Web-Only Document 135:

Protocols for Collecting and Using Traffic Data

in Bridge Design

National Cooperative Highway Research Program

Bala Sivakumar Michel Ghosn Fred Moses

Lichtenstein Consulting Engineers, Inc. Paramus, NJ

Contractor’s Final Report for NCHRP Project 12-76 Submitted July 2008

NCHRP

ACKNOWLEDGMENT This work was sponsored by the American Association of State Highway and Transportation Officials (AASHTO), in cooperation with the Federal Highway Administration, and was conducted in the National Cooperative Highway Research Program (NCHRP), which is administered by the Transportation Research Board (TRB) of the National Academies.

COPYRIGHT PERMISSION Authors herein are responsible for the authenticity of their materials and for obtaining written permissions from publishers or persons who own the copyright to any previously published or copyrighted material used herein. Cooperative Research Programs (CRP) grants permission to reproduce material in this publication for classroom and not-for-profit purposes. Permission is given with the understanding that none of the material will be used to imply TRB, AASHTO, FAA, FHWA, FMCSA, FTA, Transit Development Corporation, or AOC endorsement of a particular product, method, or practice. It is expected that those reproducing the material in this document for educational and not-for-profit uses will give appropriate acknowledgment of the source of any reprinted or reproduced material. For other uses of the material, request permission from CRP.

DISCLAIMER The opinion and conclusions expressed or implied in the report are those of the research agency. They are not necessarily those of the TRB, the National Research Council, AASHTO, or the U.S. Government. This report has not been edited by TRB.

TABLE OF CONTENTS ACKNOWLEDGMENTS ............................................................................................................iv ABSTRACT ..................................................................................................................................iv EXECUTIVE SUMMARY ...........................................................................................................1 CHAPTER 1 Background ............................................................................................................4

Problem Statement and Research Objective .............................................................................4 Scope of Study ..........................................................................................................................4 Introduction to the Final Report ................................................................................................7

CHAPTER 2 Research Approach ................................................................................................8 Research Tasks .........................................................................................................................8 Overview of Data Collection and Review ................................................................................8 State-of-Practice Summary .......................................................................................................9

State DOT Survey ..............................................................................................................9 Literature Review .............................................................................................................13

Proposed Process to Develop Vehicular Live Load Models ...................................................29

CHAPTER 3 Findings and Applications ...................................................................................35 Background to Development of Draft Recommended Protocols ............................................35 Draft Recommended Protocols for Using Traffic Data in Bridge Design ..............................41 Demonstration of Recommended Protocols Using National WIM Data ................................89

CHAPTER 4 Conclusions and Suggested Research ..............................................................138

Conclusions ...........................................................................................................................138 Suggested Research and Improvements in Data Collection ..................................................144

REFERENCES ..........................................................................................................................146 APPENDIXES

APPENDIX A National WIM Data Analyses ................................................................... A-1 APPENDIX B Main Features of Selected Studies for Collecting and Using Traffic

Data in Bridge Design ...............................................................................B-1 APPENDIX C NCHRP 12-76 Survey Questionnaires and Responses...............................C-1 APPENDIX D Potential Processes to Develop and Calibrate Vehicular Design Loads .. D-1 APPENDIX E Implementation of WIM Error Filtering Algorithm on Load Effect

Histogram ..................................................................................................E-1

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ACKNOWLEDGMENTS The research reported herein was performed under NCHRP Project 12-76 by Lichtenstein Consulting Engineers, Inc., Paramus, New Jersey, with subcontracting and consulting services provided by Drs. Michel Ghosn and Fred Moses. The Principal Investigator on this project was Bala Sivakumar from Lichtenstein Consulting Engineers, Inc. The calibration methodology, statistical analysis, and error filtration methodology were authored by Dr. Michel Ghosn with assistance from Dr. Fred Moses. The PI wishes to acknowledge the advice and guidance of the NCHRP Project Panel, with Mr. Jimmy Camp as Chairman, and the Project Manager Mr. David Beal. ABSTRACT This report documents and presents the results of a study to develop a set of protocols and methodologies for using available recent truck traffic data to develop and calibrate live load models for LRFD bridge design. The HL-93, a combination of the HS20 truck and lane loads, was developed using 1975 truck data from the Ontario Ministry of Transportation to project a 75-year live-load occurrence. Because truck traffic volume and weight have increased and truck configurations have become more complex, the 1975 Ontario data do not represent present U.S traffic loadings. The goal of this project, therefore, was to develop a set of protocols and methodologies for using available recent truck traffic data collected at different US sites and recommend a step-by-step procedure that can be followed to obtain live load models for LRFD bridge design. The protocols are geared to address the collection, processing and use of national WIM data to develop and calibrate vehicular loads for LRFD superstructure design, fatigue design, deck design and design for overload permits. These protocols are appropriate for national use or data specific to a state or local jurisdiction where the truck weight regulations and/or traffic conditions may be significantly different from national standards. The study also gives practical examples of implementing these protocols with recent national WIM data drawn from states/sites around the country with different traffic exposures, load spectra, and truck configurations.

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EXECUTIVE SUMMARY Protocols for Collecting and Using Traffic Data in Bridge Design

This report documents and presents the results of a study to develop a set of protocols and methodologies for using available recent truck traffic data to develop and calibrate live load models for LRFD bridge design. The HL-93, a combination of the HS20 truck and lane loads, was developed using 1975 truck data from the Ontario Ministry of Transportation to project a 75-year live-load occurrence. Because truck traffic volume and weight have increased and truck configurations have become more complex, the 1975 Ontario data do not represent present U.S traffic loadings. The goal of this project, therefore, was to develop a set of protocols and methodologies for using available recent truck traffic data collected at different US sites and recommend a step-by-step procedure that can be followed to obtain live load models for LRFD bridge design. The protocols are geared to address the collection, processing and use of national Weigh-In-Motion (WIM) data to develop and calibrate vehicular loads for LRFD superstructure design, fatigue design, deck design and design for overload permits. These protocols, comprised of thirteen steps with detailed instructions on their application, are appropriate for national use or use with data specific to a state or local jurisdiction where the truck weight regulations and/or traffic conditions may be significantly different from national standards. The study also gives practical examples of implementing these protocols with recent national WIM data drawn from states/sites around the country with different traffic exposures, load spectra, and truck configurations. Project recommends that truck traffic data should be collected through Weigh-In-Motion systems that can collect simultaneously headway information as well as truck weights and axle weights and axle configurations while remaining hidden from view and unnoticed by trucks drivers. Truck data surveys collected at truck weigh stations and publicized locations are not accurate, because, they are normally avoided by illegal overweight vehicles that could control the maximum loads applied on bridge structures. The selection of WIM sites should focus on sites where the owners maintain a quality assurance program that regularly checks the data for quality. WIM devices used for collecting data for live load modeling should be required to meet performance specifications for data accuracy and reliability. A year’s worth of recent continuous data is generally recommended for live load modeling. Quality information is just as important as the quantity of data collected. It is far better to collect limited amounts of well-calibrated data than to collect large amounts of data from poorly calibrated scales. Even small errors in vehicle weight measurements caused by poorly calibrated sensors could result in significant errors in measured loads. High speed WIM is prone to various errors, which need to be recognized and considered in the data review process to edit out unreliable data and unlikely trucks to ensure that only quality data is made part of the load modeling process. It is also important to recognize that unusual data is not all bad data. The WIM data should therefore be scrubbed to include only the data that meet the quality checks. Error filtering procedures provided in these protocols should be applied for screening the WIM data prior to use in the live load modeling and calibration processes. In many spans, the maximum lifetime truck-loading event is the result of more than one vehicle on the bridge at a time. Refined time stamps are critical to the accuracy of multiple presence (MP) statistics for various truck loading cases, including: single, following, side-by-side, and staggered. Many modern WIM data loggers currently in use in the U.S. have the

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capability to record and report sufficiently accurate truck arrival times for estimating multiple presence probabilities. Studies have also shown that multiple presence statistics are mostly transportable from site to site with similar truck traffic volumes and traffic flow. Load effects for single lane and two lane loadings may be obtained directly from the WIM data when accurate time arrival stamps are collected. Generalized MP statistics may be used for simulation of maximum load effects where accurate truck arrival time stamps are not available. Trucks arriving at a bridge span are grouped into bins by travel lane and run through moment and shear influence lines with their actual relative positions and the resulting load effects are normalized by dividing by the corresponding load effects for HL-93. Legal loads and routine permits are grouped under STRENGTH I. Heavy special permits are grouped under STRENGTH II.

There are several possible methods available to calculate the maximum load effect Lmax for a bridge design period (75 years) from truck WIM data collected over a shorter period of time (one year). The one implemented in these protocols is based on the assumption that the tail end of the histogram of the maximum load effect over a given return period approaches a Gumbel distribution as the return period increases. The method assumes that the WIM data is assembled over a sufficiently long period of time, preferably a year, to ensure that the data is representative of the tail end of the truck weight histograms and to factor in seasonal variations and other fluctuations in the traffic pattern. Sensitivity analyses have shown that the most important parameters for load modeling are those that describe the shape of the tail end of the truck load effects histogram. The protocols therefore recommend that a year’s worth of recent continuous data at each site be collected for use in live load modeling.

Various levels of complexity are available for utilizing the truck weight and traffic data to calibrate live load models for bridge design. A simplified calibration approach (Method I) is first proposed that focuses on the aforementioned maximum live load variable, Lmax for updating the live load factor for current traffic conditions, in a manner consistent with the LRFD calibration. The ratio, r for one-lane and for two-lanes is used to adjust the LRFD design live load factor. The ratio, r is defined as follows:

r1 = Lmax from WIM data projections for one-lane (30) Lmax used in existing LRFD calibration for one-lane

r2 = Lmax from WIM data projections for two-lanes (31) Lmax used in existing LRFD calibration for two-lanes The LRFD calibration report (NCHRP Report 368) provides mean maximum moments and shears for 75-years for simple and continuous spans. An increase in maximum expected live load based on current WIM data can be compensated in design by raising the live load factor in a corresponding manner. This simple procedure assumes that the present LRFD calibration and safety indices are adequate for the load data and site-to-site scatter or variability statistics for the WIM data is consistent with values assumed in the LRFD calibration.

When implementing the draft protocols using recent WIM data from various states, it became evident that this procedure, while simple to understand and use, had certain limitations when applied to statewide WIM data. Using a single maximum or characteristic value for Lmax for a State would be acceptable if the scatter or variability in Lmax from site-to-site for the state was equal to or less than the COV assumed in the LRFD calibration. If the variability in the WIM data is much greater than that assumed in the calibration, then the entire LRFD calibration to achieve the target 3.5 reliability index may no longer be valid for that state and a simple adjustment of the live load factor as given above should not be done. The site-to-site scatter in the Lmax values obtained from recent WIM data showed significant variability from span to span, state to state, and between one-lane and two-lane load effects. Therefore, a second more robust reliability-based

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approach (Method II) is also presented that considers both the recent load data and the site-to-site variations in WIM data in the calibration of live loads for bridge design.

The draft recommended protocols were implemented using recent traffic data (either 2005 or 2006) from 26 WIM sites in five states across the country. The states were: CA, TX, FL, IN, and MS. The states and WIM sites were chosen to capture a variety of geographic locations and functional classes, from urban interstates, rural interstates and state routes. An aim of this task was to give practical examples of using these protocols with national WIM data drawn from sites around the country with different traffic exposures, load spectra, and truck configurations. Adjustments and enhancements were made to the protocol steps based on the experience gained from this demonstration task.

Both calibration methods indicate that the lifetime maximum loading for the one lane loaded case will govern over the maximum loading for a two-lanes loaded case. This could be attributable to the increasing presence of heavy exclusion vehicles and/or routine permits in the traffic stream. The load limit enforcement environment in a state will also have a more discernible influence on the maximum single-lane loading than the maximum two-lane loading, which results from the presence of two side-by-side trucks. Additionally, with long-term WIM data with accurate truck arrival time stamps currently available, the projections of Lmax for two-lane events as undertaken in this study are based on actual side-by-side events rather than based on simulations using conservative assumed side-by-side multiple-presence probabilities as done during the AASHTO LRFD code calibration. The WIM data collected as part of this study show that the actual percentage of side-by-side multiple truck event cases is significantly lower than assumed by the AASHTO LRFD code writers who had to develop their models based on a limited set of multiple presence data.. Knowing the truck weight distribution in each lane allowed the determination of the actual relationship between the trucks weights in the main traffic lane (drive lane) and adjacent lanes and if there is a correlation between the truck properties. This study seems to indicate that there is some negative correlation between the weights of side-by-side trucks. This means that when a heavy truck is in one lane, the other lane’s truck is expected to be lighter. Here again, the conservative assumptions used during the LRFD calibration were not adequately supported by field measurements.

LRFD did not specifically address deck components in the calibration. The proposed approach to calibration of deck design loads is to assume the present LRFD safety targets are adequate for the strength design of decks and establish new nominal loads for axles based on recent WIM data. The LRFD live load factors will remain unchanged, but the axle loads and axle types will be updated to be representative of current traffic data.

Updating the LRFD fatigue load model using recent WIM data is described in the protocols. Damage accumulation laws such as Miner’s rule can be used to estimate the fatigue damage for the whole design period for the truck population at a site. Based upon the results of the WIM study changes may be proposed to the LRFD fatigue truck model, its axle configuration and/or its effective weight.

The protocols and methodologies recommended in this report can be followed to obtain live load models for bridge design using available truck traffic data collected at different US WIM sites. The models will be applicable for ultimate capacity and cyclic fatigue for main members and for bridge decks. The project was not intended to assemble sufficient data to permit recommendations about revisions to the AASHTO HL-93 design load.

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CHAPTER 1 BACKGROUND PROBLEM STATEMENT AND RESEARCH OBJECTIVE

A new vehicular live-load model was developed for the AASHTO LRFD Bridge Design Specifications because the HS20 truck from the Standard Specifications for Highway Bridges did not accurately represent service-level truck traffic. The HL-93, a combination of the HS20 truck and lane loads, was developed using 1975 truck data from the Ontario Ministry of Transportation to project a 75-year live-load occurrence. Because truck traffic volume and weight have increased and truck configurations have become more complex, the 1975 Ontario data do not represent present U.S traffic loadings. Other design live loads were based on past practice and did not consider actual or projected truck traffic and may not be consistent with the LRFD philosophy.

The present HL-93 load model, and in fact the calibration of the AASHTO LRFD specifications, is based on the top 20% of trucks in an Ontario truck weight database assembled in 1975 from a single site over only a two-week period. It reflects truck configurations and weights taken in the mid-1970s, which primarily consisted of five-axle semi trailer trucks. In the past 30 years, truck traffic has seen significant increases in volume and weight.

Updating bridge live load models needs representative samples of unbiased truck weight data that meet accepted quality standards. One method that has been developed over the last three decades to capture truck loads in an undetected manner and obtain a true unbiased representation of actual highway loads, is known as the Weigh-In-Motion, or WIM technology. Although the quality and quantity of traffic data has improved in recent years, it has not been used to update the bridge design loads. Besides information on truck weights and configurations, the design live load is highly influenced by the simultaneous presence of multiple trucks on the bridge. Such information, usually assembled from headway data, has not been traditionally collected in a manner suitable for the development of design live loads.

The goal of this project is to develop a set of protocols and methodologies for using available truck traffic data collected at different US sites and recommend a step-by-step procedure that can be followed to obtain live load models for bridge design. The models will be applicable for the design of bridge members, for both ultimate capacity and cyclic fatigue. The models will be applicable for both main structural members as well as the design of bridge decks. SCOPE OF STUDY

The original Ontario weight data from one static scale contained 10,000 truck events (2-week sample), which is a relatively small sample. More important for highway truck weight forecasting than the small sample size are the considerable site-to-site, seasonal, and other time variations in the truck weight description. These variations are not modeled in a single realization of data from one site. Heavy trucks may have avoided the static weigh station, and the degree to which this avoidance occurred in the recorded sample is also unknown. The Ontario site was assumed to have a high ADTT of 5000. With data from only one site, the influence of volume on traffic loading is also unknown.

In the LRFD development, it was seen that for two-lane bridges, loading events consisting of two side-by-side trucks govern the maximum load effect. It was calculated that the maximum load effect is equivalent to the effect of a side-by-side occurrence where each truck is about 85% of the mean maximum 75-year truck. A truck having 85% of the weight of the 75-year truck also closely corresponds to the maximum 2-month truck. The calibration of the HL93

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load model used the following assumptions for side-by-side vehicle crossings (NCHRP Report 368):

The total ADTT is assumed to be 5000 trucks/day. One out of every five trucks is a heavy truck. One out of every 15 heavy truck crossings occurs with two trucks side-by-side. Of these multiple truck events on the span, one out of 30 occurrences has

completely correlated weights. Using the product of 1/15 and 1/30 means that approximately 1/450 crossings of

a heavy truck occurs with two identical heavy vehicles alongside each other. No field data on multiple presence probabilities and truck weight correlation

were provided in the LRFD calibration report. Available literature and published reports show that there is practically little field data to support these assumptions.

No data on site-to-site variations was provided. There was no determination of the extent to which overloaded trucks may have

by-passed the static weighing operations. This project will aim to overcome the above-stated limitations in the previous load modeling study and determine the data required for establishing a representative live load model.

The first condition that any set of traffic data should meet before being used for the development of load models is the elimination of bias. Truck data surveys collected at truck weigh stations and publicized locations are not accurate, because, they are normally avoided by illegal overweight vehicles that could control the maximum loads applied on bridge structures. Furthermore, an important parameter that controls the load imposed on the structure is related to the number of simultaneous vehicles on the bridge, which is determined through data on truck headways under operating conditions. Accurate headway information cannot be obtained from fixed weigh-stations or from truck data collected at highway bypasses. For these reasons it is determined that truck traffic data should be collected through Weigh-In-Motion (WIM) systems that can collect simultaneously headway information as well as truck weights and axle weights and axle configurations while remaining hidden from view and unnoticed by trucks drivers. Simultaneous data on headways and weights is necessary to determine possible correlations between truck positions or the lanes they occupy and their weights or other characteristics such as truck type, size and numbers of axles. The 1/15 multiple presence assumption was made because of the lack of sufficient real data at the time of the LRFD calibration. Fortunately, the data needed for multiple presence estimates is presently available and already contained in the raw data files captured by many WIM data loggers.

The quality and quantity of WIM data has greatly improved in recent years. Due to the development of various weigh-in-motion technologies, unbiased truckloads are now being collected at normal highway speeds, in large quantity, and without the truck driver’s knowledge. The more advanced load modeling processes will require a more complete set of input data as discussed herein. The maximum lifetime loading requires as an input the percentage of trucks that cross the bridge side-by-side and the lane-by-lane distribution of truck weights. Assuming that the trucks in each lane have identical distribution, as in past simplified approaches, can introduce unnecessary conservatism. Using WIM data could easily improve past estimates or assumptions of various load uncertainties. Some of these uncertainties are now elaborated:

1. Knowing the truck weight distribution in each lane, including mean, COV, and distribution type can improve the input parameters needed for the load modeling process.

2. Estimation of expected maximum loading may require different distributions such as an extremal probability distribution derived from the WIM truckload histograms, rather than the normal distribution.

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3. Site-to-site variability of truckloads should be incorporated. LRFD used data from only one site in Ontario.

4. Using unbiased data is very important for the estimation of the maximum load. The data used for the LRFD calibration was obtained using a static scale operated by the Canadian province, and some trucks with excessive overloads may have deliberately bypassed the scales. The data must also not be biased by the presence of weight enforcement activity in the vicinity of the data collection site.

5. With additional WIM data, improved estimates of the tail of the probability distribution of the maximum lifetime effect can be made using Extremal distributions and other advanced reliability tools. Determining the probability distribution of the maximum effect is needed for the calibration of the live load factors. The WIM data must also be separated out ⎯ WIM measurement scatter from the actual truck weight scatter.

6. Developing and calibrating bridge live load models requires large amounts of quality WIM data. High speed WIM is prone to various errors, which need to be recognized and scrubbed / filtered out in the data review process.

7. A major advance in recent WIM operations is their ability to collect improved headway data for trucks. Clearly the headway assumptions used during the LRFD calibration were not based on actual measurements of multiple presence. Field measurements of truck arrival data to a 0.01 second resolution performed in this project and in NCHRP 12-63 consistently showed much lower side-by-side cases than those assumed in the LRFD. These new multiple presence values, can be easily incorporated in a simulation model or a simplified model for estimating the maximum lifetime loading.

8. The data must adequately represent daily and seasonal variations in the truck traffic. Hence, it should be collected for a period of one year or at random intervals over extended periods of time.

9. The relationship between the trucks weights in the main traffic lane (drive lane) and adjacent lanes must be established to determine whether passing trucks characteristics are similar to those in the main traffic lane and if there is a correlation between the truck properties. Here again, the assumptions used during the LRFD calibration were not adequately supported by field measurements. The availability of the current WIM data along with headway information and lane of occupancy will allow us to determine the level of correlation (if any) between the trucks in each lane. The relationship between truck traffic patterns and headways should be related to ADTT. Specifically, data should be collected to determine how the number of side-by-side events varies with ADTT.

The goal of this project is to develop a set of protocols and methodologies for using available current truck traffic data collected at different US sites and recommend a step-by-step procedure that can be followed to obtain live load models for bridge design. The protocols are geared to address the collection, processing and use of national WIM data to develop and calibrate vehicular loads for LRFD superstructure design, fatigue design, deck design and design for overload permits. Various levels of complexity are available for utilizing truck weight and traffic data to calibrate live load models for bridge design. A simplified calibration approach that focuses on the maximum live load variable, Lmax for updating the load factor and a more robust reliability-based approach that considers the site-to-site variations in WIM data in the calibration of live loads are proposed.

The study also gives practical examples of implementing these protocols with recent national WIM data drawn from states/sites around the country with different traffic exposures, load spectra, and truck configurations. This will give a good cross-section of WIM data for illustrative purposes. This task also allowed the updating and/or refinement of the protocols based on its applicability to WIM databases of varying quality and data standards currently being

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collected by the states. This report discusses the results of the demonstration studies in more detail. INTRODUCTION TO THE FINAL REPORT This Final Report prepared in accordance with Task 9 requirements for this project, documents the findings of Tasks 1 through 8. It contains four chapters and three Appendices. Chapter 1 gives a review of the problem statement, the research objective and scope of study. Chapter 2 describes the research tasks, findings of the literature search and survey of states, a state-of-the-art summary, and the process to develop and calibrate bridge design live load models. Chapter 3 provides the draft recommended protocols for using traffic data in bridge design and the results of the demonstration of the draft protocols using national WIM data. Chapter 4 contains the conclusions and recommendations for future research.

Appendix A includes the results of the demonstration of the draft protocols performed in Task 8 using recent national WIM data from five states. Appendix B summarizes the main features of technical publications most relevant to this project that were compiled during the literature search. Appendix C contains the questionnaires used in the surveys and tabulated responses. Appendix D summarizes the findings of Task 2, which investigated potential processes for developing live load models for bridge design. Appendix E illustrates an implementation of the error filtering algorithm described in the protocols, using recent WIM data.

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CHAPTER 2 RESEARCH APPROACH RESEARCH TASKS The research effort was organized according to the following nine tasks: Task 1. Review relevant practice, data, existing specifications, and research findings from both

foreign and domestic sources on the collection and analysis of truck weight data with particular emphasis on evaluating the stresses and deformations induced in highway bridges. This information shall be assembled from both technical literature and unpublished experiences. Information on the quantity and quality of existing WIM data from studies on or near U.S. Interstate bridges is of particular interest.

Task 2. Describe existing and potential processes to develop and calibrate vehicular loads for

superstructure design, fatigue design, deck design, and overload permitting. Task 3. Develop the vehicular traffic data requirements (type, quantity, and quality) for each of

the processes identified in Task 2. The data requirements should be validated by a sensitivity analysis of each data element.

Task 4. Assess the statistical adequacy of existing traffic data to meet the requirements

developed in Task 3. Recommend means to eliminate any inadequacies. Task 5. Using the information from Tasks 1 through 4, recommend candidate protocols for

collecting and processing traffic data to calibrate national bridge live-load models. The protocols should include guidance on selecting default values for use when the traffic data do not meet the requirements developed in Task 3. Prepare an updated, detailed work plan for developing and demonstrating the application of the protocols.

Task 6. Submit an interim report within 6 months of the contract start that documents the

results of Tasks 1 through 5 and includes the updated and expanded work plan for developing and demonstrating the protocols for collecting and processing traffic data. The contractor will be expected to meet with the NCHRP approximately 1 month later. Work may not proceed on subsequent tasks without NCHRP approval of the work plan.

Task 7. Develop the protocols in accordance with the approved work plan.

Task 8. Demonstrate the application of the protocols using existing national data to develop and calibrate vehicular loads for superstructure design, fatigue design, deck design, and overload permitting.

Task 9. Submit a final report that documents the entire research effort.

OVERVIEW OF DATA COLLECTION AND REVIEW

The first step in the live load model development process was to assemble and review recent developments and relevant information on practice, specifications, bridge live load models, weigh-in-motion systems, weigh-in-motion data, and studies of truck weights. A purpose of this

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task was to understand the state-of-the-art and the practice of collecting and utilizing traffic data in bridge design in the U.S., and in other countries. It included a survey of state highway agencies in the U.S. A search of published technical literature in the U.S. and other countries was conducted for information applicable to this research. Survey: A survey questionnaire was e-mailed to the traffic monitoring divisions of all state DOTs. The purpose of this questionnaire was to obtain detailed information and document practices on issues central to this research, such as: types of WIM equipment in use in each state and the locations of WIM sites; WIM equipment calibration procedures; the types of traffic data being collected and how they are being used. A copy of the survey questionnaire is contained in Appendix C. The questionnaire consisted of the following five sections:

SECTION 1 – Weigh-In-Motion (WIM) Program SECTION 2 – WIM Sites SECTION 3 – WIM Data SECTION 4 – WIM Data Validation and WIM System Calibration SECTION 5 – WIM Data Analysis & Applications

Completed questionnaire were received from 26 states. Responses were received from: Alaska, Arkansas, California, Connecticut, Florida, Georgia, Hawaii, Idaho, Indiana, Iowa, Kansas, Louisiana, Michigan, Minnesota, Mississippi, Missouri, Nevada, New Jersey, New Mexico, New York, North Dakota, Ohio, Oregon, South Dakota, Virginia, Washington, Wyoming. It is believed that states with significant WIM programs have responded to the questionnaire. STATE-OF-PRACTICE SUMMARY State DOT Survey

Tabulated responses to all survey questions are contained in Appendix C. Responses to certain key questions are presented in the tables below.

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Table 1 WIM Program Details State DOT WIM

Program? How Long

Has the WIM

Program Been in

Operation?

Total Number of High Speed WIM Sites

Number of WIM Sites on

Interstates

Do you Have WIM Data

Available for a Whole Year?

Alaska Yes 10+ years 7 4 Yes Arkansas No Yes California Yes 15 years 137 58 Yes Connecticut Yes 9 years 36 bi-

directional +4 LTPP

21 bi-directional +2 LTPP

Yes

Florida Yes 32 years 40 14 Yes Georgia Yes 10 years 90 30 No Hawaii Yes 18 years 7 2 Yes Idaho Yes 12 years 16 6 Yes. Lots of

available WIM data.

Indiana Yes 15 years 52 24 Yes Iowa Yes 15 years 28 9 Yes Kansas Yes 14 years 9 Perm

70 Portable 3 Perm

25 Portable Yes

Louisiana Yes 7 years 3 3 No Michigan Yes 14 years 41 21 Yes Minnesota Yes 22 years 6 2 Yes Mississippi Yes 14 years 15 7 Yes Missouri Yes 10 years 13 7 Yes Nevada Yes 20 years 4 4 Yes New Jersey Yes 13 years 64 14 Yes New Mexico Yes 17 years 18 7 Yes New York Yes 10+ years 21 11 Yes North Dakota Yes 3 years 12 4 Yes. Possibly. Ohio Yes 15 years 44 21 Yes Oregon Yes 8 years 22 18 Yes. In a text

format South Dakota Yes 15 years 14 6 Yes Virginia Yes 3 2 Yes Washington Yes 16 years 37 10 Yes Wyoming Yes 8 years 5 3 Yes

NR - No Response The responding states have maintained a WIM program over the past 3 to 32 years. The number of high-speed WIM sites varied from 3 to 137, distributed among Interstate and non-Interstate routes. Most states also indicated that they can provide a whole year’s worth of WIM data for statistical analyses. This will be an important consideration in the selection of WIM sites for load modeling data as it incorporates any seasonal variability in the traffic data. The types of sensors used at each WIM site, date installed, date last calibrated, number of traffic lanes, and the number of WIM lanes are given in Appendix C. These details were valuable when selecting WIM sites for demonstrating the use of the protocols in this project in Task 8.

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Table 2 Accuracy of Truck Arrival Time Stamps Question 3.4. What is the accuracy of truck arrival time stamps reported in the data set (1 sec, 0.01 sec, etc.)? Are time stamps available for more than one lane at a site? What is the highest resolution possible for truck arrival times? Please explain.

State DOT Time Stamp Accuracy Alaska The accuracy of the truck time arrival is .01 for all lanes of data. The time stamp is on

each vehicle record (PVR). This was an Alaska requirement to ensure that duplicate records were not loaded to the data base. This is the highest resolution possible for truck arrival times.

California 0.01 sec. Yes. Connecticut Truck arrival time stamps are reported for each lane at a site and are recorded by 1

second. The IRD software shows the data time stamp recorded to one hundredth of a second (0.01) in the individual vehicle viewing software. Additional work would be needed to determine the resolution of the data that is reported in the output file formats.

Florida Times are recorded to the nearest full second, for all lanes. Georgia Accurate to the .01 second and we weight in one lane of the roadway. At 10 locations

we collect truck traffic in the two outside lanes. Hawaii Time stamps are not checked for minute/second accuracy. We check them for date

accuracy, and we check the WIM system clock at least once per month. Observed accuracy for those can range from within 1-2 seconds to 1-2 minutes.

Idaho ECM WIM system equipment has a time resolution of one tenth of a second. The IRD/Diamond WIM systems have a “scientific” mode setting which allows for data collection with a time stamp of one hundred thousands of a second.

Indiana The timestamps for the vehicle records are to the 1/100 of a second. The ASCII report, however, will alone show the timestamp to the nearest second. This is a shortcoming that has been identified and will be corrected in future versions of the software.

Iowa They are stored by the hour. We can view the info real time to the second and can be viewed for all lanes at the site.

Kansas Accuracy varies because the on-site clock is not externally synchronized. Precision of the arrival time is 1 second, which is the finest resolution available from the equipment. Time stamps are available for each truck, regardless of lane.

Michigan The time stamp is down to the second for each lane of travel. So we have the hour, minute and second the vehicle started to cross the sensor.

Minnesota whole second Mississippi We store the data on an hourly basis in the cardw, but the img file has a time stamp

associated with each vehicle. We collect WIM data on all lanes at a permanent site. Missouri Year, month, day, hour Nevada We have never had the need to investigate this but from my experience it is within a

second New Jersey Truck arrival time stamps using the “View Vehicle” menu of the IRD office software

shows a time stamp of up to 0.01 of a second; processed weight data from the W-record cards only up to one minute.

New Mexico Hourly, for all lanes. New York All lanes are monitored and trucks are time stamped to 0.01 seconds. North Dakota 1 second resolution – Yes, time stamps available on all lanes at all times Ohio Mettler-Toledo’s time stamp is now sub second at .01 sec. The TMG does not have this

resolution and needs to be changed. The time stamp is on each vehicle so it would be by lane. Peek or Pat/IRD do not provide time stamps to the .01 second level.

Oregon Time stamp accuracy is within .01 seconds. Time stamps are available for each lane in multi-lane systems.

South Dakota unknown on accuracy of arrival time and are by lane Virginia time stamps are to the nearest second, and are available for all lanes Washington 12:00:00:00 Wyoming Time stamps are to the second and are by lane.

There is great variability in the truck arrival time data recorded by the various systems. The range is from 0.01 second to the hour. The fact that many systems record time stamps to 0.01 second

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accuracy indicates that there is sufficient availability of refined time stamps for estimating multiple-presence probabilities for truck crossings as discussed in the following chapter. Table 3 Multi-Year Traffic Data

State DOT Availability of WIM Data for a Number of Years at the Same Site?

Use of WIM data for bridge design applications?

Alaska Yes No Arkansas California Yes Yes. Caltrans has started using WIM data for

bridge design recently. Connecticut No. See answer for previous

question. No. Based loads permitted through the state.

Florida Yes No Georgia No No Hawaii Yes No Idaho Yes Yes. We provide some commercial vehicle

weight data and reports to our bridge design people.

Indiana Yes No. The data is not provided directly to them. However through Purdue University or our research section they maybe utilizing the data.

Iowa Yes No Kansas Yes No Louisiana No No Michigan Yes No. Not to my knowledge. Minnesota Yes No Mississippi No No Missouri Yes No Nevada Yes No New Jersey Yes No New Mexico Yes No New York Yes North Dakota Yes. Possibly. No Ohio Yes Yes. Maumee River crossing design & I think

for a few other applications a few years back. Oregon Yes. From “official” state weigh

records. These are available from every weigh station location, not just WIM sites.

Yes – currently the ODOT Bridge Section is conducting an analysis for Bridge re-design, and engineering standards.

South Dakota Yes Unknown Virginia No No Washington Yes No at least not to our knowledge Wyoming Possibly Not to my knowledge

The responses show that that many states have traffic data of similar quality for a number of years at the same site that may be helpful in estimating trends in truck loadings. It is also interesting to note that of the 26 responding states only CA and OR have begun using WIM data for bridge design applications. These initiatives appear to be in the early states of implementation.

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Table 4 WIM Data Quality Assurance *Question 4.5 Do you have a Quality Assurance Program in place for your WIM systems to check data accuracy?

State DOT Alaska No Arkansas California No Connecticut Yes. Through the office checks and the LTPP checks

conducted by the FHWA Regional contractors. Delaware Florida Yes Georgia No Hawaii No Idaho Yes. This is a daily ongoing part of our WIM maintenance and

processing program. Illinois NR Indiana Yes Iowa Yes Kansas No Louisiana Yes Michigan Yes Minnesota Yes Mississippi Yes Missouri Yes Nevada Yes New Jersey Yes New Mexico Yes New York Yes North Dakota No. Still under development. Ohio Yes. TKO Oregon Yes. A trouble Report system. South Dakota Yes Virginia Yes Washington Yes Wyoming The procedures explained in Section 4.1 assure data quality.

WIM data quality testing and validation is important to ensure that only quality data is made part of the load modeling process. Although WIM systems can provide massive amounts of valuable data in a relatively efficient manner, the data must be checked for accuracy. This accuracy check is a WIM user’s quality assurance (QA) program. Most states have implemented QA programs for their WIM systems to check data accuracy. A QA program adds confidence to the validity of the WIM data and alerts the data analyst to problems occurring at the WIM site. The purpose of a QA procedure is to help WIM users check data for accuracy and precision. Literature Review An investigation of published technical literature for the monitoring, collection, and analysis of bridge-related weigh-in-motion data has been performed utilizing transportation organization websites including the following resources: the TRIS, NTIS, USDOT, FHWA, and TRB. In addition, transportation engineering websites and databases, and the websites of state departments of transportation and other United States, Canadian, European, Asian, and Australian transportation institutes were explored for relevant material regarding the use of WIM data.

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This literature search concentrated on the following WIM research topics:

• The use of WIM to model bridge loads • The use of WIM to study the growth or trends in truck weights • The use of WIM to study the multiple presence of trucks • The use of WIM to study site-specific bridge loads

The technical literature search resulted in the compilation of a reference list consisting of approximately 250 abstracts, research papers, journal articles, conference papers, and reports with applicability to the project research.

The collected material was reviewed for pertinence to the areas of research under consideration. The documents determined to be the most relevant were obtained and a scan of the material was performed. Of the examined material, approximately 70 applicable documents were selected for further evaluation and possible summary preparation.

A tabulated summary of approximately 40 documents was prepared from the reviewed material (See Appendix B). Contained in each document summary is a brief study description, the study findings (if any), and recommendations for further research suggested by the authors.

A review of the summarized material (Appendix B) reveals that WIM data has been employed in numerous bridge-related applications in North America and abroad.

WIM data has been used to assess current bridge design live loads and to model new design live loads. Several studies have found that the current load models were insufficient for the actual loading experienced by the bridge population. WIM data has also been applied to the development of new fatigue models and the assessment of existing models. The results of the investigations reveal that fatigue evaluation is highly site specific and that the actual fatigue damage resulting from the use of WIM data is often underestimated or overestimated by the code-specified fatigue truck.

Truck load growth trends have been assessed utilizing WIM data. For instance, a large-scale California study has established that truck volumes have increased over time, however the gross vehicle weight in the state has remained unchanged. This study also investigated the possibility of applying WIM data that was collected at a bridge site to other nearby bridge locations. The forecasting of truck load spectra as a result of changing truck weight limits has also been investigated by the application of WIM data

The examination of truck multiple presence on bridges has employed WIM data to simulate multi-lane traffic critical loading events and extreme load effects. The studies differ in bridge span length and number of lanes investigated, however it was generally noted that as the span length increases, the critical loading event is governed by an increasing number of trucks. One study indicated that traffic density should be a deciding factor in the development of multiple presence reduction factors.

Numerous studies have investigated WIM-derived site-specific bridge loads for evaluation and design purposes. Generally, it was determined that truck loads are strongly site specific, influenced by factors such as traffic volume, gross vehicle weight, axle weight, local industry, and law enforcement effort, and that current load models for design are often not representative of actual site loading. WIM Technology: Over the last two decades, highway agencies have recognized the advantages of having automated data collection systems that can provide information on truck weights and truck traffic patterns for economic analysis, traffic management and various other purposes. The quality and quantity of WIM data has greatly improved in recent years. Due to the development of various weigh-in-motion technologies, unbiased truckloads are now being collected at normal highway speeds, in large quantity, and without truck driver’s knowledge.

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WIM systems that are utilized to provide high-speed weighing of trucks and other traffic are: Bending Plates, Load cells, Piezoelectric cables, Quartz cables, and Bridge WIM systems. One major WIM system vendor alone has approximately 500 permanent WIM sites in operation in forty seven states: 246 Piezo; 180 Bending Plate (BP); 42 Single Load Cell (SLC); 24 Kistler Quartz (Table 5). The electronics, software, and storage technologies of WIM data loggers have also advanced in pace with the sensor technology.

Weigh-in-motion equipment currently used in the United States can collect data on truck volumes, axle configurations, truck arrival times and load spectra. They usually classify the vehicles into at least the 13 FHWA classifications (bins). The majority of WIM data collection is done with permanently installed weight sensors, although some states may not collect weight data continuously at these sites. Permanent WIM stations provide more extensive datasets at geographically diverse locations over long periods. On a national or regional basis, WIM data is easily obtained from the wide network of permanent sites. If more localized site-specific characteristics are desired it may be necessary to utilize portable WIM systems for data collection. Portable devices allow flexibility in collecting site-specific traffic data at locations of interest, such as a bridge where significant illegal overloads are suspected.

There are several types of WIM technologies with varying performance and cost considerations (Table 6). Piezoelectric sensor based systems offer acceptable accuracy (usually ± 15% for gross weights) at a low cost that their use has become quite widespread for data collection purposes. They can be used as temporary or permanent sites. Strain based WIM scales and load cell WIM systems provide more accuracy at a higher cost. Strain and load-cell based systems are used primarily in permanent applications. New WIM technologies continue to be developed and brought to the market. Piezoquartz sensors were recently introduced in the United States. They are less sensitive to changes in temperature than the piezo-style sensors, and therefore generally more accurate.

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Table 5 WIM Sites and Lanes (maintained by one vendor)

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Table 6 Sensors Commonly Used for Permanent WIM Sites Type of Sensor Strengths Concerns Piezoelectric (BL) Easier, faster installation than many other

WIM systems. Generally lower cost than most other WIM sensors. Well supported by industry. Can be used for temporary WIM systems

Sensitive to temperature change. Accuracy affected by structural response of roadway. Above average maintenance requirement. Requires multiple sensors per lane

Piezoquartz Easier, faster installation than many other WIM systems. May be more cost-effective (long term) if sensors prove to be long lived. Very accurate sensor. Sensor is not temperature sensitive. Growing support by industry.

More expensive that other piezo technologies. Requires multiple sensors per lane. Above average maintenance requirement. Sensor longevity data not available. Accuracy affected by structural response of roadway.

Bending Plate Frame separates sensor from pavement structure. Entire tire fits onto sensor. Moderate sensor cost. Sensor is not temperature sensitive. Extensive industry experience with the technology.

Longer installation time required than piezo systems. Some systems have experienced premature failure, while others have been very long lived.

Load Cell Entire tire fits onto sensor. Frequently considered the “most accurate” of conventional WIM technologies. Some systems have demonstrated very long life spans.

Most expensive WIM system. Requires significant construction effort to install. Cost effective if constructed and maintained for a long life span.

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Use of In-Service Strain Measurements: Procedures for using in-service peak strain measurements to directly evaluate the safety (using the LRFR method) of existing bridges have been proposed by some researchers. A considerable part of this effort involves the statistical characterization of the live load effect using an extreme-value theory. The strains due to ambient traffic are monitored and recorded to represent the distribution of maximum load effects. The maximum load effect distribution is then projected for longer periods up to 10 years for determining the maximum expected load effect for evaluation. Because it is based on actual bridge response it eliminates a substantial part of live load modeling uncertainties, such as those related to dynamic impact and girder distribution factors. Used in combination with pavement WIM systems, this method has potential applications in other load modeling applications, particularly for fatigue design and assessment. Combining WIM data with bridge response data could significantly reduce uncertainties inherent in high speed WIM data. One problem involved in such procedures is that the projection is valid for only the stresses at the point where the stain measurements are recorded and the information cannot be generalized for stresses and strain at other locations of the same bridge let alone for application to other bridges. In any case, it is not the aim of this project to develop or recommend new WIM systems. Rather, efforts will concentrate on data now produced by operational WIM networks. LRFD Fatigue Design: Fatigue criteria for steel bridges are an important consideration for designing for heavy traffic and long expected design lives as well as for assessment of remaining life for existing bridges. As truck weight and volume increase and bridges are maintained in service for increasingly longer periods of time, the fatigue design and assessment issues becomes even more important.

The present AASHTO fatigue truck, which is based on reliability analyses, was developed by Moses, et al, in NCHRP Project 12-28 (3). The truck traffic load input was taken for some 30 WIM sites in about 8 states collected in the 1980s. For a suite of bridges, each of over 20,000 trucks was used to calculate the stress ranges and then the fatigue damage averaged according to the fatigue damage law (cubic power). The number of cycles to failure depends on the cube of the stress range and comparison with lab test data for various welded details. A variety of random variables were considered to account for material, analysis and load uncertainties. This information is used to calibrate the fatigue process to a target β for redundant and non-redundant cases. Moses, et al, describes the details of this derivation in NCHRP Report 299. The results were incorporated into two AASHTO Guide specifications for fatigue design and fatigue evaluation, respectively. Further, the fatigue truck developed for the nominal loading (54 kip, 5-axle truck) in these Guide Specifications was also incorporated into the AASHTO LRFD Specifications and the LRFR manual.

Most of the fatigue damage in a bridge is caused by passages of single trucks across the bridge. The total number of truck passages in the 75 year life of a bridge can exceed 100 million. Static strength design must be based on the most severe load effect expected to occur over the life of the bridge. Fatigue design, on the contrary, should be based on typical conditions that occur, because many repetitions are needed to cause a fatigue failure. (Ref NCHRP Report 399).

The fatigue load specified in the steel structures section of the LRFD Specifications also produces a lower calculated stress range than that of the Standard Specifications. The fatigue provisions of the new specifications are more reflective of the fatigue loads experienced by highway bridges.

In LRFD, a special vehicle is used for fatigue analysis. It consists of one design truck, as specified above, but with the rear (32-kip) axle spacing fixed at 30.0 FT and without an accompanying uniform load (Figure 1). The fatigue load is used to represent the variety of trucks of different types and weights in actual traffic. For the purposes of fatigue design, a truck is defined as any vehicle with more than either two axles or four wheels. The constant axle spacing approximates that for a 5-axle semi-trailer truck that do most of the fatigue damage to steel

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bridges. The specified fatigue loading in LRFD produces a lower calculated stress range than produced by the loadings in the Standard Specifications. This reduction in calculated stress range is offset by an increase in the number of cycles of loading to be considered in the LRFD Specifications. The lower stress range and increased number of cycles are more reflective of the actual conditions experienced by bridges. If the maximum stress a detail experiences in its lifetime is less than the constant amplitude fatigue threshold for that detail, the detail is considered to have infinite fatigue life.

In the FATIGUE load combination given in the LRFD specifications, a load factor of 0.75 is applied to the fatigue load. The factored fatigue load is equivalent to the AASHTO HS15 loading. A revision to Article 3.4.1 was adopted in 2008 to specify two separate fatigue load combinations. For infinite life design under higher traffic volume conditions, the FATIGUE I load combination would be used. In the new FATIGUE I load combination, the stress range caused by the fatigue design truck is multiplied by a load factor of 1.50 (or 2.0 * 0.75). For finite life design under lower traffic volume conditions, the FATIGUE II load combination would be used. The FATIGUE II load combination retains the load factor of 0.75 applied to the stress range caused by the fatigue design truck.

14’

Figure 1 LRFD Fatigue Truck (includes 0.75 load factor)

30’

6 k 24 k 24 k

Where the bridge is analyzed using approximate analysis methods, the specified lateral live load distribution factors for one lane loaded are used in the fatigue check, without the multiple presence factor of 1.2. Where the bridge is analyzed by any refined method, a single fatigue truck is positioned transversely and longitudinally to maximize the stress range at the detail under consideration. A reduced dynamic load allowance of 15 percent is applied to the fatigue load.

Since fatigue is defined in terms of accumulated stress-range cycles over the anticipated service life of the bridge, the fatigue load should be specified along with the frequency of load occurrence / stress cycles. For the purposes of determining the number of stress cycles per truck passage LRFD Table 6.6.1.2.5-2 may be used (Table 7). Table 7 Stress Cycles per Truck Passage

Longitudinal Members Span > 40 ft Span ≤ 40 ft Simple span girders 1.0 2.0

Continuous span girders near supports 1.5 2.0

Continuous span girders elsewhere 1.0 2.0 Transverse Members Spacing > 20 ft Spacing ≤ 20 ft

1.0 2.0

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The frequency of the fatigue load is taken as the single lane average daily truck traffic. The number of cycles to be considered is the number of cycles due to trucks actually anticipated to cross the bridge in the most heavily traveled lane over its design life. The frequency of the fatigue load is taken as the single-lane average daily truck traffic (ADTTSL). In the absence of better information, the single-lane average daily truck traffic shall be taken as: ADTTSL = p x ADTT (1) Where: ADTT = the number of trucks per day in one direction averaged over the design life p = fraction of truck traffic in a single lane. Because of the importance of the lifetime average daily truck volume parameter in fatigue design, the engineer should use whatever site data may be available for making this estimate. It should be made excluding 2-axle trucks consistent with the procedure used in calculating the fatigue truck weight. Traffic volume usually grows at an annual rate of about 2 to 5 percent until they reach a very high limiting value. It is unrealistic to project traffic growth indefinitely into the future. ADT, including all vehicles, is physically limited to about 20,000 vehicles per day per lane. AASHTO Fatigue Guide Specifications (1989, 1990): The 1989 AASHTO Guide Specifications for Fatigue Design of Steel Bridges and the 1990 AASHTO Guide Specifications for Fatigue Evaluation of Existing Steel Bridges specified a three-axle fatigue tuck having a gross weight of 54 kips to represent the variety of trucks in actual traffic seen in the WIM data collected in the early 1980s. The fatigue truck is similar to the LRFD fatigue load once the loads are scaled down using the 0.75 load factor. One key difference was that the Guide Spec allowed a variable spacing of 14 ft to 30 ft instead of the standard 30 ft main axle spacing. If used, the reduced axle spacing would have resulted in increased fatigue design stresses.

To recognize the considerable region-to-region and site-to-site differences in truck weight population, alternatives for determining the gross weight of the fatigue truck were permitted. Where the gross-weight histogram for truck traffic (excluding 2-axle trucks) was available, the guide allowed the determination of the gross weight of the fatigue truck from:

(2) ( )1/ 33i iW = f W∑

fi = fraction of gross weights within an interval i Wi = gross weight at mid-width of interval i The fatigue design was based on the passage of a single fatigue truck across the bridge in the lane under consideration. The net effect of closely spaced trucks was considered to be small for normal traffic conditions (NCHRP Report 299). Therefore, the effect of truck superpositions was neglected for span lengths typically covered by the AASHTO Standard Specifications. If unusual bunching of trucks is expected at a site, a 15% increase of the fatigue truck weight was specified. Fatigue Load Research: Research studies have been conducted to establish improved fatigue load models that will cause the same cumulative fatigue damage as the normal truck traffic distribution obtained by WIM measurements in various states. Laman and Nowak (1996) developed a fatigue load model for girder bridges from WIM measurements at five bridge sites in Michigan (Figure 2). Stress cycles were also measured at the midspan of all girders. A new three axle fatigue truck was proposed to model vehicles with 3 to 7 axles. The fatigue damage caused by the traffic consisting of 3 to 7 axles is equivalent to the damage caused by an equal number of passes of the 3 axle fatigue truck. A four axle fatigue truck was proposed for sites with 10 and 11

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axle trucks common in Michigan. The AASHTO fatigue truck was not adequate to model the traffic at these sites. It was found that a high percentage of the fatigue damage was dominated by 10 and 11 axle trucks, though they did not dominate the distribution of truck types. It was found that for these sites, two site-specific fatigue trucks could provide relatively accurate estimates of fatigue damage accumulation over a range of bridge spans. This illustrates that truck load spectra are strongly site-specific.

Chotickai and Bowman (2006) developed a new fatigue load model based on WIM data collected from three different sites in Indiana (Figure 3). The recorded truck traffic was passed over simulated bridge spans to investigate moment range responses in simple and continuous span bridges. Based on Miner’s hypotheses, fatigue damage accumulations were compared with the damage predicted for the 54 Kip AASHTO fatigue truck, a modified AASHTO fatigue truck with an equivalent effective gross weight, and other fatigue truck models. The simulation results indicate that the use of the 54 Kip gross weight in an evaluation of bridge structures can result in a considerable overestimation or underestimation of the extent of the actual fatigue damage. It was also shown that the fatigue trucks given by Laman and Nowak (1996) do not provide an accurate estimate of the fatigue damage accumulation for a wide range of span lengths when compared with fatigue damage estimated using the WIM database. Based upon the results of the Indiana WIM study, a new three axle fatigue truck and a four axle fatigue truck were proposed. The front and rear axle spacing of the new three axle fatigue truck are wider than the AASHTO fatigue truck. In addition, a higher percentage of the gross weight is distributed to the front axle compared with the AASHTO fatigue truck. These adjustments were considered to be consistent with statistics of the axle configurations of truck traffic observed. The new four-axle fatigue truck was most effective when a significant number of 8 to 11 axle trucks pass over a bridge, while the new three-axle fatigue truck was most effective otherwise.

Figure 2 Fatigue Trucks – Laman and Nowak (1996)

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Figure 3 Fatigue Trucks -- Chotickai and Bowman (2006)

LRFD Deck Design: In the LRFD Specifications, design load for decks and top slabs of culverts using the transverse strip method is the axle load, represented by a 32 kip axle of the design truck or the design tandem consisting of a pair of 25.0 Kip axles spaced 4.0 ft apart, whichever creates the most extreme force effect (Fig. 4). The two design vehicles should not be considered in the same load case ⎯ consider all trucks of one kind, design truck or design tandem, not a mix of the two. The design truck has the same weights and axle spacing as the HS20 load model, which was adopted in 1944 for bridge design, and has been carried over from the Standard Specifications. Only the truck load is required for decks and not the truck + distributed loads as required for girders. The slab may be designed by three methods: 1) Traditional strip method 2) Empirical design 3) Yield-line method. In the traditional strip method, the deck is subdivided into equivalent strips perpendicular to the supporting components. The width of equivalent strips is given in LRFD Table 4.6.2.1.3-1. The strips are analyzed as continuous beams using one or more loaded lanes to determine maximum live load moments. The empirical design requires that the designer satisfy a few simple rules regarding deck thickness and reinforcement details. An analysis for load effects is not required. Though newer deck design methods were introduced, design load effects on bridge decks have remained essentially the same in the LRFD specifications compared with the requirements of the standard Specifications. The live load modeling in LRFD did not specifically address the increasing load effects on bridge decks from the heavier and more complex axle configurations of current truck traffic.

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DECK DESIGN – LRFD CODE PROVISIONS

32 k DESIGN AXLE

25 k DESIGN TANDEM 25 k 4’

APPROXIMATE STRIP METHOD OF ANALYSIS:

+M = 26.0 + 6.6S

-M = 48.0 + 3.0S

Figure 4 LRFD Deck Design Loads and Strip Widths.

Axle groups with more than two axles are currently not considered for deck design in LRFD. However, LRFD commentary C3.6.1.3.3 states “Individual owners may choose to develop other axle weights and configurations to capture the load effects of the actual loads in their jurisdiction based upon local legal load and permitting policies. Triple axle configurations of single unit vehicles have been observed to have load effects in excess of the HL-93 tandem axle load”.

W2 W2

S2

W3 W3 W3

S3 S3

W4 W4 W4

S4 S4

W4

S4

TANDEM

TRIDEM

QUAD

Figure 5 Typical Multi-Axle Loads

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Figure 6 Concrete Ready-Mix Truck with Quad Axle

Multi-Axle Specialized Hauling Vehicle

To increase load carrying capacity and maximize productivity, the trucking industry has in recent years introduced specialized commercial vehicles with closely-spaced multiple axles (Figures 6, 7 & 8). This was the focus of the NCHRP 12-63 project (NCHRP Report 575). States have adopted a variety of short multi-axle vehicles as posting loads in response to their potential for overstressing shorter span bridges and bridge decks (Figs 9 and 10). Additionally short dump trucks are allowed loads of 60K or more in the rear tri-axle group in many states, as seen in Fig 9. Similar exemptions are granted for tandem axles on concrete mixer trucks and other work trucks (> 50 K allowed on a tandem). Such axle groups usually include lift axles, which are required to be lowered when the truck is loaded, but are not always used in this manner. This further exacerbates the overstress problem on decks and short span bridges. NCHRP 12-63 has compiled a database of over 70 trucks with complex axle configurations currently in use as legal loads in the various states. Many states exempt short hauling vehicles from Federal Formula B and axle weight limits under the grandfather rights granted when the federal weight laws were first enacted. This information intended for developing new AASHTO load models for evaluation in NCHRP 12-63 can be a valuable resource for developing new axle loads for deck design as the data represents service loads that the new decks will be subjected to on a routine basis. This has implications for the strength and fatigue design provisions for decks in the current LRFD Specifications. Current provisions may be grossly underestimating the maximum and repetitive load effects on bridge decks. Furthermore, the multiple presence probabilities for side-by-side axles could be considerably different than truck multiple presence probabilities for trucks. The former influences deck design, which could be much higher than the side-by-side probabilities for trucks as each truck may have several axle groups that could increase multiple-presence. This issue has not been adequately investigated in past calibrations of the bridge code.

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Figure 7 Multi-Axle Specialized Hauling Vehicle (Ref: NCHRP Report 575)

Figure 8 Truck with Tridem and Quad Axles

25

15 15 22.5 22.5

11’ 4’ 4’

GVW = 75 KipsAlabama Tri-Axle

13.5 18 22.5 22.5

9’-7” 4’-1” 4’-6”

GVW = 76.5 KipsConnecticut Construction Vehicle

191919164.5’4.5’8’

GVW = 73 KipsDelaware DE 4

18.7 18.7 18.713.9

4’-2”4’-2”10’

GVW = 70 KipsFlorida SU4

L = 19’

L = 17’

L = 18’-4”

L = 18’-2”

Figure 9 State Legal Loads that Exceed Federal Weight Limits (Ref: NCHRP Report 575)

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Figure 10 North Carolina Legal Loads (Ref: NCHRP Report 575) LRFD Overload Design: In addition to routine service loads, bridge owners usually have established procedures that allow the passage of vehicles above the legally established weight limitations on the highway system. Depending upon the authorization, these permit vehicles may be allowed to mix with normal traffic or may be required to be escorted in a manner which controls their speed and/or lane position, and the presence of other vehicles on the bridge. The multiple-presence probabilities for permit trucks are significantly different from those used for normal traffic. In the LRFD, the STRENGTH II limit state is specified for checking an owner-specified special design vehicle or permit vehicle during the design process with a reduced load factor of 1.35. No further guidance is given in the LRFD Specifications on how this load factor was derived, the level of safety represented by this limit state, site traffic, or how the load factor might be adjusted when design live loading characteristics (such as the gross weight of the permit load, likelihood of trucks exceeding the permitted weight, and multiple presence likelihood) differ significantly from the calibration assumptions. These kinds of information need to be obtained

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locally or regionally through WIM measurements and considered in the STRENGTH II design process since the data used for calibration of national codes are unlikely to be representative of all jurisdictions. LRFD Superstructure Design: The notional live load model used in the LRFD Specification for the design of bridges, designated HL-93, consists of a combination of the:

Design truck or design tandem, and Design lane load

Each design lane under consideration shall be occupied by either the design truck or tandem, coincident with the lane load, where applicable.

The HL-93 live load model was initially developed as a notional representation of shear and moment produced by a group of vehicles routinely permitted on highways of various states under “grandfather” exclusions to weight laws. The vehicles were based on a 1990 study conducted by the Transportation Research Board, which identified twenty-two representative configurations of vehicles allowed by states as exceptions to weight laws. The smallest and largest of which were a three-axle 48 Kip single truck and an eleven axle 149 Kip trailer truck (Kulicki 1994). The notional load model was subsequently compared to the results of truck weight studies, selected WIM data (Ontario), and the 1991 OHBDC live load model. These comparisons showed that the notional load could be scaled by appropriate load factors to be representative of these other load spectra.

Comparisons of moments and shears in simple spans and two-span continuous girders raging in span from 20 to 150 feet produced by HS20 and the envelope of results produced by the 22 representative exclusion vehicles indicated that the HS20 design loading was not representative of vehicles on U.S. highways. Five candidate notional loads were identified in the live load development for the AASHTO LRFD Specification (Kulicki 1994). Ratios of force effects for each of these live load models divided by the corresponding force effect from the envelope of exclusion loads indicated that the load model involving a combination of either a pair of 25-Kip tandem axles and the uniform load, or the HS20 and the uniform load, seem to produce the best fit to the exclusion vehicles. The tight clustering of force effect ratios for all span lengths, forming bands of data which are essentially horizontal, indicates that the live load model and load factor can be independent of span length. Thus, the combination of the tandem with uniform load and the HS20 with the uniform load, were shown to be an adequate basis for a notional design load in the LRFD Specification.

The LRFD Specification allows site-specific modifications to the design truck, design tandem, and/or the design lane load under the following conditions:

the legal load of a given jurisdiction is significantly greater than typical the roadway is expected to carry unusually high percentages of truck traffic flow control, such as stop sign, traffic signal, or toll booth, cause trucks to

collect on certain areas of a bridge, or special industrial loads are common due to the location of the bridge.

The dynamic load model was determined to be a function of three major parameters: road surface roughness, bridge dynamics (frequency of vibration) and vehicle dynamics (suspension system). The actual contribution of road roughness, bridge dynamics and vehicle dynamics varies from site to site and are difficult to predict. Therefore, the dynamic load allowance in the LRFD was specified as a constant percentage of live load (Nowak 1993).

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PROPOSED PROCESS TO DEVELOP VEHICULAR LIVE LOAD MODELS The design and load capacity evaluation of a bridge member depends on the live load model and the live load factor used in the design check equation. The live load factor γL=1.75 for Strength I provided in the AASHTO LRFD Specifications has been calibrated for use along with the HL-93 design load such that bridge members designed with the AASHTO LRFD Specifications would achieve a uniform target reliability index β=3.5. In actuality, conservative rounding up of the originally calibrated live load factor indicate that the AASHTO LRFD will produce members with reliability index values higher than 3.5. The reliability index calculations use as input a live load model that estimates the maximum expected live load effect on a bridge member. (Lmax is the expected lifetime maximum load effect on a bridge). The model includes the mean value of the maximum expected live load effect along with the standard deviation and the probability distribution type. The live load model used during the AASHTO LRD calibration was obtained from a generic set of truck weight and load effect statistics that are presumed to be valid for any typical bridge site in the U.S. Because of its generic nature, the live load model may not represent the actual loading conditions at a particular bridge site or bridges in a state where the truck weights or traffic conditions do not follow the expected typical model. Under these conditions, site-specific or state-specific live load models may need to be developed based on actual truck weight and traffic data collected at the site or within the state. Several states are currently using Weigh-In-Motion (WIM) systems to collect vast amounts of truck weight and traffic data that can be used to obtain site-specific and state-specific live load models for bridge design and load capacity evaluation. This would allow individual states to adjust the AASHTO live load factors to take into consideration the particular truck traffic conditions throughout a state, a region, or on a particular route. Task 2 of this research project was focused on existing and potential processes to develop and calibrate vehicular loads for superstructure design, fatigue design, deck design, and overload permitting. The findings are summarized in Appendix D. Several procedures of various levels of complexity exist to estimate the maximum expected load effect on a highway bridge. This section describes the recommended procedure that utilizes site-specific truck weight and traffic data to obtain estimates of the maximum live load for a specified return period. The return period for the design of a new bridge is specified to be 75 years as per the AASHTO LRFD code for Strength I limit state. A two-year return period has been used for the load capacity evaluation of existing bridges during the calibration of the AASHTO LRFR, and a one-period has been proposed for estimating the maximum live load effect for the AASHTO LRFD Strength II limit state. It should be clearly stated that it is not possible to obtain exact values of the maximum expected 75-year load due to the limitations in the available data. In fact, to obtain accurate results, one would need several cycles of WIM data collected over 75 years for each cycle which is an impossible task. Even the development of live load models for one year and two year return periods would require several cycles of one year and two year data which are currently not available due to the relative recent adoption of WIM technology in the U.S. Hence, some form of statistical projection will be needed for any practical load modeling effort as will be described in this section. The approach described in this section uses a Normal probability distribution to project the tail end of the collected WIM data histograms. The properties of the Normal distribution can then be used to obtain the statistics of the maximum load effects for any return period using extreme value distributions. This section presents the theoretical background for the proposed procedure for modeling the maximum live load effect on a highway bridge. The proposed approach for obtaining the live load model requires as input the WIM data collected at a site after being “scrubbed” and processed to remove data outliers as described in other sections of this report. For state-specific load models, data from several representative sites should be assembled. The statistics of the maximum live load effects can then be used to adjust the AASHTO live load factors so that the

29

Strength I and Strength II limit state designs would achieve safety levels similar to those intended by the AASHTO code writers while simultaneously accounting for the state-specific loading conditions. 1. Probability density function and frequency histogram of truck load effects For the single lane loading of short span bridges, a truck loading event is defined as the occurrence of a single truck on the bridge. For multiple truck presence in multi-lanes, the loading event may consist of two or more trucks simultaneously on the bridge. While all currently used WIM systems are capable of providing axle weights and axle spacings for each truck crossing, only WIM systems capable of taking continuous uninterrupted data at normal highway traffic speeds with accurate time stamps are able to identify multilane loading events and provide the axle weights, axle spacings and relative positions of all the trucks involved in each multilane loading event. For the cases when uninterrupted multilane data with accurate time stamps are not available, multilane loading events can be obtained from simulations based on estimates of the number of side-by-side and information on Average Daily Truck Traffic data. This could be achieved using an approach that will be described in Chapter 3. In a first step, using the WIM data files, the shear force or bending moment effect of each truck loading event in the WIM record is calculated by passing the trucks through the proper influence line. For multilane loadings the combined shear force or moment effect from the trucks that are simultaneously on the bridge is obtained. The shear or moment for each truck load event is then normalized by dividing the calculated value by the shear or moment of the HL-93 load model. The shear and moment data for the single lane loading and the multilane lane loading events are collected into separate percent frequency histograms. Each histogram provides a discretized form of the probability density function (pdf) of the shear or moment effects for the site. The histogram is designated as Hx(X) while the pdf is designated as fx(X). The relation between Hx(X) and fx(X) is given by:

∫=uX

lXxx dx)x(f)X(H (1)

where Xl and Xu give the upper and lower bounds of the bin within which X lies. If the bin size is small, then fx(X) can be assumed to be constant within the range of Xl to Xu and Equation (1) becomes:

( )luxxx XX)X(fX)X(f)X(H −=Δ= (2)

where ΔX is the bin size. 2. Cumulative distribution functions and cumulative frequency histograms. Using the histograms and the probability density functions fx1(…), fx2(…), fxs(…) and fz(…) the cumulative distributions for the shear or moment effects of single or multilane loading events can be obtained. The cumulative distribution is assembled from the pdf using the equation:

( ) ∫∞−

=Z

zz dy)y(fZF (3)

30

In essence, Equation (3) assembles all the bins of the histogram below a certain value Z into a single bin at Z. This is repeated for all possible values of Z. Thus, Fz(Z) will give the probability that a loading event will produce a load effect less or equal to Z. 3. Cumulative probability function for the maximum load effect over a return period of

time, treturn. For the AASHTO Strength I limit state, a bridge structure should be designed to withstand the maximum load effect expected over the design life of the bridge. The AASHTO LRFD code specifies a design life of 75 years. The LRFR bridge load rating also requires checking the capacity to resist the maximum load effects for a two-year return period. The AASHTO LRFD Strength II limit state implicitly assumes a one-year return period associated with special permit trucks. It is simply impossible to collect enough data to determine the maximum load effect expected over 75 years of loading. Even getting sufficient data for the one-year and two-year return periods would require several cycles of one-year and two-year data which are not currently available. Therefore, some form of statistical projection should be performed. The proposed calculation procedure uses the cumulative distribution function for individual loading events and then applies a statistical projection to obtain the information required for a one-year, two-year, or 75-year return period. To find the cumulative distribution for the maximum loading event in a period of time treturn we have to start by assuming that N loading events occur during this period of time. These events are designated as S1, S2, … SN. The maximum of these N events, call it Smax,N, is defined as:

Smax,N = max (S1, S2, … SN) (4)

We are interested in finding the cumulative probability distribution of Smax,N. This cumulative probability distribution, Fs max N(S), gives the probability that Smax,N is less than or equal to a value S. If Smax,N is less than S, this implies that S1 is less than S, and S2 is less than S, … and SN is less than S. Hence, assuming that the loading events are independent, the probability that Smax,N≤S can be calculated from:

( ) )S(F)...S(F).S(FSF

Ns2s1sNmaxs = (5) If S1, S2, ... SN are independent random variables that are drawn from the same probability distribution, then:

)S(F)S(F...)S(F)S(F sNs2s1s

==== (6)

and Equation (5) reduces to ( ) [ ]NsNmaxs )S(FSF = (7)

Note that Equation (7) assumes that the number of events is a known deterministic value. A sensitivity analysis performed as part of this study has however demonstrated that the results of Equation (7) are not highly sensitive to small variations in N as N becomes large. The application of Equation (7) requires high precision in Fs(S). For example, given 3000 trucks per day over a 75-year return period the number of single truck events N would be over 82 million. Thus, to obtain the median value of the maximum event Smax N corresponding to

31

( )SFNsmax

=0.5 would require to have precision up to the 9th decimal point which is not possible to obtain without executing some form of statistical projection. To perform the statistical projection a careful analysis of the tail end of

( )SFs

( )SFs is required. 4. Statistical fit of tail end of probability distribution of load effect of a single loading

event. The probability distribution of the single loading event does not follow any known probability distribution type. However, careful observations of the tail ends of the WIM data histograms assembled from several sites indicate that the tail ends match the tail ends of Normal probability distributions. For example, Figure 1 shows the plot of the data collected at the I-81 site in upstate New York on a Normal probability scale. A Normal probability plot is executed by taking the Normal inverse of represented by ( )SFs ( )[ ]SFs

1−Φ and plotting versus S. The plot would produce a straight line if S follows a Normal distribution. In this case, the mean of S would correspond to the abscissa for which ( )[ ]SFs

1−Φ is zero. The mean plus on standard

deviation would correspond to the abscissa for which ( )[ ]SFs1−Φ is equal to 1.0.

The plot of the WIM data shows that the data as a whole does not follow a Normal distribution as the curve does not follows a straight line. However, the figure shows that the upper 5% of the data (plotted in red) does approach a straight line indicating that the tail end of the data resembles the tail end of a hypothetical Normal distribution. A linear fit on the Normal probability plot of the upper 5% of the data collected at this I-81 site will produce a slope, m, and an intercept, n, which will give the mean of the equivalent Normal distribution that best fits the tail end as μevent= -n/m. The standard deviation of the best-fit Normal is σevent=1/m. For the I-81 data, single truck events give μevent=0.0232 and σevent=0.333. The regression analysis of the upper 5% of the data produces a regression coefficient R2=0.997 indicating a good linear fit.

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8-5-4-3-2-10123456

60-ft simple span moment

Stan

dard

Dev

iate

Moment/HL-93

All data Upper 5% Linear fit (upper 5%)

y=3.0049x-0.0697 (R2=0.997)

Figure 1. Normal probability plot for moment effect of trucks in drive lane of I-81 NB

32

5. Cumulative distribution of maximum load effect. To verify that the Normal fit of the tail end of the data is sufficient to obtain good estimates of the maximum load effect for long return periods, the results of Eq. (7) are plotted in Figure 2 for two cases. Cases 1 uses as input the cumulative distribution obtained from the WIM data for single loading events and case 2 plotted in red uses the that corresponds to the Normal distribution with μevent=0.0232 and σevent=0.333. The application of Eq. (7) uses different return periods varying from one day to 75 years. The number of events for the I-81 site are obtained as Nday=3200 single truck events.

( )SFs

( )SsF

Figure 2 shows good agreement between the projections obtained from the Normal fit of the tail (in red) and the WIM data for the one-day, one-week and the one-month return periods. The figure also shows that the WIM data is not sufficient to obtain the maximum load effect for return periods greater than one month. However, the use of the Normal distribution to model the tail end of WIM data would allow for obtaining the maximum load effect distribution for extended return periods.

0.8 1 1.2 1.4 1.6 1.8 2 2.20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Moment/HL-93

Freq

uenc

y

Cumulative Moment Distribution for Maximum Truck Effect in Different Return Periods

1 day1 week1 month2 years75 yearsfrom Normal

Figure 2. Cumulative distribution of maximum load effect of single lane events for different return periods.

6. Extreme value distribution of maximum load effect. Although the application of Eq. 7 can be executed numerically for any parent probability distribution, the fact that the tail end of the WIM data matches that of a Normal distribution allows for the application of extreme value theory to obtain the statistics of the maximum load effect in closed form. The approach is based on the following known concept as provided in Ang and Tang (2007): “if the parent distribution of the initial variable S has a general Normal distribution with mean μevent and standard deviation σevent, then the maximum value after N

33

repetitions approaches asymptotically an Extreme Value Type I (Gumbel) distribution” with a dispersion αN given by:

( )event

NN

σα

ln2= (8)

and a most probable value uN given by:

( ) ( )( ) ( )( ) ⎟

⎟⎠

⎞⎜⎜⎝

⎛ +−+=

NNNu eventeventN ln22

4lnlnlnln2 πσμ (9)

αN and uN can be used to find the mean of the maximum load effect, Lmax, and its standard deviation, σmax, for any return period having N repetitions as:

NNmaxmax

577216.0uLα

μ +== (10)

and

N

max 6απσ = (11)

Monte Carlo Simulation An alternative to the statistical projections approach consists of using a Monte-Carlo simulation to obtain the maximum load effect. In this approach, results of WIM data observed over a short period can be used as a basis for projections over longer periods of time. A Monte Carlo simulation requires the performance of an analysis a large number of times and then assembling the results of the analysis into a histogram that will describe the scatter in the final results. Each iteration is often referred to as a cycle. The process can be executed for the single lane-loading situation or the side-by-side loading. A step-by-step procedure for Monte Carlo Simulation is described in Step 12.3 of the Draft protocols, in the next chapter.

Monte Carlo simulation will not be accurate for large projections periods because of the limitations in the originally collected data. Also, the Monte Carlo simulation will be extremely slowed down when the number of repetitions K is very high. Furthermore, one should make sure not to exceed the random number generation limits of the software used, otherwise the generated numbers will not be independent and the final results will be erroneous. Hence, statistical projections must be made to estimate the maximum load effects for long return periods. Alternatively, one can use a smoothed tail end of the WIM histogram by fitting the tail with a known probability distribution function (such as the Normal distribution) and use that fitted distribution with the Monte Carlo simulation. It should be emphasized however, that the Monte Carlo simulation would still be very inefficient for projections over long return periods.

34

35

CHAPTER 3 FINDINGS AND APPLICATIONS. BACKGROUND TO DEVELOPMENT OF DRAFT RECOMMENDED PROTOCOLS LRFD Background

The HL-93 live load model was initially developed as a notional representation of shears and moments produced by a group of vehicles routinely permitted on highways of various states under “grandfather” exclusions to weight laws. The notional load model was subsequently compared to the results of truck weight studies, selected WIM data (Ontario), and the 1991 OHBDC (Ontario Code) live load model. These comparisons showed that the notional load could be scaled by appropriate load factors to be representative of these other load spectra.

The calibration of the AASHTO LRFD Specifications, is based on the top 20% of trucks in an Ontario truck weight database assembled in 1975 from a single site over only a two-week period. In the past 30 years, truck traffic has seen significant increases in volume and weight. The goal of this project is to develop a set of protocols and methodologies for using available current truck traffic data collected at different US sites and recommend a step-by-step procedure that can be followed to obtain live load models for bridge design. The protocols are geared to address the use of national WIM data to develop and calibrate vehicular loads for LRFD superstructure design, fatigue design, deck design and design for overload permits.

Various levels of complexity are available for utilizing the site-specific truck weight and traffic data to calibrate live load models for bridge design. A simplified calibration approach is proposed that focuses on the maximum live load variable, Lmax for updating the live load model or the load factor for current traffic conditions, in a manner consistent with the LRFD calibration. A more robust reliability-based approach is also presented that considers the site-to-site variations in WIM data in the calibration of live loads. Some key issues and traffic parameters that influence the estimation of traffic statistics and the maximum load effect are summarized as given below.

Use of High-Speed WIM Sites The first condition that any set of traffic data should meet before being used for the development of load models is the elimination of bias. Truck data surveys collected at truck weigh stations and publicized locations are not accurate, because, they are normally avoided by illegal overweight vehicles that could control the maximum loads applied on bridge structures. Furthermore, an important parameter that controls the load imposed on the structure is related to the number of simultaneous vehicles on the bridge, which is determined through data on truck headways under operating conditions. Accurate headway information cannot be obtained from fixed weigh-stations or from truck data collected at highway bypasses. For these reasons it is determined that truck traffic data should be collected through Weigh-In-Motion systems that can collect simultaneously headway information as well as truck weights and axle weights and axle configurations while remaining hidden from view and unnoticed by truck drivers.

WIM Data Quality

WIM data collection should not sacrifice quality for quantity. The selection of WIM systems sites should focus on sites where the owners maintain a quality assurance program that regularly checks the data for quality and requires system repair or recalibration when suspect data

36

is identified. Weighing accuracy is sensitive to roadway conditions. Roadway conditions at a WIM site can deteriorate after a system is installed and calibrated. Regular maintenance and recalibrations are essential for reliable WIM system performance. Vehicle dynamics plays a significant role in the force actually applied by any given axle at any given point on the roadway. Site-specific calibration is the only way that the dynamic effects of the pavement leading to the scale can be accounted for in the WIM scale calibration. The dynamic motion of trucks is also influenced by the vehicle design, gross weight, and suspension systems. The calibration approach should account for the vehicle dynamics and the truck traffic characteristics of each data collection site. Physical and software-related failures of equipment, and transmission failures are common sources of traffic data quality problems. Transmission problems can lead to gaps in the data (i.e., missing data) even though data may be continuously collected in the field. Data quality checks should be implemented to detect and fix “bad data” before processing.

WIM Scale Calibration

Heavy emphasis is placed on the calibration of WIM data collection equipment. Quality

information is more important than the quantity of data collected. It is far better to collect small amounts of well-calibrated data than to collect large amounts of data from poorly calibrated scales. Even small errors in vehicle weight measurements caused by poorly calibrated sensors could result in significant errors in measured loads. Key issues concerning the use of WIM equipment are: 1) the calibration of WIM equipment and 2) the monitoring of the data reported by WIM systems as a means of detecting drift in the calibration of weight sensors. Recommendations for WIM sensor calibration and monitoring of data are given in Appendix 5-A of the Traffic Monitoring Guide (USDOT 2001).

Auto-calibration is the practice by which software calculates and applies an adjustment to the scale calibration factor based on a comparison of the average of a number of measurements of front axle weights against its expected value. There are drawbacks to auto-calibration techniques currently used by some states to offset calibration errors, and it is recommended that direct WIM scale calibration be implemented. Only direct calibration of a WIM scale after it has been installed at a site ensures that it is measuring axle weights correctly. This includes a comparison of static axle weights with axle weights that are estimated from multiple vehicle passes with more than one vehicle. Comparison of static weights and dynamic weights will provide an effective check of system accuracy with regard to sensor errors and errors due to vehicle dynamic effects. For long duration counts, the scale should be calibrated initially, the traffic characteristics at that site should be recorded, and the scale’s performance should be monitored over time. The State should also perform additional, periodic on-site calibration checks (at least two per year). These steps will ensure that the data being collected are accurate and reliable.

WIM data scatter for axles is different from gross weight scatter and is usually much larger. This axle scatter should be assembled separately from the equipment calibration and should be used to modify the measured axle loads.

Filtration of WIM Measurement Errors

Sensitivity analyses have shown that the most important parameters affecting maximum

bridge loads are those parameters that describe the shape of the tail end of the truck load effects histogram. Current WIM technology is known to have certain levels of random measurement errors that may affect the accuracy of the load modeling results. These errors are due to the inherent inaccuracies of the WIM system itself, the difference between the dynamic weight measured and the actual static scale weight, as well as the effect of tire pressure, size and

37

configuration on the WIM results. Hence, it is advisable to use a statistical algorithm to filter out these errors. A standardized approach to executing the error filtering procedure will bring uniformity in the load modeling process that will utilize WIM data from various sites. To execute the filtering process, a calibration of the results of the WIM system should be made by comparing the results of the WIM to those of a static scale. This calibration process should be executed for a whole range of truck and axle weight types and configurations. The ratio of the measured weight to the actual weight (bias) for a large sample of readings is the calibration statistics that should be assembled into a histogram. A procedure for error filtering utilizing the scale calibration data is recommended as part of the load modeling protocols.

Site-to-Site Variability One of the largest variability in truck traffic is the site-to-site variability. Site-to-site variability of truckloads should be incorporated as the calibration of the AASHTO LRFD Specifications used data from only one site in Ontario, Canada (U.S. sites were not considered). Dividing truck routes into three functional classifications will allow a systematic assessment of truck load spectra within a state. Each route within a functional classification group is taken to experience truck weights per vehicle type that are similar to those of other routes within that group. The classification groups routes into Interstate and Non-Interstate highways. Many states allow heavier loads on non-Interstate routes under grandfather exemptions to weight laws. Interstates are further divided into urban vs. rural as many urban areas have been known to experience heavier truck loads and volume due to increased commercial activity, lack of alternate modes of freight movement and a general lack of truck weight enforcement. Truck data will be collected from WIM sites on principal arterials. The routes on the principal arterial system are sub classified as Interstate and other principal arterials (Table 8). Urban and rural areas could have fundamentally different traffic characteristics. Consequently, this workplan provides for separate classification of urban and rural functional systems.

Table 8 Proposed Classification Scheme for Truck Weight Data Collection

Protocols Functional Class

Description FHWA functional Class(es)

A Rural Interstate Principal Arterial

1

B Urban Interstate Principal Arterial

11

C Other Principal Arterial 2, 12, 14

Seasonal Variability in the Traffic Stream Traffic varies over time. Traffic varies over a number of different time scales, including: • Time of day • Day of week • Season (month) of the year. Most trucks follow a traditional urban pattern where weekday truck volumes are fairly

constant, but on weekends, truck volumes decline considerably. Long-haul trucks are not concerned with the “business day”; they travel equally on all seven days of the week. WIM sites should operate continuously throughout the year to measure temporal changes in the loads carried

38

by trucks. Where possible, more than one site within a functional group should be monitored continuously to provide a more reliable measure of seasonal change. Tracking of seasonal changes in truck traffic is necessary to obtain representative truck weight histograms needed for various analyses. Directional Variation

Most roads exhibit differences in flow by direction. Truck weights, volumes and

characteristics can also change by direction. One “classic” example of directional differences in trucks is the movement of loaded trucks in one direction along a road, with a return movement of empty trucks. This is often the case in regions where mineral resources are extracted or near port facilities. Tracking these directional movements is important to obtain the load spectra for bridge load modeling. Lane-By-Lane Variation

Vast majority of trucks (80% or more) travel in the right (drive) lane. The expected

maximum gross vehicle weight and, therefore, the expected maximum moments and shears of the trucks in the drive lane are different than those of the trucks in the passing lane. The degree of this difference seems to be dependant on the site and travel direction. The maximum lifetime loading requires as an input the percentage of trucks that cross the bridge side-by-side and the lane-by-lane distribution of truck weights. Assuming that the trucks in each lane have identical distribution (as in past simplified approaches) can introduce unnecessary conservatism. Using WIM data could easily improve past estimates or assumptions of various load uncertainties for trucks in each lane. Knowing the truck weight distribution in each lane, including mean, COV, and distribution type can improve the input parameters needed for the load modeling process.

Permit Traffic vs. Non-Permit Traffic In most states permit records are either not specific enough or detailed enough to allow separation of permit loads from non-permit loads in a large WIM database. Routine permits are not route-specific and are allowed unlimited trips. For LRFD bridge design it is not necessary to separate legal loads from Routine Permits as both are classified as unanalyzed truck loads, that should be enveloped by the HL-93 design loading. Protocols require that legal loads and routine permits be grouped under STRENGTH I and heavy special permits be grouped under STRENGTH II. The following approach was developed to grouping trucks that would be consistent from site to site:

• Do not attempt to classify trucks as permit or non-permit as customarily the permit records are not reliable enough or readily accessible to do this.

• Group all trucks with six or fewer axles in the STRENGTH I calibration. These vehicles include legal trucks and routine permits or divisible load permits. These vehicles are considered to be enveloped by the HL-93 load model.

• Group all trucks with seven or more axles in the STRENGTH II calibration. These vehicles should include the heavy special permit loads, typically in the 150 Kip GVW and above category.

For a state that maintains easily accessible permit records with a well established and enforced overweight permits program it would be possible to obtain the records for authorized permits or permit vehicles for a route for a specific data collection period and separate out these heavy vehicles (STRENGTH II) from the illegal overloads (STRENGTH I), both of which populate the

39

upper tail of the histogram. With many states moving to on-line and web-based permits processing, electronic records for permits should become more readily available in the future. Multiple-Presence Probabilities

In many spans, the maximum lifetime truck-loading event is the result of more than one

vehicle on the bridge at a time. An important step in defining nominal design load models is the modeling of multiple presence probabilities. Many modern WIM data loggers currently in use in the U.S. have the capability to record and report sufficiently accurate truck arrival times for estimating multiple presence probabilities. Many traffic counters routinely record data to 1/100 of a second or even a millisecond in their binary files. These time stamps allow the determination of headway separation of trucks in adjacent lanes or in the same lane and the occurrence of simultaneous or near-simultaneous load events in each lane. The sensitivity analysis has demonstrated that small changes in the number of multiple presence events do not have a significant effect on the estimated maximum load effect over the 75 year design life. Studies done using New York WIM data during this project show that there is a strong correlation between multiple presence and ADTT. From Figure 12 it is evident that the number of multiple presences sees a sharp drop off on days when the ADTT is low (such as weekends). Though not linear, the graph demonstrates that multiple presence statistics are related to the site traffic conditions. A recent study of truck multiple-presence at twenty-five (25) sites across NJ over a period of 11 years has also provided valuable data on the relationship between truck volume and truck multiple-presence. (Gindy, M. and Nassif, H. (2006)) Obtaining reliable multiple presence statistics requires large quantities of continuous WIM data with refined time stamps, which may not be available every site. The site ADTT could serve as one key variable for establishing a site multiple presence value. A single WIM site can provide multiple presence data for varying ADTT values due to daily variation in ADTT. , p

0

5

10

15

20

25

30

35

40

45

0 500 1000 1500 2000 2500 3000

ADTT

MP

EVEN

TS

MP Count

Figure 12 Side-by-Side Events vs. ADTT -- I-81 NB New York

40

Multiple-Presence Probabilities for Permit Loads

The multiple-presence probabilities for permit trucks are significantly different from those used for normal traffic. In the LRFD, the STRENGTH II limit state is specified for checking an owner-specified permit vehicle during the design process with a reduced load factor of 1.35. Though no guidance is given in the LRFD Specifications on how this load factor was derived, a reduced load factor is considered appropriate due to the reduced likelihood of permit trucks exceeding the authorized weight, the reduced multiple presence likelihood and the reduced exposure period of one year. The permit live load factors are derived to account for the possibility of simultaneous presence of non-permit heavy trucks on the bridge when the permit vehicle crosses the span. Information on loads and multiple-presence probabilities for permits need to be obtained locally or regionally through WIM measurements and considered in the STRENGTH II design process since the data used for calibration of national codes are unlikely to be representative of all jurisdictions. LRFD Fatigue Design

Since fatigue is defined in terms of accumulated stress-range cycles over the anticipated service life of the bridge, fatigue design is based on typical conditions that occur as many cycles are needed to cause a fatigue failure. The present AASHTO fatigue truck, which is based on reliability analyses, was developed using truck traffic load data taken for some 30 WIM sites in about eight states collected in the 1980s. Over 20,000 trucks were used to calculate the stress ranges and then the fatigue damage averaged according to the fatigue damage law (cubic power). The number of cycles to failure was compared with lab test data for various welded details. The fatigue truck developed (54 kip, 5-axle truck) from these studies has been incorporated into the AASHTO LRFD Specifications and the AASHTO LRFR manual.

As truck weight and volume increase and bridges are maintained in service for increasingly longer periods of time, the fatigue design and assessment issues becomes even more important. The AASHTO fatigue load is used to represent the variety of trucks of different types and weights in actual traffic. Applying a single truck model that may not be representative of current traffic as a standard for all fatigue design may be inaccurate or potentially unsafe. Code-based load models based on past WIM data may not adequately represent modern traffic conditions in many jurisdictions.

41

DRAFT RECOMMENDED PROTOCOLS FOR USING TRAFFIC DATA IN BRIDGE DESIGN Protocols recommended for collecting and using traffic data in bridge design can be categorized into the following steps: STEP 1 DEFINE WIM DATA REQUIREMENTS FOR LIVE LOAD MODELING STEP 2 SELECTION OF WIM SITES FOR COLLECTING TRAFFIC DATA FOR

BRIDGE DESIGN STEP 3 QUANTITIES OF WIM DATA REQUIRED FOR LOAD MODELING STEP 4 WIM CALIBRATION & VERIFICATION TESTS STEP 5 PROTOCOLS FOR DATA SCRUBBING, DATA QUALITY CHECKS &

STATISTICAL ADEQUACY OF TRAFFIC DATA STEP 6 GENERALIZED MULTIPLE-PRESENCE STATISTICS FOR TRUCKS AS A

FUNCTION OF TRAFFIC VOLUME STEP 7 PROTOCOLS FOR WIM DATA ANALYSIS FOR ONE-LANE LOAD

EFFECTS FOR SUPERSTRUCTURE DESIGN STEP 8 PROTOCOLS FOR WIM DATA ANALYSIS FOR TWO-LANE LOAD

EFFECTS FOR SUPERSTRUCTURE DESIGN STEP 9 ASSEMBLE AXLE LOAD HISTOGRAMS FOR DECK DESIGN STEP 10 FILTERING OF WIM SENSOR ERRORS / WIM SCATTER FROM WIM

HISTOGRAMS STEP 11 ACCUMULATED FATIGUE DAMAGE AND EFFECTIVE GROSS WEIGHT

FROM WIM DATA STEP 12 LIFETIME MAXIMUM LOAD EFFECT Lmax FOR SUPERSTRUCTURE

DESIGN STEP 13 DEVELOP AND CALIBRATE VEHICULAR LOAD MODELS FOR BRIDGE

DESIGN The above steps to be followed are described below in detail:

STEP 1 DEFINE WIM DATA REQUIREMENTS FOR LIVE LOAD MODELING

An aim of these processes is to capture weight data appropriate for national use or data specific to a state or local jurisdiction where the truck weight regulations and/or traffic conditions may be significantly different from national standards. The objective is to use data from existing WIM sites to develop live load models for bridge design. The models will be applicable for the strength and fatigue design of bridge members, including bridge decks and design vehicles for overload permitting. The traffic data needs for live load modeling are summarized below:

Step 1.1 Data needed for calibration of superstructure (STRENGTH I) design load models include:

Lane by lane truck type distribution, total weights, and axle weights and spacings with

particular emphasis on the tails of the weight histograms. Headways and multi-presence for single, two, or more lanes including side-by-side,

staggered and following trucks which are of particular interest for multi-span or longer single span bridges. How headways are affected by truck volumes is important for developing models that take into consideration local or regional traffic patterns.

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Calibration statistics for the WIM scale to filter out sensor errors.

Step 1.2 Data needed for overload permitting (STRENGTH II) include:

State permit policies and routine permit types authorized for a specific route. Where available, record of special permits authorized for a specific route during the data

collection period, including truck descriptions, axle weights and axle spacing Information on multiple presence for permit loads – two permits trucks side-by-side or

permit truck with a non-permit truck. WIM calibration data using overloaded test trucks, if available. If not, utilize same

calibration data as for STRENGTH I. Step 1.3 Data needed for calibration of deck design load models include:

Common axle configurations and axle weight distributions of legal trucks and permit trucks.

Frequencies of occurrences of common axle configurations. Other multi-axle axle configurations with fixed and variable axles. Headway information for side-by-side effects of axle groups or single axles. WIM scale calibration statistics for axle loads

Step 1.4 Data needed for calibration of fatigue load models (FATIGUE) include:

Truck type distribution, total weights, and axle weights and spacings with emphasis on the most common vehicles rather than on the tails. This is because the fatigue process is due to the accumulation of damage from every truck crossing and is less dependent on the extreme loading events.

Frequencies of occurrences of common truck configurations. WIM scale calibration statistics

STEP 2 SELECTION OF WIM SITES FOR COLLECTING TRAFFIC DATA FOR

BRIDGE DESIGN

Select remote WIM sites away from weigh stations. This is very important for obtaining unbiased data. Traffic monitoring unknown to the truck drivers’ is key.

Select sites that do not experience significant breakdowns and provide reliable year-round operation. Select sites that can provide a year’s worth of continuous data.

Select WIM sites that have been recently calibrated and are subject to a regular maintenance and quality assurance program. A review of recent WIM data will indicate if there is an obvious problem with the calibration. Perform a calibration check of the system. Accuracy of the weight data and the time stamps should be verified. Request a manual recalibration using a group of trucks of known weight and configuration if the system does not meet specified tolerances. Calibration data must be available for filtering out measurement errors. The project will recommended data quality requirements for WIM sites used for data collection.

Select WIM sites with free flowing traffic, where trucks usually maintain their lanes and travel speed (>10 mph), that do not experience any significant stop-and-go traffic or traffic backups. The sites should be away from exits, on level grade, with smooth roadway surfaces near the WIM installation. Avoid sites with numerous traffic stoppages.

Select sites with WIM sensors in right lane and passing lanes, in both directions. Some sites have sensors only in the drive lane.

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The user should have a good understanding of the state’s overweight permit policies that apply to the specific routes. It would be difficult to identify continuous or routine permits in the traffic stream in most states. These permits are not route-specific and are allowed unlimited trips within the period of duration for the permit. Special permits that are issued for very heavy loads are subject to restrictions on the route taken and the number of crossings made. Use records of Special permits (usually available from the permit office), to identify and remove these vehicles that populate the extreme end of the load data prior to statistical processing of “random” traffic.

Select sites equipped with current sensor and equipment technologies. Regular maintenance and periodic recalibration of any WIM system is critical for obtaining reliable traffic data. It is also important to filter out WIM data measurement errors so that they do not affect the accuracy of the load modeling results. The calibration of the WIM system will provide information on the calibration factor, ε, for use in the filtering process.

Preferably, the WIM system should be able to capture and record truck arrival times to the nearest 1/100th of a second or better to allow the determination of truck headway separations.

In general, the selection of WIM sites for bridge load modeling will depend on the geographic spread of the truck load data represented by the model. Step 2.1 Sites for National Design Live Load Modeling

• Study of truck loads can be conveniently handled by dividing the country into five regions as shown in Figure 14 below. (FHWA 2001)

• Ten states with the high truck populations are: CA, IL, TX, OH, FL, PA, OK, NY, NC, and IN (Table 9).

• Select one representative state from each region. The state should have a well established and maintained WIM program that has been in place for a number of years that could provide the data needed for load modeling. The five recommended states, one from each region are: California, Florida, Indiana, New York and Texas.

• For each representative state, select the sites and routes for WIM data collection based on functional classifications defined in Table 8.

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Figure 14 U.S. Regions for Truck Loads.

Table 9 Candidate States for National Data Collection for Live Load Modeling. State State

Ranking Based on

Truck Population

Region(See map

Fig 2)

How Long Has the WIM

Program Been in

Operation?

Total Number of High Speed WIM Sites

Number of WIM Sites

on Interstates

WIM Data Available

for a Whole Year?

California 1 WE 15 years 137 58 Yes Florida 5 SA 32 years 40 14 Yes Indiana 10 NC 15 years 52 24 Yes Michigan 11 NC 14 years 41 21 Yes Missouri 15 NC 10 years 13 7 Yes New Jersey 19 NE 13 years 64 14 Yes New York 8 NE 10+ years 21 11 Yes Ohio 4 NC 15 years 44 21 Yes Oregon 23 WE 8 years 22 18 Yes. Texas 3 SG 21 years 18 6 yes

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Table 10 Recommended Five States from Each of the Five Regions (see Fig. 14). State State

Ranking Based on

Truck Population

Region

How Long Has the WIM

Program Been in

Operation?

Total Number of High Speed WIM Sites

Number of WIM Sites

on Interstates

WIM Data Available

for a Whole Year?

California 1 WE 15 years 137 58 Yes Florida 5 SA 32 years 40 14 Yes Indiana 10 NC 15 years 52 24 Yes New York 8 NE 10+ years 21 11 Yes Texas 3 SG 21 years 18 6 yes

For each functional classification select two WIM sites, guided by the following considerations, as applicable:

o Heavy freight routes or routes known to have significant permit traffic. o Bulk cargo shipping routes o Logging routes o Specialized equipment shipping routes o WIM sites near ports, railroad terminals or other truck origination points. o WIM sites near industrial facilities or mining operations. o WIM sites near landfills or waste transfer sites. o WIM sites near military installations o WIM sites should preferable be geographically dispersed within a state o WIM sites should preferable have varied truck volumes.

Table 11 Sites by Functional Classification for WIM Data Collection

Functional Class

FHWA Functional Classes

Description WIM Sites

A 1 Rural Interstate Principal Arterial

2

B 11 Urban Interstate Principal Arterial

2

C 2, 12, 14 Other Principal Arterial 2 Step 2.2 Sites for State-Specific Design Live Load Modeling

It is important to recognize that there can be significant variations in traffic conditions within a state that should be accounted for in truck weight studies. For calibrating design load models for a specific state, some broad guidelines may be given as follows:

• Two sites from each of the three highway functional classes. Where WIM sites exist, verify that WIM data from all major truck routes within a state are included.

• Each site in a functional class should preferably be from a different region of the state. • The guidelines for selecting individual WIM sites should be as discussed above under

national design live load modeling.

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Step 2.3 Sites for Design Live Load Modeling for a Metro-Area or Transportation Hub

• For calibrating load models for a city or a transportation hub within a state, select at least

six WIM sites from within a 25-mile radius of the city or region. Where WIM sites exist, verify that WIM data from all major truck routes within the area of interest are included.

• The guidelines for selecting individual WIM sites should be as discussed above under national design live load modeling.

• Where enough permanent WIM sites are not in operation, temporary WIM sites for short-term data collection may be employed. Data should be collected to capture likely seasonal variability in truck traffic.

Step 2.4 Sites for Route-Specific Design Live Load Modeling

• For calibrating live load models for a designated hauling route, select a minimum of three WIM sites on that route or on feeder routes.

• The guidelines for selecting individual WIM sites should be as discussed above under national design live load modeling.

• Where enough permanent WIM sites are not in operation, temporary WIM sites for short-term data collection may be employed. Data should be collected to capture likely seasonal variability in truck traffic.

Step 2.5 Sites for Site-Specific Design Live Load Modeling

• This would be particularly relevant to major bridge design and/or evaluation. • For calibrating site-specific load models for a specific bridge, select three WIM sites on

that route or feeder routes, preferable within a distance of 25 miles of the bridge. • If permanent WIM sites are not available, a temporary WIM site may be deployed at the

approaches to the bridge. Data should be collected to capture likely seasonal variability in truck traffic. WIM data shall be gathered in both travel directions.

For the purposes of picking WIM data collection sites for the demonstration of the protocols for this project, one site for each functional classification in two states is proposed. In this regard, the resources available on this project were also a consideration.

STEP 3 QUANTITIES OF WIM DATA REQUIRED FOR LOAD MODELING

Some recommendations for the quantity of WIM data to be collected from each site to capture the

variability in traffic loads include:

i. A year’s worth of recent continuous data at each site to observe seasonal changes of vehicle weights and volumes is preferable.

ii. If continuous data for a year is unavailable seek a minimum of one month data for each season for each site.

iii. Data from all lanes in both directions of travel.

STEP 4 WIM CALIBRATION & VERIFICATION TESTS

To ensure that high quality data will be collected for use in bridge live load modeling, all WIM devices used for this purpose should be required to meet performance specifications for

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data accuracy and reliability. Because collection of accurate traffic loading rates throughout the year is necessary to provide the load data needed, the WIM systems used in this effort must meet the ASTM criteria all year long. Historically, many WIM systems have had problems accurately weighing vehicles when environmental conditions have changed from those that were present when the equipment was last calibrated. Changes in pavement condition at the scale location are also known to cause problems with WIM system sensor accuracy.

Pavement design procedures compute equivalent single-axle loads (ESALs) from measured axle weights using a mathematical formula developed by AASHTO. The fourth-order relationship in this formula heavily magnifies the effects of poor scale calibration, which can lead to significant errors in determining the load experienced by a pavement and thus computing the expected pavement life. Bridge design however is controlled by shear and moment effects which bear a linear relationship to axle loads and axle spacings. Therefore, errors in scale calibration are not magnified to the same extent as in pavement design.

Many States attempt to work around the cost of scale calibration by relying on a variety of auto-calibration techniques provided by WIM equipment vendors. Auto-calibration is the practice by which software calculates and applies an adjustment to the scale calibration factor. This is a common technique utilized on piezo systems to account for changing sensitivity of the scale sensors to changing environmental conditions. It is based on a comparison of the average of a number of measurements of some specific variable against its expected value. Some of these techniques adjust scale-calibration factors to known sensitivities in axle sensors for changing environmental conditions, “known” truck conditions, and equipment limitations. Although these techniques have considerable value, they are only useful after the conditions being monitored at the study site have been confirmed. State must determine whether the auto-calibration procedure used is based on assumptions that are true for a particular site and whether enough test trucks are crossing the sensor during a given period to allow the calibration technique to function as intended. Auto-calibration may not be particularly suited to low truck volume sites. Field tests to verify that a WIM system is performing within the accuracy required is an important component of data quality assurance for bridge load modeling applications. Steps to ensure that the data being collected are accurate and reliable are:

Step 4.1 Initial Calibration: Initial calibration of WIM equipment should follow LTPP calibration procedures or ASTM 1318 standards.

Step 4.2 Periodic Monitoring: Periodic monitoring of the data reported by WIM

systems as a means of detecting drift in the calibration of weight sensors.

Step 4.3 Periodic On-Site Calibration Checks: For long duration counts, the scale should be calibrated initially, the traffic characteristics at that site should be recorded, and the scale’s performance should be monitored over time. The State should also perform additional, periodic on-site calibration checks (at least two per year). Only direct calibration of a WIM scale after it has been installed at a site ensures that it is measuring axle weights correctly. This includes a comparison of static axle weights with axle weights that are estimated from multiple vehicle passes with more than one vehicle.

Assemble calibration statistics for WIM site for filtration of sensor errors during the load modeling process (see Step 11). This calibration process should be executed for a range of truck and axle weight types and configurations operating at normal highway speeds. The ratio of the measured weight to the actual weight for a large sample

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of readings is the calibration factor that should be assembled into a histogram. WIM data scatter for axles is different from gross weight scatter and is usually much larger. This axle scatter should be assembled separately from the equipment calibration and should be used to modify the measured axle loads.

STEP 5 PROTOCOLS FOR DATA SCRUBBING, DATA QUALITY CHECKS &

STATISTICAL ADEQUACY OF TRAFFIC DATA Step 5.1 Data Scrubbing

The key to developing and calibrating bridge live load models is quality of WIM data and not quantity. High speed WIM is prone to various errors, which need to be recognized and considered in the data review process. It is important to review the WIM data to edit out “bad or unreliable data” containing unlikely trucks to ensure that only quality data is made part of the load modeling process. It is also important to recognize that unusual data is not all bad data as truck configurations are becoming increasingly more complex and truck weights are getting heavier. Slow moving traffic (<10 mph) and stop-and-go traffic could cause difficulty in separating vehicles. Two or more trucks may be read as one truck. It is therefore important to check speed data. Trucks with very large axle spacings and excessive total wheelbase may be combining separate trucks. Maximum likely axle spacing must be specified. This could be done by importing the WIM text files into a database. The filters can be used the screen the database for bad data or unlikely trucks during the data transfer process.

The WIM survey data should be scrubbed to include only the data that meet the quality checks. The following is a filtering protocol that was applied for screening the WIM data used in this project. Truck records that meet the following filters were eliminated:

• Speed < 10 mph • Speed > 100 mph • Truck length > 120 ft • Total number of axles < 3 • Record where the sum of axle spacing is greater than the length of

truck. • GVW < 12 Kips (and max as required). • Record where an individual axle > 70 Kips • Record where the steer axle > 25 Kips • Record where the steer axle < 6 Kips • Record where the first axle spacing < 5 feet • Record where any axle spacing < 3.4 feet • Record where any axle < 2 Kips • Record which has GVW +/- sum of the axle weights by more than

10%. This may indicate that the axle records provided may not be complete or accurate.

The data scrubbing rules have been refined and updated as WIM data from typical sites were processed during the course of this study. Adjustments to the data scrubbing rules may need to be made to accommodate differences in traffic characteristics, truck configurations and weight limit compliance from state to state. Some newer trucks with complex axle configurations may need rules specifically tailored to fit their use. The rules do not propose a maximum GVW limit. This

49

ensures that trucks are not excluded just because they are very heavy. The test is to see if a truck configuration is “realistic” based upon an understanding of feasible axle configurations. Step 5.1.1 Review of Eliminated Suspect Data

Reviewing a sampling of trucks that were eliminated during the data scrubbing process is recommended to check if the process is performing as intended and that real trucks have not been inadvertently removed from the dataset. This is a valuable quality assurance check of the data scrubbing process. Comparing WIM data with permit data or data from any nearby weigh station would provide an additional check. Where feasible, short-duration monitoring of trucks using real time WIM data could be helpful to verify scale performance and the accuracy of truck classifications. Stopping of trucks for static weighing is not recommended during such monitoring as it may bias the WIM data, as the heavy overweight trucks may find an alternate route to avoid detection.

Step 5.2 Quality Control Checks for Scrubbed WIM Data

This section describes simple quality checks performed on WIM data to quickly confirm that a properly calibrated data collection device is working as intended. It should not be confused with calibration tests.

Perform the following quality control checks for each WIM site for each lane, for each month of data collection:

1. Check vehicle classification statistics (truck percentages by class) and compare results with historical values or manual counts where available for the site/route. Large deviations from expected values could indicate sensor problems.

2. Produce a GVW histogram of Class 9 trucks (5-axle semi-trailer trucks) using a 4 kip increment. Most sites will have two peaks in the GVW distribution (unloaded peak usually falls between 28 Kips and 32 Kips; the loaded peak falls somewhere between 72 Kips and 80 Kips). A shift in the peaks could indicate that the scale calibration may be changing or the scale may be malfunctioning. If both peaks have shifted, the scale is probably out of calibration.

3. Compute the number and percentage of Class 9 trucks over 100 Kips. If the percentage of Class 9 trucks over 100 Kips is high the scale calibration may be questionable, unless such readings could be explained by a State’s weight and permitting laws or by known movement of heavy commodities on a route. Such readings may indicate operational problems with the sensor.

4. Produce a histogram of steer axle weights for Class 9 trucks. The average front axle weight for Class 9 trucks is fairly constant for most sites. It ranges between 9 Kips and 11 Kips. Some variations are possible due to truck characteristics and GVW. Significant deviation of steer axle weights is a sign of scale operational problems.

5. Produce a histogram of Class 9 drive tandem axle weights. Compare with mean drive axle weight for Class 9 trucks given in NCHRP Report 495 (estimates wheel weights as a function of truck GVW).

6. Produce a histogram of spacing between front axles and drive tandem axles. Check mean spacing between drive tandem axles. Compare results to historical values available for class 9 trucks.

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Step 5.3 Assess the Statistical Adequacy of Traffic Data

The proposed protocols for calculating the maximum 75-year live load effect, Lmax, is based on the WIM truck weight and truck traffic database assembled at various sites within the jurisdiction for which the Lmax estimates are required. The protocols are based on collecting truck weight and truck traffic WIM data over a period of a year in order to cover all possible seasonal variations and other short-term fluctuations in truck traffic patterns.

The models used in this study assume that the WIM data is stationary in the sense that the one-year data is representative of all subsequent years within the 75-year design life of a bridge site. Possible growth in truck weights and traffic intensities must be considered using an economic projection analysis, which is beyond the scope of this study.

Furthermore, the proposed protocols assume that the tail end of the truckload effect histogram for a bridge span follows a Normal distribution the statistical properties of which are obtained from a regression analysis of the upper 5% of the data plotted on a Normal probability curve. Normal probability plots of truckload effects obtained from WIM data collected at several different sites have confirmed that the upper 5% of the data approaches a straight line with a regression coefficient R2 on the order of 0.97 to 0.99 indicating that the Normal distribution does reasonably well model the upper tail of the truck load effect histograms. The slope and intercept of the regression fit of the upper tail on the Normal probability plot can then be used to find the mean and standard deviation of the Normal distribution. However, the values of the slope and intercept depend on the estimates of the frequency of trucks in each bin of the histogram. In particular, the Normal probability plot uses the cumulative frequencies as the basis for the calculation of the slope and intercept of the regression line and thus the mean and standard deviation of the equivalent Normal distribution. The calculated values for the mean and standard deviation provide “best estimates” of these parameters. However, the process does not provide any information about the accuracy of these estimates except our understanding that these estimates will improve as the sample size increases. In order to provide some quantitative measure of the accuracy of these estimates, it is herein proposed to use statistical confidence intervals. A confidence interval of a parameter defines a range with lower and upper limits within which the true value of the parameter will lie with a prescribed probability. These confidence intervals will reflect the effect of the sample size and the number of samples that are found to lie within a bin of the truckload effect. Obviously the more data is collected, the more confidence the engineer will have in the estimated truck load effect frequencies in each category and the higher will be the accuracy of the calculated mean and standard deviations of the equivalent Normal distribution. Confidence Intervals on the Cumulative Frequencies Let us assume that the percent cumulative frequency in a particular bin of the load effect histogram at a given site is given as “ ip ” which is calculated as the total number of trucks that produced moments within the bin “i” divided by the total number of trucks, n. It can be proven that statistically speaking, this ip is an unbiased estimate of the true value pi. Thus, (according to Ang & Tang (2007)), the (1-α) lower and upper confidence intervals of pi can be obtained from:

Lower limit: ( )

np̂1p̂kp̂p ii

2/i2/i

−+= αα (14)

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Upper limit: ( )( )

np̂1p̂kp̂p ii

2/1i2/i

−+= −αα (15)

where ( )2/1k 1

2/ αΦα −−= − , and ( ) ( )2/1k 12/1 αΦα −= −

− , ( )...1−Φ is the inverse cumulative function of the Normal standard distribution. If the 95% confidence limits are desired, then 1-α=95% leading to 96.1k 2/ −=α and ( ) 96.1k 2/1 +=−α . To get the 95% confidence interval on the projected maximum live load effect Lmax,, follow Step 12.2.1 but use the upper and lower limits of the cumulative frequency pi rather than the value obtained directly from the WIM data. The evaluating engineer should decide whether the resulting confidence interval Lmax are sufficiently narrow. If the intervals are not adequate, more WIM data should be collected to further narrow the intervals. STEP 6 GENERALIZED MULTIPLE-PRESENCE STATISTICS FOR TRUCKS AS

A FUNCTION OF TRAFFIC VOLUME.

In many spans, the maximum lifetime truck-loading event is the result of more than one vehicle on the bridge at a time. Refined time stamps are critical to the accuracy of MP statistics. Accurate multiple presence data requires time stamps of truck arrival times to the hundredth of second. Many states typically report arrival times to the nearest second. A time stamp which records to the nearest second could result in an error of over a truck length for trucks traveling at highway speeds. With time stamps recorded to the nearest hundredth-of-a-second headway separations will be accurate to within a foot. As noted, multiple-presence statistics need not be developed for each site as there is a correlation between multiple presence and ADTT. There may also be a correlation between MP and the functional class of the highway. Higher MP probabilities may be more likely at urban WIM sites due to slower traffic speeds and increased congestion. Multiple presence statistics are mostly transportable from site to site with similar truck traffic volumes and traffic flow. A single WIM site can provide multiple presence data for varying ADTT values due to daily variation in ADTT. In this study, few sites with large quantities of continuous WIM data that include refined time stamps to a resolution of 0.01 second or better were investigated. A relationship between MP and traffic volume was developed to utilize the MP values from national data to any given site without performing a site-specific analysis. Where accurate time stamps are not available multiple presence events may be evaluated using MP statistics from other sites with similar traffic conditions and functional classifications. MP statistics are obtained as a function of headway separation for side-by-side and following trucks.

Definitions:

• Headway: the distance between front axles of side-by-side trucks. • Gap: the distance between the rear axle of the first truck and the first axle of the

following truck. If the gap exceeds the span length, then there is no multiple- presence on the bridge span.

• Light Volume: ADTT ≤ 1000 • Average Volume: 1000 < ADTT ≤ 2500 • Heavy Volume: 2500 < ADTT ≤ 5000 • Very Heavy Volume: ADTT > 5000

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Trucks can occur on a bridge in many different arrangements. Five loading patterns are defined as follows:

Single -- only one truck is present on the bridge in any lane. Following – two trucks in the same lane, with varying headway distances with a gap less than the span length. Side-by-Side -- two trucks in adjacent lanes with an overlap of more than one-half the truck

length of the first truck. Staggered -- two trucks in adjacent lanes with an overlap of less than one-half the truck

length of the first truck and a gap less than the span length (Figure 15) Multiple --- Simultaneous presence of trucks in adjacent lanes and in same lane

Figure 15 Staggered Truck Event with Overlap Less than One-Half Truck Length

For each WIM site with refined time stamp data, the cumulative frequencies for side-by-side, staggered and following events are obtained for headway separation from 0 ft. to 300 ft. in 20 ft increments. Report MP probabilities for each day for each site as a function of daily truck count and headway separations or gap. For each site the daily truck count will vary by day of week and by season. The study needs to be repeated for multiple WIM sites in several states with varying ADTTs (including very high ADTT > 5000) and on routes with a variety of functional classes. With a large dataset of MP statistics as a function of ADTT and highway class, guidelines for appropriate MP values for system-wide use may be developed. To calculate and report multiple presence percentages, use the following procedure:

• For each site, each direction, lump all days with light volume (daily truck counts ≤ 1000) into one bin. Find the average MP for each gap increment.

• For each site, each direction, lump all days with Average volume (daily truck counts > 1000 but ≤ 2500) into one bin. Find the average MP for each gap increment.

• For each site, each direction, lump all days with Heavy volume (daily truck counts > 2500 but ≤ 5000) into one bin. Find the average MP for each gap increment.

• For each site, each direction, lump all days with Very Heavy volume (daily truck counts > 5000) into one bin. Find the average MP for each gap increment.

Tabulate and chart the variation of MP as a function of gap and traffic volume (light, average, heavy and very heavy).

TRUCK 1

TRUCK 2

HeadwaySeparation

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Multiple-Presence Data from Published Literature (New Jersey WIM Sites) Multiple truck presence (MP) statistics based on actual truck load data from New Jersey (NJ) highways is available in the published literature (Gindy, M. and Nassif, H. (2006)). The data consist of WIM measurements from various sites located throughout New Jersey and recorded over an 11-year period, between 1993 and 2003 (with some gaps). The database included twenty-five (25) sites which are geographically dispersed across NJ and which constitute a variety of functional classes including rural and urban principal and minor arterials. The sites represent a variety of site-specific conditions including truck volume, road and area type, and number of lanes. The study did not include heavy truck traffic sites with ADTT > 5000. Timestamps of truck arrivals to the hundredth of a second were recorded. Statistics for various truck loading cases including single, following, side-by-side, and staggered are presented (see Fig. 16).

Figure 16 Variation of Multiple-Presence with Span Length – NJ WIM Sites Multiple truck presence statistics depend on factors such as truck volume, and bridge span length. The position of all trucks in the near vicinity were checked to determine whether multiple trucks simultaneously occur on the bridge The statistics shown below in Table 13 for multiple truck occurrences were extracted from Fig. 16 for various truck volumes and span lengths. As the paper

54

did not provide a tabulation of MP statistics, the values are close approximations scaled from the charts. Use a linear interpolation for other spans. Table 13 Maximum Observed Multiple Presence Probabilities as a Function of

ADTT and Bridge Span Length – NJ Sites

Maximum Side-by-Side Trucks Percent Probabilities Site Truck Traffic

Span Light: ADTT ≤ 1000

Average: 1000 < ADTT ≤ 2500

Heavy: 2500 < ADTT ≤ 5000

Very Heavy: ADTT > 5000

All Spans 0.30 0.90 1.00

Maximum Staggered Trucks Percent Probabilities Site Truck Traffic

Span Light: ADTT ≤ 1000

Average: 1000 < ADTT ≤ 2500

Heavy: 2500 < ADTT ≤ 5000

Very Heavy: ADTT > 5000

20 0.40 1.20 1.90 Not Available 40 0.60 1.60 2.30 Not Available 60 0.70 1.80 3.20 Not Available 80 0.80 2.00 3.80 Not Available 100 0.90 2.40 4.20 Not Available 120 1.00 2.60 4.60 Not Available 160 1.20 3.20 5.20 Not Available 200 1.40 3.60 5.90 Not Available

Maximum Following Trucks Percent Probabilities

Site Truck Traffic

Span Light: ADTT ≤ 1000

Average: 1000 < ADTT ≤ 2500

Heavy: 2500 < ADTT ≤ 5000

Very Heavy: ADTT > 5000

20 0.00 0.00 0.00 Not Available 40 0.00 0.00 0.10 Not Available 60 0.10 0.50 0.60 Not Available 80 0.60 1.00 1.20 Not Available 100 1.20 1.80 2.20 Not Available 120 1.80 2.40 3.40 Not Available 160 3.40 4.00 4.80 Not Available 200 4.40 5.40 7.80 Not Available

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Multiple-Presence Data from Current Research (New York WIM Sites)

By studying the occurrence of multiple trucks within a given headway separation at WIM sites with accurate time stamps, the effects of multiple trucks on a span can be simulated for WIM sites without accurate time stamps. Five WIM sites (ten directional sites) with free-flowing traffic in New York State were studied by the 12-76 Research Team in order to determine the maximum multiple presence probabilities for various truck traffic volumes. The sites chosen were Route 12 east bound and west bound (WIM site 2680), a rural state route, I-84 east bound and west bound (WIM sites 8280 and 8382), a rural interstate, I-81 north bound and south bound (WIM site 9121), a rural interstate, and Route 17 north bound and south bound (WIM site 9631), a rural state route. Two WIM sites on urban interstates (I-95and I-495) were studied, but not included in the results due to frequent traffic congestion which precludes free flowing traffic. Daily truck traffic volume was classified as light (less than 1000 trucks per day), average (more than 1000 trucks but less than 2500 trucks per day), heavy (more than 2500 trucks but less than 5000 trucks per day), and very heavy (more than 5000 trucks per day).

When considering multiple trucks on a given span, a multiple presence event is said to have occurred if the gap between two trucks, that is the distance between the last axle of the leading truck and the first axle of the trailing truck, is less than the span length. For instance, two trucks with a headway separation H ≤ 100 ft will be simultaneously on span of length = 100’ – truck length. Multiple presence probabilities were compiled for two trucks in adjacent lanes side-by-side, two trucks in adjacent lanes staggered, and two trucks in the same lane. For the purpose of simulating a multiple presence event, only the headway separation, that is the distance from the front axle of the lead truck to the front axle of the trailing truck, is important. Multiple presence probabilities were compiled for headway separations up to 300 feet, in 20-foot increments (Table 14).

For each day that truck data was captured at a WIM site, the number of multiple presence events that occurred in that day is recorded as a percentage of the total truck count for that day. The average multiple presence percentage is then calculated for all days with light truck volume, average truck volume, heavy truck volume, and very heavy truck volume, respectively. Each direction of traffic was considered separately. The maximum multiple presence percentages are summarized in the following tables.

Multiple-presence data at NY WIM sites were calculated in the NCHRP 12-76 Project using the same approach as the NJ statistics, to allow a direct comparison. The findings from the two states for side-by-side and staggered truck occurrences are quite comparable across most span lengths. The NJ values for following trucks are generally higher. The NY findings, defined in terms of headway separation intervals (Table 15), will be used in the interim to simulate multiple-presence events for sites where accurate time stamps are not available. This is achieved by categorizing the likelihood of trucks occupying various slots or headway intervals on the bridge either in the adjacent lane or in the same lane.

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Table 14 Maximum Observed Multiple Presence Cumulative Probabilities as a Function of Headway Separation and ADTT – NY Sites

Headway Light: Average: Heavy: Very Heavy:H (ft) ADTT < 1k 1k < ADTT < 2.5k 2.5k < ADTT < 5k ADTT > 5k

H < 20 0.19 0.41 0.61 0.00H < 40 0.33 0.84 1.27 0.00H < 60 0.54 1.25 1.95 0.00H < 80 0.80 1.60 2.57 0.00H < 100 1.00 2.13 3.33 0.00H < 120 1.21 2.54 4.14 0.00H < 140 1.45 2.88 4.80 0.00H < 160 1.62 3.18 5.41 0.00H < 180 1.80 3.47 5.97 0.00H < 200 1.99 3.73 6.49 0.00H < 220 2.09 3.97 6.97 0.00H < 240 2.23 4.21 7.42 0.00H < 260 2.35 4.43 7.85 0.00H < 280 2.49 4.64 8.26 0.00H < 300 2.60 4.84 8.66 0.00

Headway Light: Average: Heavy: Very Heavy:H (ft) ADTT < 1k 1k < ADTT < 2.5k 2.5k < ADTT < 5k ADTT > 5k

H < 20 0.00 0.00 0.00 0.00H < 40 0.00 0.00 0.00 0.00H < 60 0.01 0.00 0.00 0.00H < 80 0.02 0.00 0.00 0.00H < 100 0.08 0.04 0.03 0.00H < 120 0.20 0.19 0.19 0.00H < 140 0.41 0.52 0.64 0.00H < 160 0.77 1.09 1.37 0.00H < 180 1.25 1.76 2.28 0.00H < 200 1.71 2.51 3.26 0.00H < 220 2.22 3.19 4.20 0.00H < 240 2.70 3.86 5.11 0.00H < 260 3.12 4.51 5.98 0.00H < 280 3.53 5.11 6.83 0.00H < 300 3.92 5.70 7.63 0.00

Maximum Side-by-Side Truck Multiple Presence Cumulative ProbabilitiesSite Truck Traffic

Maximum Following Truck Multiple Presence Cumulative ProbabilitiesSite Truck Traffic

57

Table 15 Maximum Observed Multiple Presence Probabilities by Headway Interval as a Function of ADTT – NY Sites

Maximum MP Probabilities based on 5 WIM sites (10 directional sites) in New York State

Headway Light: Average: Heavy: Very Heavy:H (ft) ADTT < 1k 1k < ADTT < 2.5k 2.5k < ADTT < 5k ADTT > 5k

H < 20 0.19 0.41 0.61 0.0020 < H < 40 0.14 0.43 0.66 0.0040 < H < 60 0.21 0.41 0.68 0.0060 < H < 80 0.26 0.35 0.62 0.0080 < H < 100 0.20 0.53 0.76 0.00100 < H < 120 0.21 0.41 0.81 0.00120 < H < 140 0.24 0.34 0.66 0.00140 < H < 160 0.17 0.30 0.61 0.00160 < H < 180 0.18 0.29 0.56 0.00180 < H < 200 0.19 0.26 0.52 0.00200 < H < 220 0.10 0.24 0.48 0.00220 < H < 240 0.14 0.24 0.45 0.00240 < H < 260 0.12 0.22 0.43 0.00260 < H < 280 0.14 0.21 0.41 0.00280 < H < 300 0.11 0.20 0.40 0.00

Headway Light: Average: Heavy: Very Heavy:H (ft) ADTT < 1k 1k < ADTT < 2.5k 2.5k < ADTT < 5k ADTT > 5k

H < 20 0.00 0.00 0.00 0.0020 < H < 40 0.00 0.00 0.00 0.0040 < H < 60 0.01 0.00 0.00 0.0060 < H < 80 0.01 0.00 0.00 0.0080 < H < 100 0.06 0.04 0.03 0.00100 < H < 120 0.12 0.15 0.16 0.00120 < H < 140 0.21 0.33 0.45 0.00140 < H < 160 0.36 0.57 0.73 0.00160 < H < 180 0.48 0.67 0.91 0.00180 < H < 200 0.46 0.75 0.98 0.00200 < H < 220 0.51 0.68 0.94 0.00220 < H < 240 0.48 0.67 0.91 0.00240 < H < 260 0.42 0.65 0.87 0.00260 < H < 280 0.41 0.60 0.85 0.00280 < H < 300 0.39 0.59 0.80 0.00

Maximum Side-by-Side Truck Multiple Presence ProbabilitiesSite Truck Traffic

Maximum Following Truck Multiple Presence ProbabilitiesSite Truck Traffic

58

STEP 7 PROTOCOLS FOR WIM DATA ANALYSIS FOR ONE-LANE LOAD EFFECTS FOR SUPERSTRUCTURE DESIGN (SINGLE EVENTS AND FOLLOWING EVENTS)

Step 7.1 Load Effects for Single Events for Superstructure Design

a) Group data into bins by travel lane. Generate GVW relative and cumulative histograms for all trucks. Use 4 Kip bins.

b) Run the trucks (FHWA Class 6 and above – three or more axles) through moment and

shear influence lines (or structural analysis program) for simple and two-span continuous spans. Use span lengths of: 20’, 40’, 60’, 80’, 100’, 120’, 160’, and 200’.

c) Normalize maximum moment and shear values by dividing by the corresponding load

effects for HL-93. Generate a database table of normalized load effects. Make sure that each record contains GVW, class, # of axles, date, arrival time, travel lane, in addition to load effects. The date, GVW and arrival time will serve as a truck record indicator.

Step 7.2 Following Truck Events for Superstructure Design When Accurate Truck

Arrival Time Stamps are Available Load effects for following trucks may be obtained directly from the WIM data where accurate time arrival stamps are collected together with truck weight data. The load effects analysis is performed with the following trucks in their proper relative positions.

For estimating the maximum daily load effects for two random following trucks crossing the bridge as follows:

a) Combine the two trucks by superimposing the second truck on the truck first truck with the axles offset by the measured headway separation.

b) Run the combined truck through moment and shear influence lines for simple and two-span continuous spans. Use span lengths of: 20’, 40’, 60’, 80’, 100’, 120’, 160’, and 200’.

c) Repeat the process for each following truck event. d) Normalize the results by dividing by the effects of HL-93.

Step 7.3 Simulation of Following Truck Events When Accurate Truck Arrival Time

Stamps are not Available Load effects for following trucks may be obtained directly from the WIM data where accurate time arrival stamps are collected together with truck weight data. The load effects analysis is performed with the following trucks in their proper relative positions. Where accurate truck arrival time stamps are not available, generalized MP Statistics obtained in Step 6 may be used to simulate following trucks in their likely relative positions:

1. From Step 6, obtain the probabilities for following trucks in the same lane with varying headway separations (given in 20 ft increments) as a function of ADTT in each direction (see Table 15).

2. The number of expected multiple presence events in each direction for each headway

separation interval, H, can be determined from the equation:

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Number of MP Events = MP Probability x ADTT

3. Randomly select two trucks from the entire population of trucks in the desired direction. Being that there is no correlation between the truck population and travel lane, any two randomly selected trucks can be considered, regardless of lane, as long as the trucks are traveling in the desired direction.

4. Randomly select a headway separation within the desired headway separation interval.

5. With the randomly selected truck pair separated by the randomly selected headway

separation, maximum load effects can be calculated in the same manner as for trucks with accurate time stamps and measured headway separation (Step 7.2).

6. Repeat steps 3 through 5 for each headway separation interval and each direction of

travel until the expected number of multiple-presence events have been generated for each headway separation and each direction of travel.

7. Normalize by dividing the results by the effects of HL-93 loading.

STEP 7.4 Group Load Effects into STRENGTH I and STRENGTH II (One-Lane) Overloaded trucks seen in the WIM data could be either illegal overloads or authorized permit loads. It should be noted that separating permits from non-permit overloads in the WIM data is only viable where accurate permit records are available. In most jurisdictions only the special permit or single-trip permit moves are tracked in terms of their actual load configurations and travel routes. These heavy loads populate the upper tails of the load spectra and it would be beneficial to know which vehicles are authorized and which are illegal. Separating routine permits may not be possible due to the lack of necessary permit records at the state level and the sheer volume of permits in operation in most states. This is not considered a necessary requirement for live load modeling as routine permits can be taken as variations of the exclusion loads allowed under state law.

Legal loads and routine permits are grouped under STRENGTH I. Heavy special permits are grouped under STRENGTH II. For following events, if one of the trucks is a heavy special permit truck, group that loading event under STRENGTH II. Step 7.5 Assemble Single-Lane Load Effects Histograms for STRENGTH I and

STRENGTH II

a) Combine the normalized load responses of single truck events and following truck events into a single histogram for each load effect (M, V) and assemble in narrow bins of 0.02 increments for STRENGTH I and STRENGTH II. These combined histograms will represent the single lane load effects from a single truck or multiple trucks in the same lane.

b) These will constitute the single-lane measured load effects histograms

without any filtering for WIM sensor errors (see Step 10).

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STEP 8 PROTOCOLS FOR WIM DATA ANALYSIS FOR TWO-LANE LOAD EFFECTS FOR SUPERSTRUCTURE DESIGN (SIDE-BY-SIDE & STAGGERED EVENTS)

Step 8.1 Truck Load Effects from Trucks in Adjacent Lanes Using Accurate Truck

Arrival Time Stamps to the 1/100 th of a Second.

a) Determine the number of truck multiple presence (MP) events where trucks are in adjacent lanes in each direction for each day. During a MP event there could be more than one truck in a lane.

b) For each multiple-presence (MP) event obtain the headway separation between trucks in adjacent lanes and in the same lane using the WIM data.

c) For estimating the maximum daily load effects for two random trucks simultaneously crossing the bridge, proceed as follows:

1. Combine the two trucks by superimposing the second truck in the adjacent lane on the truck first truck with the axles offset by the headway separation.

2. Run the combined truck through moment and shear influence lines for simple and two-span continuous spans. Use span lengths of: 20’, 40’, 60’, 80’, 100’, 120’, 160’, and 200’.

3. Keep track of the normalized M and V 4. For each MP event, repeat the process

Step 8.2 Simulation of Load Effects of Trucks in Adjacent Lanes Using Generalized

MP Statistics.

1. From Step 6, obtain the probabilities for side-by-side/staggered trucks in adjacent lanes with varying headway separations (given in 20 ft increments) as a function of ADTT in each direction (see Table 15).

2. The number of expected multiple presence events in each direction for each headway

separation interval, H, can be determined from the equation:

Number of MP Events = MP Probability x ADTT

3. Randomly select two trucks from the entire population of trucks in the desired direction. Being that there is no correlation between the truck population and travel lane, any two randomly selected trucks can be considered, regardless of lane, as long as the trucks are traveling in the desired direction.

4. Randomly select a headway separation within the desired headway separation interval.

5. With the randomly selected truck pair separated by the randomly selected headway

separation, maximum load effects can be calculated in the same manner as for trucks with accurate time stamps and measured headway separation (Step 8.1).

6. Repeat steps 3 through 5 for each headway separation interval and each direction of

travel until the expected number of multiple-presence events have been generated for each headway separation and each direction of travel.

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Step 8.3 Group Load Effects into STRENGTH I and STRENGTH II (Two-Lane)

Overloaded trucks seen in the WIM data could be either illegal overloads or authorized permit loads. It should be noted that separating permits from non-permit overloads in the WIM data is only viable where accurate permit records are available. In most jurisdictions only the special permit or single-trip permit moves are tracked in terms of their actual load configurations and travel routes. These heavy loads populate the upper tails of the load spectra and it would be beneficial to know which vehicles are authorized and which are illegal. Separating routine permits may not be possible due to the lack of necessary permit records at the state level and the sheer volume of permits in operation in most states. This is not considered a necessary requirement for live load modeling as routine permits can be taken as variations of the exclusion loads allowed under state law.

Legal loads and routine permits are grouped under STRENGTH I. Heavy special permits are grouped under STRENGTH II. For multiple-presence events, if one of the trucks is a heavy special permit truck, group that loading event under STRENGTH II. Step 8.4 Assemble Two-Lane Load Effects Histograms for STRENGTH I and

STRENGTH II

a) Assemble normalized load effects frequency histograms for two-lane load effects for STRENGTH I and STRENGTH II in narrow bins of 0.02 increments

c) These will constitute the two-lane measured load effects histograms without

any filtering for WIM sensor errors (see Step 10). STEP 9 ASSEMBLE AXLE LOAD HISTOGRAMS FOR DECK DESIGN Step 9.1 One-Lane Axle Loads for Deck Design

a) Separate trucks into STRENGTH I and STRENGTH II groups. b) For each group, generate axle weight relative frequencies histograms for axle types:

Single, Tandem, Tridem, and Quad axles. Use a 2 Kip interval for the bins. Axles spaced at less than 6 ft to be considered as part of the same axle group.

c) This will constitute the measured axle load histogram without any filtering for

WIM sensor errors (see Step 10). d) Assuming normal distribution models for axle weight data for the filtered

histogram, determine the mean and standard deviation for: all axles, top 20% axles, top 5% axles. For each axle type report the 99th percentile statistic W99.

Step 9.2 Side-by-Side Axle Events for Two-Lanes.

Multiple-presence studies specifically for axles loads are performed for the two-lane loaded case. There will be a greater probability of side-by-side axle events than side-by-side truck events, due to the fact that each truck has two or more axles. However, an axle with a headway separation greater than the effective strip width for the slab as defined in the LRFD Specifications would not have an influence on the load effect of the axle in the adjacent lane and may be neglected. With

62

these key differences recognized, the process for multiple-presence computations for axle loads will follow an approach similar to that used for truck multiple presence studies.

a) Determine the number of side-by-side axle events in each direction for the following combinations:

• Single – Single • Single – Tandem • Tandem – Tandem • Other

STEP 10 FILTERING OF WIM SENSOR ERRORS / WIM SCATTER FROM

MEASURED HISTOGRAMS

The live load modeling protocols presented in this project rely on the weight histograms and the histograms of the corresponding load effects as collected from Weigh-In-Motion stations at various highway sites. Current WIM systems are known to have certain levels of random measurement errors that may affect the accuracy of the load modeling results. This section proposes an approach to filter out WIM measurement errors from the collected WIM data histograms. To execute the filtering process, a calibration of the results of the WIM system should be made by comparing the results of the WIM system to those of a static scale. The calibration process should be repeated several times within the WIM data collection time frame. The results of this calibration will be the basis for filtering out WIM measurement errors for each WIM data site.

10.1 WIM System Calibration Typical WIM calibration procedures consist of taking several WIM measurements from representative calibration trucks and compare the WIM measurements to those obtained from a certified static scale. Traditionally, it has been common to use a single truck for the calibration process although it would be advisable to use different trucks having different characteristics to ensure that the accuracy of the results remain consistent independent of the truck characteristics. As an example, Table 16 gives a summary sheet of the calibration data assembled for the northbound lane of site No. 7100 on I-87 in New York. The table shows the actual axle weight along with the weights estimated from the piezo-loop WIM system installed at the site. The WIM data was collected for 10 different crossings of the same calibration truck. The truck’s speeds were approximately 40 mph. Table 17 shows the ratio of the WIM weight divided by the actual weight for each of the 5 axles for the 10 crossings. The average of the ratios from all the 50 measurements is 0.97 with a standard deviation of 10%. The plot in Figure 17 of WIM error versus axle weight demonstrates that the correlation between the bias value and the axle weight is practically negligible. There appears to be a difference in the standard deviations as the axle weights change. However, more data is needed to analyze this trend more accurately. Similarly, it is not clear why the readings for axles 2 and 3 (or axles 4 and 5), which respectively have somewhat similar weights, are leading to large differences in their standard deviations.

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Table 16 Typical WIM calibration results for NY State DOT installations.

Table 17. WIM errors expressed as a ratio of measured values over actual values.

Pass 1st Axle 2nd Axle 3rd Axle 4th Axle 5th Axle Moment on 60-ft span1 0.92 1.07 0.90 1.07 1.03 1.042 0.94 0.88 0.91 0.88 0.98 0.923 0.81 0.88 0.95 1.38 1.01 1.214 0.91 0.98 0.90 1.06 0.94 1.005 0.99 1.13 0.98 0.84 1.03 1.056 1.01 0.86 0.98 1.05 1.02 1.037 1.02 1.18 1.07 0.89 0.93 1.068 0.89 1.01 0.87 1.14 1.08 1.109 0.94 0.99 0.91 1.04 1.02 1.0210 0.97 0.86 0.97 0.96 0.97 0.96 Overall Axle Moment

Average 0.94 0.98 0.94 1.03 1.00 1.04 Average 0.97 1.04Stdev 0.062 0.116 0.059 0.157 0.046 0.078 Stdev 0.100 0.078

SITE: 7100

DATE:

Sensor configuration Piezo-Loop_Piezo Contract#/Sales Order

Drive Trailer 60-ft

Steer 2nd Axle 3rd Axle Total 4th Axle 5th Axle Total GVW Moment Axle 1-2 Axle 2-3 Axle 3-4 Axle 4-5 Length

Actual 12.61 16.10 15.85 31.95 20.28 18.75 39.03 83.58 275.37 12.83 4.50 37.25 4.13 58.71

Pass 1st Axle 2nd Axle 3rd Axle Total 4th Axle 5th Axle Total GVW Moment Axle 1-2 Axle 2-3 Axle 3-4 Axle 4-5 Length

1 11.60 17.20 14.20 31.40 21.70 19.30 41.00 84.0 287.2 12.3 4.6 37.3 4.10 58.30

2 11.90 14.10 14.40 28.50 17.90 18.40 36.30 76.7 254.3 12.3 4.6 37.2 4.00 58.10

3 10.20 14.20 15.00 29.20 28.00 19.00 47.00 86.4 332.2 12.8 4.5 37.1 4.00 58.40

4 11.50 15.70 14.30 30.00 21.50 17.60 39.10 80.6 275.2 12.80 4.50 37.20 4.00 58.50

5 12.50 18.20 15.50 33.70 17.00 19.30 36.30 82.5 288.3 12.8 4.5 37.2 4.00 58.50

6 12.70 13.90 15.60 29.50 21.20 19.20 40.40 82.6 283.7 12.8 4.6 37.3 4.00 58.70

7 12.80 19.00 17.00 36.00 18.00 17.50 35.50 84.3 292.8 16.7 4.4 33.2 4.10 58.40

8 11.20 16.20 13.80 30.00 23.10 20.20 43.30 84.5 303.8 12.8 4.6 37.2 4.10 58.70

9 11.80 15.90 14.40 30.30 21.00 19.20 40.20 82.3 281.6 12.8 4.5 37.2 4.10 58.60

LOCATION: I87 Champlain Exit 42 Rt 11 (BIN 1009070) - Acc Rt 9

5/25/2006

Lane: 1 Northbound

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WIM Bias versus Axle Weight

y = 0.0121x + 0.777R2 = 0.1048

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 5 10 15 20 25

Axle weight in Kips

WIM

Bia

s (m

easu

red

wei

ght/a

ctua

l w

eigh

t)

Figure 17 Plot of WIM error ratio versus axle weight for I-84 site

Axle weight histograms are needed for modeling the live loads for deck design, while the design of main bridge members requires the maximum bending moment and shear force effect. Thus, for main bridge members, it is more important to study the influence of WIM errors on the load effect rather than on the axle weights. Because main member load effects are influenced by the weight and spacing of several axles, some of the axle weight errors will cancel out and thus the overall error may have a lower standard deviation than that for individual axles. For example, for the calibration data of the same I-87 site studied above, the maximum moment effect of the calibration truck for a 60-ft simple span beam would be equal to 275.4 kip-ft, if the actual axle weights and axle spacings were used. The maximum moment effect for the values obtained from the eighth pass would be 303.8 kip-ft. The maximum moment from the 10 different passes are provided in Table 16 showing an overall average error ratio of 1.04 and a standard deviation of 7.8%. These are compared to an average error of 0.97 and a standard deviation of 10% for the axle weights. The information provided in Table 16 can be used to filter out the errors from the axle weight and moment effect histograms as described in the next section.

The variation of the ratio with each truck crossing indicates that the measured axle weight to actual axle weight ratio is a random variable designated as ε with a mean value of 0.97 and a standard deviation of 10% for this particular site. Figure 18, shows a plot of the axle error ratio data on a Normal probability plot. With only one exception, all the data lies within the 95% confidence levels indicating that the data can be reasonably well represented by a Normal probability distribution function. This information will be required to execute the WIM error filtration as will be discussed in the next section. In the following we are assuming that these results are valid for all the trucks collected at the WIM sites independent of truck type, vehicle speed and time at which the WIM measurements were taken. A sensitivity analysis is the performed in Appendix E to study how the standard deviation of the error would affect the results.

65

0.7 0.8 0.9 1.0 1.1 1.2 1.3

1

5

10

20304050607080

90

95

99

Data

Per

cent

Normal Probability Plot for Axle Error,

ML Estimates

Mean:

StDev:

0.979369

0.0986870

Figure 18 Plot of WIM axle error ratio on Normal Probability Plot.

10.2 WIM Error Filtration Procedure Let us assume that the actual weight of an axle, or the actual moment effect of a truck, is denoted by xr, while the measured value using the WIM system is xm. Because of WIM system measurement errors, the difference between the measured value and the actual value can be represented by a calibration factor or an error ratio, ε. Because the error may depend on various random factors related to the WIM system’s characteristics and truck/structure/WIM system dynamic interaction as well as some truck features including tire size and pressure, the calibration factor ε is a random variable that relates the measured WIM data results to the “true” weight through the equation:

ε= rm xx (16) If the histogram and statistical information for ε are obtained from the calibration of the WIM system, these statistics can be used to filter out the errors in the measured raw WIM truck weight histogram collected at a given site. Our goal then is to obtain the histogram of xr given that the measured data give the histogram of xm and given the statistics of ε using the equation:

ε= m

r

xx (17)

Since the error ε varies randomly, it will not be possible to obtain xr for each particular truck. Instead, an algorithm can be developed to obtain a histogram for all the actual truck weights given the histogram of the measured weights and the probability distribution of the error ratio ε.

The WIM data collected at a site will produce a histogram for xm which can be related to the probability distribution function of xm represented by fxm(…).

Similarly, the calibration of the WIM system will provide information on the distribution function of ε represented by fε(...). For example, the WIM calibration of the I-84 NB lane 4 indicates that the error of the WIM system axle weights can be modeled as a Normal probability

66

distribution with a probability function fε(ε) with mean value 97.0=ε and a standard deviation σε=0.10.

Since xr is the ratio of two random variables with known probability distribution functions, the probability distribution function of the actual weight xr, fxr(…), can be obtained using the expression (Ang & Tang 2007):

( ) ( )∫∞

∞−ε= dyy,zyfyzf ,mXrX (18)

The analysis of the correlation of the error with the actual magnitude of the axle weight, as illustrated in Figure 17, has shown that they are practically independent i.e. the percent error does not depend on the magnitude of the actual truck weight. One should note however, that the number of readings is limited to those of a single truck. Actual statistics for ε should be obtained from runs of different trucks at normal highway speeds. If one assumes that the measured truck weight xm and the error ε are also independent random variables, then Equation 18 can be expanded as:

( ) ( ) ( )∫∞

∞−ε= dyyfzyfyzf

mXrX (19)

10.3 WIM Error Filtration Algorithm The integration of Equation 19 can be executed numerically using a simple algorithm so that the integration is changed into a simple summation and the equation can be represented as:

( ) ( ) ( )∑=

=yofvaluesall

mXrX yyfzyfyzfε

ε Δ (20)

Recalling that the probability distribution functions of ε, xr, and xm are related to the histograms by:

( ) ( ) yyfyH Δεε = ( ) ( ) zzfzH

rxrx Δ= (21)

( ) ( ) )zy(zyfzyHmxmx Δ=

where Δ(...) is the bin size for each histogram. If the bin sizes for the histogram of the actual weight xr and that of the measured weight xm are taken to be the same, so that ( )zyz ΔΔ = , then Equation 20 can be expressed as:

( ) ( ) ( ) ( ) ( )∑=

=yofvaluesall

mXrX yyfzzyfyzzfε

ε ΔΔΔ (22)

( ) ( ) ( )∑=

=yofvaluesall

mxrx yyfzyHyzHε

ε Δ (23)

Thus, given the histogram of the measured WIM data, xm, and the probability distribution of the calibration factor, ε, the integration of Equation 19 for all possible values of xr=z can be executed numerically using software tools.

67

The protocols for calculating Lmax should then be executed using the filtered histogram Hxr(z). Implementation of the above WIM Error Filtration Algorithm, based on NY calibration data, is given in Appendix E. STEP 11 ACCUMULATED FATIGUE DAMAGE AND EFFECTIVE GROSS

WEIGHT FROM WIM DATA WIM data can be used to study the stress range produced by individual trucks on a bridge component. Damage accumulation laws such as Miner’s rule can then be used to estimate the fatigue damage for the whole design period for the expected truck population at a site.

Obtain cumulative fatigue damage from WIM population and compare to LRFD fatigue truck (Fig. 19, 54 Kip gross weight) moments for each span. Use span lengths of: 20’, 40’, 60’, 80’, 100’, 120’, 160’, and 200’. Determine fatigue damage adjustment factor K, defined as:

( )

1/33

#i

FT

MK M

Trucks

⎡ ⎤⎢ ⎥× =⎢ ⎥⎣ ⎦

∑ (24)

MFT = Moment from LRFD fatigue Truck, includes 0.75 load factor K = Fatigue Damage Adjustment factor Mi = Moment range of trucks measured # Trucks = Total number of trucks measured. Figure 19 LRFD Design Fatigue Truck (54 Kips)

Obtain K for each span. For varying spans, determine the effective gross weight for trucks measured at the site using the Equation:

( )1/33eq i iW f W= ∑ (25)

Where fi is the fraction of gross weights within interval i, and Wi is the mid-width of interval i. In this calculation use trucks only with three or more axles (Class 6 and above).

14’ 30’

6 k 24 k 24 k

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STEP 12 LIFETIME MAXIMUM LOAD EFFECT Lmax FOR SUPERSTRUCTURE DESIGN (STRENGTH I)

Step 12.1 Methods for Estimating Lmax

In order to check the calibration of load models and/or load factors for a specification, it is necessary to estimate the mean maximum loading or load effect Lmax. If further calibration of the Specification is to be carried out, the corresponding COV should also be found. The estimation of the maximum load effect Lmax expected over a 75-year bridge design period can be executed through a variety of methods. Simplified analytical methods or simulations may be used to estimate the maximum loading over a longer period, from short-term WIM data. This has to be done from a limited set of data that is collected for truck weights and truck configurations as well as truck traffic headways over relatively short periods of time. These methods can be categorized as:

a) Convolution or Numerical Integrations, b) Monte Carlo Simulations, c) Simplified Statistical Projections

The models require as input the WIM data collected at a site after being scrubbed for data quality and filtered for WIM errors as described in the previous steps. The design of bridges requires the estimation of the maximum load effect over periods of 75 years. The convolution method uses numerical integrations of the collected WIM data histograms to obtain projections of the expected maximum load effect within a given return period (e.g. 75-years). The WIM data collected cannot reasonably be accurate enough in the tail of the distributions to obtain good estimates of the parameters for such extended return periods. Hence, the only possible means to obtain the parameters of the distributions of the 75-year maximum load effect is by using statistical projections. The probability distribution of the maximum value of a random variable will asymptotically approach an extreme value distribution as the number of repetitions increases. Generally a Gumbel fit can be executed on the tail of the short-term maximums for statistical projections.

An alternative to the convolution approach consists of using a Monte Carlo simulation to obtain the maximum load effect. The Monte Carlo simulation uses random sampling from the collected data to obtain the maximum load effect. A Monte Carlo simulation requires the performance of an analysis a large number of times and then assembling the results of the analysis into a histogram that will describe the scatter in the final results. Each iteration is often referred to as a cycle. The process can be executed for the single lane-loading situation or the side-by-side loading. The Monte Carlo Simulation may be performed to find Lmax in one of two ways:

Use the empirical histogram to find Lmax by simulation for a short period and then project for a longer period (use an extreme value distribution such as Gumbel distribution). As mentioned earlier, the probability distribution of the maximum value of a normal random variable will asymptotically approach the Gumbel distribution.

Alternatively, use a smoothed tail end of the WIM histogram by fitting the tail with a

known probability distribution function (such as the Normal distribution) and use that fitted distribution with the Monte Carlo simulation. This will require a very large number of repetitions.

69

It should be emphasized however, that the Monte Carlo simulation would be very inefficient for projections over long return periods when the number of repetitions are very high. (Algorithms such as Markov Chain Monte Carlo modeling may allow improved performance in such cases). Furthermore, one should make sure not to exceed the random number generation limits of the software used, otherwise the generated numbers will not be independent and the final results will be erroneous.

Simplified statistical projections for estimating the maximum load effect in a given return period can be developed based on the assumption that the tail end of the moment load effect for the original population of trucks as assembled from the WIM data approaches a Normal distribution. The method uses the properties of the extreme value distribution. Equations in closed form provide such a projection, requiring much less effort than the convolution approach. The estimation of the maximum load effect for two side-by-side trucks improves as the return period increases. This is again due to the asymptotic nature of the solution, which yields good results only as the number of load repetitions increases and as the sampling is made from the tail end of the raw WIM histogram. Step 12.2 Procedure for calculating Lmax from WIM data Using an Extreme Value

Distribution for the Upper Tail

There are several possible methods available to calculate the maximum load effect for a bridge design period from truck WIM data. The one implemented in these protocols is found to be one of the easiest methods that provide results comparable to many other methods including Monte Carlo simulations. This method is based on the assumption that the tail end of the histogram of the maximum load effect over a given return period approaches a Gumbel distribution as the return period increases. The method assumes that the WIM data is assembled over a sufficiently long period of time to ensure that the data is representative of the tail end of the truck weight histograms and to factor in seasonal variations and other fluctuations in the traffic pattern. The use of WIM data for a whole year will satisfy this requirement. In a separate analysis this study will investigate how the confidence intervals in the projection results are affected by the number of samples collected and the number of days for which the WIM data is available, especially when only limited data is available at a site.

Sensitivity analyses have shown that the most important parameters for load modeling are those that describe the shape of the tail end of the truck load effects histogram. Current WIM technology has certain levels of random measurement errors that may affect the accuracy of the load modeling results. To bring uniformity in the load modeling process, a standardized approach to executing the error filtering procedure that utilizes calibration statistics for the WIM scale is described in Step 10. This procedure should be executed on the raw data prior to calculating Lmax. Step 12.2.1 Protocols for calculating maximum load effect Lmax The process begins by assembling the WIM truck weight data and load effects for single lane events and two-lane events and filtering the data for WIM sensor errors.

• Assemble the measured load effects histograms (moment effect or shear force effect) in narrow

bins of 0.02 increments. • Execute a statistical algorithm to filter out WIM scatter / sensor errors from the load effect s

histograms as described in Step 10.

70

• Find the cumulative distribution function Fx (x) = cumulative distribution function value for each event x sample by dividing the number of samples in a bin by the total number of samples and adding the value to the value in the previous bin.

• Calculate the standard deviate of the cumulative function for each bin. In MS EXCEL this can

be achieved by taking NORMSINV(F(x)). • Take the upper 5% of the values and plot the Normal deviate versus X.

• Take the trend line and find the slope, m, and the intercept, n, of the regression line.

• Find the mean of Normal that best fits the tail end of the distribution as μevent = -n/m.

• Find the standard deviation of the best fit Normal to be σevent= (1-n)/m- μevent.

• Take the number of events per day, nday

• Find, N, the total number of events for the return period of interest. For 75-years take N=

nday*365*75 • The most probable value, u, for the Gumbel distribution that models the maximum value in 75

years Lmax is given as:

( ) ( ) ( )( ) ⎥

⎥⎦

⎤

⎢⎢⎣

⎡ +−×+=

Nln224ln)Nln(lnNln2u eventeventN

πσμ (26)

• The dispersion coefficient for the Gumbel distribution that models the maximum load effect

Lmax is given as:

( )event

N

Nln2σ

α = (27)

• The mean value of Lmax is given as:

N

uLα

μ 577216.0maxmax +== (28)

• Calculate the standard deviation of the Gumbel distribution that best models the maximum

daily effect as:

Nαπσ6max = (29)

71

Step 12.3 Alternate Method for Calculating Maximum Load Effect Lmax Using Monte-Carlo Simulation

An alternative to the statistical projections approach described in Step 12.2 consists of using a Monte-Carlo simulation to obtain the maximum load effect. If there are not enough multiple events recorded in the WIM data, one could utilize simulations to generate MP events that conform to the measured statistical MP probabilities. In this approach, results of WIM data observed over a short period can be used as a basis for projections over longer periods of time. It should be noted that the Monte-Carlo method for single-lane events will not be able to give Lmax for 75-years directly. At best a one-week or a one-month maximum single event could be obtained from a year’s worth of WIM data as the Monte-Carlo simulation will not go beyond the maximum value measured at the site. A statistical projection technique must then be executed to extend the single event results to 75 years. Alternatively, one can use the fitted Normal distribution to represent the tail end of the histogram rather than use the raw data histogram and then the projection is automatically performed by the simulation. The same is not true for the two-lane loading cases as the Monte-Carlo procedure will simulate more samples of side-by-side events based on the observed multiple-presence probabilities.

A Monte-Carlo simulation requires the performance of an analysis a large number of times and then assembling the results of the analysis into a histogram that will describe the scatter in the final results. The process can be executed for the single lane-loading situation or the side-by-side loading. Figure 20 gives a schematic representation of the Monte Carlo Simulation, which follows the procedure described in the following steps:

Figure 20 Schematic illustration of Monte Carlo simulation procedure.

1. Assemble the data representing the filtered load effects for the trucks in the drive lane

into a histogram labeled Bin I in Figure 20.

Truck in Lane 1 Truck in Lane 2

Bin I Bin II

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2. Assemble the data representing the filtered load effects for the trucks in the passing lane into a histogram labeled Bin II in Figure 20.

3. Assemble the corresponding cumulative frequency curves for the two histograms. 4. Determine a main return period, treturn, for which the expected maximum moment is

desired. For example, a one-week, one-month, a two-year, or a 75-year period may be selected. However, as noted earlier, it is unlikely that the sample size of the available WIM data will be sufficiently large to obtain results for the large return periods. Hence, it is expected that the process will be applicable for only short periods say a one-week or a one-month period the results of which can then be projected for longer periods using the extreme value projection. Alternatively, one can use the fitted Normal distribution to represent the tail end of the histogram rather than use the raw data histogram and then the projection is automatically performed by the simulation.

5. Use a uniform distribution random generator to produce a pseudo random number varying between 0 and 1. Such random generator routines are provided in all general-purpose computer software and programming tools (such as EXCEL, MATLAB).

6. The pseudo-random number of step 5 will serve to select a single value from Bin I representing the load effect of a truck arriving in the drive lane. The selection of the moment effect is executed by assuming that the pseudo-random number generated (call it ran1i) represents the cumulative frequency of the moment for this truck. Thus, to find the value of the moment, X1i, the cumulative distribution function needs to be inverted so that X1i = ( )i1

11x ranF− where ( )...F 1

1x− is the inverse of the cumulative function for the effect of

the trucks in the drive lane. (Figure 21).

Figure 21 Schematic illustration of the random generation of a sample X1i.

.

.

.

.

.

.

.

Ran1

X1i

73

7. For estimating the maximum load effect for the trucks crossing the bridge in the drive lane, follow steps a through e, otherwise skip this step and go to step 8.

a) Find the number of loading events in the drive lane, K1, corresponding to the pre-

selected return period treturn. b) Repeat steps 5 through 6 K1 times to generate K1 samples for the moments in the

drive lane in the period treturn. c) Compare the K1 values and choose the largest one of these. This will give you

one estimate of the maximum expected value in treturn, which is designated as X1mx K1.

d) Repeat steps a through c for several cycles to generate several estimates of the maximum value X1mx K1.

e) Assemble the values collected in step d in a histogram. Also, find their average value and standard deviations.

8. For estimating the maximum response for two side-by-side trucks, do the following:

a) Repeat steps 5 and 6 by generating a pseudo number ran2i, which represents the cumulative frequency of the moment for trucks in the passing lane. Find the value of the moment, X2i, by inverting the cumulative frequency, Fx2(…), for the load effects of the truck in the passing lane so that X2i = ( )i2

12x ranF− .

b) Assuming that the maximum effect of the truck in the drive lane occurs at the same time that the maximum effect of the truck in the passing lane, add the moment effects of these two trucks to produce the moment effect of a single side-by-side event Xsi=X1i+X2i.

c) Repeat the process Ks times where Ks=number of side-by-side events expected in the basic return period treturn.

d) Compare all the Ks moment effects Xs1 … XsKs and take the maximum value out of these Ks values. This will produce a single estimate of the maximum response corresponding to the basic return Xs max Ks.

e) Repeat the whole simulation process m cycles to get m estimates of Xs max Ks. f) Obtain the histogram of the m estimates of Xs max Ks and calculate the average

value and standard deviation. STEP 13 DEVELOP AND CALIBRATE VEHICULAR LOAD MODELS FOR

BRIDGE DESIGN Step 13.1 Superstructure Design live load Calibration (STRENGTH I) There are two calibration methods that can be applied to calibrate a new live load model based on recent changes in truck weights:

Method I: The first approach, which is relatively simple, is to focus on the mean or expected maximum live load variable, Lmax. That is, assume that the present LRFD calibration and safety indices are adequate for the strength and load data then available, but update the load model or the load factor for current traffic conditions in a manner consistent with the LRFD calibration approach. One key assumption in this regard is that the site-to-site variability in Lmax as measured by the COV (Coefficient of variation COV = STDEV/Mean) is the same as that used during the

74

AASHTO LRFD calibration. In AASHTO LRFD calibration, the overall live load COV was taken as 20%.

Method II: If the variability in the WIM data is much greater than that assumed in the

calibration, then the entire LRFD calibration to achieve the target 3.5 reliability index may no longer be valid for that state and a simple adjustment of the live load factor as given above should not be done. The second approach, which is more robust, is to perform a reliability analysis using the new statistical data for live loads and determine the live load factors needed to achieve the same reliability target adopted in the LRFD calibration.

Method I: Simplified Adjustment of STRENGTH I Live Load Factor

The process adjusts the loading model and/or the corresponding live load factor by the ratio:

r1 = Lmax from WIM data projections for one-lane (30) Lmax used in existing LRFD calibration for one-lane

r2 = Lmax from WIM data projections for two-lanes (31) Lmax used in existing LRFD calibration for two-lanes An increase in maximum expected live load based on current WIM data can be compensated in design by raising the live load factor in a corresponding manner. The basic steps are summarized as follows:

a) Obtain quality WIM data from a variety of jurisdictions and traffic conditions and Compute the expected lifetime maximum load, Lmax, for each data set for one-lane and for two-lane loadings

b) Compare Lmax for a suite of bridges to this expected 75-year maximum load for a similar suite of bridges given by NCHRP 368.

c) Compute the average ratio, r (Lmax WIM data, divided by Lmax Ontario data) for one-lane and for two-lanes. Compute also the corresponding COV for all sites examined.

d) Adjust the design requirements by modifying the live load factor by the average ratio, r, as given above. If r is relatively uniform over the suite of bridges used to fix Lmax then the HL-93 model can be maintained without adjustment. It is relatively easy to modify the live load factor γL but this cannot be done unless it applies to every span.

Lmax Used in Existing LRFD Calibration NCHRP Report 368 provides mean maximum moments and shears for various periods of time from one day to 75-years for simple span moments, shears and negative moments for continuous spans. Span lengths range from 10 ft to 200 ft (Table 18). Continuous spans are comprised of two equal spans. Continuous span positive moments and shears at the center pier have not been provided in the report. The maximum one lane load effect is caused either by a single truck or two or more trucks (with the weight smaller than that of the single truck) following behind each other. There was little data to verify statistical parameters for multiple presence. The maximum values of moments and shears were calculated by simulations. For two lane moments and shears, simulations indicated that the load case with two fully correlated side-by-side trucks will govern, with each truck equal to the maximum two-month truck. The ratio of the mean maximum 75-year moment (or shear) and a mean 2-month moment (or shear) is about 0.85 for all spans.

75

Table 18. Lmax Used in Existing LRFD Calibration

One-Lane Two-Lane One-Lane Two-Lane One-Lane Two-Lane

20 1.30 2.12 1.23 2.12 1.27 2.2840 1.35 2.34 1.23 2.18 1.30 2.4060 1.32 2.30 1.23 2.22 1.25 2.3080 1.32 2.28 1.27 2.26 1.21 2.24100 1.31 2.26 1.28 2.28 1.20 2.22120 1.29 2.24 1.22 2.20 1.20 2.22160 1.24 2.18 1.20 2.14 1.20 2.22200 1.23 2.16 1.17 2.08 1.20 2.22

Span (Ft)

75-Year Lmax Used in LRFD Calibration (normalized by HL-93 load effects)

Simple Span Moment Simple Span Shear Negative moment75-Year Lmax

Based on the above simple method, an increase in the maximum expected 75-year live load as estimated from current WIM data can be accounted for in the design equation by raising the live load factor in proportion to the ratio of the estimated live load projection from WIM data to the value used during the calibration of the AASHTO LRFD Specifications. Method II Reliability Analysis and Adjustment of STRENGTH I Live Load Factor The simplified approach in Method I focuses on the maximum live load variable, Lmax, assuming that the overall LRFD calibration, multiple presence factors, and target reliability indices are adequate. Hence, the approach only updates the load factors to better represent current truck traffic conditions. One key assumption in this regard is that the site-to-site variability in Lmax as measured by the COV (Coefficient of variation COV = STDEV/Mean) is the same as that used during the AASHTO LRFD calibration. In AASHTO LRFD calibration, the overall live load COV was taken as 20%. This 20% includes site-to-site variability, uncertainties in estimating the load distribution factors, uncertainties in estimating the dynamic allowance factor, the uncertainties in estimating Lmax due to the randomness of the parameter and the limitations in the data.

When implementing the draft protocols using recent WIM data in Task 8 from various States, it became evident that this procedure, while simple to understand and use, had certain limitations when applied to statewide WIM data. Using a single maximum or characteristic value for Lmax for a State would be acceptable if the scatter or variability in Lmax from site-to-site for the state was equal to (or less than to be conservative) the COV assumed in the LRFD calibration. If the variability in the WIM data is much greater than that assumed in the calibration, then the entire LRFD calibration to achieve the target 3.5 reliability index may no longer be valid for that state and a simple adjustment of the live load factor as given above should not be done. The site-to-site scatter in the Lmax values obtained from recent WIM data showed significant variability from span to span, state to state, and between one-lane and two-lane load effects as given in Table 19 for a sample set of states. For example, the data from Florida show a COV for the moments of simple span bridges under one-lane loadings that varies from 32.5% for the 20-ft simple spans to 22.3% for the 200-ft simple span. These COV’s for site-to-site must be augmented by the COV’s for the other variables that control the maximum load including within site variability, the effect of the Dynamic allowance factor, Load distribution factor, and WIM data sample size, leading to much higher overall COV for the live load than the 20% used during the AASHTO LRFD

76

calibration. For the same maximum moment of simple span bridges under one-lane loading, the site-to site variability for the data collected in California shows a COV that ranges between 19.3% for the 20-ft simple span bridges down to 5.9% for the 200-ft simple span bridges. Table 19 Site-to-Site Variability in Lmax Measured by Coefficient of Variation (COV)

State Event Type 20 40 60 80 100 120 160 200M-simple 1-Lane

FL COV 0.325 0.307 0.278 0.276 0.270 0.260 0.238 0.223IN COV 0.185 0.137 0.122 0.135 0.147 0.142 0.122 0.132CA COV 0.193 0.104 0.045 0.054 0.061 0.062 0.058 0.059

M-simple 2-LaneFL COV 0.201 0.187 0.213 0.213 0.207 0.207 0.206 0.212IN COV 0.150 0.139 0.132 0.125 0.116 0.113 0.116 0.119CA COV 0.112 0.125 0.136 0.146 0.133 0.126 0.121 0.113

V-simple 1-LaneFL COV 0.340 0.299 0.289 0.279 0.248 0.241 0.224 0.214IN COV 0.188 0.129 0.108 0.113 0.105 0.103 0.115 0.131CA COV 0.143 0.087 0.056 0.047 0.049 0.049 0.058 0.056

V-simple 2-LaneFL COV 0.203 0.204 0.205 0.183 0.174 0.175 0.180 0.189IN COV 0.140 0.119 0.122 0.133 0.134 0.136 0.135 0.140CA COV 0.109 0.127 0.137 0.120 0.113 0.112 0.107 0.109

SPAN (ft)

Overall the results of Table 19 indicate that the Florida sites evidenced the highest variability in Lmax, whereas California data was a lot more uniform. As shown by the data in Table 19, the site-to-site COV statistics alone for FL are greater than the overall live load COV used in the LRFD calibration. On the other hand, the site-to-site COV statistics for CA are lower. It should also be noted that the one-lane COV’s for Florida are higher than the Two-lane COV, whereas in California the two-lane event have a higher site-to-site variability.

The maximum Lmax values, site-to-site variability in Lmax as well as the variability in one-lane vs. two-lane events are influenced by several factors that appear to be state-specific. These factors include:

1. The presence of exclusion vehicles that are state legal loads --- these heavy hauling vehicles usually operate mostly on state truck routes. There is likely to be a greater variation in truck weights on different routes in states with exclusion vehicles such as Florida. These heavy exclusion vehicles (and routine permits) may also be resulting in high Lmax values for the one-lane loaded case. It should be noted that all trucks with six or fewer axles were grouped in the STRENGTH I calibration. This group included legal loads, exclusion loads, as well as non-flagged routine permits.

2. The load limit enforcement environment in a state will have an influence on the level of illegal overloading. For instance, California is known to have an effective truck weight monitoring (and enforcement) operation that effectively utilizes the network of weigh-in-motion systems throughout the state.

3. Site-to-site variability in truck weight data is also impacted by the quality and reliability of WIM data collected at the remote WIM sites. WIM data quality is highly dependant on the WIM quality assurance programs implemented by the State DOTs. Quality assurance programs must regularly check data for quality and require system repair or recalibration when suspect data is identified. Weighing accuracy is also sensitive to roadway conditions. Less variability in traffic data is expected when all WIM systems are maintained to the same standard of performance and data accuracy.

77

In order to incorporate the site-to-site statistical variations in WIM data collected in a given State, a reliability-based approach to adjusting the live load factors is proposed as described in this report. RELIABILITY-BASED ADJUSTMENT OF LIVE LOAD FACTORS AASHTO LRFD Background The calculation of the Lmax values is meant for use to adjust the live load factors in the LRFD design check equations. Since Lmax is a random variable with high levels of uncertainties including site-to-site variability, the most appropriate procedure for adjusting the live load factor is by applying the principles of structural reliability. A reliability-based procedure for adjusting the live load factors would explicitly account for the variations in the Lmax values as well as the other variables that control the loading of a bridge member and its capacity to resist the applied loads. The variability in the Lmax values are due to the random nature of Lmax including the projection to the 75-year design life, the limitation in the data sample size collected within each site, and site-to-site variability. For developing a new design code, the Lmax values for a wide range of nationally representative sites should be used as input. For adjusting the live load factors to reflect state-specific truck weights and truck traffic patterns, Lmax values obtained from a representative sample of sites within the state should be used. This section illustrates how the reliability-based adjustment of the live load factor can be executed given a set of Lmax values obtained from WIM data. The LRFD design equation takes the form

nLCDCWDWn LDDR γγγφ ++≥ (32) where φ and γ are the resistance and load factors, Rn is the nominal resistance, DW is the dead load effect for wearing surface, DC is the dead load effect for the components and attachments and Ln is the live load effect of the HL-93 load including dynamic allowance and load distribution factor. According to the LRFD specifications φ =1.0 for the bending moment capacities of steel and prestressed concrete members, γDW=1.50, γ DC=1.25. The current live load factor is given as γL=1.75. The dynamic allowance factor is 1.33 times the truck moment effect and the load distribution factor is calculated as a function of span length and beam spacing for different numbers of loaded lanes. If the Weigh-In-Motion data in a particular state show large differences from the standard generic data used during the calibration of the AASHTO LRFD equations, it may be necessary to adjust the LRFD live load factor to maintain the same safety levels. The adjustment requires the modeling of the live load effects and the other random variables that control the safety of bridge members. Modeling of Live Load Effect on a Single Beam For bending of typical prestressed concrete and steel girder bridges loaded by one lane of traffic, the load distribution factor equation is given as (AASHTO, LRFD, 2007):

78

1.0

3s

g3.04.0

Lt12K

LS

14S06.0.F.D ⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛+=

(33) Where S is the beam spacing, L is the span length, ts is the deck thickness, and Kg is a beam stiffness parameter. Note that Equation 33 already includes a multiple presence factor m=1.2 which accounts for the higher probability of having one heavy truck in one lane as compared to the probability of having two side-by-side heavy trucks in two adjacent lanes. For two lanes loaded, the load distribution factor equation for bending becomes (AASHTO, LRFD, 2007):

1.0

3s

g2.06.0

Lt12K

LS

5.9S075.0.F.D ⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛+=

(34) Observing that the Lmax values are for the normalized total static load effects on a bridge and observing that the D.F. of Equation 33 for a single lane already includes a multiple presence factor m=1.2, the final mean value for maximum load effect on a single beam can be calculated for one lane and two lanes loaded as:

For one lane 2.1/.F.DIMHLLLLL 93maxbeammax ×××== (35)

For two lanes 2/.F.DIMHLLLLL 93maxbeammax ×××== Dividing D.F. of one lane by 1.2 is done to remove the multiple presence factor, while dividing the D.F. of two lanes by 2 is done to account for the fact that the Lmax values for two lanes calculated in this report are normalized by dividing by the effect of one lane of HL-93 loading The COV of the maximum beam live load effect should account for the site-to-site variability represented by Vsite-to-site, the variability within a site represented by Vprojection, the uncertainty associated with the limited WIM data sample size represented by Vdata, the variability in the dynamic amplification factor, VIM and the variability in the load distribution factor VDF. The final COV for the applied live load effect on a single beam can be obtained from:

2DF

2IM

2data

2projection

2sitetositeLL VVVVVV ++++= −− (36)

Vsite-to-site is obtained by comparing the Lmax values from different WIM sites within the state. An analysis of the results of Lmax projections show that the uncertainties within a site are associated with a COV on the order of Vprojection=3.5% for the projection of the one-lane maximum effect and a COV of Vprojection=5% for the two side-by-side load effect. Additional uncertainties are associated with Lmax due to the limited number of data points used in the projections and the confidence levels associated with the number of sample points. Using the +/-95% confidence limits, it is estimated that the COV associated with the use of one year worth of WIM data is on the order of Vdata=2% for the one-lane case and about Vdata=3% for the two-lane case. Nowak (1999) also observed that the dynamic amplification factors augmented the Lmax load effect by an average of 13% for one lane of traffic and by 9% for side-by-side trucks. The dynamic amplification also resulted in a COV of VIM=9% on the one-lane load effect and VIM=5.5% on the

79

two-lane effect. In previous studies on live load modeling, Ghosn & Moses (1985) included the uncertainties in estimating the lane distribution factor which was associated with a COV equal to VDF=8% based on field measurements on typical steel and prestressed concrete bridges.

Modeling of Other Random Variables In addition to the live loads, the random variables that control the safety of a bridge member include the actual resistance and the applied dead loads. Nowak (1999) provided models to represent the mean values and the COV’s or standard deviations of these random variables that can be summarized as follows for the dead loads:

%25VD0.1D

%10VD05.1D

%8VD03.1D

DWWW

2DC2C2C

1DC1C1C

==

==

==

(37) For the bending moment resistance the mean and COV are given as:

%10VR12.1R Rn == For composite steel beams (38) %5.7VR05.1R Rn == For prestressed concrete beams

Calculation of Reliability Index and Adjustment of Live Load Factor In the LRFD specifications, safety is measured using the reliability index, β, which accounts for the uncertainties in estimating the effects of the applied loads and the resistance of bridge members. The reliability index, β, is related to the probability of failure, Pf, by:

( )fP−Φ= −1β (39)

where ( )1−Φ is the inverse of the cumulative Normal distribution function. If all the random variables representing the resistance, dead load and live load follow Gaussian (Normal) probability distributions, the reliability index, β, can be calculated as:

2LL

2DL

2R

LLDLRσσσ

β++

−−=

(40) Where the mean of the total dead load is given by:

wcc DDDDL ++= 21 , (41) the COV of the total dead load is

222

21 DWDCDCDL σσσσ ++= (42)

80

and the standard deviations are obtained as:

LLLL

DLDL

RR

VLL

VDL

VR

×=

×=

×=

σ

σ

σ

(43) The AASHTO LRFD was calibrated so that all bridge members designed using the specified load and resistance factors produce a uniform level of risk expressed in terms of a reliability index β equal to a preset target value β target. The AASHTO LRFD calibration was based on a standard set of Lmax values and live load standard deviations. If the Lmax values or their COV’s within a state are different than those used during the AASHTO LRFD calibration it may be necessary to adjust the live load factors in order to maintain the same β target. The adjustment of the live load factors requires the calculation of the reliability index for different values of the live load factor γL and adopting the γL that produces reliability index values as close to the target as possible for all material types, spans and geometric configurations.. During the calibration of the AASHTO LRFD, Nowak (1999) assumed that the resistance is Lognormal while the combined effect of the dead and live loads is Normal. The reliability index calculations were then executed using a First Order Reliability Method (FORM) algorithm instead of using Eq. (40). However, in order to illustrate the procedure and keep the calculations as simple as possible, it is herein assumed that all the random variables representing the resistance, dead load and live load follow Gaussian (Normal) probability distributions. In such a case, the reliability index, β, can be directly calculated from equation (40). Note that the data and models used by Nowak (1999) led to a target reliability index β target=3.5. Method II Reliability Based Adjustment Procedure for Live Load Factors

1. Assemble a set of representative bridge samples for the state comprising steel and concrete bridges of different span lengths, number of beams and beam spacing.

2. Assume a value for γL 3. Choose one bridge from the representative sample of bridges 4. Find the nominal dead loads of components, and wearing surface: DC1, DC2

and DW. 5. Find the nominal live load effect for the HL-93 loading. 6. Apply the new value of γL into Eq. 32 to obtain the required nominal

resistance value Rn. 7. Find the mean resistance R using Eq. (38) 8. Find the COV VR also using Eq. (38) 9. Find the mean dead load effects using Eq. (37) 10. Find the COV for the dead loads using Eq. (37) and find the standard

deviations 11DC1DC DCV=σ 22DC2DC DCV=σ DWVDWDW =σ

11. Use the protocols for the WIM data analysis to get Lmax for 75 years for one-lane loadings and two-lane loadings for several sites within the state.

12. Take the average Lmax and find Vsite-to-site the COV for one-lane loading and two-lane loading for site-to-site variability.

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13. Find the mean value of the live load effect for one lane and two lanes using Eq. 35

14. Find the COV of the live load effect for one-lane loading and two-lane loading using Eq. 36

The proposed adjustment of the live load factor is based on the following assumptions:

• The target reliability index βtarget=3.50 is a satisfactory target and does not need to be modified. This target was established by the AASHTO LRFD code writers based on the generic live load data available at the time. Future research could lead to selecting of a different target.

• Although the changes in γL would lead to different bridge member capacities Rn, it is assumed that these changes would not lead to changes in the dead loads applied on the bridge members.

• Equation (40) is based on the assumption that the resistance, dead load effects and live load effects follow Normal (Gaussian) probability functions. Otherwise one should use a First Order Reliability Method (FORM) algorithm as described by Nowak (1999).

• The models used to obtain the statistical data on the mean values and COV’s of the moment and shear capacity of steel composite and prestressed concrete members as well as the dynamic amplification factors and load distribution factors used during the AASHTO LRFD calibration are still valid.

• The goal of the calibration is to adjust the live load factor only so that the representative sample of bridges would on the average match the target reliability index. In general, the target reliability index should be matched as closely as possible for all representative span lengths and bridge configurations. However, this may not be always possibly by changing the live load factor only.

Step 13.2 Deck Design Load Calibration (STRENGTH I)

The data base upon which the present AASHTO LRFD deck provisions were fixed is less defined than for bending and shear in longitudinal members. LRFD design loads for decks represented by a 32 kip axle or a pair of 25.0 Kip axles (Fig. 22) were not based on the Ontario WIM data. The design truck has the same weights and axle spacing as the HS20 load model, which was adopted in 1944 for bridge design, and has been carried over from the Standard Specifications. WIM data was not used to validate these axle load models during the LRFD development. NCHRP Report 368 on LRFD calibration is focused on bridge loads for superstructure design and does not specifically address calibration of loads models for deck design, fatigue design or overload permitting.

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DECK DESIGN – LRFD CODE PROVISIONS

32 k DESIGN AXLE

25 k DESIGN TANDEM 25 k 4’

Figure 22 LRFD Deck Design Loads Axle groups with more than two axles are currently not considered for deck design in LRFD. However, LRFD commentary C3.6.1.3.3 states “Individual owners may choose to develop other axle weights and configurations to capture the load effects of the actual loads in their jurisdiction based upon local legal load and permitting policies. Triple axle configurations of single unit vehicles have been observed to have load effects in excess of the HL-93 tandem axle load”.

W3 W3 W3

S3 S3

W4 W4 W4

S4 S4

W4

S4

TRIDEM

QUAD

Figure 23 Common Axle Group Loads A relevant issue which is beyond the scope of this project is the conservative nature of the present checking rules on the resistance side. The simple strip flexural model is conservative with respect to the true capacity of a deck which actually fails in a punching shear mode. Introducing an accurate strength model would require a change in nominal strength formulas as well as the calibrated factors, which require research beyond the current scope. Resistance factors vary with design methods and are not constant.

Rigorous calibration of load and resistance factors for deck design requires the availability of statistical data beyond live loads. LRFD did not specifically address deck components in the calibration. It is important to note that there are no β calculations or database of loads/load effects used for the calibration of decks in the LRFD available for use in this project.

One reasonable approach to calibration of deck design loads is to assume the present LRFD safety targets are adequate for the strength design of decks and establish new nominal loads for axles based on recent WIM data. The LRFD live load factors will remain unchanged, but the axle loads and axle types will be updated to be representative of current traffic data. For instance, tri-axles and quad-axles that are currently not included in the LRFD loadings may need to be considered.

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Axle weight statistics from WIM data will first be assembled. The measured axle weights should be adjusted for WIM scatter and measurement errors as detailed in Step 10. This procedure will be repeated for multiple WIM sites to determine the governing nominal loads, taken as:

• For single axles, 32 Kips or the 99th percentile statistic W99, whichever is higher. • For tandem axles, 50 Kips (2 x 25 Kips) or the 99th percentile statistic W99, whichever

is higher. • For tridem axles, the 99th percentile statistic W99 • For quad axles, the 99th percentile statistic W99

The nominal axle loads derived using WIM data are used instead of the code specified

values, where the W99 statistic is higher than the code values. W99 represents an axle load with a 1% probability of exceedance in a year. This approach provides realistic axle loads for deck design based on current WIM data while keeping all other factors unchanged (load factor, deck dynamic load allowance, Table 20). It also allows the introduction of three and four axle configurations for deck design in a consistent manner. WIM data will also be applied to define nominal axle spacings for the multi-axle groups. Table 20 Deck Design Load Calibration Using WIM AXLE TYPE DESIGN AXLE LOAD AXLE SPACING LOAD FACTOR Single W99 not less than 32 K N/A 1.75 Tandem W99 not less than 50 K 4 Ft 1.75 Tridem W99 from WIM 4 Ft 1.75 Quad W99 from WIM 4 Ft 1.75

Step 13.3 Repetitive live load Calibration (FATIGUE) The LRFD fatigue truck configuration will be checked and updated to ensure that it produces fatigue damage similar to that obtained from actual trucks from the traffic data, for typical bridge configurations and fatigue details. Adjustments to the fatigue load model could include changes to:

Effective gross weight Axle configuration and axle loads

Fatigue adjustment factor K for each span using site WIM data could provide the basis for calibrating fatigue design load models, as given below:

1. Use LRFD fatigue truck if K values are uniform and equal to 1.0 2. LRFD fatigue truck should be modified using the effective gross weight if K

values are uniform but not equal to 1.0. 3. Recommend site-specific fatigue trucks if K varies from 1.0 for varying

spans.

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Step 13.4 Superstructure Design Overload Calibration (STRENGTH II) Live Load Modeling for Strength II The AASHTO LRFD Strength II limit state is used when checking the safety of bridge members under the effect of owner-specified special design vehicles or evaluation permit vehicles. The return period implicit in Strength II is equal to one year. To develop appropriate live load factors for the AASHTO LRFD Strength II limit state, three loading scenarios must be considered:

I. Permit vehicle alone II. Permit vehicle along another permit III. Permit vehicle along random vehicle.

Case I is exclusively used if the permit vehicle is escorted and traffic is controlled such that no other heavy vehicle is allowed to cross the bridge when the permit is on. Otherwise, Case I should be compared to Cases II and III and the most critical case would govern. Case II may control the loading if a high number of permits are allowed over a certain route or are allowed to travel freely within a jurisdiction. Case III may control depending on the relative weights of the permit as compared to the heavy legal and illegal vehicles that normally cross the bridge.

Case I – Permit vehicle alone In this case, we can assume that the axle weights and axle configuration of the permit truck are perfectly known so that the total maximum static live load effect on the bridge of the permit truck designated by P is a deterministic value. However, this does not imply that the total live load effect on a bridge member is deterministic due to the uncertainties in estimating the dynamic effect represented by the dynamic amplification factor, IM, and the uncertainties in the structural analysis process that allocates the fraction of the total load to the most critical member. For multi-girder bridges, the structural analysis is represented by the load distribution factor, D.F. The equations for the D.F. of multi-girder bridges loaded by a single lane given in the AASHTO LRFD specifications already include a multiple presence factor m=1.2. Therefore, the expression for the maximum load effect on the most critical beam when a single vehicle is on the bridge can be calculated from:

For case I 2.1/..max FDIMPLLL beam ××== (44) Nowak (1999) observed that the dynamic amplification factor augments the load effect by an average of 13% for one lane of traffic. Assuming that the weight and axle configuration of the permit vehicle are exactly known, the COV’s of the maximum beam live load effect is obtained from the COV of IM and the COV of DF:

2DF

2IMLL VVV += (45)

Using the data for VIM and VDF for one lane proposed by Nowak (1999) and Ghosn & Moses (1985) the loading of a single permit vehicle, the live load COV becomes:

( ) ( ) %12%8%9V 22LL =+=

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Case II – Two Permits side-by-side In this case, we can assume that the axle weights and axle configurations of the two permit trucks are the same and are perfectly known so that the total maximum static live load effect on the bridge is a deterministic value equal to 2P. However, this does not imply that the total live load effect on a bridge member is deterministic due to the uncertainties in estimating the dynamic effect represented by the dynamic amplification factor, IM, and the uncertainties in the structural analysis process that allocates the fraction of the total load to the most critical member. The structural analysis is represented by the load distribution factor, D.F. The equations for the D.F. of multi-girder bridges loaded in two lanes given in the AASHTO LRFD specifications assume that the two lanes are loaded by the same vehicle and give the load on the most critical beam as a function of the load in one of the lanes. Thus, the live load effect on one member can be given as:

For case II ..max FDIMPLLL beam ××== (46) According to Nowak (1999), the dynamic amplification factor augments the load effect by an average of 9% for side-by-side trucks. The dynamic amplification also results in a COV of VIM=5.5% on the two-lane effect. We will also assume that the same COV for the lane distribution factor VDF=8% obtained by Moses & Ghosn (1986) from field measurements on typical steel and prestressed concrete bridges is still valid. Therefore, for the loading of a single

permit vehicle, the live load COV becomes ( ) ( ) %71.9%8%5.5V 22

LL =+=.

The reliability index conditional on the arrival of two side-by-side permits on the bridge can then

calculated using Eq. (40) where R is the mean resistance when the bridge member is designed for

two side-by-side permits and LL is the live load effect on the beam due to two side-by-side permits. The reliability index calculated from Eq. (40) in this case is conditional on having two side-by-side trucks. The probability that a bridge member would fail given that two permit vehicles are side-by-side can be calculated from the inverse of Eq. (39). However, the final unconditional probability of failure will depend on the conditional probability given two side-by-side events and the probability of having a situation with side-by-side permits. Thus:

sidebysideeventssidebyside/ff PPP −−−− ×= (47) The probability of having two-side-by-side permits depends on the number of permit trucks expected to cross the bridge within the return period within which the permits are granted. The percentage of these permits that will be side-by-side is related to the total number of permit crossings. Tables relating the percentage of side-by-side events, Pside-by-side as a function of the number of truck crossings can be obtained from the WIM data. The final unconditional reliability index is then obtained by inserting the results of Eq. (47) into Eq, (39)

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Case III –Permit Truck Alongside a Random Truck For case III, the maximum live load effect is due to the permit truck alongside the maximum truck expected to occur simultaneously in the other lane. The maximum total load effect depends on the number of side-by-side events expected within the return period. To determine the number of side-by-side permit-random truck events that would occur within a one-year period we assume that NP gives the number of permit truck crossings expected in a return period T. The final number of random trucks along side a permit will be:

PsidebysideR NPN ×= −− (48) where Pside-by-side is the percentage of side-by-side events which depends on the ADTT and Np is the number of permits within the return period of interest. The maximum live load effect is obtained from:

( )IMDFLDFPLL RNP R×+×= max (49)

where P is the load effect of the permit truck, DFP is the distribution factor for the load P,

RNmaxL is the maximum load effect of random trucks for NR events which correspond to the one-year return period applicable for the Strength II case, DFR is the distribution factor for the random load, and IM is the impact factor for side-by-side events. The problem in this case is that the DF tables provided in the AASHTO LRFD for two lanes assume that the two side-by-side trucks are of equal weight, which is clearly not the case. Following the AASHTO LRFD approach for permit trucks alongside random trucks, Moses (2001) suggested that DFP be obtained from the AASHTO LRFD tables for single lane while DFR be obtained from the difference between the DF of two lanes and that of a single lane.

The coefficient of variation for RRNmax DFL × is estimated as:

2222max* DFdataproejctionsitetositeL VVVVV +++= −− (50)

where all the values are taken for the single lane case. Assuming the effect of the permit load is deterministic, the coefficient of variation for PxDFP is estimated as: VP*=8% (51) which is the COV for the load distribution factor, DFP. Hence, the standard deviation of LL without the Impact factor is:

( ) ( )2maxmax

2* ** RNLPPLL DFLVDFPV

R××+××=σ

(52)

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and the COV for the live load effect on the critical beam including the effect of the impact IM is given by:

2IM

2

*

*LLLL V

LLV +⎟⎟

⎠

⎞⎜⎜⎝

⎛=

σ

(53)

where ( )RRNmaxP* DFLDFPLL ×+×= is the static live load effect on the most critical bridge

member. The mean live load obtained form Eq. (49) and the COV obtained from Eq. (53) are then used to find the reliability index from Eq. (40). The calibration of the appropriate live load factor would consist of finding the γL that will lead to reliability index values equal to the target value for Cases I, II and III. Method II: Reliability Based Adjustment Procedure for Overload Live Load

Factors

1. Assemble a set of representative bridge samples for the state comprising steel and concrete bridges of different span lengths, number of beams and beam spacing.

2. Determine the permit vehicle configuration. 3. Assume a value for γL 4. Choose one bridge from the representative sample of bridges 5. Find the nominal dead loads of components, and wearing surface: DC1,

DC2 and DW. 6. Find the nominal live load effect, P, for the permit vehicle 7. Apply the new value of γL into Eq. 32 to obtain the required nominal

resistance value Rn. 8. Find the mean resistance R using Eq. (38) 9. Find the COV VR also using Eq. (38) 10. Find the mean dead load effects using Eq. (37) 11. Find the COV of the dead loads from Eq. (37) and Find the standard

deviations 11DC1DC DCV=σ 22DC2DC DCV=σ DWVDWDW =σ 12. Use the protocols for the WIM data analysis to get Lmax NR for one-lane

loadings for a one year return period. 13. Calculate LL for Case I, Case II, and Case III from Equations 44, 46,

and 49. 14. Find the COV for LL for each case using Eq. (45) or (53). 15. Find the standard deviations using Equations 42 and 43. 16. Apply the mean and standard deviation values of loads and resistance

into Eq. (40) to calculate the reliability index, β, for the bridge configuration selected in step 4 for each of the three Cases.

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• For Cases I and III the reliability index is obtained from Eq. (40) directly.

• For Case II, the conditional reliability index, βcond is obtained from Eq. (40). The final unconditional reliability index, β, is obtained from ( )fP−Φ= −1β where fP is obtained from Equation 47 and ( )condsidebysidefP β−Φ=−−/ where Φ is the Standard Normal cumulative distribution function.

17. Go to step 4 to select another bridge and repeat steps 4 to 16 until you exhaust all the bridges in the representative sample.

18. Find the average βave of each load case for the representative sample of bridges.

19. If βave=βtarget=3.50 stop otherwise go to step 3 and start the process over.

20. Determine the value of γL that leads to βave=βtarget=3.50 for each of the three Cases.

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DEMONSTRATION OF RECOMMENDED PROTOCOLS USING NATIONAL WIM DATA Introduction In this Chapter, draft protocols including step-by-step procedures for collecting and using traffic data in bridge design were developed. They are geared to address the use of national WIM data to develop and calibrate vehicular loads for LRFD superstructure design, fatigue design, deck design and design for overload permits.

The aim of this section is to give practical examples of using these protocols with national WIM data drawn from sites around the country with different traffic exposures, load spectra, and truck configurations. This will give a good cross-section of WIM data for illustrative purposes. This step will allow the updating and/or refinement of the protocols based on its applicability to WIM databases of varying quality and data standards currently being collected by the states. This section of the report discusses the results of the demonstration studies in more detail. Selection of Sites for National WIM Data Collection The protocols established in this Chapter were implemented using recent traffic data (either 2005 or 2006) from 26 WIM sites (47 directional sites) in five states across the country (Table 21). The sites were chosen to capture a variety of geographic locations and functional classes, from urban interstates, rural interstates and state routes. Requests for WIM data needed for the studies were sent out to certain selected States based on the National survey findings. The requirements for selection of WIM sites were are as follows: WIM data for a whole year (2006 or 2005) from the following highway functional classifications:

a. Two WIM sites on Rural Interstates b. Two WIM sites on Urban Interstates c. Two WIM sites on Principal Arterials (non-Interstate routes)

Table 39 lists the sites studied along with their respective ADTT’s. For consistency, lanes one and two are eastbound or northbound lanes; lanes three and four are westbound or south bound lanes.

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Table 21 WIM Sites Studied in Task 8 State Site ID Route Dir # Truck

RecordsADTT State Site ID Route Dir # Truck

RecordsADTT

CA 0001 Lodi E/N 1537613 5058 MS 2606 I-55 N 564393 1622CA 0001 Lodi W/S 1470924 4839 MS 2606 I-55 S 604919 1733CA 0003 Antelop

e E 719834 2790 MS 3015 I-10 E 750814 2248

CA 0004 Antelope

W 806122 3149 MS 3015 I-10 W 667560 1999

CA 0059 LA710 S 4243780 11627 MS 4506 I-55 N 530517 2002CA 0060 LA710 N 3806748 11432 MS 4506 I-55 S 477931 1804CA 0072 Bowma

n E/N 310596 2318 MS 6104 US-49 N 462301 1288

CA 0072 Bowman

W/S 289319 2159 MS 6104 US-49 S 498054 1387

FL 9916 US-29 N 175905 498 MS 7900 US-61 N 69996 220FL 9919 I-95 N 939637 2708 MS 7900 US-61 S 68198 216FL 9919 I-95 S 875766 2524 TX 0506 US-287 E/N 559663 1701FL 9926 I-75 N 1096076 4136 TX 0506 US-287 W/S 520092 1581FL 9926 I-75 S 1032680 3897 TX 0516 I-35 E/N 717666 2384FL 9927 SR-546 E 204549 567 TX 0516 I-35 W/S 707744 2449FL 9927 SR-546 W 168114 466 TX 0523 US-281 E/N 430227 1429FL 9936 I-10 E 700774 1980 TX 0523 US-281 W/S 394804 1312FL 9936 I-10 W 723512 2044 TX 0526 I-20 E/N 1330799 4070IN 9511 I-65 N 2119022 5919 TX 0526 I-20 W/S 1174954 3593IN 9511 I-65 S 2068073 5777 IN 9512 I-74 E 931971 2596 IN 9512 I-74 W 1003443 2795 IN 9532 US-31 N 224506 629 IN 9532 US-31 S 229532 643 IN 9534 I-65 N 2128577 5929 IN 9534 I-65 S 2162874 6025 IN 9544 I-80/I-

94 E 3786127 11235

IN 9544 I-80/I-94

W 4032537 11966

IN 9552 US-50 E 95900 278 IN 9552 US-50 W 102212 296

Data Filtering and Quality Control (Protocol Steps 5.1 and 5.2) The same data scrubbing criteria established in Steps 5.1 and 5.2, were employed. That is, truck records that met any one of the following criteria were eliminated as unlikely or unwanted trucks for the purposes of this study. The following is a filtering protocol was applied for screening the WIM data used in this project. Truck records that meet the following filters were eliminated:

• Speed < 10 mph • Speed > 100 mph • Truck length > 120 ft • Total number of axles > 12 • Total number of axles < 3 • Record where the sum of axle spacing is greater than the length of truck

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• GVW < 12 Kips • Record where an individual axle > 70 Kips • Record where the steer axle > 25 Kips • Record where the steer axle < 6 Kips • Record where the first axle spacing < 5 feet • Record where any axle spacing < 3.4 feet • Record where any axle < 2 Kips • Record which has GVW +/- sum of the axle weights by more than 10%

The two most common criteria used to eliminate records were “number of axles < 3” (2-axle light vehicles) and “steer axle < 6 kips”. Typically, one of these two criteria was responsible for 75% to 90% of all scrubbed records at a given WIM site. Further more, the gross vehicle weight of these trucks tends to be low. Therefore, their removal from the study has very little effect on the analysis which tends to concentrate on the upper tail of the data. Table 22 shows the number of trucks, as well as the percentage of the total truck population, eliminated from each WIM site for meeting one or more of the above criteria. Also shown is the mean gross vehicle weight, in kips, of all the eliminated trucks. Table 22 Trucks Eliminated by Data Filtering State Site Number % GVW State Site Number % GVWCA 0001 1671347 35.7 12.0 IN 9511 984044 19.0 14.6CA 0003 643461 47.2 11.2 IN 9512 421592 17.9 13.2CA 0004 771032 48.9 11.4 IN 9532 839445 64.9 10.9CA 0059 1242393 22.6 14.3 IN 9534 1952426 31.3 10.9CA 0060 1366271 26.4 14.8 IN 9544 1855062 19.2 12.9CA 0072 407724 40.5 10.9 IN 9552 162192 45.0 11.0FL 9916 533513 73.0 16.5 MS 2606 380794 24.6 27.8FL 9919 457426 20.1 22.5 MS 3015 1712866 53.4 25.9FL 9926 1752902 45.2 13.7 MS 4506 458419 31.3 19.1FL 9927 276965 42.6 16.5 MS 6104 488899 33.7 24.3FL 9936 330745 18.8 26.3 MS 7900 86777 38.6 13.6 TX 0506 584553 35.1 10.9 TX 0516 881932 38.2 9.6 TX 0523 465556 36.1 10.7 TX 0526 1261244 33.5 11.4

The scrubbed WIM data was passed through various quality control checks. The quality control checks established in Step 5.2 were employed for each WIM site studied. The quality control checks look specifically at Class 9 trucks (5-axle semi-trailer trucks). Since Class 9 trucks are so prevalent in the population and their configurations are well defined, deviations from their expected characteristics can be noted and corrective measures taken. The quality control checks are described as follows:

1. Percentage of trucks by class. Class 9 trucks should be the most prevalent truck class in the population.

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2. Class 9 truck GVW histogram. The characteristic bi-modal shape of the GVW histogram should show an “unloaded” peak between 28 kips and 32 kips, and a “loaded” peak between 72 kips and 80 kips.

3. Over-weight Class 9 trucks. The percentage of Class 9 trucks over 100 kips should be small.

4. Class 9 truck steer axle weight histogram. The weight of the front axle of Class 9 trucks should be between 9 kips and 11 kips. There should not be a significant deviation from this range.

5. Class 9 drive tandem weight histogram. The weight of the drive tandem should not deviate significantly from the estimated values given in NCHRP Report 495.

6. Class 9 axle spacing histogram. The spacing between the steer axle and the drive tandem axle as well as the spacing between the drive tandem axles should be fairly consistent.

The traffic in each lane at a WIM site is recorded by it own sensor. If a sensor malfunctions or begins to lose its calibration it will manifest itself in one or more of the results of the quality control checks. By segregating the data of these quality control checks by lane and by month, deviations from the normal, expected values can be more easily identified and isolated. If a sensor appears to be malfunctioning or providing less reliable data, then the data collected by the offending sensor is eliminated from the population.

Of all the sites studied, only two required additional data scrubbing due to non-conformance during the quality control checks. At WIM Site 3015 in Mississippi, all data from Lane 3 during the months of January through June were eliminated. This accounted for 74,351 trucks, or 5.0% of the filtered truck data. At WIM Site 9916 in Florida, all data from Lane 1 during the month of January were eliminated. This accounted for 14,521 trucks, or 7.6% of the filtered truck data.

After this second round of data scrubbing due to sensor issues, all remaining data is considered reliable and ready for processing. Truck Multiple-Presence (Protocol Step 6) Accurate multiple presence data requires time stamps of truck arrival times to the hundredth of second. We did request this time stamp resolution, but the WIM data records were mostly to a second accuracy. Multiple-presence (MP) statistics need not be developed for each site. Multiple presence statistics are mostly transportable from site to site with similar truck traffic volumes and traffic flow. A relationship between MP and ADTT was developed in this Study, which could be applied to any given site without performing a site-specific analysis (see Step 7 below). WIM Data Analysis for One-Lane Loading ( Step 7) Grouping Trucks into STRENGTH I Protocols developed in Task 7 require that legal loads and routine permits be grouped under STRENGTH I and heavy special permits be grouped under STRENGTH II. The following approach to grouping trucks in the WIM databases was used:

• Do not attempt to classify NY trucks as permit or non-permits based on permit records when using large scale WIM databases. The permit data is not reliable, incomplete or not easily accessed to allow this to be achieved.

• Group all trucks with six or fewer axles in the STRENGTH I calibration. These vehicles include legal trucks and routine permits. These vehicles are considered to be enveloped by the HL-93 load model.

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• Group all trucks with seven or more axles in the STRENGTH II calibration. These vehicles should include the heavy special permit loads, typically in the 150 Kip GVW and above category. An analysis of WIM data from several states indicates a big drop off in truck population for vehicles with seven or greater axles. Only a very small percentage of trucks belong to this permit group.

Gross Vehicle Weight Histograms (Step 7.1) Gross Vehicle Weight (GVW) histograms were generated by direction of travel for each WIM site. Figure 24 shows, as a sample, the GVW histogram for WIM Site 9926 in Florida (I-75). Appendix C contains the GVW histograms for all other WIM sites studied in this task.

Figure 24 – GVW Histogram. WIM Site 9926 in Florida The bi-modal shape of this histogram is typical of GVW histograms with the first major peak representing un-loaded or lightly loaded trucks and the second major peak representing trucks loaded near the legal limit of 80 kips. One Lane Load Effects (Step 7.1) The load effects of each truck individually were calculated for eight span lengths from 20 feet to 200 feet for both simple spans and two-span continuous spans. The load effects calculated were maximum mid-span moment for a simple span, shear at a support for a simple span, maximum positive moment for a two-span continuous span, maximum negative moment for a two-span continuous span, and shear at the center support of a two-span continuous span. All load effects were normalized to those of HL-93 loading. Figure 25 shows, as a sample, the single truck maximum mid-span moment histogram for a simple 60-ft span for WIM Site 9926 in Florida (I-75). Similarly, Figure 26 shows the single truck maximum shear histogram for a simple 60-ft span for WIM Site 9926. Appendix C contains the moment histograms for all other WIM sites studied in this task.

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Figure 25 – Single Truck Simple-Span Moment Histogram. WIM Site 9926 in Florida

Figure 26 – Single Truck Simple-Span Shear Histogram. WIM Site 9926 in Florida

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As would be expected, the general shape of these histograms is similar to that of the GVW histogram; that is, bi-modal with the first major peak representing unloaded or lightly loaded trucks and the second major peak representing trucks loaded near the legal limit. WIM Data Analysis for Two-Lane Loading (Step 8) Simulation of Truck Events using Generalized Multiple Presence Statistics (Step 8.2) All the New York WIM sites studied captured accurate time stamps with each truck record. This allowed for the analysis of two trucks existing simultaneously on a span. Additional data was also available from several WIM sites in New Jersey. None of the WIM sites included reported time stamps with sufficient precision (to the nearest 1/100th of a second) to accurately model the relative positions of two trucks on a span. However, the probabilities of two trucks existing within various headway separations were determined. These probabilities, shown in Table 23, were used to simulate the simultaneous presence of two trucks on a span. Table 23 – Multiple Presence Probabilities

Headway(ft) Light Average Heavy Very Heavy Light Average Heavy Very Heavy

0 to 20 0.19 0.41 0.61 0.60 0.00 0.00 0.00 0.0020 to 40 0.14 0.43 0.66 0.63 0.00 0.00 0.00 0.0040 to 60 0.21 0.41 0.68 0.66 0.01 0.00 0.00 0.0160 to 80 0.26 0.35 0.62 0.64 0.01 0.00 0.00 0.0980 to 100 0.20 0.53 0.76 0.74 0.06 0.04 0.03 0.49100 to 120 0.21 0.41 0.81 0.64 0.12 0.15 0.16 1.81120 to 140 0.24 0.34 0.66 0.61 0.21 0.33 0.45 3.04140 to 160 0.17 0.30 0.61 0.56 0.36 0.57 0.73 3.29160 to 180 0.18 0.29 0.56 0.53 0.48 0.67 0.91 3.03180 to 200 0.19 0.26 0.52 0.50 0.46 0.75 0.98 2.74200 to 220 0.10 0.24 0.48 0.48 0.51 0.68 0.94 2.52220 to 240 0.14 0.24 0.45 0.43 0.48 0.67 0.91 2.28240 to 260 0.12 0.22 0.43 0.41 0.42 0.65 0.87 2.18260 to 280 0.14 0.21 0.41 0.39 0.41 0.60 0.85 1.98280 to 300 0.11 0.20 0.40 0.36 0.39 0.59 0.80 1.87

** Light: ADTT < 1000Average: 1000 < ADTT < 2500Heavy: 2500 < ADTT < 5000Very Heavy: ADTT > 5000

Multiple Presence Probabilities (%)Two-Lane Events (Side-by-Side) One-Lane Events (Following)

Site Truck Traffic (ADTT)** Site Truck Traffic (ADTT)**

Note that the very heavy ADTT MP was based only on one site in New York City and has some anomalies that should be addressed by additional studies at other U.S sites. Based on a WIM site’s ADTT and the multiple presence probabilities established as shown in Table 23, the number of expected multiple presence events for the given WIM site were determined. For each expected multiple presence event two trucks traveling in the desired direction were chosen at random from the entire population of trucks traveling in that direction and positioned to achieve the required headway separation. The load effects of the simulated multiple presence events were calculated as for the single truck events.

For the purpose of design, in consideration of distribution factors, load effects were segregated into one-lane and two-lane; one-lane load effects are those due to a single truck as well as two trucks in the same lane, while two-lane load effects are those due to two trucks in

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adjacent lanes. Figure 27 shows, as a sample, the one-lane and two-lane moment histograms for a 60-foot simple span for lanes one and two of WIM Site 9926 in Florida (I-75). Figure 28 and Figure 29 are similar, but show the histograms for simple span shear and negative moment, respectively. Appendix C contains the load effect histograms for all other WIM sites studied in this task.

Figure 27 – Simple-Span Moment Histogram. WIM Site 9926 in Florida

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Figure 28 – Simple-Span Shear Histogram. WIM Site 9926 in Florida

Figure 29 – Two-Span Continuous Negative Moment Histogram. WIM Site 9926 in Florida Since it is unlikely that two trucks traveling in the same lane will be separated by less than 60 feet, the load effects histograms for the one-lane events are very similar to the single-truck load effects histograms; that is, they display the typical bi-modal shape. The same cannot be said of

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the two-lane events. Here, the distinction between unloaded trucks and loaded trucks is blended resulting in a unimodal distribution. Accumulated Fatigue Damage and Effective Gross Weight (Step 11) Damage accumulation laws such as Miner’s rule can then be used to estimate the fatigue damage for the whole design period for the expected truck population at a site. For varying spans, the effective gross weight for trucks measured at the site was determined using the Equation:

( )1/33eq i iW f W= ∑ (54)

Where fi is the fraction of gross weights within interval i, and Wi is the mid-width of interval i. In this calculation use trucks only with three or more axles (Class 6 and above). The LRFD fatigue truck, has a 54 Kip effective gross weight. Table 24 shows the effective gross weights calculated for the various WIM sites. Table 24 – Effective Gross Vehicle Weight for All WIM Sites Studied in Task 8 State Site ID Route Dir Weff State Site ID Route Dir Weff CA 0001 Lodi E/N 61.5 MS 2606 I-55 N 73.7 CA 0001 Lodi W/S 60.3 MS 2606 I-55 S 66.0 CA 0003 Antelope E 56.3 MS 3015 I-10 E 56.9 CA 0004 Antelope W 56.4 MS 3015 I-10 W 61.7 CA 0059 LA710 S 45.8 MS 4506 I-55 N 67.1 CA 0060 LA710 N 54.4 MS 4506 I-55 S 56.9 CA 0072 Bowman E/N 56.0 MS 6104 US-49 N 65.5 CA 0072 Bowman W/S 57.2 MS 6104 US-49 S 66.0 FL 9916 US-29 N 56.1 MS 7900 US-61 N 58.9 FL 9919 I-95 N 49.3 MS 7900 US-61 S 60.7 FL 9919 I-95 S 50.0 TX 0506 E/N 63.1 FL 9926 I-75 N 56.2 TX 0506 W/S 62.7 FL 9926 I-75 S 59.6 TX 0516 E/N 55.6 FL 9927 SR-546 E 52.9 TX 0516 W/S 58.4 FL 9927 SR-546 W 47.2 TX 0523 E/N 60.9 FL 9936 I-10 E 73.9 TX 0523 W/S 62.2 FL 9936 I-10 W 50.2 TX 0526 E/N 60.8 IN 9511 I-65 N 51.4 TX 0526 W/S 61.9 IN 9511 I-65 S 47.4 IN 9512 I-74 E 64.5 IN 9512 I-74 W 65.1 IN 9532 US-31 N 47.4 IN 9532 US-31 S 50.7 IN 9534 I-65 N 49.0 IN 9534 I-65 S 51.6 IN 9544 I-80/I-94 E 53.5 IN 9544 I-80/I-94 W 50.1 IN 9552 US-50 E 55.7 IN 9552 US-50 W 46.3

99

Accumulated fatigue damage was studied, as in Step 11, by calculating the fatigue adjustment factor, K. The fatigue adjustment factor K was calculated relative to three reference trucks: the LRFD fatigue truck, the modified LRFD fatigue truck, and the site-specific fatigue truck.

( )1/33

#i

FT

MK M

Trucks

⎡ ⎤⎢ ⎥× =⎢ ⎥⎣ ⎦

∑ (55)

The modified LRFD fatigue truck has the same number of axles, the same axle spacing, and the same axle weight distribution as the LRFD fatigue truck, but a GVW equal to the effective gross weight of the truck population at the WIM site. For the site-specific fatigue truck, the most common axle spacings and axle weight distributions were determined for the 5-axle trucks (the most common truck type) and used to define an equivalent 3-axle fatigue truck. That is, the drive tandem axles were combined into an equivalent single axle (with an axle weight equal to the combined weight of the tandem, located mid-way between the two tandem axles), and the trailer tandem axles were combined into an equivalent single axle. This is a slight adjustment to the definition of the site-specific fatigue truck used. The effective gross weight of the truck population was still used for the GVW of this fatigue truck. Table 24 shows the effective gross vehicle weight, in kips, used in calculating K for each directional WIM site studied in this task.

The most common axle configuration of the five-axle trucks was gathered from histograms of axle weights and axle spacing for each WIM site. This information was used to define a site-specific fatigue truck for each site. Figure 30 shows, as a sample, the typical configuration of 5-axle trucks and the equivalent 3-axle fatigue truck derived from it for WIM Site 9926 in Florida (I-75). Table 25 shows, as a sample, the values of the fatigue adjustment factor, K, for the northbound lanes of WIM Site 9926. Appendix C contains the fatigue adjustment factor values for all other WIM sites studied in this task.

The more closely the reference truck represents the actual truck traffic at a site, the closer the value of the fatigue adjustment factor is to unity. Values of K greater than 1.0 indicate that the reference truck underestimates the accumulated fatigue damage of the traffic, while values of K less than 1.0 indicate that the reference truck overestimates the accumulated fatigue damage. As would be expected, the site-specific fatigue truck most closely represents the entire truck population in regards to accumulated fatigue damage.

16.5 ft 4 ft 31.5 ft 4 ft

0.214 W 0.213 W 0.204 W 0.187 W 0.182 W

Typical 5-Axle Truck Configuration

18.5 ft 35.5 ft

0.21 W 0.42 W 0.37 W

Site-Specific Fatigue Truck Configuration

Figure 30 – Site Specific Truck Configurations. WIM Site 9926 in Florida (I-75)

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Table 25 – Fatigue Adjustment Factor, K. WIM Site 9926 in Florida (I-75) Lanes 1 and 2LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8965 0.9933 1.0718 0.9749 0.9846 0.9944 1.0069 1.0142K (pos.) 0.875 0.9761 0.9988 0.967 0.9789 0.9885 1.0014 1.0094K (neg.) 1.1614 0.9462 1.0834 1.0868 0.9887 1.0004 1.0175 1.0257Modified LRFD Fatigue Truck GVW = 56.203 kips (effective gross weight)

Axle Weight: Steer = 6.245 kips Drive = 24.979 kips Trailer = 24.979 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8613 0.9544 1.0298 0.9367 0.946 0.9554 0.9675 0.9745K (pos.) 0.8407 0.9378 0.9596 0.9291 0.9406 0.9498 0.9622 0.9698K (neg.) 1.1158 0.9091 1.0409 1.0442 0.95 0.9612 0.9777 0.9855Site-Specific Fatigue Truck GVW = 56.203 kips (effective gross weight)

Axle Weight: Steer = 11.803 kips Drive = 23.605 kips Trailer = 20.795 kipsAxle Spacing: 18.5 ft 35.5 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.9115 1.0464 1.0364 1.0236 1.0072 1.0028 1.0002 0.9995K (pos.) 0.8896 1.0024 1.0203 1.0128 1.0051 1.0021 1 0.9994K (neg.) 0.9749 1.0111 0.9887 1.0052 1.029 1.0147 1.0073 1.0045

Lanes 3 and 4LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.9928 1.1091 1.1941 1.0721 1.0701 1.0739 1.0804 1.0848K (pos.) 0.9649 1.0879 1.1129 1.0638 1.0657 1.0695 1.0763 1.0811K (neg.) 1.2809 1.0062 1.149 1.1622 1.0599 1.0688 1.0831 1.0901Modified LRFD Fatigue Truck GVW = 59.573 kips (effective gross weight)

Axle Weight: Steer = 6.619 kips Drive = 26.477 kips Trailer = 26.477 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8999 1.0054 1.0824 0.9718 0.97 0.9734 0.9794 0.9833K (pos.) 0.8746 0.9861 1.0088 0.9643 0.966 0.9695 0.9756 0.9799K (neg.) 1.1611 0.9121 1.0415 1.0535 0.9607 0.9688 0.9818 0.9881Site-Specific Fatigue Truck GVW = 59.573 kips (effective gross weight)

Axle Weight: Steer = 12.51 kips Drive = 25.021 kips Trailer = 22.042 kipsAxle Spacing: 18.5 ft 35.5 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.9523 1.1023 1.0894 1.0619 1.0327 1.0217 1.0125 1.0086K (pos.) 0.9255 1.0541 1.0726 1.0512 1.0323 1.0229 1.014 1.0099K (neg.) 1.0144 1.0143 0.9893 1.0142 1.0406 1.0228 1.0115 1.0071 Lifetime Maximum Load Effect Lmax for Strength I (Step 12.2) Statistical projections with a Gumbel distribution fit to the upper tail of the load effects histograms were used to determine the lifetime maximum load effects, Lmax, for Strength I superstructure design. Lmax was calculated for all five load effects, for all eight span lengths, for all 47 directional WIM sites, and segregated by one-lane and two-lane events. The results of the calculation of Lmax based on the data assembled from several WIM sites are provided in Tables 26 to 30 for different span lengths. The results show a slight decrease in the value of Lmax with span length. The average value of Lmax tends to be more closely related to its minimum value than to its maximum value indicating a bias to less heavily loaded spans. Where the information is available, the 75-year Lmax values used in the LRFD calibration are also shown. With the exception of negative moment in a two-span continuous span, the Lmax values used in the LRFD calibration are unconservative, being less than the maximum values observed in this study. The degree to which these values are unconservative is more pronounced in the one-lane events where the Lmax values used in the LRFD calibration are less than the average values

101

observed in this study. Appendix B contains the Lmax results for all the WIM sites studied in this task.

Table 26 through Table 30 show, for each state studied in this task respectively, the maximum values of Lmax calculated for each load effect and span length (The maximum value shown in a cell in the table is the maximum for all WIM sites in that state.). Although in many cases the maximum Lmax value for a 2-Lane event is larger than that of the equivalent 1-Lane event, this is not a generality that holds true for all load effects, all span lengths, or even all states. It is, however, evident that the truck traffic is state dependant resulting in a broad range of Lmax values among the states.

Table 31 shows the 75-year Lmax values used in the LRFD calibration. Here the Lmax values remain fairly constant with span length and even with load effect. One apparent trend is for the Lmax value of the 2-Lane event to be nearly 2x0.85 that of the equivalent 1-Lane event. Table 26 – Maximum Lmax Values for California

Load Effect 20 40 60 80 100 120 160 2001-Lane 1.989 1.635 1.413 1.392 1.351 1.311 1.227 1.1682-Lane 1.955 1.823 1.844 1.891 1.859 1.783 1.676 1.5441-Lane 1.861 1.526 1.483 1.427 1.391 1.349 1.258 1.1752-Lane 1.930 1.843 1.904 1.870 1.842 1.796 1.662 1.5491-Lane 1.861 1.526 1.483 1.427 1.391 1.349 1.258 1.1752-Lane 1.867 1.859 1.859 1.894 1.854 1.806 1.697 1.5641-Lane 1.599 1.557 1.364 1.346 1.250 1.078 0.939 0.8462-Lane 2.017 2.013 1.446 1.086 1.020 0.973 0.895 0.8121-Lane 1.752 1.508 1.506 1.439 1.344 1.208 1.020 0.9152-Lane 1.906 1.846 1.896 1.848 1.757 1.520 1.356 1.200

Maximum Lmax Values of 8 Directional WIM Sites in CaliforniaSpan (ft)

M-simple

V-simple

M-positive

M-negative

V-center

Table 27 - Maximum Lmax Values for Florida

Load Effect 20 40 60 80 100 120 160 2001-Lane 2.860 2.571 2.234 2.240 2.178 2.112 1.939 1.8002-Lane 2.511 2.478 2.471 2.451 2.405 2.365 2.244 2.1411-Lane 2.955 2.515 2.456 2.395 2.290 2.193 2.008 1.8542-Lane 2.444 2.467 2.493 2.380 2.297 2.273 2.199 2.1011-Lane 2.880 2.586 2.273 2.230 2.220 2.145 2.003 1.8292-Lane 2.407 2.423 2.496 2.497 2.429 2.361 2.260 2.1511-Lane 2.640 2.336 1.807 1.582 1.396 1.195 1.025 0.9582-Lane 2.480 2.577 1.814 1.615 1.489 1.361 1.279 1.1281-Lane 2.851 2.436 2.404 2.306 2.204 1.903 1.588 1.4212-Lane 2.506 2.270 2.288 2.371 2.280 2.074 1.821 1.649

Maximum Lmax Values of 9 Directional WIM Sites in FloridaSpan (ft)

M-simple

V-simple

M-positive

M-negative

V-center

102

Table 28 - Maximum Lmax Values for Indiana

Load Effect 20 40 60 80 100 120 160 2001-Lane 2.302 2.207 1.932 1.896 1.859 1.806 1.702 1.6362-Lane 2.219 1.958 1.814 1.765 1.706 1.749 1.740 1.6691-Lane 2.422 2.079 1.899 1.883 1.839 1.789 1.687 1.6182-Lane 2.134 1.820 1.885 2.019 2.057 2.034 1.914 1.7981-Lane 2.352 2.175 1.961 1.891 1.858 1.807 1.736 1.6362-Lane 2.278 1.952 1.800 1.735 1.739 1.768 1.742 1.6721-Lane 1.861 1.917 1.608 1.505 1.302 1.153 1.009 0.9392-Lane 1.841 2.335 1.853 1.324 1.076 1.073 1.017 0.9341-Lane 2.392 2.024 1.831 1.810 1.764 1.581 1.395 1.3022-Lane 2.100 1.791 1.837 1.971 1.991 1.799 1.555 1.416

Maximum Lmax Values of 12 Directional WIM Sites in IndianaSpan (ft)

M-simple

V-simple

M-positive

M-negative

V-center

Table 29 - Maximum Lmax Values for Mississippi

Load Effect 20 40 60 80 100 120 160 2001-Lane 1.687 1.679 1.666 1.674 1.678 1.796 1.989 2.0102-Lane 2.255 2.156 1.930 1.935 2.025 2.031 1.954 1.8561-Lane 1.683 1.689 1.790 1.781 1.957 2.083 2.158 2.1332-Lane 2.309 2.135 2.054 2.097 2.104 2.093 1.981 1.8611-Lane 1.618 1.659 1.660 1.646 1.626 1.791 1.955 2.0122-Lane 2.237 2.182 1.979 1.989 2.034 2.035 1.973 1.8731-Lane 1.905 1.816 2.164 1.972 1.733 1.466 1.240 1.1862-Lane 2.059 2.490 1.911 1.353 1.228 1.193 1.118 1.0151-Lane 1.711 1.702 1.853 1.839 1.940 1.920 1.824 1.7642-Lane 2.260 2.086 2.054 2.069 2.071 1.864 1.635 1.467

Maximum Lmax Values of 10 Directional WIM Sites in MississippiSpan (ft)

M-simple

V-simple

M-positive

M-negative

V-center

Table 30 - Maximum Lmax Values for Texas

Load Effect 20 40 60 80 100 120 160 2001-Lane 1.718 1.844 1.793 1.647 1.524 1.463 1.313 1.1902-Lane 1.966 1.763 1.598 1.557 1.600 1.611 1.559 1.4621-Lane 1.742 1.694 1.648 1.578 1.515 1.454 1.345 1.2602-Lane 1.996 1.655 1.706 1.776 1.785 1.759 1.666 1.5541-Lane 1.688 1.741 1.798 1.674 1.570 1.479 1.331 1.2332-Lane 1.937 1.698 1.579 1.561 1.609 1.612 1.575 1.4901-Lane 1.642 1.605 1.206 0.864 0.941 0.966 0.906 0.8502-Lane 1.567 2.028 1.536 1.098 0.978 0.993 0.952 0.8381-Lane 1.666 1.706 1.670 1.569 1.447 1.242 1.057 0.9662-Lane 1.951 1.605 1.682 1.732 1.733 1.560 1.356 1.224

Maximum Lmax Values of 8 Directional WIM Sites in TexasSpan (ft)

M-simple

V-simple

M-positive

M-negative

V-center

103

Table 31 – 75-year Lmax Values Used in LRFD Calibration

Load Effect 20 40 60 80 100 120 160 2001-Lane 1.300 1.350 1.320 1.320 1.310 1.290 1.240 1.2302-Lane 2.120 2.340 2.300 2.280 2.260 2.240 2.180 2.1601-Lane 1.230 1.230 1.230 1.270 1.280 1.220 1.200 1.1702-Lane 2.120 2.180 2.220 2.260 2.280 2.200 2.140 2.0801-Lane 1.270 1.300 1.250 1.210 1.200 1.200 1.200 1.2002-Lane 2.280 2.400 2.300 2.240 2.220 2.220 2.220 2.220

75-year Lmax Values Used in LRFD CalibrationSpan (ft)

M-simple

V-simple

M-negative

Discussion and Analysis of Lmax Results

The ratio of 2-lane Lmax divided by one lane Lmax is reasonably constant for shear and moments within a range of 1.05 to 1.13 (Fig 31).

The ratio of Lmax for 2-lane/Lmax for 1-lane for moments and shear of simple spans are

relatively small, compared with the LRFD calibration data. This would indicate that in many cases the single event may govern design load effects. This would also depend on the LRFD live load distribution factors for one and two lane loaded conditions.

Average Lmax seems to decrease with span length (Fig. 32) indicating that HL-93 loading

is not entirely consistent with current truck weight data.

Lmax 2/ LMax 1

0

0.2

0.4

0.6

0.8

1

1.2

0 50 100 150 200 250

S pa n l e ngt h

MS

VS

Figure 31 - Lmax for 2-lane / Lmax for 1-lane for moments and shear of simple spans

104

Average Lmax Vs. Span Length

0.000

0.500

1.000

1.500

2.000

2.500

0 50 100 150 200 250

Span in Ft

Lmax

2 lane VS

2 lane Ms

1 lane vs

1 lane MS

Figure 32 – Average Lmax vs Span Length

The spread in Lmax is very high with a Coefficient of Variation (COV) 0.36 to 0.24 with a

tendency to go lower with span length. This COV expresses the site-to-site variability. Also, the COV accounts for the extreme distribution property (obtained from the projections protocols). The one lane COV is lower and decreases faster with span length than the 2-lane COV.

COV of Lmax versus Span Length

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 50 100 150 200 250

Span Length

CO

V of

Lm

ax 2 lane VS

2 lane MS

1 lane Vs

1 lane ms

Figure 33 – COV of Lmax vs Span Length

105

There seems to be no correlation between Lmax and ADTT. R2 is approximately zero for

all the cases (Figures 34 thru 37).

Lmax vs ADTT All sites Simple Moments 80-ft span

y = 7E-06x + 1.5401

R2 = 0.002

0.000

0.500

1.000

1.500

2.000

2.500

3.000

0 2000 4000 6000 8000 10000 12000 14000

ADTT

Series1

Linear (Series1)

Figure 34 – Lmax vs ADTT for One-Lane Simple Span Moment

80-ft Simple Span Lmax for Shear

y = -4E-08x + 1.6447

R2 = 5E-08

0.000

0.500

1.000

1.500

2.000

2.500

3.000

0 2000 4000 6000 8000 10000 12000 14000

ADTT

Series1

Linear (Series1)

Figure 35 – Lmax vs ADTT for One-Lane Simple Span Moment

106

2 Lanes 80-ft simple MS

y = -5E-07x + 1.6726

R2 = 7E-06

0.000

0.500

1.000

1.500

2.000

2.500

3.000

3.500

4.000

0 2000 4000 6000 8000 10000 12000 14000

ADTT

Series1

Linear (Series1)

Figure 36 – Lmax vs ADTT for Two-Lane Simple Span Moment

2 -lane 80-ft VS

y = -9E-06x + 1.8324

R2 = 0.0021

0.000

0.500

1.000

1.500

2.000

2.500

3.000

3.500

4.000

0 2000 4000 6000 8000 10000 12000 14000

ADTT

Series1

Linear (Series1)

Figure 37 – Lmax vs. ADTT for Two-Lane Simple Span Shear

107

Calibrate Vehicular Load Factors for Bridge Design Strength I (Step 13.1) Method I An increase in maximum expected live load based on current WIM data can be compensated in design by raising the live load factor in a corresponding manner. The calibration process adjusts the corresponding live load factor by the ratios r1 and r2 of Eq. (30) and (31):

L,StrengthI StrengthIγ = 1.75 x r (62) The value r is taken to be the ratio of the Lmax value as calculated from WIM data to the Lmax value used in the LRFD calibration. It can be used to determine the effectiveness of HL93 for lifetime maximum loading. One key assumption with regard to this simplified procedure for adjusting live load factors is that the site-to-site variability in Lmax as measured by the COV is the same as that used during the AASHTO LRFD calibration. In AASHTO LRFD calibration, the overall live load COV was taken as 20%. Table 32 through Table 36 show, for each state studied in this task respectively, the maximum values of r calculated for each load effect and span length. Table 32 - Maximum r Values for California

Load Effect 20 40 60 80 100 120 160 2001-Lane 1.530 1.211 1.070 1.055 1.031 1.016 0.990 0.9502-Lane 0.922 0.779 0.802 0.829 0.823 0.796 0.769 0.7151-Lane 1.513 1.241 1.206 1.124 1.087 1.106 1.048 1.0042-Lane 0.910 0.845 0.858 0.827 0.808 0.816 0.777 0.7451-Lane 1.259 1.198 1.091 1.112 1.042 0.898 0.783 0.7052-Lane 0.885 0.839 0.629 0.485 0.459 0.438 0.403 0.366

Maximum r Values of 8 Directional WIM Sites in CaliforniaSpan (ft)

M-simple

V-simple

M-negative

Table 33 - Maximum r Values for Florida

Load Effect 20 40 60 80 100 120 160 2001-Lane 2.200 1.904 1.692 1.697 1.663 1.637 1.564 1.4632-Lane 1.184 1.059 1.074 1.075 1.064 1.056 1.029 0.9911-Lane 2.402 2.045 1.997 1.886 1.789 1.798 1.673 1.5852-Lane 1.153 1.132 1.123 1.053 1.007 1.033 1.028 1.0101-Lane 2.079 1.797 1.446 1.307 1.163 0.996 0.854 0.7982-Lane 1.088 1.074 0.789 0.721 0.671 0.613 0.576 0.508

Maximum r Values of 9 Directional WIM Sites in FloridaSpan (ft)

M-simple

V-simple

M-negative

108

Table 34 - Maximum r Values for Indiana

Load Effect 20 40 60 80 100 120 160 2001-Lane 1.771 1.635 1.464 1.436 1.419 1.400 1.373 1.3302-Lane 1.047 0.837 0.789 0.774 0.755 0.781 0.798 0.7731-Lane 1.969 1.690 1.544 1.483 1.437 1.466 1.406 1.3832-Lane 1.007 0.835 0.849 0.893 0.902 0.925 0.894 0.8641-Lane 1.465 1.475 1.286 1.244 1.085 0.961 0.841 0.7832-Lane 0.807 0.973 0.806 0.591 0.485 0.483 0.458 0.421

Maximum r Values of 12 Directional WIM Sites in IndianaSpan (ft)

M-simple

V-simple

M-negative

Table 35 - Maximum r Values for Mississippi

Load Effect 20 40 60 80 100 120 160 2001-Lane 1.298 1.244 1.262 1.268 1.281 1.392 1.604 1.6342-Lane 1.064 0.921 0.839 0.849 0.896 0.907 0.896 0.8591-Lane 1.368 1.373 1.455 1.402 1.529 1.707 1.798 1.8232-Lane 1.089 0.979 0.925 0.928 0.923 0.951 0.926 0.8951-Lane 1.500 1.397 1.731 1.630 1.444 1.222 1.033 0.9882-Lane 0.903 1.038 0.831 0.604 0.553 0.537 0.504 0.457

Maximum r Values of 10 Directional WIM Sites in MississippiSpan (ft)

M-simple

V-simple

M-negative

Table 36 - Maximum r Values for Texas

Load Effect 20 40 60 80 100 120 160 2001-Lane 1.322 1.366 1.358 1.248 1.163 1.134 1.059 0.9672-Lane 0.927 0.753 0.695 0.683 0.708 0.719 0.715 0.6771-Lane 1.416 1.377 1.340 1.243 1.184 1.192 1.121 1.0772-Lane 0.942 0.759 0.768 0.786 0.783 0.800 0.779 0.7471-Lane 1.293 1.235 0.965 0.714 0.784 0.805 0.755 0.7082-Lane 0.687 0.845 0.668 0.490 0.441 0.447 0.429 0.377

Maximum r Values of 8 Directional WIM Sites in TexasSpan (ft)

M-simple

V-simple

M-negative

Summary of Method I Results As with Lmax, the value of r is state dependant. Unlike Lmax, however, there is a significant, and consistent, difference between the r-values for 1-Lane events and 2-Lane events. The r-values for 1-Lane events are significantly greater than those for 2-Lane events. Whereas the maximum r-values for 2-Lane events exceed 1.0 in some cases, its maximum value among all WIM sites is 1.184. This indicates that the HL93 loading defined in the LRFD specification is fairly adequate in modeling the lifetime maximum loading on a span with two lanes loaded. For 1-Lane events, the maximum r-values are often greater than 1.5 with a maximum value among all WIM sites of 2.402. This indicates that the HL93 loading defined in the LRFD specification underestimates the lifetime maximum loading on a span with only one lane loaded. It should be noted that HL-93 load effects are being compared with routine truck traffic at a site, defined as all trucks with six or fewer axles that will include legal loads and routine permits. These un-analyzed routine permits are a form of exclusion traffic for a particular state and should be enveloped by the HL-93 design live load model. This simplified procedure for adjusting live load factors assumes that the site-to-

109

site variability in Lmax is within the AASHTO LRFD calibration limits. This needs to be verified as a precondition for the use of Method I. Adjustment of Live Load Factors Using Method II An example illustrating the application of the protocols for adjusting the load factors for Strength I using the reliability-based approach is presented. The illustration is provided for a set of bridges varying in span length between 60 ft to 200 ft with beam spacing varying between 4 ft and 12 ft. Composite steel and prestressed concrete simple span bridges are selected. The procedure follows the protocols provided in Step 13.1 Method II using the equations of Chapter 2 and the results are given in Tables 37 through 46. For example, using the data provided by Nowak (1999) for a typical 60-ft simple span composite steel bridge with beams at 4-ft spacing, the wearing surface dead load is estimated to be DW=49 kip-ft (referred to as D3 in Tables 31 and 32), the other dead loads are combined into DC=284 kip-ft (with DC1=39 kip-ft for factory made members (referred to as D1 in Tables 31 and 32, and DC2=245 kip-ft for cast in place

members referred to as D2 in Tables 31 and 32). Assuming that 0.1Lt12

K3s

g =⎟⎟⎠

⎞⎜⎜⎝

⎛ as suggested by

the AASHTO LRFD (2007) for the cases when the detailed design is not available, Eq. (34) will yield a distribution factor D.F. =0.42 for two lanes loaded and Eq. (33) gives D.F. =0.33 for one lane loaded. Given that the AASHTO HL-93 lane load moment for a 60-ft simple span is 288 kip-ft and the HL-93 truck load is 805 kip-ft and applying the dynamic allowance factor IM=1.33 on the truck load, Equation 32 would lead to a nominal required resistance for a single beam Rn=1430 kip-ft for the two-lane case and Rn=1210 kip-ft for the one lane case. Since in this case the Rn value for two lanes is higher than that obtained for one-lane loading, the two-lane case governs the design. Similar calculations can be executed to find the required nominal bending moment capacity of steel and prestressed concrete bridges having different span lengths and beam spacings. For example, Tables 31 and 32 show the nominal bending moment resistances obtained using Equation 32 with the AASHTO LRFD specified live load factor γL=1.75 for a sample of simple span bridge configurations. The configurations selected and the corresponding values for the dead weights are adopted from the report of the AASHTO LRFD calibration study (Nowak; 1999).

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Table 37. Calculation of Nominal Resistance, Rn, using current LRFD for a sample of typical composite steel bridges.

Composite steel Dead Loads HL-93 Required Nominal Resist.Span Spacing D1 D2 D3 Truck load lane load two lanes one lane ft ft kip-ft kip-ft kip-ft kip-ft kip-ft kip-ft kip-ft

60 4 39 245 49 805 288 1430.07 1210.4460 6 48 335 73 805 288 1905.25 1580.0060 8 70 414 97 805 288 2362.18 1931.6760 10 84 521 122 805 288 2831.06 2295.9960 12 103 639 146 805 288 3307.38 2668.51

Composite steel Dead Loads HL-93 Required Nominal Resist.Span Spacing D1 D2 D3 Truck load lane load one lane two lanesft ft kip-ft kip-ft kip-ft kip-ft kip-ft kip-ft kip-ft

120 4 502 981 194 1882 1152 4552.49 3925.44120 6 607 1341 292 1882 1152 6019.48 5112.16120 8 650 1656 389 1882 1152 7302.59 6119.07120 10 681 2083 486 1882 1152 8676.66 7220.72120 12 773 2556 583 1882 1152 10158.57 8433.60

Composite steel Dead Loads HL-93 Required Nominal Resist.Span Spacing D1 D2 D3 Truck load lane load one lane two lanesft ft kip-ft kip-ft kip-ft kip-ft kip-ft kip-ft kip-ft

200 4 2780 2725 540 3320 3200 12317.82 10987.92200 6 3303 3725 810 3320 3200 16016.30 14116.20200 8 3790 4600 1080 3320 3200 19422.06 16963.58200 10 4190 5788 1350 3320 3200 23046.27 20039.36200 12 4875 7100 1620 3320 3200 27132.98 23586.16

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Table 38. Calculation of Nominal Resistance, Rn, using current LRFD for a sample of typical prestressed concrete bridges.

Prestressed Concrete Dead Loads HL-93 Required Nominal Resist.Span Spacing D1 D2 D3 Truck load lane load two lanes one laneft ft kip-ft kip-ft kip-ft kip-ft kip-ft kip-ft kip-ft

60 4 262 245 49 805 288 1708.82 1489.1960 6 262 335 73 805 288 2172.75 1847.5060 8 262 414 97 805 288 2602.18 2171.6760 10 262 521 122 805 288 3053.56 2518.4960 12 262 639 146 805 288 3506.13 2867.26

Prestressed Concrete Dead Loads HL-93 Required Nominal Resist.Span Spacing D1 D2 D3 Truck load lane load one lane two lanesft ft kip-ft kip-ft kip-ft kip-ft kip-ft kip-ft kip-ft

120 4 1899 981 194 1882 1152 6298.74 5671.69120 6 1899 1341 292 1882 1152 7634.48 6727.16120 8 1899 1656 389 1882 1152 8863.84 7680.32120 10 1899 2083 486 1882 1152 10199.16 8743.22120 12 1899 2556 583 1882 1152 11566.07 9841.10

Prestressed Concrete Dead Loads HL-93 Required Nominal Resist.Span Spacing D1 D2 D3 Truck load lane load one lane two lanesft ft kip-ft kip-ft kip-ft kip-ft kip-ft kip-ft kip-ft

200 4 5650 2725 540 3320 3200 15905.32 14575.42200 6 5650 3725 810 3320 3200 18950.05 17049.95200 8 5650 4600 1080 3320 3200 21747.06 19288.58200 10 5650 5788 1350 3320 3200 24871.27 21864.36200 12 5650 7100 1620 3320 3200 28101.73 24554.91

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Live Load Effect Modeling The work performed as part of NCHRP 12-76 consisted of collecting WIM truck traffic data on various sites within the U.S. and using these data to project for the maximum expected live load effects, Lmax, over the 75-year design life of a new bridge. For example, Table 33 provides a set of Lmax values obtained for the maximum bending moments of 60-ft, 120-ft and 200-ft simple span bridges from 8 sites in California. The Lmax values were calculated for one lane of traffic and for two lanes of traffic and they are normalized with respect to the effect of one lane of HL-93 loading. For example the results of Table 33 for the 60-ft span, show that on the average the 75-year maximum load effect will be equal to 1.321 times the static load effect of the HL-93 design load. The values vary from site to site showing a standard deviation for site-to-site variability of 0.060 or a Coefficient of Variation COV Vsite-to-site=4.5%. Table 34 gives the calculated Lmax values for the same sites for the cases when two lanes are loaded simultaneously. Notice that the 60-ft span the two-lane Lmax is on the average equal to 1.44 times the effect of one lane of HL-93 with a site-to-site variability expressed through a COV, Vsite-to-site=13.6%. The higher COV for the two-lane effects is partially due to the differences in the number of two-lane events collected at each site over the one year WIM data collection period as compared to the number of data samples collected for single truck events in the main traffic lane. Other factors that influence the differences in the COV’s include the Average Daily Truck Traffic at the sites, the frequency of heavy legal and overloaded vehicles (illegal, exclusion, or permit) in the truck traffic stream, and the probability of having two lanes loaded by such vehicles. Table 39. Lmax values for one lane for the moment effect of simple span beams

MaxState Site ID Direction ADTT 20 40 60 80 100 120 160 200 ValueCA 0001 E/N 5058 1.370 1.278 1.239 1.206 1.173 1.164 1.137 1.086 1.370CA 0001 W/S 4839 1.400 1.354 1.305 1.237 1.174 1.161 1.124 1.069 1.400CA 0003 E 2790 1.190 1.216 1.293 1.268 1.219 1.191 1.149 1.106 1.293CA 0004 W 3149 1.365 1.354 1.382 1.337 1.253 1.189 1.114 1.051 1.382CA 0059 S 11627 1.340 1.291 1.368 1.358 1.338 1.293 1.212 1.127 1.368CA 0060 N 11432 1.989 1.635 1.413 1.392 1.351 1.311 1.227 1.168 1.989CA 0072 E/N 2318 1.138 1.228 1.297 1.255 1.221 1.140 1.052 1.003 1.297CA 0072 W/S 2159 1.217 1.227 1.272 1.213 1.149 1.094 1.046 0.976 1.272

Min Value 1.138 1.216 1.239 1.206 1.149 1.094 1.046 0.976Avg Value 1.376 1.323 1.321 1.283 1.235 1.193 1.132 1.073Max Value 1.989 1.635 1.413 1.392 1.351 1.311 1.227 1.168

stand. Dev. 0.266 0.137 0.060 0.070 0.076 0.074 0.065 0.063 0.101COV 0.193 0.104 0.045 0.054 0.061 0.062 0.058 0.059 0.057

1-Lane Event Lmax for Simple Span MomentSpan Length (ft)

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Table 40. Lmax values for two lanes for the moment effect of simple span beams In addition to the site-to-site variability, the uncertainties associated with the estimated values for Lmax include the uncertainties within a site due to the random nature of Lmax and the fact that the WIM data histograms do not necessarily include all the extreme load events that may occur within the 75-year design period of the bridge. An analysis of the results of the projections show that the uncertainties within a site are associated with a COV on Lmax on the order of Vprojection=3.5% for the projection of the one-lane maximum effect and a COV of Vprojection=5% for the two side-by-side load effect. Vprojection was obtained from the analysis of the WIM data described in the draft protocols, by taking the ratio of the standard deviation σmax obtained from Eq. (29) divided by the mean Lmax=μmax=of Eq. (28). Additional uncertainties are associated with Lmax due to the limited number of data points used in the projections and the confidence levels associated with the number of sample points. Using the +/-95% confidence limits, it is estimated that the COV is on the order of Vdata=2% for the one-lane case and about Vdata=3% for the two-lane case. Vdata is an estimate obtained from the upper and lower 95% confidence intervals calculated as presented earlier in the report entitled under Step 5.3 “Assessing the Statistical Adequacy of WIM Data”. We took the upper and lower 95% values and assumed that they fall within +/- 1.96 standard deviations from the mean. So, by dividing the difference between the mean value and the upper and lower 95% values by 1.96 we obtain estimates of the standard deviation which when divided by the mean value give estimates of the COV. For example, the upper and lower 95% limits for the WIM data collected at the I-81 site in New York State for Lmax of the one lane loading for the moment at the midpoint a 60-ft simple span are 1.964 and 1.839. The mean Lmax for the one lane loading case is obtained as 1.906. Thus, one estimate of the standard deviation is obtained as (1.906-1.839)/1.96=0.034. The estimate of the COV, Vdata, becomes 0.034/1.906=0.018 or about 1.8%. Another estimate is obtained as (1.964-1.906)/1.96/1.906=1.6%. The final Vdata used is rounded up to 2%. Similarly for the two-lane loading, the mean is Lmax=3.276, the lower 95% limit is 3.058 and the upper 95% limit is 3.462. One estimate for the standard deviation is (3.276-3.058)/1.96=0.111 and the estimate for the COV is 0.111/3.276=3.40% another estimate is obtained as (3.462-3.276)/1.96/3.276=2.90% and the final Vdata used is 3%. Strictly speaking, the approach followed for finding Vdata is not exact, but the Vdata calculated gives some measure of the uncertainty related to the size of the data sample.

MaxState Site ID Direction ADTT 20 40 60 80 100 120 160 200 ValueCA 0001 E/N 5058 1.663 1.706 1.515 1.412 1.456 1.450 1.386 1.299 1.706CA 0001 W/S 4839 1.592 1.475 1.324 1.382 1.445 1.460 1.410 1.341 1.592CA 0003 E 2790 1.447 1.421 1.429 1.392 1.374 1.332 1.281 1.213 1.447CA 0004 W 3149 1.575 1.441 1.440 1.460 1.515 1.529 1.479 1.388 1.575CA 0059 S 11627 1.678 1.665 1.490 1.553 1.562 1.578 1.506 1.419 1.678CA 0060 N 11432 1.955 1.823 1.844 1.891 1.859 1.783 1.676 1.544 1.955CA 0072 E/N 2318 1.368 1.235 1.172 1.199 1.224 1.233 1.177 1.122 1.368CA 0072 W/S 2159 1.499 1.428 1.335 1.265 1.286 1.247 1.198 1.125 1.499

Min Value 1.368 1.235 1.172 1.199 1.224 1.233 1.177 1.122Avg Value 1.597 1.524 1.444 1.444 1.465 1.452 1.389 1.306Max Value 1.955 1.823 1.844 1.891 1.859 1.783 1.676 1.544

stand. Dev. 0.179 0.191 0.196 0.211 0.195 0.183 0.168 0.148COV 0.112 0.125 0.136 0.146 0.133 0.126 0.121 0.113 0.127

2-Lane Event Lmax for Simple Span MomentSpan Length (ft)

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Nowak (1999) also observed that the dynamic amplification factors augmented the Lmax load effect by an average of 13% for one lane of traffic and by 9% for side-by-side trucks. The dynamic amplification also resulted in a COV of VIM=9% on the one-lane load effect and VIM=5.5% on the two-lane effect. In previous studies on live load modeling, Ghosn & Moses (1985) included the uncertainties in estimating the lane distribution factor which was associated with a COV equal to VDF=8% based on field measurements on typical steel and prestressed concrete bridges. This information is used in Eq. (35) and (36) to find the mean value of the live load and the COV. For example, the application of Equation (35) for the average load effect on a 60-ft simple span bridge with beams at 4-ft from the California sites would lead to:

For one lane: ( ) ftkip4482.1/33.013.180528832.1HLLLL 93beammax −=××+×=×= For two lanes: ( ) ftkip3602/42.009.180528844.1HLLLL 93beammax −=××+×=×=

For the one-lane case, Lmax=1.32 is obtained from Table 39 as the average value for the California sites for 60-ft spans. Lmax=1.44 for two lanes is obtained from Table 40 as the average value for the 60-ft spans from all the sites. Notice that the mean live load effect for the one lane case is higher than that of the two-lane case. This is due to the fact that the number of side-by-side events is generally low compared to the number of single lane events, thus the projection to the 75-year maximum for one lane of traffic would lead to the possibility of having a very heavy single truck load (1.32 times the effect of the HL-93 load) as compared to having two very heavy side-by-side trucks the maximum for each one being on the order of 0.72 (1.44/2) times the effect of the HL-93 live load. Also, the load distribution factor D.F. indicates that the effect of a single truck would more likely load a single beam by 27% of the weight of one truck (D.F.=0.33/1.2=0.27) as compared to the weights of two trucks side-by-side which would be more evenly spread over all the beams of the bridge such that the most loaded beam would carry 21% of the lane load (D.F=0.42/2=0.21). Furthermore, the dynamic amplification peaks of two trucks are not likely to coincide due to the different natural frequencies, which would lead to a lower overall dynamic allowance factor for the two-lane case (1.09) as compared to the one-lane case (1.13). Note, that in these calculations and following the procedure of Nowak (1999), it has been assumed that the load distribution factors provided by AASHTO LRFD are the expected (mean) values. It should also be mentioned that the data for the dynamic allowance and for the load distribution factors as used by Nowak (1999) are based on very limited data and much more research is needed on these topics to study how these factors change from site to site and how they relate to the truck weights and traffic data. However, these issues are beyond the scope of this study and in this case, this study uses the same data applied during the AASHTO LRFD calibration. The application of Equation 36 for the 60-ft Lmax yields:

For two lanes: ( ) ( ) ( ) ( ) ( ) %18%8%5.5%3%5%5.13V 22222LL =++++=

For one lane: ( ) ( ) ( ) ( ) ( ) %13%8%9%2%5.3%5.4V 22222LL =++++=

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Vsite-to-site values of 4.5% and 13.5% for one-lane and two-lane cases are respectively obtained from Tables 39 and 40 for the 60-ft spans. The standard deviation for the two-lane case becomes σLL =VLL* LL =65 kip-ft and for the one-lane case σLL=58 kip-ft. Thus, the COV of the two-lane effect for the California sites is comparable to the VLL=19% to 20% obtained by Ghosn & Moses (1985) and subsequently used by Nowak (1999) during the calibration of the AASHTO LRFD specifications. Note that the COV for the single lane effect is lower than that of the two-lane effect indicating that the estimation of the maximum load effect for one lane is associated with lower levels of uncertainty. The difference in the two VLL COV’s is primarily due to the site-to-site variability, which is much higher for the two-lane loading as compared to that for the one-lane loading. Modeling of Other Random Variables The application of Equations (37) and (38) for the beams of the 60-ft composite steel bridge at 4-ft spacing will yield mean dead loads: 1CD =40 kip-ft, 2CD =257 kip-ft and WD =49 kip-ft. The standard deviations are: σDC1=3.2 kip-ft, σDC2=25.7kip-ft and σDW=12.3 kip-ft. The mean of the total dead load becomes DL =346 kip-ft and using the square root of the sum of the square, the standard deviation for the total dead load is σDL=29 kip-ft. The mean nominal resistance for a two-lane bridge is R =1602 kip-ft and for a one-lane bridge, R =1355 kip-ft. The standard deviation for the resistance for the two lane bridge is σR=160 kip-ft and for the one-lane bridge σR=136 kip-ft. For the maximum moment of the sample of simple span bridges studied in this report, Equations 37 and 38 will yield the mean and standard deviation values provided in Tables 35 and 36 for the bending moment of simple span composite steel and prestressed concrete bridges. Calculation of Reliability Index and Calibration of Live Load Factor The adjustment of the live load factors requires the calculation of the reliability index for different values of the live load factor γL. The γL that produces reliability index values as close to the target as possible for all material types, spans and geometric configurations will be adopted as the final γL. Using γL=1.75 for the one-lane 60-ft bridge with beams at 4-ft spacing the reliability index is calculated from Eq. (40) as:

One lane: 72.35829136

44834613552L

2L

2=

++

−−=β

For the two-lane 60-ft bridge with beams at 4-ft spacing the reliability index is calculated as:

Two lanes: 12.56529160

3603461602222

=++

−−=β

The results for this example indicate that, based on the WIM data collected on the California sites, the use of the AASHTO LRFD strength design equation with a live load factor γL=1.75 and the HL-93 loading leads to a reliability index β=3.72 for the 75-year design life of a 60-ft simple span steel bridge with beams at 4-ft spacing. In this case, the one-lane load governs the safety of the bridge beams producing a reliability index value of β=3.72 which is higher than the target β=3.50 set during the calibration of the AASHTO LRFD specifications. It should be emphasized that the target β=3.50 was set during the AASHTO LRFD code calibration based on the

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observation made at the time that under the generic live loading data, typical bridge configurations that were designed to satisfy the AASHTO LFD specifications, produced an average reliability index β=3.50. Thus, the new LRFD code was developed in order for new designs to match this β=3.50 as closely as possible for all bridge spans, configurations and material types. The two-lane loading leads to a much higher reliability index value of β=5.12. This indicates that for the two-lane case, the AASHTO LRFD is conservative. It is noted that for the sake of simplicity this report assumed that the resistance, dead load and live load follow Normal (Gaussian) distributions. The work of Nowak (1999) assumed that the resistance is lognormal while the combination of all the loads is Normal. A preliminary sensitivity analysis was performed indicating that the Normal model produces lower reliability index values than the LogNormal model. The calculation of the reliability index can be executed using Monte Carlo simulations (or other simulation techniques) if the probability distributions of all the random variables are available. Previous sensitivity analyses performed by this research team has demonstrated that the calibration of LRFD design equations is not sensitive to the probability distribution type used as long as the new equations are designed to match an average reliability index calculated using the same models and probability distributions (Ghosn & Moses 1985 and 1986)

California Data Tables 35 and 36 show the reliability index values obtained for the maximum bending moment of a sample of simple span steel composite and prestressed bridge configurations. The results show that for the California truck traffic conditions, the reliability index for one lane is on the average equal to β=3.55 which is close to the target β=3.50. For two lanes of truck traffic, the average reliability index is β=4.63. This indicates that for the two-lane loading of California bridges, the current AASHTO LRFD is conservative producing higher reliability index values than the target β=3.50 set by the AASHTO LRFD code writers. The range of the β’s however is large varying between a β=5.32 for short span prestressed concrete bridges with closely spaced beams to β=4.0 for long span prestressed concrete bridges with closely spaced beams. The fact that the loading of the short span bridges is dominated by the live loads while the long span bridges’ loading is dominated by the dead load indicates that for California bridges, the HL-93 nominal design live load is conservative. If one wishes to reduce the reliability index for the two lane cases and achieve an average reliability index for the two-lane cases equal to the target β=3.5, then a live load factor γL=1.20 should be used. This would mean that the HL-93 loading should be associated with a multiple lane reduction factor =1.46 (1.75/1.20) when checking the design for two lanes of traffic. Alternatively, for the California WIM data, one could keep the current AASHTO LRFD live load factor γL=1.75 and accept the fact that the design will yield the target reliability index for one lane of traffic with the understanding that the design would be conservative for multiple lanes. The adjusted γL=1.20 for the two-lane loading conditions is obtained by trial and error using the protocols steps 13.1 Method II. These steps are based on: 1) having established a representative sample of bridge configurations that represent the most common bridge spans, types, and configurations in the state; and 2) having pre-determined an appropriate reliability index target βtarget, that bridges evaluated using the adjusted live load factor should meet. In usual reliability-based adjustments of design and evaluation equations, the reliability index after adjusting the live load factor should match the target reliability, βtarget, as closely as possible for all representative span ranges, bridge types, loading cases, etc. Given the large

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spread in the calculated reliability index values observed in Tables 35 and 36, this may not be possible to achieve by only adjusting the live load factor. Furthermore, the sample of bridges selected for analysis may not actually be representative of the California bridges. However, to illustrate the process, the steps provided in 13.1 outline a reliability-based live load adjustment procedure that assumes that the target reliability index has already been established as βtarget=3.5 for the sample of bridges analyzed in the previous section, and the goal of the trial and error analysis process is to adjust the live load factor γL so that the average reliability index of the bridges analyzed after adjusting the live load factor will produce the target index.

Florida Data The results presented above for the California WIM data may not be consistent with the data from other states or jurisdictions. The differences are mainly due to the legal truck weight limits or exemptions and the permit overload frequencies and weight regulations that may vary from state to state. For example, if the Lmax values generated from the Florida WIM data sites are used as input for the live load modeling, the reliability index values shown in Tables 37 and 38 are obtained. These tables show that the reliability index for one lane of loading drops to an average of β=2.58. The two-lane Lmax would lead to an average reliability index β=3.96. The latter value is still higher than the target β=3.5 while the one lane reliability is lower than the target. It is noted that the Florida data shows high variations from the results of different sites leading to a high COV for Lmax and subsequently lower reliability index values than those observed from the California data. It is noted that if the live load factor is raised to γL=2.37 the reliability indexes for the Florida sites would increase to β=3.50 for the one-lane cases, and β=4.95 for the two-lane cases, bringing the reliability indexes more in line with the California results.

Indiana Data Using the Lmax values generated from the Indiana WIM data sites, the reliability index values shown in Tables 39 and 40 are obtained. These tables show that the reliability index for one lane of loading is on the average equal to β=3.16 for one-lane loading. The two-lane Lmax would lead to an average reliability index β=4.71. The latter value is higher than the target β=3.5 while the one lane reliability is slightly lower than the target. The Indiana data shows a site-to-site variability in COV’s on the order of 11% to 15% for both one-lane and two-lanes loadings. This is compared to the CA data that shows low site-to-site variability in the one-lane loading cases (typically less than 10% for spans greater than 40ft) and the Florida data that shows high COV’s for both the one-lane and two-lane cases (typically greater than 20%). Summary Using a single maximum or characteristic value for Lmax for a State would be acceptable if the scatter or variability in Lmax from site-to-site for the state was equal to (or less than to be conservative) the COV assumed in the LRFD calibration. If the variability in the WIM data is much greater than that assumed in the calibration, then the entire LRFD calibration to achieve the target 3.5 reliability index may no longer be valid for that state and a simple adjustment of the live load factor as given in the Method I of Step 13.1 protocols should not be done. This example presented a reliability-based procedure to adjust the live load factors based on the Lmax values assembled for each state. The results show that the average reliability index values vary considerably from state to state as a function of the average Lmax values, the live load case that governs, and the site-to-site variability expressed in terms of the COV of Lmax. Also, the results reflect the fact that current WIM data indicates that one-lane loadings are often dominating the

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safety of bridge members due to the lower number of side-by-side events and the lower load effects produced by these events when compared to the data used during the calibration of the AASHTO LRFD. The Method II procedure outlined provides a more robust method for updating live load factors for LRFD design using recent WIM data.

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Table 41. Reliability index calculation for bending moment of simple span composite steel bridges based on California WIM data

Span spacing Ave. Res. 1 Av. Res. 2 σ Res. 1 σ Res. 2 Mean DL σ DL Mean LL 1 Mean LL 2 σ LL 1 σ LL 2 beta 1-lane beta 2-lane60 4 1356 1602 136 160 346 28 447 362 60 64 3.73 5.1160 6 1770 2134 177 213 474 38 567 476 76 84 3.71 5.0960 8 2163 2646 216 265 604 48 675 583 91 103 3.69 5.0760 10 2572 3171 257 317 756 61 776 684 105 121 3.66 5.0260 12 2989 3704 299 370 923 74 870 782 117 138 3.63 4.97

Span spacing Ave. Res. 1 Av. Res. 2 σ Res. 1 σ Res. 2 Mean DL σ DL Mean LL 1 Mean LL 2 σ LL 1 σ LL 2 beta 1-lane beta 2-lane120 4 4396 5099 440 510 1741 117 949 904 134 153 3.60 4.50120 6 5726 6742 573 674 2325 160 1193 1181 169 200 3.57 4.49120 8 6853 8179 685 818 2797 199 1414 1440 200 244 3.57 4.50120 10 8087 9718 809 972 3375 247 1618 1686 229 286 3.53 4.47120 12 9446 11378 945 1138 4063 301 1811 1923 256 326 3.49 4.42

Span spacing Ave. Res. 1 Av. Res. 2 σ Res. 1 σ Res. 2 Mean DL σ DL Mean LL 1 Mean LL 2 σ LL 1 σ LL 2 beta 1-lane beta 2-lane200 4 12306 13796 1231 1380 6265 377 1630 1611 228 258 3.38 4.07200 6 15810 17938 1581 1794 8123 500 2035 2095 285 335 3.36 4.08200 8 18999 21753 1900 2175 9814 614 2401 2547 336 408 3.35 4.09200 10 22444 25812 2244 2581 11743 749 2740 2977 384 476 3.32 4.06200 12 26416 30389 2642 3039 14096 906 3059 3390 428 542 3.28 4.01

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Table 42. Reliability index calculation for bending moment of simple span prestressed concrete bridges based on California WIM data

Span spacing Ave. Res. 1 Av. Res. 2 σ Res. 1 σ Res. 2 Mean DL σ DL Mean LL 1 Mean LL 2 σ LL 1 σ LL 2 beta 1-lane beta 2-lane60 4 1564 1794 125 144 576 34 447 362 60 64 3.78 5.3260 6 1940 2281 155 183 695 44 567 476 76 84 3.80 5.4060 8 2280 2732 182 219 802 52 675 583 91 103 3.82 5.4560 10 2644 3206 212 256 939 64 776 684 105 121 3.80 5.4560 12 3011 3681 241 295 1087 77 870 782 117 138 3.78 5.43

prestressed concrete

Span spacing Ave. Res. 1 Av. Res. 2 σ Res. 1 σ Res. 2 Mean DL σ DL Mean LL 1 Mean LL 2 σ LL 1 σ LL 2 beta 1-lane beta 2-lane120 4 5955 6614 476 529 3180 187 949 904 134 153 3.45 4.35120 6 7064 8016 565 641 3656 215 1193 1181 169 200 3.53 4.51120 8 8064 9307 645 745 4084 245 1414 1440 200 244 3.57 4.61120 10 9180 10709 734 857 4629 285 1618 1686 229 286 3.58 4.64120 12 10333 12144 827 972 5223 331 1811 1923 256 326 3.56 4.64

prestressed concrete

Span spacing Ave. Res. 1 Av. Res. 2 σ Res. 1 σ Res. 2 Mean DL σ DL Mean LL 1 Mean LL 2 σ LL 1 σ LL 2 beta 1-lane beta 2-lane200 4 15304 16701 1224 1336 9221 545 1630 1611 228 258 3.28 4.00200 6 17902 19898 1432 1592 10541 620 2035 2095 285 335 3.36 4.17200 8 20253 22834 1620 1827 11730 699 2401 2547 336 408 3.41 4.28200 10 22958 26115 1837 2089 13247 808 2740 2977 384 476 3.41 4.32200 12 25783 29507 2063 2361 14895 934 3059 3390 428 542 3.40 4.32

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Table 43. Reliability index calculation for bending moment of simple span composite steel bridges based on Florida WIM data

Span spacing Ave. Res. 1 Av. Res. 2 σ Res. 1 σ Res. 2 Mean DL σ DL Mean LL 1 Mean LL 2 σ LL 1 σ LL 2 beta 1-lane beta 2-lane60 4 1356 1602 136 160 346 28 566 425 151 134 2.25 4.0260 6 1770 2134 177 213 474 38 718 558 192 177 2.27 4.0260 8 2163 2646 216 265 604 48 855 683 229 216 2.30 4.0260 10 2572 3171 257 317 756 61 982 802 263 254 2.32 4.0160 12 2989 3704 299 370 923 74 1102 916 295 290 2.34 3.99

Span spacing Ave. Res. 1 Av. Res. 2 σ Res. 1 σ Res. 2 Mean DL σ DL Mean LL 1 Mean LL 2 σ LL 1 σ LL 2 beta 1-lane beta 2-lane120 4 4396 5099 440 510 1741 117 1201 1036 315 269 2.69 4.01120 6 5726 6742 573 674 2325 160 1510 1354 397 351 2.71 4.00120 8 6853 8179 685 818 2797 199 1789 1651 470 429 2.71 4.01120 10 8087 9718 809 972 3375 247 2048 1934 538 502 2.72 3.99120 12 9446 11378 945 1138 4063 301 2292 2205 602 572 2.72 3.96

Span spacing Ave. Res. 1 Av. Res. 2 σ Res. 1 σ Res. 2 Mean DL σ DL Mean LL 1 Mean LL 2 σ LL 1 σ LL 2 beta 1-lane beta 2-lane200 4 12306 13796 1231 1380 6265 377 2120 1851 565 498 2.82 3.78200 6 15810 17938 1581 1794 8123 500 2648 2407 706 648 2.83 3.79200 8 18999 21753 1900 2175 9814 614 3123 2926 833 788 2.83 3.79200 10 22444 25812 2244 2581 11743 749 3565 3420 950 921 2.83 3.78200 12 26416 30389 2642 3039 14096 906 3980 3894 1061 1049 2.82 3.74

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Table 44. Reliability index calculation for bending moment of simple span prestressed concrete bridges based on Florida WIM data

Span spacing Ave. Res. 1 Av. Res. 2 σ Res. 1 σ Res. 2 Mean DL σ DL Mean LL 1 Mean LL 2 σ LL 1 σ LL 2 beta 1-lane beta 2-lane60 4 1564 1794 125 144 576 34 1201 1036 151 134 2.21 4.0760 6 1940 2281 155 183 695 44 1510 1354 192 177 2.20 4.0960 8 2280 2732 182 219 802 52 1789 1651 229 216 2.19 4.1060 10 2644 3206 212 256 939 64 2048 1934 263 254 2.20 4.1060 12 3011 3681 241 295 1087 77 2292 2205 295 290 2.21 4.09

prestressed concrete

Span spacing Ave. Res. 1 Av. Res. 2 σ Res. 1 σ Res. 2 Mean DL σ DL Mean LL 1 Mean LL 2 σ LL 1 σ LL 2 beta 1-lane beta 2-lane120 4 5955 6614 476 529 3180 187 2120 1851 315 269 2.67 3.91120 6 7064 8016 565 641 3656 215 2648 2407 397 351 2.68 4.01120 8 8064 9307 645 745 4084 245 3123 2926 470 429 2.69 4.07120 10 9180 10709 734 857 4629 285 3565 3420 538 502 2.69 4.09120 12 10333 12144 827 972 5223 331 3980 3894 602 572 2.68 4.09

prestressed concrete

Span spacing Ave. Res. 1 Av. Res. 2 σ Res. 1 σ Res. 2 Mean DL σ DL Mean LL 1 Mean LL 2 σ LL 1 σ LL 2 beta 1-lane beta 2-lane200 4 15304 16701 1224 1336 9221 545 1630 1611 565 498 2.75 3.71200 6 17902 19898 1432 1592 10541 620 2035 2095 706 648 2.79 3.84200 8 20253 22834 1620 1827 11730 699 2401 2547 833 788 2.80 3.92200 10 22958 26115 1837 2089 13247 808 2740 2977 950 921 2.80 3.94200 12 25783 29507 2063 2361 14895 934 3059 3390 1061 1049 2.80 3.94

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Table 45. Reliability index calculation for bending moment of simple span composite steel bridges based on Indiana WIM data

Span spacing Ave. Res. 1 Av. Res. 2 σ Res. 1 σ Res. 2 Mean DL σ DL Mean LL 1 Mean LL 2 σ LL 1 σ LL 2 beta 1-lane beta 2-lane60 4 1356 1602 136 160 346 28 508 376 62 50 3.31 5.1760 6 1770 2134 177 213 474 38 644 495 79 65 3.30 5.1460 8 2163 2646 216 265 604 48 767 606 94 80 3.29 5.1260 10 2572 3171 257 317 756 61 881 711 107 94 3.28 5.0760 12 2989 3704 299 370 923 74 988 812 121 107 3.26 5.01

Span spacing Ave. Res. 1 Av. Res. 2 σ Res. 1 σ Res. 2 Mean DL σ DL Mean LL 1 Mean LL 2 σ LL 1 σ LL 2 beta 1-lane beta 2-lane120 4 4396 5099 440 510 1741 117 1137 888 162 100 3.15 4.64120 6 5726 6742 573 674 2325 160 1430 1161 203 131 3.14 4.62120 8 6853 8179 685 818 2797 199 1695 1415 241 160 3.14 4.63120 10 8087 9718 809 972 3375 247 1940 1657 275 187 3.12 4.59120 12 9446 11378 945 1138 4063 301 2170 1890 308 214 3.09 4.54

Span spacing Ave. Res. 1 Av. Res. 2 σ Res. 1 σ Res. 2 Mean DL σ DL Mean LL 1 Mean LL 2 σ LL 1 σ LL 2 beta 1-lane beta 2-lane200 4 12306 13796 1231 1380 6265 377 1999 1598 264 190 3.08 4.11200 6 15810 17938 1581 1794 8123 500 2496 2078 329 247 3.07 4.12200 8 18999 21753 1900 2175 9814 614 2944 2526 389 301 3.07 4.13200 10 22444 25812 2244 2581 11743 749 3360 2952 444 351 3.05 4.10200 12 26416 30389 2642 3039 14096 906 3752 3362 495 400 3.02 4.05

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Table 46. Reliability index calculation for bending moment of simple span prestressed concrete bridges based on IndianaWIM data

Span spacing Ave. Res. 1 Av. Res. 2 σ Res. 1 σ Res. 2 Mean DL σ DL Mean LL 1 Mean LL 2 σ LL 1 σ LL 2 beta 1-lane beta 2-lane60 4 1564 1794 125 144 576 34 508 376 62 50 3.34 5.4060 6 1940 2281 155 183 695 44 644 495 79 65 3.35 5.5060 8 2280 2732 182 219 802 52 767 606 94 80 3.36 5.5560 10 2644 3206 212 256 939 64 881 711 107 94 3.36 5.5560 12 3011 3681 241 295 1087 77 988 812 121 107 3.34 5.53

prestressed concrete

Span spacing Ave. Res. 1 Av. Res. 2 σ Res. 1 σ Res. 2 Mean DL σ DL Mean LL 1 Mean LL 2 σ LL 1 σ LL 2 beta 1-lane beta 2-lane120 4 5955 6614 476 529 3180 187 1137 888 162 100 3.05 4.46120 6 7064 8016 565 641 3656 215 1430 1161 203 131 3.10 4.64120 8 8064 9307 645 745 4084 245 1695 1415 241 160 3.13 4.76120 10 9180 10709 734 857 4629 285 1940 1657 275 187 3.13 4.80120 12 10333 12144 827 972 5223 331 2170 1890 308 214 3.12 4.80

prestressed concrete

Span spacing Ave. Res. 1 Av. Res. 2 σ Res. 1 σ Res. 2 Mean DL σ DL Mean LL 1 Mean LL 2 σ LL 1 σ LL 2 beta 1-lane beta 2-lane200 4 15304 16701 1224 1336 9221 545 1999 1598 264 190 2.99 4.04200 6 17902 19898 1432 1592 10541 620 2496 2078 329 247 3.05 4.22200 8 20253 22834 1620 1827 11730 699 2944 2526 389 301 3.09 4.34200 10 22958 26115 1837 2089 13247 808 3360 2952 444 351 3.09 4.37200 12 25783 29507 2063 2361 14895 934 3752 3362 495 400 3.08 4.38

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Calibrate Overload Load Factors for Strength II (Step 13.4) Reliability Analysis and Adjustment of Live Load Factor for Case I – Permit vehicle alone

T4A

T5A

T6A

T7A

T8

Bridge Formula Truck (BFT)

10' 4' 4'

10' 4' 4' 4'

10' 4' 4' 4' 4'

10' 4' 4' 4' 4' 4'

6' 4' 4' 4' 4' 4' 4'

6' to 14' 4' 4' 4' 4' 4' 4'

12 8 17 17

12 8 8 17 17

11.5

11.5

8 8 17 17 8

8171788 8

6.5

6

10.5

8

10.5

8

10.5

17 17

10.5 10.5

8

10.5

8

10.5

8

GVW=54Kips

GVW=62Kips

GVW=69.5Kips

GVW=77.5Kips

GVW=80Kips

GVW=80Kips

Legal Limit Permit Weight

GVW=120Kips

GVW=120Kips

GVW=116.3Kips

GVW=104.3Kips

GVW=93Kips

GVW=81Kips

Figure 38. Examples of Permit Truck Configurations To execute the reliability calculations, we will use a set of typical permit vehicles configurations as shown in Figure 38. These configurations are for typical Special Hauling Vehicles (SHV) and are adopted from the work performed for NCHRP 12-63 (Sivakumar et al; 2006). The weights of these SHV’s are increased by 150% from the legal limits to be considered as special permit loads. For 60-ft, 120-ft and 200-ft simple spans, these hypothetical permit vehicles produce the maximum moments of Table 47. Table 47. Moment Effect for Set of Permit Trucks Moments in kip-ft Span length T4A T5A T6A T7A T8 BFT 60 ft 1016 1116 1240 1346 1336 1405 120 ft 2230 2508 2802 3090 3134 3205 200 ft 3850 4366 4887 5415 5534 5604 The nominal resistance that would be required for a set of multi-beam simple span steel bridges can be calculated by applying Eq. 32 with γD=1.25 for component dead weights and γD=1.50 for the wearing surface. In Eq. 32, the effect of the permit trucks is multiplied by a load factor γL=1.35 after applying the D.F. of Eq. 33 and the impact factor specified in the AASHTO LRFD as IM=1.33. The required nominal resistance values for the cases considered in this example are provided in Table 48. In these calculations we are assuming that the dead loads of the components remain essentially unchanged when the applied live loads are changed. The application of Eq. 40 leads to the reliability index values provided in Table 49.

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Table 48. Nominal Resistance for Beams of Simple Span Bridges under a Single Permit

Composite steel

Dead weight effect (kip-ft)

RN Nominal resistance (kip-ft)

Span (ft) space (ft) DC1 DC2 DW T4A T5A T6A T7A T8 BFT 60 4 39 245 49 928 978 1038 1091 1086 112060 6 48 335 73 1222 1285 1362 1428 1422 146560 8 70 414 97 1506 1580 1672 1751 1743 179560 10 84 521 122 1806 1892 1998 2089 2080 213960 12 103 639 146 2119 2215 2334 2436 2426 2492

Span (ft) space (ft) DC1 DC2 DW T4A T5A T6A T7A T8 BFT

120 4 502 981 194 3074 3190 3312 3432 3450 3480120 6 607 1341 292 4041 4187 4341 4491 4515 4552120 8 650 1656 389 4850 5023 5205 5384 5411 5455120 10 681 2083 486 5768 5966 6175 6379 6411 6461120 12 773 2556 583 6808 7029 7263 7492 7527 7583

Span (ft) space (ft) DC1 DC2 DW T4A T5A T6A T7A T8 BFT

200 4 2780 2725 540 9116 9307 9500 9695 9740 9765200 6 3303 3725 810 11779 12018 12259 12502 12558 12590200 8 3790 4600 1080 14206 14488 14772 15060 15125 15163200 10 4190 5788 1350 16893 17214 17538 17867 17941 17984200 12 4875 7100 1620 20073 20432 20794 21160 21243 21292

Table 49. Reliability Index for a Single Permit with γL=1.35 Composite steel Reliability index, β Span (ft) space (ft) T4A T5A T6A T7A T8 BFT

60 4 3.31 3.34 3.37 3.39 3.39 3.40 60 6 3.30 3.33 3.36 3.38 3.38 3.39 60 8 3.28 3.31 3.34 3.37 3.37 3.38 60 10 3.25 3.29 3.32 3.34 3.34 3.36 60 12 3.22 3.26 3.29 3.32 3.31 3.33

Span (ft) space (ft)

120 4 3.01 3.05 3.08 3.12 3.12 3.13 120 6 2.99 3.03 3.07 3.10 3.11 3.11 120 8 2.99 3.03 3.07 3.10 3.10 3.11 120 10 2.96 3.00 3.04 3.07 3.08 3.09 120 12 2.93 2.97 3.01 3.04 3.05 3.06

Span (ft) space (ft)

200 4 2.78 2.81 2.84 2.86 2.87 2.87 200 6 2.77 2.80 2.83 2.86 2.87 2.87 200 8 2.78 2.81 2.83 2.86 2.87 2.87 200 10 2.76 2.79 2.82 2.84 2.85 2.85 200 12 2.74 2.77 2.80 2.82 2.83 2.83

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The results of Table 49 illustrate the following points:

• For a given span length and beam spacing, the different vehicle configurations produce little change in the reliability index. The largest difference in β being on the order of 0.11 when the range is between β=3.22 to β=3.33 for the 60-ft span with beams at 12ft.

• Increasing the beam spacing leads to slightly lower reliability index values. • Increasing span length leads to lower reliability index values. • The average reliability index for the span lengths and beam spacings considered is on

the order of βave=3.07 with a minimum value of β=2.74 and a maximum value β=3.40.

• Using a live load factor γL=1.35 for Strength II produces an average reliability index βave=3.07 for a single permit on the bridge. This average value is lower than the βtarget=3.50 used for the calibration of the AASHTO LRFD equations. If an average reliability βave=3.50 is desired for the bridge configurations considered in this example, then a γL=1.62 should be used when considering the case of a permit load alone on the bridge. The γL=1.62 is obtained using a trial and error procedure. The process is repeated until a βave=3.5 is obtained.

• An average reliability index βave=2.5 was used for the calibration of the operating rating live load factor in the LRFR code. If an average reliability βave=2.5 is desired for the bridge configurations considered in this example, then a γL=1.04 should be used when considering the case of a permit load alone on the bridge.

Reliability Analysis and Adjustment of Live Load Factor for Case II – Two Permits side-by-side In this case, we can assume that the axle weights and axle configurations of the two permit trucks are the same and are perfectly known so that the total maximum static live load effect on the bridge Lmax is a deterministic value. However, this does not imply that the total live load effect on a bridge member is deterministic due to the uncertainties in estimating the dynamic effect represented by the dynamic amplification factor, IM, and the uncertainties in the structural analysis process that allocates the fraction of the total load to the most critical member. The structural analysis is represented by the load distribution factor, D.F. The equations for the D.F. of multi-girder bridges loaded in two lanes given in the AASHTO LRFD specifications assume that the two lanes are loaded by the same vehicle and give the load on the most critical beam as a function of the load in one of the lanes. Thus, the live load effect on one member can be given from Equation (46). According to Nowak (1999), the dynamic amplification factor augments the load effect by an average of 9% for side-by-side trucks. The dynamic amplification also resulted in a COV of VIM=5.5% on the two-lane effect. We will also assume that the same COV for the lane distribution factor VDF=8% obtained by Moses & Ghosn (1986) from field measurements on typical steel and prestressed concrete bridges is still valid. Therefore, for the loading of a single

permit vehicle, the live load COV becomes: ( ) ( ) %71.9%8%5.5V 22LL =+= .

The reliability index conditional on the arrival of two side-by-side permits on the bridge can then calculated using Eq. (40) where R is the mean resistance when the bridge member is designed for

128

two side-by-side permits and LL is the live load effect on the beam due to two side-by-side permits.

The reliability index calculated from Eq. (40) in this case is conditional on having two side-by-side trucks. The probability that a bridge member would fail given that two permit vehicles are side-by-side can be calculated from ( )condsidebysidefP β−Φ=−−/ . However, the final unconditional probability of failure will depend on the conditional probability given two side-by-side events and the probability of having a situation with side-by-side permits as shown in Eq. (47). The probability of having two-side-by-side permits depends on the number of permit trucks expected to cross the bridge within the return period within which the permits are granted. In this example, we will assume that all the permits will likely cross the same bridges so that the number of permits crossing a certain bridge within a one-year period is equal to the number of permits granted. The percentage of these permits that will be side-by-side is related to the total number of crossings as provided in Table 50. For example, assuming that the number of permit-vehicles expected on a bridge during the return period when the permits are in effect will be on the order of 1000 vehicles then, according to Table 50, the probability of having side-by-side events is 0.54% (=0.19+0.14+0.21). This value is obtained by conservatively assuming that trucks within a headway distance H<60 ft are actually side-by-side. Table 50. Multiple presence probabilities for side-by-side events as a function of

headway distance

To execute the reliability calculations, we will use a set of typical permit vehicles configurations as shown in Figure 38. These configurations were adopted from the work performed for NCHRP 12-63 (Sivakumar et al; 2006) and multiplying the legal weights of each SHV by 150%. For 60-ft, 120-ft and 200-ft simple spans, these vehicles produce maximum moments as shown in Table 47.

129

Table 51. Conditional Reliability Index for Case II Composite steel Conditional Reliability index, , β Span (ft) space (ft) T4A T5A T6A T7A T8 BFT

60 4 3.65 3.69 3.72 3.74 3.74 3.76 60 6 3.64 3.68 3.71 3.74 3.73 3.75 60 8 3.64 3.67 3.70 3.73 3.73 3.74 60 10 3.61 3.65 3.68 3.71 3.71 3.72 60 12 3.59 3.62 3.66 3.69 3.68 3.70

Span (ft) space (ft)

120 4 3.29 3.34 3.39 3.43 3.44 3.45 120 6 3.29 3.34 3.39 3.43 3.43 3.44 120 8 3.29 3.35 3.39 3.44 3.44 3.45 120 10 3.27 3.33 3.38 3.42 3.42 3.43 120 12 3.25 3.30 3.35 3.39 3.40 3.41

Span (ft) space (ft)

200 4 2.97 3.02 3.06 3.10 3.11 3.12 200 6 2.98 3.03 3.07 3.11 3.12 3.13 200 8 2.99 3.04 3.08 3.12 3.13 3.13 200 10 2.98 3.02 3.07 3.11 3.12 3.12 200 12 2.96 3.00 3.04 3.08 3.09 3.10

Table 52. Final (unconditional) Reliability Index for Case II Composite steel Reliability index, β Span (ft) space (ft) T4A T5A T6A T7A T8 BFT

60 4 4.83 4.85 4.88 4.90 4.89 4.91 60 6 4.82 4.84 4.87 4.89 4.89 4.90 60 8 4.81 4.84 4.86 4.88 4.88 4.89 60 10 4.79 4.82 4.85 4.87 4.87 4.88 60 12 4.77 4.80 4.83 4.85 4.85 4.86

Span (ft) space (ft)

120 4 4.55 4.59 4.62 4.66 4.66 4.67 120 6 4.55 4.58 4.62 4.65 4.66 4.66 120 8 4.55 4.59 4.63 4.66 4.66 4.67 120 10 4.54 4.58 4.61 4.65 4.65 4.66 120 12 4.52 4.55 4.59 4.62 4.63 4.64

Span (ft) space (ft)

200 4 4.32 4.35 4.38 4.41 4.42 4.42 200 6 4.32 4.35 4.39 4.42 4.42 4.43 200 8 4.33 4.36 4.39 4.42 4.43 4.43 200 10 4.32 4.35 4.38 4.41 4.42 4.42 200 12 4.30 4.34 4.37 4.40 4.40 4.41

130

The nominal resistance that would be required for a set of multi-beam simple span steel bridges can be calculated by applying Eq. 32 with γD=1.25 for component dead weights and γD=1.50 for the wearing surface. In Eq. 32, the effect of the permit trucks is multiplied by a load factor γL=1.35 after applying the D.F. of Eq. 34 and the impact factor specified in the AASHTO LRFD as IM=1.33. In these calculations we are assuming that the dead loads of the components remain essentially unchanged when the applied live loads are changed. The conditional reliability index is given in Table 51. Eq.47 is then used to find the unconditional probability of failure that is then inverted using Eq. 39 to find the unconditional reliability index β. The final (unconditional) reliability index values are provided in Table 52 for the bridge configurations analyzed in this example. The results of Tables 51 and 52 illustrate the following points:

• For a given span length and beam spacing, the different vehicle configurations produce little change in the reliability index. The largest difference in the unconditional β being on the order of 0.12 for the 120-ft span bridges.

• Increasing the beam spacing leads to small changes of less than 0.06 in the reliability index values.

• Increasing the span length leads to lower reliability index values. • The average unconditional reliability index for the span lengths and beam spacings

considered is on the order of βave=4.62 with a minimum value of β=4.30 and a maximum value β=4.91

• The higher reliability index obtained for the two side-by-side permits as compared to the single permit is primarily due to the low probability of having side-by-side events. If one looks at the conditional reliability index, then the average βconditional=3.38 is closer to but still higher than the βave=3.07 obtained for a single permit truck. In this case, the still higher conditional reliability index value is partially due to the lower mean impact factor ( IM =1.09 versus 1.13) and the lower corresponding COV (VIM=5.5% versus 9%) for side-by-side events which are justified by the low likelihood of having the peaks of the dynamic oscillations of the two side-by-side vehicles occur simultaneously.

Reliability Analysis and Adjustment of Live Load Factor for Case III –Permit Truck Alongside a Random Truck For case III, the maximum live load effect is due to the permit truck alongside the maximum truck expected to occur simultaneously in the other lane. The maximum total load effect depends on the number of side-by-side events expected within the return period. To determine the number of side-by-side permit-random truck events that would occur within a one-year period we will assume that the number of side-by-side events involving one random truck is obtained from Table 44 based on the ADTT. For example, we assume that NP gives the number of permit truck crossings expected in a return period T. The average number of random trucks in one day is given by the ADTT. For ADTT between 1,000 and 2500 trucks per day, the percentage of side-by-side events involving a random truck (assumed to be those within a headway H ≤ 60 ft) is taken from Table 44 to be 1.25% (=0.41%+0.43%+0.41%). Thus, within a one-year return period, there will be 4.56 x ADTT (=1.25%x365xADTT) random trucks alongside another truck. Assuming that there will be 1000 permits on this route within this one-year period, the percentage of permits in the total truck population will be 2.74/ADTT

131

⎟⎠⎞

⎜⎝⎛

×=

365ADTT1000

. This indicates that the number of random trucks alongside a permit truck

will be on the average NR=12.5 (=4.56x2.74) events within a one-year return period. The maximum live load effect expected within this one-year period will be due to the heaviest of these 12.5 random trucks combined with the effect of the permit. Table 53 gives the Lmax NR values for the maximum moment effect on simple spans obtained for the maximum of 12.5 events for single lanes for WIM data collected at 6 California sites. These are obtained by applying the protocls steps 12.2.1 with N=Nr=12.5 in Equations 26 and 27. The values in Table 53 are normalized as a function of the effect of the HL-93 vehicle. Table 53. Lmax values for the maximum moment effect on simple spans obtained for the maximum of 12.5 events for single lanes

RNmaxL for NR=12.5 events

Site 60-ft 120-ft 200-ft Lodi 1 0.67 0.70 0.67Lodi 2 0.69 0.71 0.63Antelope 1 0.67 0.66 0.59Antelope 2 0.72 0.70 0.62LA710 1 0.70 0.68 0.63LA 710 2 0.74 0.71 0.66Bowman 1 0.64 0.62 0.56Bowman 2 0.63 0.64 0.58

Average 0.68 0.68 0.62Std. Dev. 0.04 0.03 0.04

The maximum live load effect is obtained from Eq. (49) where P is the load effect of the permit truck, DFP is the distribution factor for the load P,

RNmaxL is the maximum load effect of random trucks for NR events, DFR is the distribution factor for the random load, and IM is the impact factor for side-by-side events. The coefficient of variation for RRNmax DFL × is estimated using Eq. (50) as:

( ) ( ) ( ) ( ) %6.10%8%2%5.3%6.5V 2222*maxL

=+++=

where the 5.6% is the COV for site to site variability, the 3.5% is due to randomness in the WIM data and the 2% is due to the limitation in the WIM sample size, the 8% is due to the uncertainties in estimating DFR Assuming the effect of the permit load is deterministic, the coefficient of variation for PxDFP is estimated as VP*=8% which is the COV for the load distribution factor, DFP. Hence, the standard deviation of LL without the Impact factor is obtained using Eq. (52):

( ) ( )2RRNmax

2P*LL

DFL%6.10DFP%8 ××+××=σ

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and the COV for the live load effect on the critical beam including the effect of the impact IM is given by Eq. (53). The live load mean obtained from Eq. (49) and the COV obtained from Eq. (53) are then used to find the reliability index from Eq. (40). In these example calculations, the same bridge configurations used fro Case II are assumed and the nominal Rn values are obtained from two side-by-side permit loads as traditionally done. The reliability calculations produce the results shown in Table 54. The results in Table 54 show a large range for β varying between 2.93 and 4.51 with an average β=3.72. To reduce the average to βtarget=3.5, the live load factor would need to be reduced from γL=1.35 to 1.25. Table 48. Reliability Index for Case III Composite steel Reliability index, β Span (ft) space (ft) T4A T5A T6A T7A T8 BFT

60 4 4.03 4.16 4.30 4.41 4.40 4.47 60 6 4.04 4.17 4.32 4.44 4.43 4.49 60 8 4.04 4.18 4.33 4.45 4.44 4.51 60 10 4.01 4.16 4.32 4.43 4.42 4.49 60 12 3.98 4.13 4.29 4.41 4.40 4.47

Span (ft) space (ft)

120 4 3.37 3.52 3.67 3.80 3.82 3.85 120 6 3.37 3.53 3.68 3.81 3.83 3.86 120 8 3.38 3.54 3.70 3.84 3.86 3.89 120 10 3.36 3.52 3.68 3.82 3.84 3.87 120 12 3.33 3.49 3.65 3.79 3.81 3.84

Span (ft) space (ft)

200 4 2.95 3.07 3.18 3.28 3.30 3.31 200 6 2.96 3.08 3.19 3.30 3.32 3.33 200 8 2.97 3.09 3.20 3.31 3.34 3.35 200 10 2.95 3.08 3.19 3.30 3.32 3.34 200 12 2.93 3.05 3.16 3.27 3.30 3.31

Summary The reliability analysis executed in this report for the limit state of Strength II with a live load factor γL=1.35 shows large variations in the reliability index depending on whether the permit load crosses the bridge with no other trucks alongside of it, or the permit is alongside another permit, or the permit is alongside a random truck. When the permit crossing is controlled such that no other trucks are alongside, the average reliability index for the span lengths and beam spacings considered in this report is on the order of βave=3.07. The average reliability index for two permits side by side is on the order of βave=4.62. The results for a permit alongside a random truck is on average β=3.72. A high average reliability index for two side-by-side permits is due to the low probability of the occurrence of such cases. If the number of permits is such that the chances of their side-by-side occurrences is close to 100%, then the average reliability index becomes β=3.38 which is lower than the random-permit reliability index of 3.72. In this latter

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case, the reliability index β=3.38 is lower than the 3.72 because in the random-permit case it is unlikely that the random truck will be as heavy as the permit truck. Adjustments to the live load factor γL=1.35 can be made to match a target reliability index. It should be noted that the determination of the target reliability index and the sample of bridge configurations for which the adjustment of the live load factor need to be made should be based on the experience of bridge owners with the performance of the bridges in their jurisdiction. The calculations performed as part of this report assume that the resistance, dead loads and live loads follow normal (Gaussian) probability distributions. This assumption was made to illustrate the procedure and can be adjusted as more information on these variables is assembled from on going and recent research studies. Axle Loads for Deck Design from WIM Data (Step 9) Axle Group Weight (Step 9.1 and 9.2) One-lane (single truck) and two-lane (side-by-side trucks) axle events were analyzed for the purpose of calibrating deck design loads. For the one-lane events, single, tandem, tridem and quad axle groups were considered. For the two-lane events, single-single, single-tandem and tandem-tandem axle group combinations were considered. All other axle group combinations were consolidated into one group. Single axles and tandem axles are, by far, the most common axle groups.

Figure 39 shows, as a sample, the one-lane axle group weight histograms for WIM Site 9926 in Florida (I-75). Table 55 shows summary statistics for the data. Figure 40 shows the two-lane axle group weight histograms for the same site and Table 56 shows summary statistics for this data. In addition to the mean and standard deviation of the entire population, top 20% of the population, and top 5% of the population, the 99th percentile is shown. This upper extreme is taken in this project as the maximum anticipated load for design. Table 57 shows the 99th percentile of the one-lane axle group weights for all the WIM sites studied in this task. Table 58 shows the 99th percentile of the two-lane axle group weights for all the WIM sites studied in this task. As would be expected, the combined load of the two-lane events is less than sum of the constituent one-lane events indicating that the heaviest axles loads are not, necessarily, involved in side-by-side events. Appendix C contains axle group weight histograms for all other WIM sites studied in this task.

Rigorous calibration of load and resistance factors for deck design requires the availability of statistical data beyond live loads. LRFD did not specifically address deck components in the calibration. In the protocols developed in this study, the nominal axle loads derived using WIM data are used instead of the code specified values, where the W99 statistic is higher than the code values. All other factors are kept unchanged (load factor, deck dynamic load allowance). The governing nominal axle loads for LRFD deck design, are taken as:

• For single axles, 32 Kip load given in LRFD or the 99th percentile statistic W99, whichever is higher

• For tandem axles, 50 Kips (2 x 25 Kips given in LRFD) or the 99th percentile statistic W99, whichever is higher

• For tridem axles, the 99th percentile statistic W99 • For quad axles, the 99th percentile statistic W99

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The 99th percentile axle weights are as given in the tables for each axle type at each WIM site.

Figure 39 – 1-Lane Axle Group Weight Histogram. WIM Site 9926 in Florida Table 55– 1-Lane Axle Group Weight Statistics. WIM Site 9926 in Florida

WIM Site 9926 Axle Group Weight Statistics Statistics Single Tandem Tridem Quad Axle Count 2986536 3293111 94115 1077 Mean All Axles 10.831 21.773 46.649 43.899 Std Dev All Axles 3.494 9.847 13.955 22.070 COV All Axles 0.323 0.452 0.299 0.503 Mean Top 20% Axles 16.039 36.285 63.111 70.777 Std Dev Top 20% Axles 2.932 3.763 3.976 6.282 COV Top 20% Axles 0.183 0.104 0.063 0.089 Mean Top 5% Axles 20.152 41.357 68.343 79.444 Std Dev Top 5% Axles 2.008 3.913 3.817 6.380 COV Top 5% Axles 0.100 0.095 0.056 0.080 99th Percentile 20 42 68 82

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Figure 40 - 2-Lane Axle Group Weight Histogram. WIM Site 9926 in Florida Table 56 - 2-Lane Axle Group Weight Statistics. WIM Site 9926 in Florida

WIM Site 9926 Two-Lane Multiple Presence Axle Load Statistics

Statistics Single-Single

Single-Tandem

Tandem-Tandem All Others

Event Count 13124 29735 16306 1801 Mean All Events 21.585 32.535 43.445 63.314 Std Dev All Events 4.994 10.486 14.111 17.759 COV All Events 0.231 0.322 0.325 0.280 Mean Top 20% Events 29.141 47.916 64.044 87.483 Std Dev Top 20% Events 3.345 4.509 6.522 8.462 COV Top 20% Events 0.115 0.094 0.102 0.097 Mean Top 5% Events 33.655 54.181 72.988 99.089 Std Dev Top 5% Events 3.003 4.094 5.088 7.489 COV Top 5% Events 0.089 0.076 0.070 0.076 99th Percentile 34 54 74 102

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Table 57 – 99th Percentile One-Lane Axle Group Weight State Site ID Route Single Tandem Tridem Quad CA 0001 Lodi 18 36 50 40 CA 0003 Antelope 16 32 52 62 CA 0004 Antelope 18 34 56 64 CA 0059 LA710 16 34 46 54 CA 0060 LA710 18 36 46 60 CA 0072 Bowman 16 32 50 54 FL 9916 US-29 20 46 78 88 FL 9919 I-95 14 32 50 62 FL 9926 I-75 20 42 68 82 FL 9927 SR-546 18 38 58 64 FL 9936 I-10 22 44 74 94 IN 9511 I-65 14 30 52 62 IN 9512 I-74 18 38 58 68 IN 9532 US-31 16 34 58 72 IN 9534 I-65 16 34 56 66 IN 9544 I-80/I-94 16 34 54 64 IN 9552 US-50 16 34 56 62 MS 2606 I-55 20 48 76 78 MS 3015 I-10 16 36 52 68 MS 4506 I-55 18 40 60 78 MS 6104 US-49 16 36 52 74 MS 7900 US-61 16 40 56 78 TX 0506 18 36 56 -- TX 0516 18 36 56 -- TX 0523 18 36 62 -- TX 0526 18 36 60 --

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Table 58 - 99th Percentile Two-Lane Axle Group Weight State Site ID Route Single-

Single Single-Tandem

Tandem-Tandem

Other

CA 0001 Lodi 34 50 66 76 CA 0003 Antelope 30 46 62 82 CA 0004 Antelope 32 48 64 78 CA 0059 LA710 26 44 62 72 CA 0060 LA710 30 48 66 74 CA 0072 Bowman 30 46 62 80 FL 9916 US-29 36 60 78 90 FL 9919 I-95 26 42 58 74 FL 9926 I-75 32 58 74 120 FL 9927 SR-546 30 50 70 76 FL 9936 I-10 38 60 84 106 IN 9511 I-65 26 40 54 78 IN 9512 I-74 34 52 72 90 IN 9532 US-31 28 46 64 84 IN 9534 I-65 28 44 58 86 IN 9544 I-80/I-94 28 46 60 80 IN 9552 US-50 28 46 64 70 MS 2606 I-55 36 62 86 92 MS 3015 I-10 28 46 66 78 MS 4506 I-55 34 54 72 84 MS 6104 US-49 32 50 68 90 MS 7900 US-61 32 52 68 76 TX 0506 32 50 68 84 TX 0516 30 48 66 82 TX 0523 30 50 70 96 TX 0526 32 50 68 96

CHAPTER 4 CONCLUSIONS AND SUGGESTED RESEARCH CONCLUSIONS The present HL-93 load model, and in fact the calibration of the AASHTO LRFD specifications, is based on the top 20% of trucks in an Ontario truck weight database assembled in 1975 from a single site over only a two-week period. It reflects truck configurations and weights taken in the mid-1970s, which primarily consisted of five-axle semi trailer trucks. In the past 30 years, truck traffic has seen significant increases in volume and weight. Therefore, current AASHTO specified live load models, that are based on past Canadian traffic data, may not represent modern and future traffic conditions in some US jurisdictions.

Bridge engineers often focus on enhancing the knowledge of member and system resistances with less effort expended on understanding the live load demand on bridge elements and systems. Enhancement of bridge live load models needs representative samples of unbiased truck weight data that meet accepted quality standards. It also requires information on simultaneous presence of multiple trucks on bridges. Traditionally, the latter has been assembled from headway data, and has not been collected in a manner suitable for the development of design live loads. Due to the development of various weigh-in-motion technologies, the quality and quantity of WIM data has greatly improved in recent years. Unbiased truckloads are now being collected at normal highway speeds, in large quantity, and without truck driver’s knowledge. Modern WIM data loggers have the capability to record and report truck arrival times to an accuracy of 0.01 second, sufficient for estimating multiple presence probabilities. This information, however, has not been used to update the bridge design loads. In this regard, the lack of nationally accepted protocols may have been a contributing factor.

The goal of this project, therefore, was to develop a set of protocols and methodologies for using available recent truck traffic data collected at different US sites and recommend a step-by-step procedure that can be followed to obtain live load models for LRFD bridge design. The protocols are geared to address the collection, processing and use of national WIM data to develop and calibrate vehicular loads for LRFD superstructure design, fatigue design, deck design and design for overload permits. The study also gives practical examples of implementing these protocols with recent national WIM data drawn from states/sites around the country with different traffic exposures, load spectra, and truck configurations. Truck traffic data should be collected through Weigh-In-Motion systems that can collect simultaneously headway information as well as truck weights and axle weights and axle configurations while remaining hidden from view and unnoticed by trucks drivers. Truck data surveys collected at truck weigh stations and publicized locations are not reliable for use in live load modeling, because, they are normally avoided by illegal overweight vehicles that could control the maximum loads applied on bridge structures.

The selection of WIM systems sites should focus on sites where the owners maintain a quality assurance program that regularly checks the data for quality and requires system repair or recalibration when suspect data is identified. Weighing accuracy is sensitive to roadway conditions. Roadway conditions at a WIM site can deteriorate after a system is installed and calibrated. Regular maintenance and recalibrations are essential for reliable WIM system performance. Quality information is more important than the quantity of traffic data collected. It is far better to collect small amounts of well-calibrated data than to collect large amounts of data from poorly calibrated scales. Even small errors in vehicle weight measurements caused by poorly calibrated sensors could result in significant errors in measured loads. For long duration

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counts, the scale should be calibrated initially, the traffic characteristics at that site should be recorded, and the scale’s performance should be monitored over time. The State should also perform additional, periodic on-site calibration checks (at least two per year). These steps will ensure that the data being collected are accurate and reliable. Site-specific calibration is the only way that the dynamic effects of the pavement leading to the scale can be accounted for in the WIM scale calibration. This calibration process should be executed for a whole range of truck and axle weight types and configurations.

In many spans, the maximum lifetime truck-loading event is the result of more than one vehicle on the bridge at a time. Obtaining reliable multiple presence statistics requires large quantities of continuous WIM data with refined time stamps, which may not be available at every site. Studies done using New York WIM data during this project show that there is a strong correlation between multiple presence and ADTT. The multiple presence statistics are mostly transportable from site to site with similar truck traffic volumes and traffic flow and need not be repeated for each site. The site ADTT could serve as a key variable for establishing a site multiple presence value. The multiple-presence probabilities for permit trucks are significantly different from those used for normal traffic. Information on loads and multiple-presence probabilities for permits need to be obtained locally or regionally through WIM measurements and considered in the STRENGTH II design process since the data used for calibration of national codes are unlikely to be representative of all jurisdictions. Draft Recommended Protocols for Using Traffic Data in Bridge Design An aim of these processes is to capture weight data appropriate for national use or data specific to a state or local jurisdiction where the truck weight regulations and/or traffic conditions may be significantly different from national standards. The objective is to use data from existing WIM sites to develop live load models for bridge design. The models will be applicable for the strength, serviceability and fatigue design of bridge members, including bridge decks and design vehicles for overload permitting. Based on the research findings of this project, step-by-step protocols for collecting and using traffic data in bridge design have been developed. The recommended protocols are summarized as follows: STEP 1 DEFINE WIM DATA REQUIREMENTS FOR LIVE LOAD MODELING

This step defines the types of traffic data and WIM sensor calibration statistics needed for live load modeling of superstructure design load models (STRENGTH I), overload permitting (STRENGTH II), deck design, and for calibration of fatigue load models.

STEP 2 SELECTIONS OF WIM SITES FOR COLLECTING TRAFFIC DATA FOR

BRIDGE DESIGN

This step defines the criteria to be used for selecting WIM sites for national, state-specific, route-specific, and for site-specific design live load modeling. National study of truck loads can be conveniently handled by dividing the country into five regions. Representative states are selected from each region and the sites and routes for WIM data collection are selected based on roadway functional classifications. Some of the criteria for selecting WIM sites include: remote WIM sites away from weigh stations with free flowing traffic; sites that can provide a year’s worth of continuous data; sites that have been recently calibrated and are subject to a regular maintenance and quality assurance program; and sites equipped with current sensor and equipment technologies (preferably able to capture and record truck arrival times to the nearest 1/100th of a second or better).

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STEP 3 QUANTITIES OF WIM DATA REQUIRED FOR LOAD MODELING

There are several possible methods available to calculate the maximum load effect for a bridge design period from truck WIM data. The one implemented in these protocols is based on the assumption that the tail end of the histogram of the maximum load effect over a given return period approaches a Gumbel distribution as the return period increases. The method assumes that the WIM data is assembled over a sufficiently long period of time, preferably a year, to ensure that the data is representative of the tail end of the truck weight histograms and to factor in seasonal variations and other fluctuations in the traffic pattern. Sensitivity analyses have shown that the most important parameters for load modeling are those that describe the shape of the tail end of the truck load effects histogram. Step 3 provides recommendations for the quantity of WIM data to be collected from each site. They include: 1) A year’s worth of recent continuous data at each site to observe seasonal changes of vehicle weights and volumes is preferable; 2) If continuous data for a year is unavailable seek a minimum of one month data for each season for each site; 3) Data from all lanes in both directions of travel.

STEP 4 WIM CALIBRATION & VERIFICATION TESTS

WIM devices used for collecting data for live load modeling should be required to meet performance specifications for data accuracy and reliability. Field tests to verify that a WIM system is performing within the accuracy required is an important component of data quality assurance for bridge load modeling applications. Steps to ensure that the data being collected are accurate and reliable include: 1) Initial calibration of WIM equipment 2) Periodic monitoring of the data reported by WIM systems as a means of detecting drift in the calibration of weight sensors, and 3) Periodic on-site calibration checks for long duration counts, where, in addition to Steps 1 and 2 above, the scale is subjected to periodic on-site calibration checks at least two per year and the calibration statistics retained for use in filtration of sensor errors.

STEP 5 PROTOCOLS FOR DATA SCRUBBING, DATA QUALITY CHECKS &

STATISTICAL ADEQUACY OF TRAFFIC DATA

High speed WIM is prone to various errors, which need to be recognized and considered in the data review process to edit out unreliable data and unlikely trucks to ensure that only quality data is made part of the load modeling process. It is also important to recognize that unusual data is not all bad data. The WIM data should therefore be scrubbed to include only the data that meet the quality checks. Filtering protocols provided in this step should be applied for screening the WIM data prior to use in the live load modeling and calibration processes. Adjustments to the data scrubbing rules may need to be made to accommodate changes in truck configurations from state to state. Reviewing a sampling of trucks that were eliminated during the data scrubbing process is also recommended to check if the process is performing as intended. Ongoing simple quality checks are also performed on the WIM data to detect any operational problems with the sensors.

STEP 6 GENERALIZED MULTIPLE-PRESENCE STATISTICS FOR TRUCKS AS A

FUNCTION OF TRAFFIC VOLUME In many spans, the maximum lifetime truck-loading event is the result of more than one vehicle on the bridge at a time. Refined time stamps are critical to the accuracy of MP

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statistics for various truck loading cases including: single, following, side-by-side, and staggered. However, multiple presence statistics are mostly transportable from site to site with similar truck traffic volumes and traffic flow. A relationship between MP and traffic volume could be developed to utilize the MP values from national data to any given site without performing a site-specific analysis. In this step, relationship between the trucks weights in the drive lane and passing lanes must be established to determine whether passing trucks characteristics are similar to those in the main traffic lane and if there is a correlation between the truck properties.

STEP 7 PROTOCOLS FOR WIM DATA ANALYSIS FOR ONE-LANE LOAD

EFFECTS FOR SUPERSTRUCTURE DESIGN

In this step single lane load effects for single truck events and for following truck events for superstructure design are determined. Load effects for following trucks may be obtained directly from the WIM data where accurate time arrival stamps are collected. Generalized MP Statistics obtained in Step 6 may be used for simulation of load effects where accurate truck arrival time stamps are not available. The trucks are grouped into bins by travel lane and run through moment and shear influence lines (or structural analysis program) for simple and two-span continuous spans. The results are normalized by dividing by the corresponding load effects for HL-93.

Legal loads and routine permits are grouped under STRENGTH I. Heavy special permits are grouped under STRENGTH II. In most states permit records are either not specific enough or detailed enough to allow separation of permit loads from non-permit loads in a large WIM database. The protocols recommend that in such cases to group trucks with six or fewer axles in the STRENGTH I calibration. Vehicles in this group include legal trucks and routine permits or divisible load permits. These vehicles (legal loads and un-analyzed permits) are considered to be enveloped by the HL-93 load model. Group all trucks with seven or more axles in the STRENGTH II calibration.

STEP 8 PROTOCOLS FOR WIM DATA ANALYSIS FOR TWO-LANE LOAD

EFFECTS FOR SUPERSTRUCTURE DESIGN

Determine the number of side-by-side or staggered truck multiple presence events where trucks are in adjacent lanes in each direction. Run the combined truck with the trucks offset by their actual headway separation through moment and shear influence lines for simple and two-span continuous spans. Estimate the maximum daily load effects for two random trucks simultaneously crossing the bridge. The results are normalized by dividing by the corresponding load effects for HL-93. Where accurate time arrival stamps are not available, generalized MP Statistics obtained in Step 6 may be used for simulation of load effects. Legal loads and routine permits are grouped under STRENGTH I. Heavy special permits are grouped under STRENGTH II. As in Step 7, the protocols recommend that in cases where reliable permit record are unavailable to group trucks with six or fewer axles in the STRENGTH I calibration and trucks with seven or greater axles in the STRENGTH II calibration.

STEP 9 ASSEMBLE AXLE LOAD HISTOGRAMS FOR DECK DESIGN

As before, separate trucks into STRENGTH I and STRENGTH II groups for single events and for two-lane loaded cases. For each group, generate axle weight relative frequencies

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histograms for axle types: Single, Tandem, Tridem, and Quad axles. Multiple-presence probabilities are determined for side-by-side axle events.

STEP 10 FILTERING OF WIM SENSOR ERRORS / WIM SCATTER FROM WIM

HISTOGRAMS

Current WIM systems are known to have certain levels of random measurement errors that may affect the accuracy of the load modeling results. This step proposes an approach to filter out WIM measurement errors from the collected WIM data histograms. To execute the filtering process, calibration data for the WIM system for a whole range of trucks should be obtained. The results of these sensor calibration tests will be the basis for filtering out WIM measurement errors for each WIM data site. The Protocols present a procedure to filter out the WIM calibration errors from the measured WIM histograms of gross weights (or load effects) to obtain WIM data histograms that reflect the actual truck weights rather than the measured weights.

STEP 11 ACCUMULATED FATIGUE DAMAGE AND EFFECTIVE GROSS WEIGHT FROM WIM DATA

Updating the LRFD fatigue load model using recent WIM data is described in this step. Damage accumulation laws such as Miner’s rule can then be used to estimate the fatigue damage for the whole design period for the truck population at a site. Cumulative fatigue damage from the WIM population is compared to the LRFD fatigue truck to determine the fatigue damage adjustment factor K. Based upon the results of the WIM study changes may be proposed to the LRFD fatigue truck model, its axle configuration and/or its effective weight.

STEP 12 LIFETIME MAXIMUM LOAD EFFECT Lmax FOR SUPERSTRUCTURE DESIGN

In order to check the calibration of load models and/or load factors for strength design, it is necessary to estimate the mean maximum lifetime loading or load effect Lmax. There are several possible methods available to calculate the maximum load effect for a bridge design period from truck WIM data. Simplified analytical methods or simulations may be used to estimate the maximum loading over a longer period (75 years), from short-term WIM data. The approach implemented in these protocols is found to be one of the easiest methods that provide results comparable to many other computationally intensive methods, including Monte Carlo simulations. This statistical projection method is based on the assumption that the tail end of the histogram of the maximum load effect over a given return period approaches a Gumbel (extreme value) distribution as the return period increases.

STEP 13 DEVELOP AND CALIBRATE VEHICULAR LOAD MODELS FOR BRIDGE

DESIGN

Various levels of complexity are available for utilizing the site-specific truck weight and traffic data to calibrate live load models for bridge design. A simplified calibration approach (Method I) is proposed that focuses on the maximum live load variable, Lmax for updating the live load model or the load factor for current traffic conditions, in a manner consistent with the LRFD calibration. The ratio, r (Lmax WIM data, divided by Lmax Ontario data) for one-lane and for two-lanes is used to adjust the live load factor. This procedure assumes that the present LRFD calibration and safety indices are adequate for the load data

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and that the site-to-site variability (COV) of the present data and the data then available are consistent. A more robust reliability-based approach (Method II) is also presented that considers both the recent load data and the site-to-site variations in WIM data in the calibration of live loads.

During the development of the step-by-step protocols, recent long-term WIM data collected at several NY WIM sites by NYSDOT were obtained and used to test the validity and applicability of the protocols. The testing process was very helpful in ensuring that the recommended draft protocols were practical and could be effectively implemented using already available national WIM data.

Demonstration of Protocols Using National WIM Data

The draft recommended protocols were implemented using recent traffic data for a whole year (either 2005 or 2006) from 26 WIM sites in five states across the country. The states were: CA, TX, FL, IN, and MS. The states and WIM sites were chosen to capture a variety of geographic locations and functional classes, from urban interstates, rural interstates and state routes. An aim of this task was to give practical examples of using these protocols with national WIM data drawn from sites around the country with different traffic exposures, load spectra, and truck configurations. Adjustments and enhancements were made to the several protocol steps based on the experience gained from this demonstration task.

The lifetime maximum Lmax and r values (ratio of Lmax values) determined using Step 12 and Method I of Step 13 showed a significant, and consistent difference between the r-values for the 1-Lane events and 2-Lane events. The r-values for 1-Lane events are significantly greater than those for 2-Lane events. Whereas the maximum r-values for 2-Lane events had a maximum value of 1.184, the 1-Lane events had a maximum r-value among all WIM sites of 2.402. This seems to indicate that the live loading defined in the LRFD specification is fairly adequate in modeling the lifetime maximum loading on a span with two lanes loaded, but underestimates the lifetime maximum loading on a span with only one lane loaded. However, as discussed in Step 13, using a single maximum or characteristic value for Lmax for a State would be acceptable if the scatter or variability in Lmax from site-to-site for the state was equal to or less than the COV assumed in the LRFD calibration. The site-to-site scatter in the Lmax values obtained from recent WIM data showed significant variability from span to span, state to state, and between one-lane and two-lane load effects, well above the overall 20% COV used during the LRFD calibration. For example, the data from Florida show a COV for the moments of simple span bridges under one-lane loadings that varies from 32.5% for the 20-ft simple spans to 22.3% for the 200-ft simple span. (On the other hand, the site-to-site COV statistics for California are lower). Live load modeling using Method II was then implemented to reflect the site-to-site variability.

The results show that for the California truck traffic conditions, the reliability index for one lane is on the average equal to β=3.55 which is close to the LRFD target β=3.50. For two lanes of truck traffic, the average reliability index is β=4.63. This indicates that for the two-lane loading of California bridges, the current AASHTO LRFD is conservative producing higher reliability index values than the target β=3.50 set by the AASHTO LRFD code writers. If the intent is to reduce the reliability index for the two lane cases to the target β=3.5, then an adjusted live load factor γL=1.20 would result using the steps provided in the protocols. The reliability index for Florida for one lane loading drops to an average of β=2.58. The two-lane Lmax would lead to an average reliability index β=3.96. The latter value is still higher than the target β=3.5 while the one lane reliability is lower than the target. If the live load factor is raised to γL=2.37 then the reliability indices for the Florida sites would increase to β=3.50 for the one-lane cases. For Indiana, the reliability index for one lane of loading is on the average equal to β=3.16 for

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one-lane loading and the two-lane loading would lead to an average reliability index β=4.71. The Indiana data shows a site-to-site variability in COV’s on the order of 11% to 15% for both one-lane and two-lanes loadings.

Both calibration methods indicate that the live loading defined in the LRFD specification is generally adequate or even conservative in modeling the lifetime maximum loading on a span with two lanes loaded, but it underestimates the lifetime maximum loading for the one lane loaded case. This could be attributable to the increasing presence of heavy exclusion vehicles and/or routine permits in the traffic stream. The load limit enforcement environment in a state will also have a more discernible influence on the maximum single-lane loading than the maximum two-lane loading, which results from the presence of two side-by-side trucks. Additionally, with more multiple presence and WIM data currently available, the projections of Lmax for two-lane events as undertaken in this study are based on actual side-by-side events rather than based on simulations using conservative assumed side-by-side multiple-presence probabilities as done during the AASHTO LRFD code calibration. The WIM data collected as part of this study show that the actual percentage of side-by-side multiple truck event cases is significantly lower than assumed by the AASHTO LRFD code writers who had to develop their models based on a limited set of multiple presence data.

Knowing the actual truck weight distribution in each lane allowed the determination of the relationship between the trucks weights in the main traffic lane (drive lane) and adjacent lanes and if there is a correlation between the truck properties. This study seems to indicate that there is some negative correlation between the weights of side-by-side trucks. This means that when a heavy truck is in one lane, the other lane’s truck is expected to be lighter. Here again, the conservative assumptions used during the LRFD calibration were not adequately supported by field measurements. SUGGESTED RESEARCH AND IMPROVEMENTS IN DATA COLLECTION Developing and calibrating bridge live load models requires large amounts of quality WIM data. Improvements in WIM data collection is needed to allow the effective implementation of these protocols. Suggested research on this topic for the future and recommendations for improving WIM data collection are as follows:

• States should evaluate their WIM data collection equipment to ascertain if it can provide the quantity and quality of data to implement these protocols. It may be necessary to upgrade the WIM technology and data collection system at specific sites selected for data collection.

• DOT’s should carefully consider the locations of WIM sites within a state. Remote WIM sites away from weigh stations are needed to provide un-biased WIM data. Availability of WIM sites on heavy freight routes, hauling routes, or routes known to have significant permit traffic is important for live load modeling purposes.

• WIM devices should be required to meet ASTM performance specifications for data accuracy and reliability. The WIM sites should be subject to a regular maintenance and quality assurance program. The system components should be reliable enough to be able to provide a year’s worth of continuous data.

• The WIM system should be able to capture and record truck arrival times to the nearest 1/100th of a second or better to allow the determination of truck headway separations. Sensors should be placed in the drive lane and passing lanes at sites used for data collection.

• The WIM system should not cut off trucks having more than a certain number of axles or heavier than a certain upper weight limit. It is important to record the long heavy

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superloads that may have a dozen or more axles and weigh over 200 Kips. These trucks populate the upper tail of the truck weight distribution and have a significant influence on bridge safety.

• WIM calibration and verification testing requirements defined in Step 4 should be implemented as part of an overall Quality Assurance Program. Regular maintenance and periodic recalibration of any WIM system is critical for obtaining reliable traffic data. Initial calibration and periodic recalibration every six months are recommended for sites selected for data collection. Calibration of WIM equipment should follow LTPP calibration procedures or ASTM 1318 standards. Periodic monitoring and quality check of the data reported by WIM systems should be performed as a means of detecting drift in the calibration of weight sensors. Calibration statistics should be maintained for each WIM site for use in the error filtration process during the data analysis.

• Separating permit vehicles from non-permit traffic in large scale WIM data requires the availability of reliable electronic permits database/records of special permits authorized in a given period for a State. DOT surveys have indicated that such permit databases are not currently being maintained, at least in an electronic form. States should make necessary changes to their permit operations / management to create and maintain a comprehensive electronic database of overweight permits authorized that will allow these vehicles to be properly grouped as either STRENGTH I or STRENGTH II for live load modeling.

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18. AASHTO (1987): Guide for Maximum Dimensions and Weights of Motor Vehicles and

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33. Nowak, A. S. and Y.-K. Hong, “Bridge Live-Load Models,” Journal of Structural Engineering, v 117, n 9, Sept, 1991, p 2757-2767.

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148

48. Nowak, A. S., “Live Load Model for Highway Bridges,” Structural Safety, v 13, n 1-2, Dec, 1993, p 53-66.

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53. Fu, G. and O. Hag-Elsafi, “Overweight Trucks and Safety of Bridges,” Proceedings of the ASCE Structures Congress ’94, Atlanta, GA USA, Apr 24-28 1994, p 284-289.

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56. Ghosn, M. and F. Moses, “Reliability Calibration of Bridge Design Code,” Journal of

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57. Ghosn, M. and D. M. Frangopol, “Site-Specific Live Load Models for Bridge Evaluation,” Probabilistic Mechanics and Structural and Geotechnical Reliability, Proceedings of the 7th ASCE Specialty Conference, Worcester, MA USA, Aug 7-9 1996, p 30-33.

58. Laman, J. A. and A. S. Nowak, “Site-Specific Truck Loads on Bridges and Roads,”

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59. Harman, D. J. and A. G. Davenport, “Statistical Approach to Traffic Loading on

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60. Brameld, G. H., “Statistical Formulation of Highway Bridge Live Loads,” Pitagora

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61. Harman, D. J., A. G. Davenport, and W. S. S. Wong, “Traffic Loads on Medium and Long Span Bridges,” Canadian Journal of Civil Engineering, v 11, n 3, Sept, 1984, p 556-573.

149

62. Nowak, A. S. and D. M. Ferrand, “Truck Load Models for Bridges,” Proceedings of the 2004 Structures Congress – Building on the Past: Securing the Future, Nashville, TN USA, May 22-26 2004, p 1147-1156.

63. Frangopol, D. M., G. G. Goble, and N. Tan, “Truck Loading Data for a Probabilistic

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64. Jacobsohn, A. P., “Truck Weights: A Long and Winding Road,” Waste Age, v 28, n 6,

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65. Fu, G. and O. Hag-Elsafi, “Vehicular Overloads: Load Model, Bridge Safety, and Permit Checking,” Journal of Bridge Engineering, v 5, n 1, Feb, 2000, p 49-57.

66. Kim, S., A. S. Nowak, and R. Till, “Verification of Site-Specific Live Load on Bridges,”

Probabilistic Mechanics and Structural and Geotechnical Reliability, Proceedings of the 7th ASCE Specialty Conference, Worcester, MA USA, Aug 7-9 1996, p 214-217.

67. Laman, J. A. and A. S. Nowak, “Verification of Truck Loads for Girder Bridges,”

Proceedings of the 13th Structures Conference, Part 1 of 2, Boston, MA USA, Apr 3-5 1995, p 907-920.

68. Daniels, J. H., J. L. Wilson, B. T. Yen, L. Y. Lai, and R. Abbaszadeh, “WIM Plus

Response Study of Four In-Service Bridges,” Engineer’s Society of Western Pennsylvania, Official Proceedings – 3rd Annual International Bridge Conference, Pittsburgh, PA USA, p 136-142.

69. Bez, R., R. Cantieni, and J. Jacquemoud, “Modeling of Highway Traffic Loads in

Switzerland,” IABSE Proceedings P-117/87, 1987, p 153-168. Publisher: International Association for Bridge and Structural Engineering.

70. Ghosn, M., F. Moses, and F. Gabriel, “Truck Data for Bridge Load Modeling,” Second

Workshop on Bridge Engineering Research in Progress, Reno, Nevada USA, Oct 29-30 1990, p 71-74.

71. Lui, W. D., C. A. Cornell, and R. A. Imbsen, “Analysis of Bridge Truck Loads,”

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72. Kulicki, J. M. and D. R. Mertz, “New Live Load for Bridge Design,” Proceedings of the

8th Annual International Bridge Conference, Pittsburgh, PA USA, Jun 10-12 1991, p 238.

73. Hwang, E.-S., H.-M. Koh, and D.-B. Bae, “A Proposal for New Design Live Load Model in Korea,” Structural Safety and Reliability: Proceedings of the Eighth International Conference, ICOSSAR’01, Newport Beach, CA USA, Jun 17-22 2001, 1 page abstract (paper on CD-ROM).

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75. Nyman, W. E., “Calibration of Bridge Fatigue Design Model,” Journal of Structural Engineering, v 111, n 6, Jun, 1985, p 1251-1266.

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and Measured Data,” Joint International Conference on Computing and Decision Making in Civil Engineering, Montreal, Canada, Jun 14-16 2006.

77. Caprani, C. C., S. A. Grave, E. J. O’Brien, and A. J. O’Connor, “Critical Loading Events

for the Assessment of Medium Span Bridges,” ICCST ’02: Proceedings of the 6th International Conference on Computational Structures Technology, Prague, Czech Republic, Sept 4-6 2002, p 343-344 (abstract) (paper on CD-ROM). Editor: B.H.V. Topping and Z. Bittnar, Publisher: Civil Comp Press.

78. Laman, J. A. and A. S. Nowak, “Fatigue-Load Models for Girder Bridges,” Journal of

Structural Engineering, v 122, issue 7, Jul, 1996, p 726-733.

79. Au, A., C. Lam, A. C. Agarwal, and B. Tharmabala, “Bridge Evaluation by Mean Load Method per the Canadian Highway Bridge Design Code,” Canadian Journal of Civil Engineering, v 32, n 4, Aug, 2005, p 678-686.

80. Laman, J. A. and A. S. Nowak, “Live Load Spectra for Bridge Evaluation,” Proceedings

of the Symposium on Practical Solutions for Bridge Strengthening and Rehabilitation, Des Moines, IA USA, Apr 5-6 1993, p 13-22.

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Detroit, Michigan Area,” Transportation Research Record 1541, 1996, p 58-63.

83. Cohen, H., G. Fu, W. Dekelbab, and F. Moses, “Predicting Truck Load Spectra Under Weigh Limit Changes and its Application to Steel Bridge Fatigue Assessment,” Journal of Bridge Engineering, v 8, n 5, Sept, 2003, p 312-322.

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Appendix A

Implementation of Draft Protocols WIM Data Analysis

California

• WIM Site 0001 – Lodi

• WIM Site 0003 – Antelope EB

• WIM Site 0004 – Antelope WB

• WIM Site 0059 – LA710SB

• WIM Site 0060 – LA710NB

• WIM Site 0072 – Bowman

Florida

• WIM Site 9916 – US29

• WIM Site 9919 – I-95

• WIM Site 9926 – I-75

• WIM Site 9927 – State Route

• WIM Site 9936 – I-10

Indiana

• WIM Site 9511

• WIM Site 9512

• WIM Site 9532

• WIM Site 9534

• WIM Site 9544

• WIM Site 9552

Mississippi

• WIM Site 2606 – I-55

• WIM Site 3015 – I-10

• WIM Site 4506 – I-55

• WIM Site 6104 – US49

• WIM Site 7900 – US61

Texas

• WIM Site 0506

• WIM Site 0516

• WIM Site 0523

• WIM Site 0526

A - 1

Implementation of Draft Protocols WIM Data Analysis

California

WIM Site 0001 – Lodi

• GVW Histogram

• Single Truck Moment Histogram

• One-Lane and Two-Lane Moment Histogram

• One-Lane and Two-Lane Shear Histogram

• One-Lane and Two-lane Negative Moment Histogram

• Fatigue Adjustment Factor

• Axle Group Weight Histogram

A - 2

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 1536017 1469224

Mean All Trucks 55.988 53.188Std Dev All Trucks 18.309 20.446

CoV All Trucks 0.327 0.384

Mean Top 20% Trucks 78.306 79.692Std Dev Top 20% Trucks 3.509 3.121

CoV Top 20% Trucks 0.045 0.039

Mean Top 5% Trucks 82.282 83.600Std Dev Top 5% Trucks 4.367 3.793

CoV Top 5% Trucks 0.053 0.045

WIM Site 0001 Gross Vehicle Weight Statistics

WIM Site 0001Single Truck GVW Relative Frequencies

0

2

4

6

8

10

12

14

16

0 50 100 150 200

GVW (kips)

Freq

uenc

y %

Lanes 1 & 2Lanes 3 & 4

A - 3

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 1536017 1469224

Mean All Trucks 0.363 0.347Std Dev All Trucks 0.108 0.120

CoV All Trucks 0.296 0.345

Mean Top 20% Trucks 0.496 0.505Std Dev Top 20% Trucks 0.029 0.030

CoV Top 20% Trucks 0.059 0.060

Mean Top 5% Trucks 0.534 0.544Std Dev Top 5% Trucks 0.034 0.035

CoV Top 5% Trucks 0.063 0.064

WIM Site 0001 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 0001HL93 Single Truck Simple-Span Moment

60 ft Span

0

2

4

6

8

10

12

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Moment Ratio (Mtruck/MHL93)

Freq

uenc

y %

Lanes 1&2Lanes 3&4

A - 4

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 1569126 58014

Mean All Trucks 0.365 0.533Std Dev All Trucks 0.108 0.157

CoV All Trucks 0.295 0.294

Mean Top 20% Trucks 0.497 0.777Std Dev Top 20% Trucks 0.030 0.077

CoV Top 20% Trucks 0.060 0.099

Mean Top 5% Trucks 0.535 0.884Std Dev Top 5% Trucks 0.035 0.047

CoV Top 5% Trucks 0.065 0.054

WIM Site 0001 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 0001HL93 Simple-Span Moment Lanes 1&2

60 ft Span

0

2

4

6

8

10

12

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 5

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 1569126 58014

Mean All Trucks 0.404 0.585Std Dev All Trucks 0.122 0.168

CoV All Trucks 0.303 0.287

Mean Top 20% Trucks 0.560 0.844Std Dev Top 20% Trucks 0.032 0.086

CoV Top 20% Trucks 0.058 0.102

Mean Top 5% Trucks 0.599 0.965Std Dev Top 5% Trucks 0.040 0.052

CoV Top 5% Trucks 0.067 0.054

WIM Site 0001 HL93 Simple-Span Shear Statistics - 60 ft Span

WIM Site 0001HL93 Simple-Span Shear Lanes 1&2

60 ft Span

0123456789

10

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Shear Ratio (VWIM/VHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 6

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 1569126 58014

Mean All Trucks 0.356 0.542Std Dev All Trucks 0.119 0.149

CoV All Trucks 0.334 0.276

Mean Top 20% Trucks 0.503 0.764Std Dev Top 20% Trucks 0.024 0.078

CoV Top 20% Trucks 0.048 0.102

Mean Top 5% Trucks 0.531 0.875Std Dev Top 5% Trucks 0.031 0.056

CoV Top 5% Trucks 0.058 0.064

WIM Site 0001 HL93 Negative Moment Statistics - 60 ft Span

WIM Site 0001HL93 Negative Moment Lanes 1&2

60 ft Span

0

2

4

6

8

10

12

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 7

WIM Site: 0001 Fatigue Adjustment Factor

Lanes 1 and 2LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8642 0.9554 1.0481 0.9801 1.0182 1.0417 1.0681 1.0823K (pos.) 0.8448 0.94 0.974 0.9673 1.0047 1.0287 1.057 1.0731K (neg.) 1.142 0.995 1.1649 1.1573 1.0388 1.0648 1.0924 1.1057Modified LRFD Fatigue Truck GVW = 61.46 kips

Axle Weight: Steer = 6.829 kips Drive = 27.315 kips Trailer = 27.315 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7593 0.8395 0.9208 0.8611 0.8947 0.9153 0.9384 0.9509K (pos.) 0.7422 0.8259 0.8558 0.8499 0.8827 0.9038 0.9287 0.9428K (neg.) 1.0034 0.8743 1.0235 1.0168 0.9127 0.9355 0.9598 0.9715Site-Specific Fatigue Truck GVW = 61.46 kips

Axle Weight: Steer = 12.907 kips Drive = 25.813 kips Trailer = 22.74 kipsAxle Spacing: 19 ft 37 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8035 0.9317 0.9333 0.9688 0.9719 0.9756 0.9804 0.9832K (pos.) 0.7854 0.8898 0.9155 0.9473 0.9603 0.9678 0.9758 0.9799K (neg.) 0.88 0.9936 0.9654 0.9627 1.0062 0.9993 0.9953 0.9942

Lanes 3 and 4LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8421 0.9312 1.0281 0.9657 1.002 1.0245 1.0497 1.0634K (pos.) 0.8233 0.9146 0.9542 0.9509 0.9876 1.011 1.0386 1.0541K (neg.) 1.1177 0.9698 1.1356 1.1311 1.0218 1.0465 1.0729 1.0858Modified LRFD Fatigue Truck GVW = 60.329 kips

Axle Weight: Steer = 6.703 kips Drive = 26.813 kips Trailer = 26.813 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7538 0.8335 0.9203 0.8644 0.8969 0.917 0.9396 0.9518K (pos.) 0.7369 0.8186 0.8541 0.8512 0.884 0.905 0.9296 0.9436K (neg.) 1.0005 0.868 1.0165 1.0125 0.9146 0.9367 0.9604 0.9719Site-Specific Fatigue Truck GVW = 60.329 kips

Axle Weight: Steer = 12.669 kips Drive = 25.338 kips Trailer = 22.322 kipsAxle Spacing: 19 ft 37 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7977 0.9251 0.9327 0.9725 0.9744 0.9775 0.9817 0.9841K (pos.) 0.7798 0.8819 0.9137 0.9487 0.9617 0.969 0.9768 0.9807K (neg.) 0.8774 0.9865 0.9588 0.9586 1.0083 1.0006 0.9959 0.9946

A - 8

Statistics Single Tandem Tridem QuadAxle Count 5364440 4655865 18889 61

Mean All Axles 10.975 22.249 26.651 19.951Std Dev All Axles 3.866 9.091 10.356 7.254

CoV All Axles 0.352 0.409 0.389 0.364

Mean Top 20% Axles 16.780 33.630 40.461 28.833Std Dev Top 20% Axles 1.872 1.901 5.021 11.892

CoV Top 20% Axles 0.112 0.057 0.124 0.412

Mean Top 5% Axles 19.243 36.050 47.475 43.667Std Dev Top 5% Axles 1.032 2.145 5.237 18.148

CoV Top 5% Axles 0.054 0.060 0.110 0.416

99th Percentile 18 36 50 40

WIM Site 0001 Axle Group Weight Statistics

WIM Site 0001Axle Group Weight Relative Frequency

Histogram

05

1015202530354045

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

Axle Group Weight (kips)

Freq

uenc

y %

SingleTandemTridemQuad

A - 9

Statistics Single-Single Single-Tandem Tandem-Tandem All OthersEvent Count 30468 52923 22722 406

Mean All Events 21.928 33.127 44.592 43.350Std Dev All Events 5.527 9.914 12.881 14.551

CoV All Events 0.252 0.299 0.289 0.336

Mean Top 20% Events 29.717 46.243 62.580 64.630Std Dev Top 20% Events 2.690 3.183 3.753 7.976

CoV Top 20% Events 0.091 0.069 0.060 0.123

Mean Top 5% Events 33.482 50.747 67.350 75.000Std Dev Top 5% Events 2.285 2.476 2.753 8.778

CoV Top 5% Events 0.068 0.049 0.041 0.117

99th Percentile 34 50 66 76

WIM Site 0001 Two-Lane Multiple Presence Axle Load Statistics

WIM Site 0001Two-Lane MP Axle Loads

02468

101214161820

0 20 40 60 80 100 120 140 160 180 200

Axle Load (kips)

Freq

uenc

y %

Single-Single

Single-Tandem

Tandem-Tandem

AllOthers

A - 10

Implementation of Draft Protocols WIM Data Analysis

California

WIM Site 0003 – Antelope EB

• GVW Histogram

• Single Truck Moment Histogram

• One-Lane and Two-Lane Moment Histogram

• One-Lane and Two-Lane Shear Histogram

• One-Lane and Two-lane Negative Moment Histogram

• Fatigue Adjustment Factor

• Axle Group Weight Histogram

A - 11

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 719057 0

Mean All Trucks 50.279 0.000Std Dev All Trucks 18.288 0.000

CoV All Trucks 0.364 0.000

Mean Top 20% Trucks 73.550 0.000Std Dev Top 20% Trucks 3.269 0.000

CoV Top 20% Trucks 0.044 0.000

Mean Top 5% Trucks 77.012 0.000Std Dev Top 5% Trucks 3.905 0.000

CoV Top 5% Trucks 0.051 0.000

WIM Site 0003 Gross Vehicle Weight Statistics

WIM Site 0003Single Truck GVW Relative Frequencies

0

2

4

6

8

10

12

14

0 50 100 150 200

GVW (kips)

Freq

uenc

y %

Lanes 1 & 2Lanes 3 & 4

A - 12

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 719057 0

Mean All Trucks 0.328 0.000Std Dev All Trucks 0.106 0.000

CoV All Trucks 0.322 0.000

Mean Top 20% Trucks 0.466 0.000Std Dev Top 20% Trucks 0.033 0.000

CoV Top 20% Trucks 0.070 0.000

Mean Top 5% Trucks 0.509 0.000Std Dev Top 5% Trucks 0.037 0.000

CoV Top 5% Trucks 0.072 0.000

WIM Site 0003 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 0003HL93 Single Truck Simple-Span Moment

60 ft Span

0123456789

10

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Moment Ratio (Mtruck/MHL93)

Freq

uenc

y %

Lanes 1&2Lanes 3&4

A - 13

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 720470 28267

Mean All Trucks 0.328 0.483Std Dev All Trucks 0.106 0.148

CoV All Trucks 0.322 0.306

Mean Top 20% Trucks 0.467 0.712Std Dev Top 20% Trucks 0.033 0.078

CoV Top 20% Trucks 0.071 0.110

Mean Top 5% Trucks 0.509 0.821Std Dev Top 5% Trucks 0.037 0.049

CoV Top 5% Trucks 0.073 0.060

WIM Site 0003 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 0003HL93 Simple-Span Moment Lanes 1&2

60 ft Span

0123456789

10

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 14

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 720470 28267

Mean All Trucks 0.367 0.531Std Dev All Trucks 0.121 0.158

CoV All Trucks 0.330 0.298

Mean Top 20% Trucks 0.530 0.771Std Dev Top 20% Trucks 0.032 0.088

CoV Top 20% Trucks 0.061 0.114

Mean Top 5% Trucks 0.569 0.897Std Dev Top 5% Trucks 0.037 0.054

CoV Top 5% Trucks 0.065 0.061

WIM Site 0003 HL93 Simple-Span Shear Statistics - 60 ft Span

WIM Site 0003HL93 Simple-Span Shear Lanes 1&2

60 ft Span

012345678

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Shear Ratio (VWIM/VHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 15

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 720470 28267

Mean All Trucks 0.318 0.489Std Dev All Trucks 0.118 0.143

CoV All Trucks 0.372 0.292

Mean Top 20% Trucks 0.472 0.701Std Dev Top 20% Trucks 0.022 0.078

CoV Top 20% Trucks 0.047 0.111

Mean Top 5% Trucks 0.500 0.811Std Dev Top 5% Trucks 0.024 0.057

CoV Top 5% Trucks 0.048 0.071

WIM Site 0003 HL93 Negative Moment Statistics - 60 ft Span

WIM Site 0003HL93 Negative Moment Lanes 1&2

60 ft Span

0123456789

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 16

WIM Site: 0003 Fatigue Adjustment Factor

Lanes 1 and 2LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7971 0.8753 0.9592 0.8933 0.9273 0.9495 0.9745 0.9881K (pos.) 0.7776 0.8609 0.8894 0.8821 0.916 0.9382 0.9647 0.9798K (neg.) 1.0473 0.9087 1.0649 1.0605 0.9518 0.974 0.9995 1.0117Modified LRFD Fatigue Truck GVW = 56.26 kips

Axle Weight: Steer = 6.251 kips Drive = 25.004 kips Trailer = 25.004 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7651 0.8402 0.9207 0.8574 0.8901 0.9113 0.9354 0.9484K (pos.) 0.7463 0.8263 0.8537 0.8466 0.8792 0.9005 0.926 0.9404K (neg.) 1.0053 0.8722 1.0221 1.0179 0.9136 0.9349 0.9594 0.9711Site-Specific Fatigue Truck GVW = 56.26 kips

Axle Weight: Steer = 12.377 kips Drive = 21.941 kips Trailer = 21.941 kipsAxle Spacing: 19 ft 37 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8719 1.001 0.9853 1.0066 0.9956 0.9933 0.9921 0.9918K (pos.) 0.8505 0.9523 0.965 0.9844 0.9867 0.9881 0.9895 0.9902K (neg.) 0.9109 1 0.9626 0.9614 1.0202 1.0068 0.9989 0.9962

Lanes 3 and 4LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0 0 0 0 0 0 0 0K (pos.) 0 0 0 0 0 0 0 0K (neg.) 0 0 0 0 0 0 0 0Modified LRFD Fatigue Truck GVW = 0 kips

Axle Weight: Steer = 0 kips Drive = 0 kips Trailer = 0 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0 0 0 0 0 0 0 0K (pos.) 0 0 0 0 0 0 0 0K (neg.) 0 0 0 0 0 0 0 0Site-Specific Fatigue Truck GVW = 0 kips

Axle Weight: Steer = 0 kips Drive = 0 kips Trailer = 0 kipsAxle Spacing: 19 ft 37 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0 0 0 0 0 0 0 0K (pos.) 0 0 0 0 0 0 0 0K (neg.) 0 0 0 0 0 0 0 0

A - 17

Statistics Single Tandem Tridem QuadAxle Count 1197849 1127692 2407 14

Mean All Axles 10.624 20.488 27.225 34.714Std Dev All Axles 3.230 8.575 11.635 16.415

CoV All Axles 0.304 0.419 0.427 0.473

Mean Top 20% Axles 15.486 31.208 43.299 56.333Std Dev Top 20% Axles 1.930 1.963 5.904 6.110

CoV Top 20% Axles 0.125 0.063 0.136 0.108

Mean Top 5% Axles 17.704 33.827 51.650 63.000Std Dev Top 5% Axles 1.160 1.884 2.912 0.000

CoV Top 5% Axles 0.066 0.056 0.056 0.000

99th Percentile 16 32 52 62

WIM Site 0003 Axle Group Weight Statistics

WIM Site 0003Axle Group Weight Relative Frequency

Histogram

0

5

10

15

20

25

30

35

40

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

Axle Group Weight (kips)

Freq

uenc

y %

SingleTandemTridemQuad

A - 18

Statistics Single-Single Single-Tandem Tandem-Tandem All OthersEvent Count 6371 12274 5586 46

Mean All Events 21.216 30.982 40.720 46.348Std Dev All Events 4.500 9.176 12.250 14.016

CoV All Events 0.212 0.296 0.301 0.302

Mean Top 20% Events 27.725 43.101 57.994 67.222Std Dev Top 20% Events 2.427 2.810 3.799 12.468

CoV Top 20% Events 0.088 0.065 0.066 0.185

Mean Top 5% Events 30.906 47.016 63.093 83.000Std Dev Top 5% Events 2.348 2.278 2.747 0.000

CoV Top 5% Events 0.076 0.048 0.044 0.000

99th Percentile 30 46 62 82

WIM Site 0003 Two-Lane Multiple Presence Axle Load Statistics

WIM Site 0003Two-Lane MP Axle Loads

0

5

10

15

20

25

0 20 40 60 80 100 120 140 160 180 200

Axle Load (kips)

Freq

uenc

y %

Single-Single

Single-Tandem

Tandem-Tandem

AllOthers

A - 19

Implementation of Draft Protocols WIM Data Analysis

California

WIM Site 0004 – Antelope WB

• GVW Histogram

• Single Truck Moment Histogram

• One-Lane and Two-Lane Moment Histogram

• One-Lane and Two-Lane Shear Histogram

• One-Lane and Two-lane Negative Moment Histogram

• Fatigue Adjustment Factor

• Axle Group Weight Histogram

A - 20

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 0 804963

Mean All Trucks 0.000 50.058Std Dev All Trucks 0.000 18.375

CoV All Trucks 0.000 0.367

Mean Top 20% Trucks 0.000 76.971Std Dev Top 20% Trucks 0.000 3.801

CoV Top 20% Trucks 0.000 0.049

Mean Top 5% Trucks 0.000 81.168Std Dev Top 5% Trucks 0.000 4.404

CoV Top 5% Trucks 0.000 0.054

WIM Site 0004 Gross Vehicle Weight Statistics

WIM Site 0004Single Truck GVW Relative Frequencies

0

2

4

6

8

10

12

14

16

0 50 100 150 200

GVW (kips)

Freq

uenc

y %

Lanes 1 & 2Lanes 3 & 4

A - 21

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 0 804963

Mean All Trucks 0.000 0.334Std Dev All Trucks 0.000 0.106

CoV All Trucks 0.000 0.316

Mean Top 20% Trucks 0.000 0.488Std Dev Top 20% Trucks 0.000 0.036

CoV Top 20% Trucks 0.000 0.074

Mean Top 5% Trucks 0.000 0.532Std Dev Top 5% Trucks 0.000 0.044

CoV Top 5% Trucks 0.000 0.084

WIM Site 0004 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 0004HL93 Single Truck Simple-Span Moment

60 ft Span

0

2

4

6

8

10

12

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Moment Ratio (Mtruck/MHL93)

Freq

uenc

y %

Lanes 1&2Lanes 3&4

A - 22

Statistics Lanes 3&4 - 1 Lane Event Lanes 3&4 - 2 Lane EventTruck Count 806307 31128

Mean All Trucks 0.335 0.489Std Dev All Trucks 0.106 0.152

CoV All Trucks 0.316 0.311

Mean Top 20% Trucks 0.488 0.724Std Dev Top 20% Trucks 0.036 0.086

CoV Top 20% Trucks 0.074 0.119

Mean Top 5% Trucks 0.532 0.847Std Dev Top 5% Trucks 0.045 0.060

CoV Top 5% Trucks 0.084 0.071

WIM Site 0004 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 0004HL93 Simple-Span Moment Lanes 3&4

60 ft Span

0

2

4

6

8

10

12

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 23

Statistics Lanes 3&4 - 1 Lane Event Lanes 3&4 - 2 Lane EventTruck Count 806307 31128

Mean All Trucks 0.369 0.535Std Dev All Trucks 0.122 0.164

CoV All Trucks 0.330 0.307

Mean Top 20% Trucks 0.552 0.784Std Dev Top 20% Trucks 0.038 0.096

CoV Top 20% Trucks 0.068 0.123

Mean Top 5% Trucks 0.597 0.921Std Dev Top 5% Trucks 0.045 0.065

CoV Top 5% Trucks 0.075 0.070

WIM Site 0004 HL93 Simple-Span Shear Statistics - 60 ft Span

WIM Site 0004HL93 Simple-Span Shear Lanes 3&4

60 ft Span

0

2

4

6

8

10

12

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Shear Ratio (VWIM/VHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 24

Statistics Lanes 3&4 - 1 Lane Event Lanes 3&4 - 2 Lane EventTruck Count 806307 31128

Mean All Trucks 0.316 0.490Std Dev All Trucks 0.119 0.147

CoV All Trucks 0.378 0.299

Mean Top 20% Trucks 0.492 0.708Std Dev Top 20% Trucks 0.026 0.080

CoV Top 20% Trucks 0.053 0.113

Mean Top 5% Trucks 0.523 0.822Std Dev Top 5% Trucks 0.027 0.062

CoV Top 5% Trucks 0.052 0.075

WIM Site 0004 HL93 Negative Moment Statistics - 60 ft Span

WIM Site 0004HL93 Negative Moment Lanes 3&4

60 ft Span

0

2

4

6

8

10

12

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 25

WIM Site: 0004 Fatigue Adjustment Factor

Lanes 1 and 2LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0 0 0 0 0 0 0 0K (pos.) 0 0 0 0 0 0 0 0K (neg.) 0 0 0 0 0 0 0 0Modified LRFD Fatigue Truck GVW = 0 kips

Axle Weight: Steer = 0 kips Drive = 0 kips Trailer = 0 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0 0 0 0 0 0 0 0K (pos.) 0 0 0 0 0 0 0 0K (neg.) 0 0 0 0 0 0 0 0Site-Specific Fatigue Truck GVW = 0 kips

Axle Weight: Steer = 0 kips Drive = 0 kips Trailer = 0 kipsAxle Spacing: 18.5 ft 36.5 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0 0 0 0 0 0 0 0K (pos.) 0 0 0 0 0 0 0 0K (neg.) 0 0 0 0 0 0 0 0

Lanes 3 and 4LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8008 0.8884 0.9777 0.9137 0.944 0.9631 0.9848 0.9967K (pos.) 0.7824 0.8749 0.9079 0.9013 0.9318 0.9516 0.9752 0.9886K (neg.) 1.0751 0.9159 1.0674 1.0611 0.9587 0.9809 1.0044 1.0158Modified LRFD Fatigue Truck GVW = 56.407 kips

Axle Weight: Steer = 6.267 kips Drive = 25.07 kips Trailer = 25.07 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7666 0.8505 0.936 0.8747 0.9037 0.922 0.9428 0.9541K (pos.) 0.749 0.8376 0.8692 0.8629 0.892 0.911 0.9336 0.9464K (neg.) 1.0293 0.8768 1.0218 1.0158 0.9178 0.939 0.9616 0.9725Site-Specific Fatigue Truck GVW = 56.407 kips

Axle Weight: Steer = 12.41 kips Drive = 23.691 kips Trailer = 20.307 kipsAxle Spacing: 18.5 ft 36.5 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8112 0.9309 0.9348 0.9638 0.9677 0.972 0.9777 0.9809K (pos.) 0.7926 0.8928 0.9174 0.946 0.9579 0.9652 0.9734 0.9778K (neg.) 0.8847 0.9904 0.9649 0.9644 1.0026 0.9972 0.9939 0.9933

A - 26

Statistics Single Tandem Tridem QuadAxle Count 1334146 1264006 3097 8

Mean All Axles 10.555 20.446 29.421 58.000Std Dev All Axles 3.319 8.571 12.080 7.559

CoV All Axles 0.314 0.419 0.411 0.130

Mean Top 20% Axles 15.336 32.684 45.943 64.000Std Dev Top 20% Axles 2.333 2.025 6.132 1.414

CoV Top 20% Axles 0.152 0.062 0.133 0.022

Mean Top 5% Axles 18.423 34.967 54.923 0.000Std Dev Top 5% Axles 1.332 2.543 3.463 0.000

CoV Top 5% Axles 0.072 0.073 0.063 0.000

99th Percentile 18 34 56 64

WIM Site 0004 Axle Group Weight Statistics

WIM Site 0004Axle Group Weight Relative Frequency

Histogram

0

5

10

15

20

25

30

35

40

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

Axle Group Weight (kips)

Freq

uenc

y %

SingleTandemTridemQuad

A - 27

Statistics Single-Single Single-Tandem Tandem-Tandem All OthersEvent Count 7026 13541 6316 79

Mean All Events 21.147 30.949 40.680 45.025Std Dev All Events 4.776 9.197 12.168 14.754

CoV All Events 0.226 0.297 0.299 0.328

Mean Top 20% Events 28.159 44.143 58.425 66.375Std Dev Top 20% Events 2.641 3.108 4.967 8.785

CoV Top 20% Events 0.094 0.070 0.085 0.132

Mean Top 5% Events 31.655 48.291 65.177 78.500Std Dev Top 5% Events 2.256 3.049 2.924 3.416

CoV Top 5% Events 0.071 0.063 0.045 0.044

99th Percentile 32 48 64 78

WIM Site 0004 Two-Lane Multiple Presence Axle Load Statistics

WIM Site 0004Two-Lane MP Axle Loads

0

5

10

15

20

25

0 20 40 60 80 100 120 140 160 180 200

Axle Load (kips)

Freq

uenc

y %

Single-Single

Single-Tandem

Tandem-Tandem

AllOthers

A - 28

Implementation of Draft Protocols WIM Data Analysis

California

WIM Site 0059 – LA710SB

• GVW Histogram

• Single Truck Moment Histogram

• One-Lane and Two-Lane Moment Histogram

• One-Lane and Two-Lane Shear Histogram

• One-Lane and Two-lane Negative Moment Histogram

• Fatigue Adjustment Factor

• Axle Group Weight Histogram

A - 29

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 0 4234050

Mean All Trucks 0.000 38.201Std Dev All Trucks 0.000 17.252

CoV All Trucks 0.000 0.452

Mean Top 20% Trucks 0.000 69.139Std Dev Top 20% Trucks 0.000 7.449

CoV Top 20% Trucks 0.000 0.108

Mean Top 5% Trucks 0.000 78.176Std Dev Top 5% Trucks 0.000 3.661

CoV Top 5% Trucks 0.000 0.047

WIM Site 0059 Gross Vehicle Weight Statistics

WIM Site 0059Single Truck GVW Relative Frequencies

0

5

10

15

20

25

0 50 100 150 200

GVW (kips)

Freq

uenc

y %

Lanes 1 & 2Lanes 3 & 4

A - 30

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 0 4234050

Mean All Trucks 0.000 0.274Std Dev All Trucks 0.000 0.110

CoV All Trucks 0.000 0.402

Mean Top 20% Trucks 0.000 0.473Std Dev Top 20% Trucks 0.000 0.052

CoV Top 20% Trucks 0.000 0.110

Mean Top 5% Trucks 0.000 0.542Std Dev Top 5% Trucks 0.000 0.038

CoV Top 5% Trucks 0.000 0.070

WIM Site 0059 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 0059HL93 Single Truck Simple-Span Moment

60 ft Span

02468

101214161820

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Moment Ratio (Mtruck/MHL93)

Freq

uenc

y %

Lanes 1&2Lanes 3&4

A - 31

Statistics Lanes 3&4 - 1 Lane Event Lanes 3&4 - 2 Lane EventTruck Count 4307371 149544

Mean All Trucks 0.275 0.402Std Dev All Trucks 0.111 0.150

CoV All Trucks 0.402 0.373

Mean Top 20% Trucks 0.475 0.631Std Dev Top 20% Trucks 0.052 0.094

CoV Top 20% Trucks 0.109 0.149

Mean Top 5% Trucks 0.543 0.764Std Dev Top 5% Trucks 0.039 0.083

CoV Top 5% Trucks 0.072 0.109

WIM Site 0059 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 0059HL93 Simple-Span Moment Lanes 3&4

60 ft Span

02468

101214161820

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 32

Statistics Lanes 3&4 - 1 Lane Event Lanes 3&4 - 2 Lane EventTruck Count 4307371 149544

Mean All Trucks 0.300 0.434Std Dev All Trucks 0.124 0.163

CoV All Trucks 0.414 0.376

Mean Top 20% Trucks 0.527 0.683Std Dev Top 20% Trucks 0.056 0.100

CoV Top 20% Trucks 0.106 0.146

Mean Top 5% Trucks 0.598 0.823Std Dev Top 5% Trucks 0.036 0.090

CoV Top 5% Trucks 0.060 0.110

WIM Site 0059 HL93 Simple-Span Shear Statistics - 60 ft Span

WIM Site 0059HL93 Simple-Span Shear Lanes 3&4

60 ft Span

02468

1012141618

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Shear Ratio (VWIM/VHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 33

Statistics Lanes 3&4 - 1 Lane Event Lanes 3&4 - 2 Lane EventTruck Count 4307371 149544

Mean All Trucks 0.240 0.387Std Dev All Trucks 0.111 0.138

CoV All Trucks 0.463 0.355

Mean Top 20% Trucks 0.438 0.601Std Dev Top 20% Trucks 0.051 0.080

CoV Top 20% Trucks 0.116 0.133

Mean Top 5% Trucks 0.501 0.713Std Dev Top 5% Trucks 0.027 0.073

CoV Top 5% Trucks 0.053 0.102

WIM Site 0059 HL93 Negative Moment Statistics - 60 ft Span

WIM Site 0059HL93 Negative Moment Lanes 3&4

60 ft Span

02468

101214161820

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 34

WIM Site: 0059 Fatigue Adjustment Factor

Lanes 1 and 2LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0 0 0 0 0 0 0 0K (pos.) 0 0 0 0 0 0 0 0K (neg.) 0 0 0 0 0 0 0 0Modified LRFD Fatigue Truck GVW = 0 kips

Axle Weight: Steer = 0 kips Drive = 0 kips Trailer = 0 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0 0 0 0 0 0 0 0K (pos.) 0 0 0 0 0 0 0 0K (neg.) 0 0 0 0 0 0 0 0Site-Specific Fatigue Truck GVW = 0 kips

Axle Weight: Steer = 0 kips Drive = 0 kips Trailer = 0 kipsAxle Spacing: 19.5 ft 33.5 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0 0 0 0 0 0 0 0K (pos.) 0 0 0 0 0 0 0 0K (neg.) 0 0 0 0 0 0 0 0

Lanes 3 and 4LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.6817 0.7678 0.8506 0.7934 0.8031 0.8103 0.8187 0.8233K (pos.) 0.664 0.7554 0.789 0.7813 0.7944 0.8029 0.813 0.8188K (neg.) 0.9331 0.7586 0.8597 0.8584 0.8001 0.8105 0.823 0.8288Modified LRFD Fatigue Truck GVW = 45.752 kips

Axle Weight: Steer = 5.084 kips Drive = 20.334 kips Trailer = 20.334 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8046 0.9062 1.004 0.9365 0.9479 0.9564 0.9662 0.9717K (pos.) 0.7838 0.8916 0.9312 0.9221 0.9376 0.9476 0.9596 0.9664K (neg.) 1.1013 0.8954 1.0147 1.0131 0.9444 0.9566 0.9713 0.9783Site-Specific Fatigue Truck GVW = 45.752 kips

Axle Weight: Steer = 11.438 kips Drive = 19.216 kips Trailer = 15.098 kipsAxle Spacing: 19.5 ft 33.5 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8514 1.0157 0.9965 0.977 0.9769 0.9789 0.9819 0.9838K (pos.) 0.8294 0.9599 0.9755 0.9767 0.9778 0.9794 0.9819 0.9836K (neg.) 0.9151 1.0219 0.9845 0.9894 1.008 1.0004 0.9957 0.9939

A - 35

Statistics Single Tandem Tridem QuadAxle Count 5203584 7194357 58357 4

Mean All Axles 9.062 15.530 22.940 50.000Std Dev All Axles 2.514 8.297 12.119 3.830

CoV All Axles 0.277 0.534 0.528 0.077

Mean Top 20% Axles 12.170 30.437 40.000 55.000Std Dev Top 20% Axles 2.261 3.534 3.520 0.000

CoV Top 20% Axles 0.186 0.116 0.088 0.000

Mean Top 5% Axles 15.554 35.006 44.856 0.000Std Dev Top 5% Axles 2.221 2.421 3.364 0.000

CoV Top 5% Axles 0.143 0.069 0.075 0.000

99th Percentile 16 34 46 54

WIM Site 0059 Axle Group Weight Statistics

WIM Site 0059Axle Group Weight Relative Frequency

Histogram

0

10

20

30

40

50

60

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

Axle Group Weight (kips)

Freq

uenc

y %

SingleTandemTridemQuad

A - 36

Statistics Single-Single Single-Tandem Tandem-Tandem All OthersEvent Count 20731 59070 39636 1158

Mean All Events 18.008 24.452 30.937 36.204Std Dev All Events 3.585 8.630 11.736 14.347

CoV All Events 0.199 0.353 0.379 0.396

Mean Top 20% Events 22.907 39.495 49.103 56.578Std Dev Top 20% Events 2.677 4.092 7.173 8.189

CoV Top 20% Events 0.117 0.104 0.146 0.145

Mean Top 5% Events 26.819 44.973 59.895 68.793Std Dev Top 5% Events 2.170 2.799 5.108 6.049

CoV Top 5% Events 0.081 0.062 0.085 0.088

99th Percentile 26 44 62 72

WIM Site 0059 Two-Lane Multiple Presence Axle Load Statistics

WIM Site 0059Two-Lane MP Axle Loads

0

5

10

15

20

25

30

35

0 20 40 60 80 100 120 140 160 180 200

Axle Load (kips)

Freq

uenc

y %

Single-Single

Single-Tandem

Tandem-Tandem

AllOthers

A - 37

Implementation of Draft Protocols WIM Data Analysis

California

WIM Site 0060 – LA710NB

• GVW Histogram

• Single Truck Moment Histogram

• One-Lane and Two-Lane Moment Histogram

• One-Lane and Two-Lane Shear Histogram

• One-Lane and Two-lane Negative Moment Histogram

• Fatigue Adjustment Factor

• Axle Group Weight Histogram

A - 38

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 3800854 0

Mean All Trucks 47.518 0.000Std Dev All Trucks 19.273 0.000

CoV All Trucks 0.406 0.000

Mean Top 20% Trucks 75.339 0.000Std Dev Top 20% Trucks 4.731 0.000

CoV Top 20% Trucks 0.063 0.000

Mean Top 5% Trucks 81.250 0.000Std Dev Top 5% Trucks 4.042 0.000

CoV Top 5% Trucks 0.050 0.000

WIM Site 0060 Gross Vehicle Weight Statistics

WIM Site 0060Single Truck GVW Relative Frequencies

0123456789

10

0 50 100 150 200

GVW (kips)

Freq

uenc

y %

Lanes 1 & 2Lanes 3 & 4

A - 39

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 3800854 0

Mean All Trucks 0.337 0.000Std Dev All Trucks 0.123 0.000

CoV All Trucks 0.364 0.000

Mean Top 20% Trucks 0.523 0.000Std Dev Top 20% Trucks 0.048 0.000

CoV Top 20% Trucks 0.091 0.000

Mean Top 5% Trucks 0.589 0.000Std Dev Top 5% Trucks 0.038 0.000

CoV Top 5% Trucks 0.065 0.000

WIM Site 0060 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 0060HL93 Single Truck Simple-Span Moment

60 ft Span

0

1

2

3

4

5

6

7

8

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Moment Ratio (Mtruck/MHL93)

Freq

uenc

y %

Lanes 1&2Lanes 3&4

A - 40

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 3858180 132583

Mean All Trucks 0.339 0.497Std Dev All Trucks 0.123 0.163

CoV All Trucks 0.364 0.327

Mean Top 20% Trucks 0.523 0.746Std Dev Top 20% Trucks 0.048 0.099

CoV Top 20% Trucks 0.091 0.133

Mean Top 5% Trucks 0.590 0.887Std Dev Top 5% Trucks 0.039 0.072

CoV Top 5% Trucks 0.066 0.081

WIM Site 0060 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 0060HL93 Simple-Span Moment Lanes 1&2

60 ft Span

012345678

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 41

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 3858180 132583

Mean All Trucks 0.368 0.540Std Dev All Trucks 0.138 0.175

CoV All Trucks 0.375 0.323

Mean Top 20% Trucks 0.580 0.802Std Dev Top 20% Trucks 0.048 0.105

CoV Top 20% Trucks 0.082 0.131

Mean Top 5% Trucks 0.646 0.951Std Dev Top 5% Trucks 0.040 0.074

CoV Top 5% Trucks 0.062 0.078

WIM Site 0060 HL93 Simple-Span Shear Statistics - 60 ft Span

WIM Site 0060HL93 Simple-Span Shear Lanes 1&2

60 ft Span

012345678

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Shear Ratio (VWIM/VHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 42

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 3858180 132583

Mean All Trucks 0.297 0.478Std Dev All Trucks 0.120 0.145

CoV All Trucks 0.404 0.304

Mean Top 20% Trucks 0.469 0.694Std Dev Top 20% Trucks 0.036 0.078

CoV Top 20% Trucks 0.077 0.113

Mean Top 5% Trucks 0.516 0.805Std Dev Top 5% Trucks 0.029 0.057

CoV Top 5% Trucks 0.057 0.071

WIM Site 0060 HL93 Negative Moment Statistics - 60 ft Span

WIM Site 0060HL93 Negative Moment Lanes 1&2

60 ft Span

0123456789

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 43

WIM Site: 0060 Fatigue Adjustment Factor

Lanes 1 and 2LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7991 0.9053 1.0122 0.9538 0.9635 0.9704 0.9787 0.9834K (pos.) 0.7748 0.888 0.9366 0.9357 0.9511 0.9606 0.9717 0.9779K (neg.) 1.1068 0.9051 1.0117 1.013 0.9586 0.9702 0.9829 0.9888Modified LRFD Fatigue Truck GVW = 54.426 kips

Axle Weight: Steer = 6.047 kips Drive = 24.189 kips Trailer = 24.189 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7928 0.8983 1.0043 0.9464 0.956 0.9628 0.971 0.9757K (pos.) 0.7687 0.881 0.9293 0.9284 0.9436 0.9531 0.9641 0.9703K (neg.) 1.0981 0.898 1.0038 1.005 0.9511 0.9626 0.9752 0.9811Site-Specific Fatigue Truck GVW = 54.426 kips

Axle Weight: Steer = 10.885 kips Drive = 22.859 kips Trailer = 20.682 kipsAxle Spacing: 19 ft 33 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.839 0.9981 1.0254 1.0044 0.9972 0.9949 0.9932 0.9926K (pos.) 0.8135 0.9515 1.0013 0.9922 0.9917 0.9915 0.9915 0.9915K (neg.) 0.9791 0.9827 0.9743 1.0025 1.011 1.0031 0.9975 0.9953

Lanes 3 and 4LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0 0 0 0 0 0 0 0K (pos.) 0 0 0 0 0 0 0 0K (neg.) 0 0 0 0 0 0 0 0Modified LRFD Fatigue Truck GVW = 0 kips

Axle Weight: Steer = 0 kips Drive = 0 kips Trailer = 0 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0 0 0 0 0 0 0 0K (pos.) 0 0 0 0 0 0 0 0K (neg.) 0 0 0 0 0 0 0 0Site-Specific Fatigue Truck GVW = 0 kips

Axle Weight: Steer = 0 kips Drive = 0 kips Trailer = 0 kipsAxle Spacing: 19 ft 33 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0 0 0 0 0 0 0 0K (pos.) 0 0 0 0 0 0 0 0K (neg.) 0 0 0 0 0 0 0 0

A - 44

Statistics Single Tandem Tridem QuadAxle Count 4749881 6405697 72236 21

Mean All Axles 10.465 19.931 27.078 31.095Std Dev All Axles 3.022 8.396 11.223 13.630

CoV All Axles 0.289 0.421 0.414 0.438

Mean Top 20% Axles 15.019 32.276 41.497 49.500Std Dev Top 20% Axles 2.904 2.889 3.512 8.062

CoV Top 20% Axles 0.193 0.090 0.085 0.163

Mean Top 5% Axles 18.427 36.147 46.239 61.000Std Dev Top 5% Axles 1.390 2.511 3.674 0.000

CoV Top 5% Axles 0.075 0.069 0.079 0.000

99th Percentile 18 36 46 60

WIM Site 0060 Axle Group Weight Statistics

WIM Site 0060Axle Group Weight Relative Frequency

Histogram

05

1015202530354045

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

Axle Group Weight (kips)

Freq

uenc

y %

SingleTandemTridemQuad

A - 45

Statistics Single-Single Single-Tandem Tandem-Tandem All OthersEvent Count 18437 51020 33902 1247

Mean All Events 20.857 30.294 39.924 42.817Std Dev All Events 4.296 8.868 11.882 13.849

CoV All Events 0.206 0.293 0.298 0.323

Mean Top 20% Events 27.694 43.187 57.074 62.333Std Dev Top 20% Events 2.528 3.661 5.333 6.467

CoV Top 20% Events 0.091 0.085 0.093 0.104

Mean Top 5% Events 30.911 48.229 64.542 71.581Std Dev Top 5% Events 2.585 3.077 3.820 4.699

CoV Top 5% Events 0.084 0.064 0.059 0.066

99th Percentile 30 48 66 74

WIM Site 0060 Two-Lane Multiple Presence Axle Load Statistics

WIM Site 0060Two-Lane MP Axle Loads

0

5

10

15

20

25

30

0 20 40 60 80 100 120 140 160 180 200

Axle Load (kips)

Freq

uenc

y %

Single-Single

Single-Tandem

Tandem-Tandem

AllOthers

A - 46

Implementation of Draft Protocols WIM Data Analysis

California

WIM Site 0072 – Bowman

• GVW Histogram

• Single Truck Moment Histogram

• One-Lane and Two-Lane Moment Histogram

• One-Lane and Two-Lane Shear Histogram

• One-Lane and Two-lane Negative Moment Histogram

• Fatigue Adjustment Factor

• Axle Group Weight Histogram

A - 47

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 310301 289105

Mean All Trucks 51.529 52.865Std Dev All Trucks 15.737 15.917

CoV All Trucks 0.305 0.301

Mean Top 20% Trucks 72.557 72.224Std Dev Top 20% Trucks 3.416 3.747

CoV Top 20% Trucks 0.047 0.052

Mean Top 5% Trucks 76.693 77.014Std Dev Top 5% Trucks 3.726 4.385

CoV Top 5% Trucks 0.049 0.057

WIM Site 0072 Gross Vehicle Weight Statistics

WIM Site 0072Single Truck GVW Relative Frequencies

0

2

4

6

8

10

12

14

0 50 100 150 200

GVW (kips)

Freq

uenc

y %

Lanes 1 & 2Lanes 3 & 4

A - 48

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 310301 289105

Mean All Trucks 0.336 0.342Std Dev All Trucks 0.091 0.092

CoV All Trucks 0.270 0.268

Mean Top 20% Trucks 0.460 0.456Std Dev Top 20% Trucks 0.032 0.031

CoV Top 20% Trucks 0.070 0.069

Mean Top 5% Trucks 0.501 0.496Std Dev Top 5% Trucks 0.036 0.035

CoV Top 5% Trucks 0.072 0.071

WIM Site 0072 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 0072HL93 Single Truck Simple-Span Moment

60 ft Span

0

2

4

6

8

10

12

14

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Moment Ratio (Mtruck/MHL93)

Freq

uenc

y %

Lanes 1&2Lanes 3&4

A - 49

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 310894 7652

Mean All Trucks 0.336 0.487Std Dev All Trucks 0.091 0.140

CoV All Trucks 0.270 0.286

Mean Top 20% Trucks 0.460 0.704Std Dev Top 20% Trucks 0.032 0.070

CoV Top 20% Trucks 0.070 0.099

Mean Top 5% Trucks 0.501 0.802Std Dev Top 5% Trucks 0.036 0.045

CoV Top 5% Trucks 0.072 0.057

WIM Site 0072 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 0072HL93 Simple-Span Moment Lanes 1&2

60 ft Span

0123456789

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 50

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 310894 7652

Mean All Trucks 0.366 0.531Std Dev All Trucks 0.102 0.149

CoV All Trucks 0.279 0.281

Mean Top 20% Trucks 0.508 0.760Std Dev Top 20% Trucks 0.033 0.078

CoV Top 20% Trucks 0.066 0.103

Mean Top 5% Trucks 0.552 0.871Std Dev Top 5% Trucks 0.033 0.048

CoV Top 5% Trucks 0.060 0.055

WIM Site 0072 HL93 Simple-Span Shear Statistics - 60 ft Span

WIM Site 0072HL93 Simple-Span Shear Lanes 1&2

60 ft Span

0123456789

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Shear Ratio (VWIM/VHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 51

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 310894 7652

Mean All Trucks 0.326 0.495Std Dev All Trucks 0.103 0.135

CoV All Trucks 0.316 0.272

Mean Top 20% Trucks 0.466 0.697Std Dev Top 20% Trucks 0.023 0.073

CoV Top 20% Trucks 0.050 0.105

Mean Top 5% Trucks 0.495 0.800Std Dev Top 5% Trucks 0.024 0.056

CoV Top 5% Trucks 0.049 0.070

WIM Site 0072 HL93 Negative Moment Statistics - 60 ft Span

WIM Site 0072HL93 Negative Moment Lanes 1&2

60 ft Span

0123456789

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 52

WIM Site: 0072 Fatigue Adjustment Factor

Lanes 1 and 2LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7814 0.8645 0.9586 0.8859 0.9214 0.944 0.9691 0.9827K (pos.) 0.7631 0.8536 0.8905 0.8749 0.9095 0.932 0.9588 0.974K (neg.) 1.0608 0.8909 1.0624 1.0627 0.9378 0.962 0.9907 1.0041Modified LRFD Fatigue Truck GVW = 55.969 kips

Axle Weight: Steer = 6.219 kips Drive = 24.875 kips Trailer = 24.875 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7539 0.8341 0.9249 0.8547 0.889 0.9107 0.935 0.9481K (pos.) 0.7363 0.8236 0.8592 0.8442 0.8775 0.8992 0.9251 0.9397K (neg.) 1.0235 0.8596 1.0251 1.0253 0.9048 0.9281 0.9558 0.9687Site-Specific Fatigue Truck GVW = 55.969 kips

Axle Weight: Steer = 11.754 kips Drive = 22.947 kips Trailer = 21.268 kipsAxle Spacing: 19 ft 37 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8172 0.9477 0.9566 0.9778 0.977 0.9794 0.9827 0.9847K (pos.) 0.7981 0.9077 0.9381 0.9559 0.9659 0.9719 0.9783 0.9816K (neg.) 0.9122 0.9775 0.9661 0.971 1.0021 0.9942 0.9925 0.9921

Lanes 3 and 4LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.805 0.8841 0.9737 0.9015 0.9386 0.9621 0.9885 1.0028K (pos.) 0.7866 0.8721 0.9049 0.8908 0.9268 0.9502 0.9781 0.994K (neg.) 1.0728 0.9152 1.0872 1.0861 0.9597 0.9836 1.0127 1.0262Modified LRFD Fatigue Truck GVW = 57.178 kips

Axle Weight: Steer = 6.353 kips Drive = 25.413 kips Trailer = 25.413 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7602 0.835 0.9196 0.8514 0.8864 0.9086 0.9336 0.9471K (pos.) 0.7429 0.8236 0.8546 0.8413 0.8753 0.8974 0.9238 0.9387K (neg.) 1.0131 0.8644 1.0267 1.0258 0.9063 0.929 0.9564 0.9691Site-Specific Fatigue Truck GVW = 57.178 kips

Axle Weight: Steer = 12.007 kips Drive = 23.443 kips Trailer = 21.728 kipsAxle Spacing: 19 ft 37 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8241 0.9487 0.9511 0.974 0.9741 0.9771 0.9812 0.9836K (pos.) 0.8053 0.9078 0.9331 0.9526 0.9635 0.9699 0.9769 0.9806K (neg.) 0.903 0.983 0.9676 0.9714 1.0038 0.9951 0.993 0.9925

A - 53

Statistics Single Tandem Tridem QuadAxle Count 981999 973669 2069 4

Mean All Axles 10.606 21.145 25.720 49.500Std Dev All Axles 2.911 7.518 10.175 7.550

CoV All Axles 0.274 0.356 0.396 0.153

Mean Top 20% Axles 14.796 30.518 39.691 55.000Std Dev Top 20% Axles 1.836 1.905 6.146 0.000

CoV Top 20% Axles 0.124 0.062 0.155 0.000

Mean Top 5% Axles 17.444 32.835 48.961 0.000Std Dev Top 5% Axles 1.043 2.133 4.087 0.000

CoV Top 5% Axles 0.060 0.065 0.083 0.000

99th Percentile 16 32 50 54

WIM Site 0072 Axle Group Weight Statistics

WIM Site 0072Axle Group Weight Relative Frequency

Histogram

0

10

20

30

40

50

60

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

Axle Group Weight (kips)

Freq

uenc

y %

SingleTandemTridemQuad

A - 54

Statistics Single-Single Single-Tandem Tandem-Tandem All OthersEvent Count 3219 6518 3284 29

Mean All Events 21.112 31.461 42.163 46.862Std Dev All Events 4.141 7.968 10.774 14.162

CoV All Events 0.196 0.253 0.256 0.302

Mean Top 20% Events 27.084 42.037 57.134 66.000Std Dev Top 20% Events 2.280 2.675 3.249 9.011

CoV Top 20% Events 0.084 0.064 0.057 0.137

Mean Top 5% Events 30.329 45.663 61.378 81.000Std Dev Top 5% Events 1.816 2.192 2.664 0.000

CoV Top 5% Events 0.060 0.048 0.043 0.000

99th Percentile 30 46 62 80

WIM Site 0072 Two-Lane Multiple Presence Axle Load Statistics

WIM Site 0072Two-Lane MP Axle Loads

0

5

10

15

20

25

30

0 20 40 60 80 100 120 140 160 180 200

Axle Load (kips)

Freq

uenc

y %

Single-Single

Single-Tandem

Tandem-Tandem

AllOthers

A - 55

Implementation of Draft Protocols WIM Data Analysis

Florida

WIM Site 9916 – US29

• GVW Histogram

• Single Truck Moment Histogram

• One-Lane and Two-Lane Moment Histogram

• One-Lane and Two-Lane Shear Histogram

• One-Lane and Two-lane Negative Moment Histogram

• Fatigue Adjustment Factor

• Axle Group Weight Histogram

A - 56

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 175865 0

Mean All Trucks 46.355 0.000Std Dev All Trucks 21.804 0.000

CoV All Trucks 0.470 0.000

Mean Top 20% Trucks 81.155 0.000Std Dev Top 20% Trucks 15.450 0.000

CoV Top 20% Trucks 0.190 0.000

Mean Top 5% Trucks 102.057 0.000Std Dev Top 5% Trucks 14.524 0.000

CoV Top 5% Trucks 0.142 0.000

WIM Site 9916 Gross Vehicle Weight Statistics

WIM Site 9916Single Truck GVW Relative Frequencies

0123456789

10

0 50 100 150 200

GVW (kips)

Freq

uenc

y %

Lanes 1 & 2Lanes 3 & 4

A - 57

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 175865 0

Mean All Trucks 0.355 0.000Std Dev All Trucks 0.156 0.000

CoV All Trucks 0.439 0.000

Mean Top 20% Trucks 0.601 0.000Std Dev Top 20% Trucks 0.114 0.000

CoV Top 20% Trucks 0.190 0.000

Mean Top 5% Trucks 0.760 0.000Std Dev Top 5% Trucks 0.105 0.000

CoV Top 5% Trucks 0.138 0.000

WIM Site 9916 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 9916HL93 Single Truck Simple-Span Moment

60 ft Span

0

1

2

3

4

5

6

7

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Moment Ratio (Mtruck/MHL93)

Freq

uenc

y %

Lanes 1&2Lanes 3&4

A - 58

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 176104 1869

Mean All Trucks 0.355 0.516Std Dev All Trucks 0.156 0.192

CoV All Trucks 0.438 0.373

Mean Top 20% Trucks 0.601 0.816Std Dev Top 20% Trucks 0.114 0.126

CoV Top 20% Trucks 0.190 0.155

Mean Top 5% Trucks 0.760 0.994Std Dev Top 5% Trucks 0.105 0.105

CoV Top 5% Trucks 0.138 0.105

WIM Site 9916 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 9916HL93 Simple-Span Moment Lanes 1&2

60 ft Span

0

1

2

3

4

5

6

7

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 59

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 176104 1869

Mean All Trucks 0.380 0.548Std Dev All Trucks 0.161 0.197

CoV All Trucks 0.423 0.359

Mean Top 20% Trucks 0.637 0.851Std Dev Top 20% Trucks 0.113 0.123

CoV Top 20% Trucks 0.177 0.145

Mean Top 5% Trucks 0.793 1.024Std Dev Top 5% Trucks 0.097 0.101

CoV Top 5% Trucks 0.123 0.099

WIM Site 9916 HL93 Simple-Span Shear Statistics - 60 ft Span

WIM Site 9916HL93 Simple-Span Shear Lanes 1&2

60 ft Span

0

1

2

3

4

5

6

7

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Shear Ratio (VWIM/VHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 60

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 176104 1869

Mean All Trucks 0.300 0.488Std Dev All Trucks 0.143 0.173

CoV All Trucks 0.478 0.355

Mean Top 20% Trucks 0.530 0.755Std Dev Top 20% Trucks 0.100 0.114

CoV Top 20% Trucks 0.188 0.151

Mean Top 5% Trucks 0.667 0.910Std Dev Top 5% Trucks 0.086 0.108

CoV Top 5% Trucks 0.129 0.119

WIM Site 9916 HL93 Negative Moment Statistics - 60 ft Span

WIM Site 9916HL93 Negative Moment Lanes 1&2

60 ft Span

012345678

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 61

WIM Site: 9916 Fatigue Adjustment Factor

Lanes 1 and 2LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.9027 1.0271 1.1222 1.0003 0.9969 1.0014 1.0099 1.0156K (pos.) 0.8796 1.0095 1.0427 0.9893 0.9913 0.9962 1.005 1.0111K (neg.) 1.2362 0.9177 1.0887 1.1105 0.9969 0.9993 1.0136 1.0224Modified LRFD Fatigue Truck GVW = 56.116 kips

Axle Weight: Steer = 6.235 kips Drive = 24.941 kips Trailer = 24.941 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8687 0.9883 1.0799 0.9626 0.9593 0.9636 0.9718 0.9773K (pos.) 0.8464 0.9714 1.0034 0.952 0.9539 0.9587 0.9671 0.973K (neg.) 1.1895 0.8831 1.0476 1.0686 0.9593 0.9616 0.9753 0.9838Site-Specific Fatigue Truck GVW = 56.116 kips

Axle Weight: Steer = 15.151 kips Drive = 23.008 kips Trailer = 17.957 kipsAxle Spacing: 19.5 ft 38 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.9416 1.1331 1.0782 1.0707 1.034 1.021 1.0112 1.0073K (pos.) 0.9175 1.0654 1.0579 1.0599 1.0356 1.0243 1.0141 1.0096K (neg.) 0.9733 1.0677 0.9918 0.9909 1.0487 1.0332 1.0151 1.0094

Lanes 3 and 4LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0 0 0 0 0 0 0 0K (pos.) 0 0 0 0 0 0 0 0K (neg.) 0 0 0 0 0 0 0 0Modified LRFD Fatigue Truck GVW = 0 kips

Axle Weight: Steer = 0 kips Drive = 0 kips Trailer = 0 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0 0 0 0 0 0 0 0K (pos.) 0 0 0 0 0 0 0 0K (neg.) 0 0 0 0 0 0 0 0Site-Specific Fatigue Truck GVW = 0 kips

Axle Weight: Steer = 0 kips Drive = 0 kips Trailer = 0 kipsAxle Spacing: 19.5 ft 38 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0 0 0 0 0 0 0 0K (pos.) 0 0 0 0 0 0 0 0K (neg.) 0 0 0 0 0 0 0 0

A - 62

Statistics Single Tandem Tridem QuadAxle Count 234426 262344 8161 132

Mean All Axles 11.497 19.526 42.941 46.212Std Dev All Axles 4.278 10.828 16.030 21.876

CoV All Axles 0.372 0.555 0.373 0.473

Mean Top 20% Axles 17.338 36.530 64.493 77.769Std Dev Top 20% Axles 2.504 5.924 7.421 7.758

CoV Top 20% Axles 0.144 0.162 0.115 0.100

Mean Top 5% Axles 20.814 44.770 74.559 88.143Std Dev Top 5% Axles 2.099 4.433 7.506 5.757

CoV Top 5% Axles 0.101 0.099 0.101 0.065

99th Percentile 20 46 78 88

WIM Site 9916 Axle Group Weight Statistics

WIM Site 9916Axle Group Weight Relative Frequency

Histogram

0

5

10

15

20

25

0 8 16 24 32 40 48 56 64 72 80 88 96

Axle Group Weight (kips)

Freq

uenc

y %

SingleTandemTridemQuad

A - 63

Statistics Single-Single Single-Tandem Tandem-Tandem All OthersEvent Count 303 672 356 42

Mean All Events 23.185 30.839 38.624 54.857Std Dev All Events 6.345 11.636 15.188 15.601

CoV All Events 0.274 0.377 0.393 0.284

Mean Top 20% Events 31.623 48.806 61.394 79.750Std Dev Top 20% Events 2.794 7.001 8.643 7.479

CoV Top 20% Events 0.088 0.143 0.141 0.094

Mean Top 5% Events 35.400 57.588 73.667 90.000Std Dev Top 5% Events 2.414 7.699 6.362 1.414

CoV Top 5% Events 0.068 0.134 0.086 0.016

99th Percentile 36 60 78 90

WIM Site 9916 Two-Lane Multiple Presence Axle Load Statistics

WIM Site 9916Two-Lane MP Axle Loads

0

2

4

6

8

10

12

14

0 20 40 60 80 100 120 140 160 180 200

Axle Load (kips)

Freq

uenc

y %

Single-Single

Single-Tandem

Tandem-Tandem

AllOthers

A - 64

Implementation of Draft Protocols WIM Data Analysis

Florida

WIM Site 9919 – I-95

• GVW Histogram

• Single Truck Moment Histogram

• One-Lane and Two-Lane Moment Histogram

• One-Lane and Two-Lane Shear Histogram

• One-Lane and Two-lane Negative Moment Histogram

• Fatigue Adjustment Factor

• Axle Group Weight Histogram

A - 65

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 939503 875732

Mean All Trucks 44.779 46.185Std Dev All Trucks 14.745 14.021

CoV All Trucks 0.329 0.304

Mean Top 20% Trucks 67.171 65.088Std Dev Top 20% Trucks 5.465 4.867

CoV Top 20% Trucks 0.081 0.075

Mean Top 5% Trucks 74.255 71.293Std Dev Top 5% Trucks 5.375 5.079

CoV Top 5% Trucks 0.072 0.071

WIM Site 9919 Gross Vehicle Weight Statistics

WIM Site 9919Single Truck GVW Relative Frequencies

0

2

4

6

8

10

12

14

16

0 50 100 150 200

GVW (kips)

Freq

uenc

y %

Lanes 1 & 2Lanes 3 & 4

A - 66

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 939503 875732

Mean All Trucks 0.304 0.306Std Dev All Trucks 0.095 0.082

CoV All Trucks 0.313 0.269

Mean Top 20% Trucks 0.446 0.421Std Dev Top 20% Trucks 0.060 0.038

CoV Top 20% Trucks 0.135 0.090

Mean Top 5% Trucks 0.528 0.471Std Dev Top 5% Trucks 0.065 0.041

CoV Top 5% Trucks 0.123 0.087

WIM Site 9919 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 9919HL93 Single Truck Simple-Span Moment

60 ft Span

0

2

4

6

8

10

12

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Moment Ratio (Mtruck/MHL93)

Freq

uenc

y %

Lanes 1&2Lanes 3&4

A - 67

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 941044 36733

Mean All Trucks 0.304 0.440Std Dev All Trucks 0.095 0.137

CoV All Trucks 0.313 0.310

Mean Top 20% Trucks 0.446 0.651Std Dev Top 20% Trucks 0.060 0.083

CoV Top 20% Trucks 0.135 0.127

Mean Top 5% Trucks 0.528 0.767Std Dev Top 5% Trucks 0.065 0.067

CoV Top 5% Trucks 0.123 0.087

WIM Site 9919 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 9919HL93 Simple-Span Moment Lanes 1&2

60 ft Span

0

2

4

6

8

10

12

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 68

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 941044 36733

Mean All Trucks 0.333 0.479Std Dev All Trucks 0.107 0.145

CoV All Trucks 0.323 0.303

Mean Top 20% Trucks 0.499 0.700Std Dev Top 20% Trucks 0.053 0.086

CoV Top 20% Trucks 0.105 0.124

Mean Top 5% Trucks 0.572 0.823Std Dev Top 5% Trucks 0.047 0.065

CoV Top 5% Trucks 0.083 0.079

WIM Site 9919 HL93 Simple-Span Shear Statistics - 60 ft Span

WIM Site 9919HL93 Simple-Span Shear Lanes 1&2

60 ft Span

0

2

4

6

8

10

12

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Shear Ratio (VWIM/VHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 69

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 941044 36733

Mean All Trucks 0.289 0.441Std Dev All Trucks 0.097 0.127

CoV All Trucks 0.335 0.289

Mean Top 20% Trucks 0.437 0.631Std Dev Top 20% Trucks 0.038 0.072

CoV Top 20% Trucks 0.086 0.114

Mean Top 5% Trucks 0.486 0.733Std Dev Top 5% Trucks 0.036 0.059

CoV Top 5% Trucks 0.073 0.080

WIM Site 9919 HL93 Negative Moment Statistics - 60 ft Span

WIM Site 9919HL93 Negative Moment Lanes 1&2

60 ft Span

0

2

4

6

8

10

12

14

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 70

WIM Site: 9919 Fatigue Adjustment Factor

Lanes 1 and 2LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7422 0.82 0.8881 0.8117 0.8347 0.8506 0.8689 0.879K (pos.) 0.7255 0.808 0.8272 0.8045 0.827 0.8425 0.8615 0.8726K (neg.) 0.9759 0.812 0.9548 0.9518 0.8467 0.864 0.8855 0.8955Modified LRFD Fatigue Truck GVW = 49.32 kips

Axle Weight: Steer = 5.48 kips Drive = 21.92 kips Trailer = 21.92 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8127 0.8978 0.9723 0.8887 0.9139 0.9313 0.9514 0.9624K (pos.) 0.7943 0.8847 0.9057 0.8808 0.9054 0.9224 0.9433 0.9554K (neg.) 1.0685 0.889 1.0454 1.0421 0.927 0.946 0.9695 0.9804Site-Specific Fatigue Truck GVW = 49.32 kips

Axle Weight: Steer = 10.357 kips Drive = 20.221 kips Trailer = 18.742 kipsAxle Spacing: 19 ft 37 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8809 1.02 1.0057 1.0167 1.0043 1.0015 0.9999 0.9995K (pos.) 0.861 0.9751 0.9889 0.9974 0.9967 0.9969 0.9976 0.998K (neg.) 0.9523 1.011 0.9852 0.9869 1.0267 1.0134 1.0067 1.0041

Lanes 3 and 4LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.737 0.8083 0.8715 0.8005 0.8315 0.8514 0.8737 0.8858K (pos.) 0.7213 0.7965 0.8121 0.7944 0.8233 0.8425 0.8655 0.8787K (neg.) 0.9561 0.8239 0.9695 0.9619 0.851 0.8711 0.8952 0.9063Modified LRFD Fatigue Truck GVW = 50.004 kips

Axle Weight: Steer = 5.556 kips Drive = 22.224 kips Trailer = 22.224 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7959 0.8729 0.9412 0.8645 0.8979 0.9194 0.9435 0.9566K (pos.) 0.7789 0.8602 0.877 0.8579 0.8891 0.9098 0.9347 0.9489K (neg.) 1.0325 0.8897 1.0469 1.0388 0.919 0.9408 0.9668 0.9787Site-Specific Fatigue Truck GVW = 50.004 kips

Axle Weight: Steer = 10.501 kips Drive = 20.502 kips Trailer = 19.002 kipsAxle Spacing: 19 ft 37 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8628 0.9918 0.9735 0.989 0.9867 0.9887 0.9917 0.9935K (pos.) 0.8444 0.9481 0.9576 0.9714 0.9787 0.9833 0.9885 0.9912K (neg.) 0.9202 1.0118 0.9867 0.9837 1.0178 1.0077 1.0038 1.0023

A - 71

Statistics Single Tandem Tridem QuadAxle Count 2560154 3081702 29973 354

Mean All Axles 9.382 18.745 32.450 37.328Std Dev All Axles 2.570 6.910 11.581 17.050

CoV All Axles 0.274 0.369 0.357 0.457

Mean Top 20% Axles 12.875 28.610 45.819 57.761Std Dev Top 20% Axles 1.866 2.522 2.995 3.336

CoV Top 20% Axles 0.145 0.088 0.065 0.058

Mean Top 5% Axles 15.517 32.157 49.882 62.333Std Dev Top 5% Axles 1.273 1.799 2.707 2.058

CoV Top 5% Axles 0.082 0.056 0.054 0.033

99th Percentile 14 32 50 62

WIM Site 9919 Axle Group Weight Statistics

WIM Site 9919Axle Group Weight Relative Frequency

Histogram

0

5

10

15

20

25

30

35

40

0 8 16 24 32 40 48 56 64 72 80 88 96

Axle Group Weight (kips)

Freq

uenc

y %

SingleTandemTridemQuad

A - 72

Statistics Single-Single Single-Tandem Tandem-Tandem All OthersEvent Count 11169 27976 16663 627

Mean All Events 18.641 27.998 37.470 46.094Std Dev All Events 3.634 7.336 9.766 13.856

CoV All Events 0.195 0.262 0.261 0.301

Mean Top 20% Events 23.767 38.437 51.477 64.616Std Dev Top 20% Events 2.149 2.976 4.235 6.333

CoV Top 20% Events 0.090 0.077 0.082 0.098

Mean Top 5% Events 26.595 42.614 57.545 73.710Std Dev Top 5% Events 1.845 2.296 2.892 5.100

CoV Top 5% Events 0.069 0.054 0.050 0.069

99th Percentile 26 42 58 74

WIM Site 9919 Two-Lane Multiple Presence Axle Load Statistics

WIM Site 9919Two-Lane MP Axle Loads

0

5

10

15

20

25

30

0 20 40 60 80 100 120 140 160 180 200

Axle Load (kips)

Freq

uenc

y %

Single-Single

Single-Tandem

Tandem-Tandem

AllOthers

A - 73

Implementation of Draft Protocols WIM Data Analysis

Florida

WIM Site 9926 – I-75

• GVW Histogram

• Single Truck Moment Histogram

• One-Lane and Two-Lane Moment Histogram

• One-Lane and Two-Lane Shear Histogram

• One-Lane and Two-lane Negative Moment Histogram

• Fatigue Adjustment Factor

• Axle Group Weight Histogram

A - 74

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 1096047 1032644

Mean All Trucks 48.389 53.488Std Dev All Trucks 20.281 18.976

CoV All Trucks 0.419 0.355

Mean Top 20% Trucks 80.263 80.216Std Dev Top 20% Trucks 6.242 6.701

CoV Top 20% Trucks 0.078 0.084

Mean Top 5% Trucks 87.183 88.317Std Dev Top 5% Trucks 8.090 7.876

CoV Top 5% Trucks 0.093 0.089

WIM Site 9926 Gross Vehicle Weight Statistics

WIM Site 9926Single Truck GVW Relative Frequencies

0

2

4

6

8

10

12

14

16

0 50 100 150 200

GVW (kips)

Freq

uenc

y %

Lanes 1 & 2Lanes 3 & 4

A - 75

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 1096047 1032644

Mean All Trucks 0.349 0.392Std Dev All Trucks 0.139 0.149

CoV All Trucks 0.398 0.380

Mean Top 20% Trucks 0.564 0.619Std Dev Top 20% Trucks 0.086 0.117

CoV Top 20% Trucks 0.152 0.189

Mean Top 5% Trucks 0.688 0.792Std Dev Top 5% Trucks 0.084 0.091

CoV Top 5% Trucks 0.123 0.114

WIM Site 9926 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 9926HL93 Single Truck Simple-Span Moment

60 ft Span

0

2

4

6

8

10

12

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Moment Ratio (Mtruck/MHL93)

Freq

uenc

y %

Lanes 1&2Lanes 3&4

A - 76

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 1097694 40956

Mean All Trucks 0.349 0.510Std Dev All Trucks 0.139 0.181

CoV All Trucks 0.398 0.356

Mean Top 20% Trucks 0.564 0.788Std Dev Top 20% Trucks 0.086 0.117

CoV Top 20% Trucks 0.152 0.148

Mean Top 5% Trucks 0.688 0.953Std Dev Top 5% Trucks 0.084 0.099

CoV Top 5% Trucks 0.123 0.104

WIM Site 9926 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 9926HL93 Simple-Span Moment Lanes 1&2

60 ft Span

0

2

4

6

8

10

12

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 77

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 1097694 40956

Mean All Trucks 0.381 0.552Std Dev All Trucks 0.154 0.194

CoV All Trucks 0.403 0.350

Mean Top 20% Trucks 0.628 0.843Std Dev Top 20% Trucks 0.076 0.119

CoV Top 20% Trucks 0.121 0.141

Mean Top 5% Trucks 0.736 1.013Std Dev Top 5% Trucks 0.067 0.097

CoV Top 5% Trucks 0.091 0.096

WIM Site 9926 HL93 Simple-Span Shear Statistics - 60 ft Span

WIM Site 9926HL93 Simple-Span Shear Lanes 1&2

60 ft Span

0

2

4

6

8

10

12

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Shear Ratio (VWIM/VHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 78

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 1097694 40956

Mean All Trucks 0.311 0.493Std Dev All Trucks 0.132 0.163

CoV All Trucks 0.424 0.330

Mean Top 20% Trucks 0.520 0.734Std Dev Top 20% Trucks 0.043 0.092

CoV Top 20% Trucks 0.082 0.125

Mean Top 5% Trucks 0.569 0.864Std Dev Top 5% Trucks 0.053 0.076

CoV Top 5% Trucks 0.093 0.088

WIM Site 9926 HL93 Negative Moment Statistics - 60 ft Span

WIM Site 9926HL93 Negative Moment Lanes 1&2

60 ft Span

0

2

4

6

8

10

12

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 79

WIM Site: 9926 Fatigue Adjustment Factor

Lanes 1 and 2LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8965 0.9933 1.0718 0.9749 0.9846 0.9944 1.0069 1.0142K (pos.) 0.875 0.9761 0.9988 0.967 0.9789 0.9885 1.0014 1.0094K (neg.) 1.1614 0.9462 1.0834 1.0868 0.9887 1.0004 1.0175 1.0257Modified LRFD Fatigue Truck GVW = 56.203 kips

Axle Weight: Steer = 6.245 kips Drive = 24.979 kips Trailer = 24.979 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8613 0.9544 1.0298 0.9367 0.946 0.9554 0.9675 0.9745K (pos.) 0.8407 0.9378 0.9596 0.9291 0.9406 0.9498 0.9622 0.9698K (neg.) 1.1158 0.9091 1.0409 1.0442 0.95 0.9612 0.9777 0.9855Site-Specific Fatigue Truck GVW = 56.203 kips

Axle Weight: Steer = 11.803 kips Drive = 23.605 kips Trailer = 20.795 kipsAxle Spacing: 18.5 ft 35.5 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.9115 1.0464 1.0364 1.0236 1.0072 1.0028 1.0002 0.9995K (pos.) 0.8896 1.0024 1.0203 1.0128 1.0051 1.0021 1 0.9994K (neg.) 0.9749 1.0111 0.9887 1.0052 1.029 1.0147 1.0073 1.0045

Lanes 3 and 4LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.9928 1.1091 1.1941 1.0721 1.0701 1.0739 1.0804 1.0848K (pos.) 0.9649 1.0879 1.1129 1.0638 1.0657 1.0695 1.0763 1.0811K (neg.) 1.2809 1.0062 1.149 1.1622 1.0599 1.0688 1.0831 1.0901Modified LRFD Fatigue Truck GVW = 59.573 kips

Axle Weight: Steer = 6.619 kips Drive = 26.477 kips Trailer = 26.477 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8999 1.0054 1.0824 0.9718 0.97 0.9734 0.9794 0.9833K (pos.) 0.8746 0.9861 1.0088 0.9643 0.966 0.9695 0.9756 0.9799K (neg.) 1.1611 0.9121 1.0415 1.0535 0.9607 0.9688 0.9818 0.9881Site-Specific Fatigue Truck GVW = 59.573 kips

Axle Weight: Steer = 12.51 kips Drive = 25.021 kips Trailer = 22.042 kipsAxle Spacing: 18.5 ft 35.5 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.9523 1.1023 1.0894 1.0619 1.0327 1.0217 1.0125 1.0086K (pos.) 0.9255 1.0541 1.0726 1.0512 1.0323 1.0229 1.014 1.0099K (neg.) 1.0144 1.0143 0.9893 1.0142 1.0406 1.0228 1.0115 1.0071

A - 80

Statistics Single Tandem Tridem QuadAxle Count 2986536 3293111 94115 1077

Mean All Axles 10.831 21.773 46.649 43.899Std Dev All Axles 3.494 9.847 13.955 22.070

CoV All Axles 0.323 0.452 0.299 0.503

Mean Top 20% Axles 16.039 36.285 63.111 70.777Std Dev Top 20% Axles 2.932 3.763 3.976 6.282

CoV Top 20% Axles 0.183 0.104 0.063 0.089

Mean Top 5% Axles 20.152 41.357 68.343 79.444Std Dev Top 5% Axles 2.008 3.913 3.817 6.380

CoV Top 5% Axles 0.100 0.095 0.056 0.080

99th Percentile 20 42 68 82

WIM Site 9926 Axle Group Weight Statistics

WIM Site 9926Axle Group Weight Relative Frequency

Histogram

0

5

10

15

20

25

30

35

40

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

Axle Group Weight (kips)

Freq

uenc

y %

SingleTandemTridemQuad

A - 81

Statistics Single-Single Single-Tandem Tandem-Tandem All OthersEvent Count 2271836 932101 2365640 142081

Mean All Events 21.165 33.837 43.648 71.052Std Dev All Events 3.741 11.633 14.045 20.000

CoV All Events 0.177 0.344 0.322 0.281

Mean Top 20% Events 26.326 50.500 64.065 98.280Std Dev Top 20% Events 3.812 4.688 6.660 11.014

CoV Top 20% Events 0.145 0.093 0.104 0.112

Mean Top 5% Events 31.651 56.848 73.199 114.340Std Dev Top 5% Events 3.795 3.971 5.302 9.101

CoV Top 5% Events 0.120 0.070 0.072 0.080

99th Percentile 32 58 74 120

WIM Site 9926 Two-Lane Multiple Presence Axle Load Statistics

WIM Site 9926Two-Lane MP Axle Loads

0

5

10

15

20

25

30

35

0 20 40 60 80 100 120 140 160 180 200

Axle Load (kips)

Freq

uenc

y %

Single-Single

Single-Tandem

Tandem-Tandem

AllOthers

A - 82

Implementation of Draft Protocols WIM Data Analysis

Florida

WIM Site 9927 – State Route

• GVW Histogram

• Single Truck Moment Histogram

• One-Lane and Two-Lane Moment Histogram

• One-Lane and Two-Lane Shear Histogram

• One-Lane and Two-lane Negative Moment Histogram

• Fatigue Adjustment Factor

• Axle Group Weight Histogram

A - 83

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 204547 168114

Mean All Trucks 45.264 41.108Std Dev All Trucks 19.545 16.454

CoV All Trucks 0.432 0.400

Mean Top 20% Trucks 76.642 67.934Std Dev Top 20% Trucks 4.723 6.308

CoV Top 20% Trucks 0.062 0.093

Mean Top 5% Trucks 82.508 76.265Std Dev Top 5% Trucks 4.186 3.973

CoV Top 5% Trucks 0.051 0.052

WIM Site 9927 Gross Vehicle Weight Statistics

WIM Site 9927Single Truck GVW Relative Frequencies

02468

1012141618

0 50 100 150 200

GVW (kips)

Freq

uenc

y %

Lanes 1 & 2Lanes 3 & 4

A - 84

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 204547 168114

Mean All Trucks 0.337 0.312Std Dev All Trucks 0.125 0.118

CoV All Trucks 0.373 0.378

Mean Top 20% Trucks 0.537 0.499Std Dev Top 20% Trucks 0.065 0.083

CoV Top 20% Trucks 0.121 0.166

Mean Top 5% Trucks 0.626 0.618Std Dev Top 5% Trucks 0.071 0.080

CoV Top 5% Trucks 0.113 0.129

WIM Site 9927 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 9927HL93 Single Truck Simple-Span Moment

60 ft Span

0

2

4

6

8

10

12

14

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Moment Ratio (Mtruck/MHL93)

Freq

uenc

y %

Lanes 1&2Lanes 3&4

A - 85

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 204813 2167

Mean All Trucks 0.337 0.485Std Dev All Trucks 0.126 0.169

CoV All Trucks 0.373 0.348

Mean Top 20% Trucks 0.537 0.743Std Dev Top 20% Trucks 0.065 0.108

CoV Top 20% Trucks 0.121 0.146

Mean Top 5% Trucks 0.626 0.901Std Dev Top 5% Trucks 0.071 0.080

CoV Top 5% Trucks 0.113 0.089

WIM Site 9927 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 9927HL93 Simple-Span Moment Lanes 1&2

60 ft Span

0

2

4

6

8

10

12

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 86

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 204813 2167

Mean All Trucks 0.364 0.524Std Dev All Trucks 0.139 0.182

CoV All Trucks 0.383 0.346

Mean Top 20% Trucks 0.593 0.797Std Dev Top 20% Trucks 0.064 0.113

CoV Top 20% Trucks 0.108 0.142

Mean Top 5% Trucks 0.685 0.964Std Dev Top 5% Trucks 0.056 0.083

CoV Top 5% Trucks 0.081 0.086

WIM Site 9927 HL93 Simple-Span Shear Statistics - 60 ft Span

WIM Site 9927HL93 Simple-Span Shear Lanes 1&2

60 ft Span

0

2

4

6

8

10

12

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Shear Ratio (VWIM/VHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 87

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 204813 2167

Mean All Trucks 0.292 0.472Std Dev All Trucks 0.127 0.157

CoV All Trucks 0.436 0.332

Mean Top 20% Trucks 0.497 0.706Std Dev Top 20% Trucks 0.033 0.093

CoV Top 20% Trucks 0.066 0.131

Mean Top 5% Trucks 0.539 0.838Std Dev Top 5% Trucks 0.027 0.079

CoV Top 5% Trucks 0.050 0.095

WIM Site 9927 HL93 Negative Moment Statistics - 60 ft Span

WIM Site 9927HL93 Negative Moment Lanes 1&2

60 ft Span

0

2

4

6

8

10

12

14

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 88

WIM Site: 9927 Fatigue Adjustment Factor

Lanes 1 and 2LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8389 0.9452 1.0187 0.9298 0.9388 0.9463 0.9555 0.9608K (pos.) 0.8221 0.9282 0.9503 0.9229 0.9331 0.9407 0.9506 0.9566K (neg.) 1.0988 0.9065 1.0207 1.0177 0.9364 0.9476 0.9614 0.9679Modified LRFD Fatigue Truck GVW = 52.911 kips

Axle Weight: Steer = 5.879 kips Drive = 23.516 kips Trailer = 23.516 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8562 0.9647 1.0396 0.9489 0.9582 0.9658 0.9752 0.9806K (pos.) 0.839 0.9473 0.9699 0.9419 0.9523 0.9601 0.9702 0.9763K (neg.) 1.1215 0.9251 1.0417 1.0386 0.9557 0.9671 0.9812 0.9878Site-Specific Fatigue Truck GVW = 52.911 kips

Axle Weight: Steer = 11.64 kips Drive = 22.223 kips Trailer = 19.048 kipsAxle Spacing: 18 ft 36 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.906 1.0428 1.0308 1.0324 1.017 1.0113 1.0066 1.0045K (pos.) 0.8878 1.0013 1.0171 1.0215 1.014 1.0103 1.0066 1.0048K (neg.) 0.9608 1.0322 0.9842 0.9911 1.0358 1.0214 1.0113 1.007

Lanes 3 and 4LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7762 0.882 0.9491 0.8569 0.8561 0.8582 0.8618 0.8642K (pos.) 0.7576 0.865 0.8853 0.8499 0.8516 0.8542 0.8584 0.8613K (neg.) 1.0197 0.8088 0.913 0.9161 0.8436 0.8511 0.8608 0.8655Modified LRFD Fatigue Truck GVW = 47.21 kips

Axle Weight: Steer = 5.246 kips Drive = 20.982 kips Trailer = 20.982 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8879 1.0088 1.0856 0.9801 0.9792 0.9816 0.9857 0.9884K (pos.) 0.8665 0.9894 1.0126 0.9722 0.9741 0.977 0.9818 0.9851K (neg.) 1.1664 0.9251 1.0443 1.0479 0.9649 0.9735 0.9846 0.9899Site-Specific Fatigue Truck GVW = 47.21 kips

Axle Weight: Steer = 10.386 kips Drive = 19.828 kips Trailer = 16.996 kipsAxle Spacing: 18 ft 36 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.9395 1.0905 1.0765 1.0664 1.0393 1.0279 1.0174 1.0126K (pos.) 0.917 1.0458 1.062 1.0543 1.0373 1.0281 1.0186 1.0139K (neg.) 0.9993 1.0321 0.9867 1 1.0458 1.0282 1.0148 1.0092

A - 89

Statistics Single Tandem Tridem QuadAxle Count 456993 591335 6875 65

Mean All Axles 10.250 19.025 39.152 22.262Std Dev All Axles 2.667 8.909 13.085 14.801

CoV All Axles 0.260 0.468 0.334 0.665

Mean Top 20% Axles 13.927 33.270 54.244 46.538Std Dev Top 20% Axles 2.984 3.550 3.262 17.666

CoV Top 20% Axles 0.214 0.107 0.060 0.380

Mean Top 5% Axles 18.206 37.930 58.680 71.667Std Dev Top 5% Axles 2.265 3.340 2.981 17.010

CoV Top 5% Axles 0.124 0.088 0.051 0.237

99th Percentile 18 38 58 64

WIM Site 9927 Axle Group Weight Statistics

WIM Site 9927Axle Group Weight Relative Frequency

Histogram

05

1015202530354045

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

Axle Group Weight (kips)

Freq

uenc

y %

SingleTandemTridemQuad

A - 90

Statistics Single-Single Single-Tandem Tandem-Tandem All OthersEvent Count 570 1402 831 24

Mean All Events 20.421 29.127 38.658 51.667Std Dev All Events 3.773 9.281 13.605 16.029

CoV All Events 0.185 0.319 0.352 0.310

Mean Top 20% Events 26.316 43.814 59.566 69.800Std Dev Top 20% Events 3.067 3.789 7.960 5.215

CoV Top 20% Events 0.117 0.086 0.134 0.075

Mean Top 5% Events 30.643 48.914 70.095 77.000Std Dev Top 5% Events 1.967 3.395 5.323 0.000

CoV Top 5% Events 0.064 0.069 0.076 0.000

99th Percentile 30 50 70 76

WIM Site 9927 Two-Lane Multiple Presence Axle Load Statistics

WIM Site 9927Two-Lane MP Axle Loads

0

5

10

15

20

25

30

35

0 20 40 60 80 100 120 140 160 180 200

Axle Load (kips)

Freq

uenc

y %

Single-Single

Single-Tandem

Tandem-Tandem

AllOthers

A - 91

Implementation of Draft Protocols WIM Data Analysis

Florida

WIM Site 9936 – I-10

• GVW Histogram

• Single Truck Moment Histogram

• One-Lane and Two-Lane Moment Histogram

• One-Lane and Two-Lane Shear Histogram

• One-Lane and Two-lane Negative Moment Histogram

• Fatigue Adjustment Factor

• Axle Group Weight Histogram

A - 92

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 700288 723053

Mean All Trucks 67.740 44.815Std Dev All Trucks 21.466 15.896

CoV All Trucks 0.317 0.355

Mean Top 20% Trucks 95.777 69.125Std Dev Top 20% Trucks 7.034 7.592

CoV Top 20% Trucks 0.073 0.110

Mean Top 5% Trucks 104.262 79.336Std Dev Top 5% Trucks 8.759 6.569

CoV Top 5% Trucks 0.084 0.083

WIM Site 9936 Gross Vehicle Weight Statistics

WIM Site 9936Single Truck GVW Relative Frequencies

0

2

4

6

8

10

12

14

0 50 100 150 200

GVW (kips)

Freq

uenc

y %

Lanes 1 & 2Lanes 3 & 4

A - 93

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 700288 723053

Mean All Trucks 0.442 0.300Std Dev All Trucks 0.126 0.096

CoV All Trucks 0.286 0.319

Mean Top 20% Trucks 0.612 0.444Std Dev Top 20% Trucks 0.055 0.052

CoV Top 20% Trucks 0.090 0.116

Mean Top 5% Trucks 0.684 0.511Std Dev Top 5% Trucks 0.064 0.054

CoV Top 5% Trucks 0.094 0.106

WIM Site 9936 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 9936HL93 Single Truck Simple-Span Moment

60 ft Span

0123456789

10

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Moment Ratio (Mtruck/MHL93)

Freq

uenc

y %

Lanes 1&2Lanes 3&4

A - 94

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 701548 17274

Mean All Trucks 0.442 0.651Std Dev All Trucks 0.126 0.192

CoV All Trucks 0.286 0.296

Mean Top 20% Trucks 0.612 0.949Std Dev Top 20% Trucks 0.055 0.097

CoV Top 20% Trucks 0.090 0.102

Mean Top 5% Trucks 0.684 1.086Std Dev Top 5% Trucks 0.064 0.068

CoV Top 5% Trucks 0.094 0.063

WIM Site 9936 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 9936HL93 Simple-Span Moment Lanes 1&2

60 ft Span

0

1

2

3

4

5

6

7

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 95

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 701548 17274

Mean All Trucks 0.495 0.721Std Dev All Trucks 0.155 0.206

CoV All Trucks 0.312 0.285

Mean Top 20% Trucks 0.706 1.035Std Dev Top 20% Trucks 0.057 0.111

CoV Top 20% Trucks 0.080 0.107

Mean Top 5% Trucks 0.782 1.191Std Dev Top 5% Trucks 0.060 0.078

CoV Top 5% Trucks 0.076 0.066

WIM Site 9936 HL93 Simple-Span Shear Statistics - 60 ft Span

WIM Site 9936HL93 Simple-Span Shear Lanes 1&2

60 ft Span

0

1

2

3

4

5

6

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Shear Ratio (VWIM/VHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 96

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 701548 17274

Mean All Trucks 0.440 0.665Std Dev All Trucks 0.142 0.183

CoV All Trucks 0.322 0.275

Mean Top 20% Trucks 0.627 0.938Std Dev Top 20% Trucks 0.047 0.100

CoV Top 20% Trucks 0.075 0.107

Mean Top 5% Trucks 0.685 1.081Std Dev Top 5% Trucks 0.055 0.078

CoV Top 5% Trucks 0.081 0.072

WIM Site 9936 HL93 Negative Moment Statistics - 60 ft Span

WIM Site 9936HL93 Negative Moment Lanes 1&2

60 ft Span

0

1

2

3

4

5

6

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 97

WIM Site: 9936 Fatigue Adjustment Factor

Lanes 1 and 2LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 1.1098 1.2007 1.2694 1.1631 1.2129 1.2456 1.2826 1.3026K (pos.) 1.0863 1.1808 1.1844 1.1598 1.2046 1.2348 1.2714 1.2925K (neg.) 1.352 1.2292 1.4363 1.419 1.2544 1.2858 1.3222 1.3389Modified LRFD Fatigue Truck GVW = 73.908 kips

Axle Weight: Steer = 8.212 kips Drive = 32.848 kips Trailer = 32.848 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8109 0.8773 0.9275 0.8498 0.8862 0.9101 0.9371 0.9517K (pos.) 0.7937 0.8627 0.8653 0.8474 0.8801 0.9022 0.929 0.9444K (neg.) 0.9878 0.8981 1.0494 1.0368 0.9165 0.9394 0.9661 0.9783Site-Specific Fatigue Truck GVW = 73.908 kips

Axle Weight: Steer = 13.303 kips Drive = 31.78 kips Trailer = 28.824 kipsAxle Spacing: 19 ft 38 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8381 0.9548 0.9419 0.9807 0.9797 0.9831 0.988 0.9907K (pos.) 0.8204 0.9156 0.9268 0.9566 0.9686 0.9759 0.9836 0.9876K (neg.) 0.8941 1.0096 0.9818 0.9768 1.0175 1.0079 1.004 1.0025

Lanes 3 and 4LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7505 0.8212 0.8802 0.805 0.835 0.8547 0.8769 0.8889K (pos.) 0.734 0.809 0.8206 0.8012 0.8286 0.847 0.8694 0.8823K (neg.) 0.951 0.8322 0.9739 0.9648 0.8559 0.8751 0.8987 0.9096Modified LRFD Fatigue Truck GVW = 50.163 kips

Axle Weight: Steer = 5.574 kips Drive = 22.295 kips Trailer = 22.295 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8079 0.884 0.9475 0.8666 0.8989 0.9201 0.944 0.9569K (pos.) 0.7902 0.8709 0.8834 0.8625 0.8919 0.9118 0.9359 0.9498K (neg.) 1.0237 0.8959 1.0484 1.0386 0.9213 0.9421 0.9675 0.9792Site-Specific Fatigue Truck GVW = 50.163 kips

Axle Weight: Steer = 9.029 kips Drive = 21.57 kips Trailer = 19.564 kipsAxle Spacing: 19 ft 38 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8351 0.9621 0.9622 1 0.9937 0.9939 0.9952 0.9962K (pos.) 0.8167 0.9243 0.9461 0.9737 0.9816 0.9862 0.991 0.9933K (neg.) 0.9266 1.0071 0.9808 0.9785 1.0229 1.0107 1.0055 1.0034

A - 98

Statistics Single Tandem Tridem QuadAxle Count 2025154 2469487 12092 261

Mean All Axles 10.515 23.613 35.722 51.130Std Dev All Axles 3.899 10.409 16.626 22.434

CoV All Axles 0.371 0.441 0.465 0.439

Mean Top 20% Axles 16.481 39.285 59.945 82.923Std Dev Top 20% Axles 3.425 4.178 8.631 8.317

CoV Top 20% Axles 0.208 0.106 0.144 0.100

Mean Top 5% Axles 21.353 44.924 72.064 93.923Std Dev Top 5% Axles 2.117 3.200 6.969 3.121

CoV Top 5% Axles 0.099 0.071 0.097 0.033

99th Percentile 22 44 74 94

WIM Site 9936 Axle Group Weight Statistics

WIM Site 9936Axle Group Weight Relative Frequency

Histogram

0

5

10

15

20

25

30

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

Axle Group Weight (kips)

Freq

uenc

y %

SingleTandemTridemQuad

A - 99

Statistics Single-Single Single-Tandem Tandem-Tandem All OthersEvent Count 5743 14379 8755 199

Mean All Events 20.916 34.210 47.303 55.824Std Dev All Events 6.137 11.861 16.322 21.147

CoV All Events 0.293 0.347 0.345 0.379

Mean Top 20% Events 30.466 52.032 72.017 86.300Std Dev Top 20% Events 4.286 5.344 7.341 9.856

CoV Top 20% Events 0.141 0.103 0.102 0.114

Mean Top 5% Events 36.324 59.512 82.160 99.800Std Dev Top 5% Events 3.379 3.960 4.480 7.254

CoV Top 5% Events 0.093 0.067 0.055 0.073

99th Percentile 38 60 84 106

WIM Site 9936 Two-Lane Multiple Presence Axle Load Statistics

WIM Site 9936Two-Lane MP Axle Loads

0

2

4

6

8

10

12

14

16

0 20 40 60 80 100 120 140 160 180 200

Axle Load (kips)

Freq

uenc

y %

Single-Single

Single-Tandem

Tandem-Tandem

AllOthers

A - 100

Implementation of Draft Protocols WIM Data Analysis

Indiana

WIM Site 9511

• GVW Histogram

• Single Truck Moment Histogram

• One-Lane and Two-Lane Moment Histogram

• One-Lane and Two-Lane Shear Histogram

• One-Lane and Two-lane Negative Moment Histogram

• Fatigue Adjustment Factor

• Axle Group Weight Histogram

A - 101

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 2118346 2067410

Mean All Trucks 48.149 44.662Std Dev All Trucks 13.063 11.589

CoV All Trucks 0.271 0.259

Mean Top 20% Trucks 65.534 59.970Std Dev Top 20% Trucks 4.318 5.358

CoV Top 20% Trucks 0.066 0.089

Mean Top 5% Trucks 71.220 67.246Std Dev Top 5% Trucks 4.459 4.841

CoV Top 5% Trucks 0.063 0.072

WIM Site 9511 Gross Vehicle Weight Statistics

WIM Site 9511Single Truck GVW Relative Frequencies

0

2

4

6

8

10

12

14

16

0 50 100 150 200

GVW (kips)

Freq

uenc

y %

Lanes 1 & 2Lanes 3 & 4

A - 102

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 2118346 2067410

Mean All Trucks 0.311 0.291Std Dev All Trucks 0.075 0.071

CoV All Trucks 0.242 0.246

Mean Top 20% Trucks 0.416 0.391Std Dev Top 20% Trucks 0.045 0.050

CoV Top 20% Trucks 0.109 0.128

Mean Top 5% Trucks 0.467 0.458Std Dev Top 5% Trucks 0.065 0.056

CoV Top 5% Trucks 0.139 0.121

WIM Site 9511 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 9511HL93 Single Truck Simple-Span Moment

60 ft Span

0

2

4

6

8

10

12

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Moment Ratio (Mtruck/MHL93)

Freq

uenc

y %

Lanes 1&2Lanes 3&4

A - 103

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 2164771 80338

Mean All Trucks 0.312 0.454Std Dev All Trucks 0.075 0.128

CoV All Trucks 0.241 0.282

Mean Top 20% Trucks 0.417 0.650Std Dev Top 20% Trucks 0.045 0.068

CoV Top 20% Trucks 0.108 0.105

Mean Top 5% Trucks 0.468 0.740Std Dev Top 5% Trucks 0.065 0.066

CoV Top 5% Trucks 0.140 0.089

WIM Site 9511 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 9511HL93 Simple-Span Moment Lanes 1&2

60 ft Span

0

2

4

6

8

10

12

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 104

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 2164771 80338

Mean All Trucks 0.342 0.494Std Dev All Trucks 0.086 0.134

CoV All Trucks 0.253 0.271

Mean Top 20% Trucks 0.466 0.699Std Dev Top 20% Trucks 0.046 0.072

CoV Top 20% Trucks 0.098 0.103

Mean Top 5% Trucks 0.526 0.798Std Dev Top 5% Trucks 0.053 0.060

CoV Top 5% Trucks 0.101 0.075

WIM Site 9511 HL93 Simple-Span Shear Statistics - 60 ft Span

WIM Site 9511HL93 Simple-Span Shear Lanes 1&2

60 ft Span

0123456789

10

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Shear Ratio (VWIM/VHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 105

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 2164771 80338

Mean All Trucks 0.312 0.467Std Dev All Trucks 0.086 0.120

CoV All Trucks 0.277 0.257

Mean Top 20% Trucks 0.429 0.647Std Dev Top 20% Trucks 0.028 0.065

CoV Top 20% Trucks 0.065 0.101

Mean Top 5% Trucks 0.466 0.740Std Dev Top 5% Trucks 0.029 0.051

CoV Top 5% Trucks 0.061 0.069

WIM Site 9511 HL93 Negative Moment Statistics - 60 ft Span

WIM Site 9511HL93 Negative Moment Lanes 1&2

60 ft Span

0123456789

10

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 106

WIM Site: 9511 Fatigue Adjustment Factor

Lanes 1 and 2LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7225 0.7992 0.8781 0.8058 0.8426 0.8658 0.8915 0.9053K (pos.) 0.7072 0.7877 0.8162 0.7977 0.8322 0.8548 0.8816 0.8969K (neg.) 0.9774 0.8257 0.9932 0.9929 0.8667 0.8871 0.9154 0.9282Modified LRFD Fatigue Truck GVW = 51.393 kips

Axle Weight: Steer = 5.71 kips Drive = 22.841 kips Trailer = 22.841 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7591 0.8398 0.9226 0.8467 0.8853 0.9097 0.9367 0.9512K (pos.) 0.7431 0.8277 0.8576 0.8381 0.8744 0.8982 0.9264 0.9424K (neg.) 1.027 0.8675 1.0436 1.0432 0.9107 0.9322 0.9618 0.9753Site-Specific Fatigue Truck GVW = 51.393 kips

Axle Weight: Steer = 11.306 kips Drive = 20.557 kips Trailer = 19.529 kipsAxle Spacing: 19 ft 37 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8435 0.9762 0.9668 0.977 0.9787 0.9827 0.9876 0.9902K (pos.) 0.8256 0.9314 0.9491 0.9589 0.9696 0.9762 0.9835 0.9873K (neg.) 0.9155 0.994 0.9836 0.9858 1.0123 1.001 1.0001 0.9997

Lanes 3 and 4LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.6589 0.7376 0.8213 0.7556 0.7859 0.8053 0.8269 0.8386K (pos.) 0.6448 0.7277 0.7625 0.7455 0.7751 0.7946 0.8177 0.8308K (neg.) 0.9268 0.7587 0.9145 0.9168 0.8038 0.8207 0.8457 0.8571Modified LRFD Fatigue Truck GVW = 47.416 kips

Axle Weight: Steer = 5.268 kips Drive = 21.074 kips Trailer = 21.074 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7504 0.84 0.9354 0.8606 0.8951 0.9172 0.9418 0.955K (pos.) 0.7343 0.8288 0.8684 0.8491 0.8828 0.9049 0.9313 0.9462K (neg.) 1.0555 0.8641 1.0414 1.0442 0.9154 0.9347 0.9631 0.9761Site-Specific Fatigue Truck GVW = 47.416 kips

Axle Weight: Steer = 10.432 kips Drive = 18.966 kips Trailer = 18.018 kipsAxle Spacing: 19 ft 37 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8338 0.9765 0.9802 0.9931 0.9895 0.9908 0.9929 0.9942K (pos.) 0.8159 0.9327 0.961 0.9714 0.9789 0.9836 0.9887 0.9913K (neg.) 0.9409 0.9901 0.9816 0.9867 1.0175 1.0037 1.0014 1.0005

A - 107

Statistics Single Tandem Tridem QuadAxle Count 6153587 7146399 28976 13222

Mean All Axles 10.024 18.377 28.800 42.145Std Dev All Axles 2.106 5.853 10.482 7.743

CoV All Axles 0.210 0.318 0.364 0.184

Mean Top 20% Axles 12.647 26.746 43.054 54.663Std Dev Top 20% Axles 1.697 2.232 5.721 4.638

CoV Top 20% Axles 0.134 0.083 0.133 0.085

Mean Top 5% Axles 14.823 29.803 50.891 60.888Std Dev Top 5% Axles 1.493 2.039 4.886 4.555

CoV Top 5% Axles 0.101 0.068 0.096 0.075

99th Percentile 14 30 52 62

WIM Site 9511 Axle Group Weight Statistics

WIM Site 9511Axle Group Weight Relative Frequency

Histogram

05

1015202530354045

0 8 16 24 32 40 48 56 64 72 80 88 96

Axle Group Weight (kips)

Freq

uenc

y %

SingleTandemTridemQuad

A - 108

Statistics Single-Single Single-Tandem Tandem-Tandem All OthersEvent Count 28573 66698 37822 905

Mean All Events 20.122 28.377 36.686 47.290Std Dev All Events 2.983 6.190 8.291 13.539

CoV All Events 0.148 0.218 0.226 0.286

Mean Top 20% Events 24.233 37.267 48.608 66.669Std Dev Top 20% Events 1.779 2.605 3.848 6.817

CoV Top 20% Events 0.073 0.070 0.079 0.102

Mean Top 5% Events 26.576 40.854 53.916 76.778Std Dev Top 5% Events 1.802 2.296 2.953 4.139

CoV Top 5% Events 0.068 0.056 0.055 0.054

99th Percentile 26 40 54 78

WIM Site 9511 Two-Lane Multiple Presence Axle Load Statistics

WIM Site 9511Two-Lane MP Axle Loads

0

5

10

15

20

25

30

35

0 20 40 60 80 100 120 140 160 180 200

Axle Load (kips)

Freq

uenc

y %

Single-Single

Single-Tandem

Tandem-Tandem

AllOthers

A - 109

Implementation of Draft Protocols WIM Data Analysis

Indiana

WIM Site 9512

• GVW Histogram

• Single Truck Moment Histogram

• One-Lane and Two-Lane Moment Histogram

• One-Lane and Two-Lane Shear Histogram

• One-Lane and Two-lane Negative Moment Histogram

• Fatigue Adjustment Factor

• Axle Group Weight Histogram

A - 110

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 930734 1002375

Mean All Trucks 60.589 60.084Std Dev All Trucks 15.905 18.043

CoV All Trucks 0.263 0.300

Mean Top 20% Trucks 79.664 83.868Std Dev Top 20% Trucks 4.605 4.806

CoV Top 20% Trucks 0.058 0.057

Mean Top 5% Trucks 84.477 89.324Std Dev Top 5% Trucks 6.433 5.671

CoV Top 5% Trucks 0.076 0.063

WIM Site 9512 Gross Vehicle Weight Statistics

WIM Site 9512Single Truck GVW Relative Frequencies

0

2

4

6

8

10

12

14

0 50 100 150 200

GVW (kips)

Freq

uenc

y %

Lanes 1 & 2Lanes 3 & 4

A - 111

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 930734 1002375

Mean All Trucks 0.412 0.403Std Dev All Trucks 0.093 0.109

CoV All Trucks 0.227 0.269

Mean Top 20% Trucks 0.528 0.549Std Dev Top 20% Trucks 0.036 0.034

CoV Top 20% Trucks 0.068 0.063

Mean Top 5% Trucks 0.570 0.592Std Dev Top 5% Trucks 0.047 0.037

CoV Top 5% Trucks 0.083 0.062

WIM Site 9512 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 9512HL93 Single Truck Simple-Span Moment

60 ft Span

0

2

4

6

8

10

12

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Moment Ratio (Mtruck/MHL93)

Freq

uenc

y %

Lanes 1&2Lanes 3&4

A - 112

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 932504 37630

Mean All Trucks 0.412 0.581Std Dev All Trucks 0.093 0.156

CoV All Trucks 0.227 0.268

Mean Top 20% Trucks 0.528 0.826Std Dev Top 20% Trucks 0.036 0.073

CoV Top 20% Trucks 0.068 0.088

Mean Top 5% Trucks 0.570 0.927Std Dev Top 5% Trucks 0.047 0.052

CoV Top 5% Trucks 0.083 0.056

WIM Site 9512 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 9512HL93 Simple-Span Moment Lanes 1&2

60 ft Span

0

2

4

6

8

10

12

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 113

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 932504 37630

Mean All Trucks 0.437 0.627Std Dev All Trucks 0.104 0.165

CoV All Trucks 0.238 0.264

Mean Top 20% Trucks 0.571 0.884Std Dev Top 20% Trucks 0.038 0.077

CoV Top 20% Trucks 0.066 0.088

Mean Top 5% Trucks 0.619 0.993Std Dev Top 5% Trucks 0.042 0.052

CoV Top 5% Trucks 0.068 0.052

WIM Site 9512 HL93 Simple-Span Shear Statistics - 60 ft Span

WIM Site 9512HL93 Simple-Span Shear Lanes 1&2

60 ft Span

0123456789

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Shear Ratio (VWIM/VHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 114

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 932504 37630

Mean All Trucks 0.394 0.586Std Dev All Trucks 0.105 0.148

CoV All Trucks 0.266 0.252

Mean Top 20% Trucks 0.520 0.807Std Dev Top 20% Trucks 0.028 0.074

CoV Top 20% Trucks 0.054 0.091

Mean Top 5% Trucks 0.552 0.913Std Dev Top 5% Trucks 0.035 0.055

CoV Top 5% Trucks 0.063 0.061

WIM Site 9512 HL93 Negative Moment Statistics - 60 ft Span

WIM Site 9512HL93 Negative Moment Lanes 1&2

60 ft Span

0

2

4

6

8

10

12

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 115

WIM Site: 9512 Fatigue Adjustment Factor

Lanes 1 and 2LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.9567 1.0574 1.1529 1.0418 1.079 1.1032 1.1301 1.1447K (pos.) 0.9313 1.0431 1.0734 1.0354 1.0697 1.0926 1.1202 1.136K (neg.) 1.2641 1.0486 1.2525 1.25 1.0939 1.1185 1.1509 1.166Modified LRFD Fatigue Truck GVW = 64.475 kips

Axle Weight: Steer = 7.164 kips Drive = 28.655 kips Trailer = 28.655 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8013 0.8856 0.9656 0.8725 0.9037 0.9239 0.9465 0.9587K (pos.) 0.78 0.8737 0.899 0.8672 0.8959 0.9151 0.9382 0.9515K (neg.) 1.0588 0.8782 1.0491 1.047 0.9162 0.9368 0.9639 0.9766Site-Specific Fatigue Truck GVW = 64.475 kips

Axle Weight: Steer = 12.895 kips Drive = 28.369 kips Trailer = 23.211 kipsAxle Spacing: 19 ft 38 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8094 0.9403 0.9475 0.9729 0.9757 0.9802 0.9858 0.9888K (pos.) 0.7879 0.9027 0.9307 0.9523 0.9652 0.9728 0.9812 0.9855K (neg.) 0.9138 1.0006 0.9843 0.9823 1.0114 1.0017 1.0003 0.9998

Lanes 3 and 4LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.9571 1.058 1.1483 1.0403 1.0802 1.1066 1.136 1.1519K (pos.) 0.9352 1.0437 1.0691 1.0348 1.0715 1.0961 1.1258 1.1429K (neg.) 1.2556 1.0623 1.2646 1.2591 1.1024 1.1284 1.1615 1.1769Modified LRFD Fatigue Truck GVW = 65.07 kips

Axle Weight: Steer = 7.23 kips Drive = 28.92 kips Trailer = 28.92 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7943 0.878 0.953 0.8633 0.8965 0.9183 0.9428 0.9559K (pos.) 0.7761 0.8661 0.8872 0.8587 0.8892 0.9096 0.9343 0.9485K (neg.) 1.042 0.8816 1.0494 1.0449 0.9149 0.9364 0.9639 0.9767Site-Specific Fatigue Truck GVW = 65.07 kips

Axle Weight: Steer = 13.014 kips Drive = 28.631 kips Trailer = 23.425 kipsAxle Spacing: 19 ft 38 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8023 0.9322 0.9351 0.9627 0.9679 0.9743 0.9818 0.9859K (pos.) 0.7839 0.8949 0.9185 0.943 0.9579 0.9671 0.9771 0.9825K (neg.) 0.8993 1.0045 0.9847 0.9803 1.01 1.0013 1.0003 0.9999

A - 116

Statistics Single Tandem Tridem QuadAxle Count 2672423 3431095 12263 334

Mean All Axles 11.736 24.714 34.721 54.749Std Dev All Axles 2.924 8.575 12.489 9.754

CoV All Axles 0.249 0.347 0.360 0.178

Mean Top 20% Axles 15.851 35.796 51.699 64.522Std Dev Top 20% Axles 2.704 2.430 4.494 2.561

CoV Top 20% Axles 0.171 0.068 0.087 0.040

Mean Top 5% Axles 19.570 38.968 58.044 67.941Std Dev Top 5% Axles 1.857 2.103 3.642 2.015

CoV Top 5% Axles 0.095 0.054 0.063 0.030

99th Percentile 18 38 58 68

WIM Site 9512 Axle Group Weight Statistics

WIM Site 9512Axle Group Weight Relative Frequency

Histogram

05

101520253035404550

0 8 16 24 32 40 48 56 64 72 80 88 96

Axle Group Weight (kips)

Freq

uenc

y %

SingleTandemTridemQuad

A - 117

Statistics Single-Single Single-Tandem Tandem-Tandem All OthersEvent Count 11589 30556 19294 322

Mean All Events 23.532 36.411 49.363 58.248Std Dev All Events 4.124 9.017 12.130 16.173

CoV All Events 0.175 0.248 0.246 0.278

Mean Top 20% Events 29.687 48.327 66.073 81.469Std Dev Top 20% Events 2.973 3.162 4.248 5.874

CoV Top 20% Events 0.100 0.065 0.064 0.072

Mean Top 5% Events 33.680 52.751 71.935 89.625Std Dev Top 5% Events 2.850 2.678 2.983 4.177

CoV Top 5% Events 0.085 0.051 0.041 0.047

99th Percentile 34 52 72 90

WIM Site 9512 Two-Lane Multiple Presence Axle Load Statistics

WIM Site 9512Two-Lane MP Axle Loads

0

5

10

15

20

25

30

35

0 20 40 60 80 100 120 140 160 180 200

Axle Load (kips)

Freq

uenc

y %

Single-Single

Single-Tandem

Tandem-Tandem

AllOthers

A - 118

Implementation of Draft Protocols WIM Data Analysis

Indiana

WIM Site 9532

• GVW Histogram

• Single Truck Moment Histogram

• One-Lane and Two-Lane Moment Histogram

• One-Lane and Two-Lane Shear Histogram

• One-Lane and Two-lane Negative Moment Histogram

• Fatigue Adjustment Factor

• Axle Group Weight Histogram

A - 119

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 224192 229077

Mean All Trucks 42.344 44.619Std Dev All Trucks 14.949 16.824

CoV All Trucks 0.353 0.377

Mean Top 20% Trucks 64.755 70.519Std Dev Top 20% Trucks 6.062 7.002

CoV Top 20% Trucks 0.094 0.099

Mean Top 5% Trucks 72.614 79.244Std Dev Top 5% Trucks 6.092 7.609

CoV Top 5% Trucks 0.084 0.096

WIM Site 9532 Gross Vehicle Weight Statistics

WIM Site 9532Single Truck GVW Relative Frequencies

0

2

4

6

8

10

12

14

16

0 50 100 150 200

GVW (kips)

Freq

uenc

y %

Lanes 1 & 2Lanes 3 & 4

A - 120

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 224192 229077

Mean All Trucks 0.304 0.325Std Dev All Trucks 0.113 0.126

CoV All Trucks 0.370 0.389

Mean Top 20% Trucks 0.478 0.522Std Dev Top 20% Trucks 0.101 0.107

CoV Top 20% Trucks 0.211 0.205

Mean Top 5% Trucks 0.630 0.684Std Dev Top 5% Trucks 0.081 0.083

CoV Top 5% Trucks 0.129 0.122

WIM Site 9532 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 9532HL93 Single Truck Simple-Span Moment

60 ft Span

0

2

4

6

8

10

12

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Moment Ratio (Mtruck/MHL93)

Freq

uenc

y %

Lanes 1&2Lanes 3&4

A - 121

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 224553 2491

Mean All Trucks 0.305 0.443Std Dev All Trucks 0.113 0.152

CoV All Trucks 0.370 0.343

Mean Top 20% Trucks 0.478 0.679Std Dev Top 20% Trucks 0.101 0.105

CoV Top 20% Trucks 0.211 0.155

Mean Top 5% Trucks 0.630 0.825Std Dev Top 5% Trucks 0.081 0.099

CoV Top 5% Trucks 0.129 0.120

WIM Site 9532 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 9532HL93 Simple-Span Moment Lanes 1&2

60 ft Span

0

2

4

6

8

10

12

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 122

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 224553 2491

Mean All Trucks 0.328 0.473Std Dev All Trucks 0.113 0.152

CoV All Trucks 0.346 0.322

Mean Top 20% Trucks 0.508 0.705Std Dev Top 20% Trucks 0.082 0.100

CoV Top 20% Trucks 0.161 0.142

Mean Top 5% Trucks 0.625 0.847Std Dev Top 5% Trucks 0.070 0.079

CoV Top 5% Trucks 0.113 0.093

WIM Site 9532 HL93 Simple-Span Shear Statistics - 60 ft Span

WIM Site 9532HL93 Simple-Span Shear Lanes 1&2

60 ft Span

0

2

4

6

8

10

12

14

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Shear Ratio (VWIM/VHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 123

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 224553 2491

Mean All Trucks 0.273 0.434Std Dev All Trucks 0.099 0.129

CoV All Trucks 0.362 0.297

Mean Top 20% Trucks 0.423 0.628Std Dev Top 20% Trucks 0.040 0.074

CoV Top 20% Trucks 0.094 0.117

Mean Top 5% Trucks 0.475 0.734Std Dev Top 5% Trucks 0.041 0.055

CoV Top 5% Trucks 0.086 0.075

WIM Site 9532 HL93 Negative Moment Statistics - 60 ft Span

WIM Site 9532HL93 Negative Moment Lanes 1&2

60 ft Span

0

2

4

6

8

10

12

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 124

WIM Site: 9532 Fatigue Adjustment Factor

Lanes 1 and 2LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7405 0.8481 0.9275 0.8308 0.834 0.8404 0.8494 0.855K (pos.) 0.7201 0.8328 0.8619 0.8212 0.8279 0.8345 0.8442 0.8504K (neg.) 1.0041 0.7731 0.9178 0.9307 0.83 0.8383 0.8546 0.8623Modified LRFD Fatigue Truck GVW = 47.376 kips

Axle Weight: Steer = 5.264 kips Drive = 21.056 kips Trailer = 21.056 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8441 0.9667 1.0572 0.947 0.9506 0.9579 0.9682 0.9745K (pos.) 0.8207 0.9492 0.9824 0.9361 0.9437 0.9512 0.9622 0.9693K (neg.) 1.1445 0.8812 1.0461 1.0608 0.9461 0.9555 0.9741 0.9829Site-Specific Fatigue Truck GVW = 47.376 kips

Axle Weight: Steer = 10.896 kips Drive = 19.424 kips Trailer = 17.055 kipsAxle Spacing: 19 ft 37.5 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.915 1.0958 1.0772 1.0746 1.0388 1.0256 1.0146 1.0099K (pos.) 0.8897 1.041 1.0573 1.0539 1.0342 1.0244 1.015 1.0105K (neg.) 0.9885 1.0221 0.9851 0.9952 1.0507 1.026 1.0129 1.0078

Lanes 3 and 4LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.806 0.9177 1.0013 0.8893 0.8911 0.8979 0.9079 0.9141K (pos.) 0.7826 0.9017 0.9312 0.8802 0.8859 0.8925 0.9027 0.9094K (neg.) 1.074 0.8212 0.9829 1.0017 0.8878 0.8948 0.9131 0.922Modified LRFD Fatigue Truck GVW = 50.726 kips

Axle Weight: Steer = 5.636 kips Drive = 22.545 kips Trailer = 22.545 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8581 0.977 1.0659 0.9467 0.9486 0.9558 0.9665 0.9731K (pos.) 0.8331 0.9599 0.9913 0.937 0.9431 0.9501 0.9609 0.9681K (neg.) 1.1433 0.8742 1.0463 1.0663 0.9451 0.9526 0.972 0.9815Site-Specific Fatigue Truck GVW = 50.726 kips

Axle Weight: Steer = 11.667 kips Drive = 20.798 kips Trailer = 18.261 kipsAxle Spacing: 19 ft 37.5 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.9302 1.1074 1.0861 1.0742 1.0366 1.0234 1.0128 1.0085K (pos.) 0.9031 1.0527 1.0669 1.0549 1.0335 1.0232 1.0136 1.0093K (neg.) 0.9874 1.014 0.9853 1.0004 1.0496 1.0228 1.0108 1.0064

A - 125

Statistics Single Tandem Tridem QuadAxle Count 687022 653757 22461 4226

Mean All Axles 10.026 17.942 39.424 50.008Std Dev All Axles 2.846 7.654 10.894 9.248

CoV All Axles 0.284 0.427 0.276 0.185

Mean Top 20% Axles 14.042 29.672 52.453 62.444Std Dev Top 20% Axles 2.247 3.583 4.298 5.639

CoV Top 20% Axles 0.160 0.121 0.082 0.090

Mean Top 5% Axles 16.972 34.353 58.305 70.062Std Dev Top 5% Axles 2.040 3.698 4.255 5.931

CoV Top 5% Axles 0.120 0.108 0.073 0.085

99th Percentile 16 34 58 72

WIM Site 9532 Axle Group Weight Statistics

WIM Site 9532Axle Group Weight Relative Frequency

Histogram

0

5

10

15

20

25

30

35

40

0 8 16 24 32 40 48 56 64 72 80 88 96

Axle Group Weight (kips)

Freq

uenc

y %

SingleTandemTridemQuad

A - 126

Statistics Single-Single Single-Tandem Tandem-Tandem All OthersEvent Count 1067 1879 901 143

Mean All Events 20.110 28.098 36.352 53.769Std Dev All Events 3.948 8.158 11.146 14.259

CoV All Events 0.196 0.290 0.307 0.265

Mean Top 20% Events 25.761 40.553 53.089 71.897Std Dev Top 20% Events 2.481 4.041 5.544 5.870

CoV Top 20% Events 0.096 0.100 0.104 0.082

Mean Top 5% Events 29.000 46.106 61.000 79.857Std Dev Top 5% Events 2.572 3.752 4.285 6.094

CoV Top 5% Events 0.089 0.081 0.070 0.076

99th Percentile 28 46 64 84

WIM Site 9532 Two-Lane Multiple Presence Axle Load Statistics

WIM Site 9532Two-Lane MP Axle Loads

0

5

10

15

20

25

0 20 40 60 80 100 120 140 160 180 200

Axle Load (kips)

Freq

uenc

y %

Single-Single

Single-Tandem

Tandem-Tandem

AllOthers

A - 127

Implementation of Draft Protocols WIM Data Analysis

Indiana

WIM Site 9534

• GVW Histogram

• Single Truck Moment Histogram

• One-Lane and Two-Lane Moment Histogram

• One-Lane and Two-Lane Shear Histogram

• One-Lane and Two-lane Negative Moment Histogram

• Fatigue Adjustment Factor

• Axle Group Weight Histogram

A - 128

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 2126739 2160704

Mean All Trucks 43.752 46.924Std Dev All Trucks 15.698 15.395

CoV All Trucks 0.359 0.328

Mean Top 20% Trucks 66.489 68.224Std Dev Top 20% Trucks 6.933 6.549

CoV Top 20% Trucks 0.104 0.096

Mean Top 5% Trucks 75.546 77.326Std Dev Top 5% Trucks 7.643 5.958

CoV Top 5% Trucks 0.101 0.077

WIM Site 9534 Gross Vehicle Weight Statistics

WIM Site 9534Single Truck GVW Relative Frequencies

0

2

4

6

8

10

12

0 50 100 150 200

GVW (kips)

Freq

uenc

y %

Lanes 1 & 2Lanes 3 & 4

A - 129

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 2126739 2160704

Mean All Trucks 0.291 0.311Std Dev All Trucks 0.096 0.096

CoV All Trucks 0.331 0.310

Mean Top 20% Trucks 0.432 0.449Std Dev Top 20% Trucks 0.063 0.070

CoV Top 20% Trucks 0.147 0.155

Mean Top 5% Trucks 0.514 0.540Std Dev Top 5% Trucks 0.076 0.082

CoV Top 5% Trucks 0.147 0.152

WIM Site 9534 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 9534HL93 Single Truck Simple-Span Moment

60 ft Span

0123456789

10

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Moment Ratio (Mtruck/MHL93)

Freq

uenc

y %

Lanes 1&2Lanes 3&4

A - 130

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 2174979 80810

Mean All Trucks 0.292 0.428Std Dev All Trucks 0.096 0.135

CoV All Trucks 0.330 0.316

Mean Top 20% Trucks 0.433 0.636Std Dev Top 20% Trucks 0.063 0.083

CoV Top 20% Trucks 0.146 0.130

Mean Top 5% Trucks 0.515 0.751Std Dev Top 5% Trucks 0.075 0.075

CoV Top 5% Trucks 0.146 0.100

WIM Site 9534 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 9534HL93 Simple-Span Moment Lanes 1&2

60 ft Span

0123456789

10

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 131

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 2174979 80810

Mean All Trucks 0.317 0.461Std Dev All Trucks 0.103 0.142

CoV All Trucks 0.325 0.309

Mean Top 20% Trucks 0.471 0.678Std Dev Top 20% Trucks 0.065 0.086

CoV Top 20% Trucks 0.137 0.127

Mean Top 5% Trucks 0.560 0.799Std Dev Top 5% Trucks 0.066 0.072

CoV Top 5% Trucks 0.119 0.090

WIM Site 9534 HL93 Simple-Span Shear Statistics - 60 ft Span

WIM Site 9534HL93 Simple-Span Shear Lanes 1&2

60 ft Span

0123456789

10

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Shear Ratio (VWIM/VHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 132

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 2174979 80810

Mean All Trucks 0.286 0.436Std Dev All Trucks 0.104 0.130

CoV All Trucks 0.364 0.299

Mean Top 20% Trucks 0.436 0.631Std Dev Top 20% Trucks 0.045 0.075

CoV Top 20% Trucks 0.104 0.119

Mean Top 5% Trucks 0.496 0.737Std Dev Top 5% Trucks 0.048 0.063

CoV Top 5% Trucks 0.097 0.085

WIM Site 9534 HL93 Negative Moment Statistics - 60 ft Span

WIM Site 9534HL93 Negative Moment Lanes 1&2

60 ft Span

0123456789

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 133

WIM Site: 9534 Fatigue Adjustment Factor

Lanes 1 and 2LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7077 0.7829 0.8584 0.7726 0.8013 0.823 0.8478 0.8613K (pos.) 0.6922 0.7721 0.7982 0.7655 0.7941 0.8143 0.8392 0.8537K (neg.) 0.9558 0.7775 0.9532 0.9618 0.8325 0.8422 0.8701 0.8832Modified LRFD Fatigue Truck GVW = 48.994 kips

Axle Weight: Steer = 5.444 kips Drive = 21.775 kips Trailer = 21.775 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7801 0.8629 0.9461 0.8515 0.8831 0.9071 0.9344 0.9493K (pos.) 0.7629 0.851 0.8797 0.8437 0.8752 0.8975 0.9249 0.9409K (neg.) 1.0535 0.857 1.0506 1.0601 0.9176 0.9283 0.959 0.9734Site-Specific Fatigue Truck GVW = 48.994 kips

Axle Weight: Steer = 11.269 kips Drive = 19.598 kips Trailer = 18.128 kipsAxle Spacing: 19 ft 39 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8667 1.0019 0.984 1.0086 0.9938 0.9932 0.9941 0.995K (pos.) 0.8477 0.9552 0.9665 0.9817 0.9845 0.9874 0.9909 0.9928K (neg.) 0.925 1.0142 0.9821 0.9797 1.0091 1.0099 1.0045 1.0024

Lanes 3 and 4LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7499 0.8327 0.9086 0.8172 0.8472 0.8693 0.8945 0.9083K (pos.) 0.7332 0.8202 0.8452 0.811 0.84 0.8605 0.8858 0.9006K (neg.) 1 0.8254 1.0043 1.0109 0.8767 0.889 0.9177 0.931Modified LRFD Fatigue Truck GVW = 51.6 kips

Axle Weight: Steer = 5.733 kips Drive = 22.933 kips Trailer = 22.933 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7848 0.8714 0.9509 0.8553 0.8866 0.9097 0.9361 0.9505K (pos.) 0.7673 0.8583 0.8845 0.8487 0.8791 0.9005 0.927 0.9425K (neg.) 1.0465 0.8638 1.051 1.058 0.9175 0.9303 0.9604 0.9743Site-Specific Fatigue Truck GVW = 51.6 kips

Axle Weight: Steer = 11.868 kips Drive = 20.64 kips Trailer = 19.092 kipsAxle Spacing: 19 ft 39 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.872 1.0118 0.9889 1.013 0.9977 0.9961 0.9959 0.9963K (pos.) 0.8525 0.9634 0.9718 0.9875 0.9889 0.9908 0.9931 0.9945K (neg.) 0.9189 1.0222 0.9825 0.9777 1.009 1.0122 1.006 1.0034

A - 134

Statistics Single Tandem Tridem QuadAxle Count 6007791 7280125 51604 16657

Mean All Axles 10.093 18.037 34.661 46.949Std Dev All Axles 2.665 7.463 11.751 8.361

CoV All Axles 0.264 0.414 0.339 0.178

Mean Top 20% Axles 13.751 28.597 48.667 57.972Std Dev Top 20% Axles 2.155 3.192 4.671 4.997

CoV Top 20% Axles 0.157 0.112 0.096 0.086

Mean Top 5% Axles 16.557 33.111 55.194 65.214Std Dev Top 5% Axles 1.997 2.765 4.695 3.270

CoV Top 5% Axles 0.121 0.084 0.085 0.050

99th Percentile 16 34 56 66

WIM Site 9534 Axle Group Weight Statistics

WIM Site 9534Axle Group Weight Relative Frequency

Histogram

0

5

10

15

20

25

30

35

40

0 8 16 24 32 40 48 56 64 72 80 88 96

Axle Group Weight (kips)

Freq

uenc

y %

SingleTandemTridemQuad

A - 135

Statistics Single-Single Single-Tandem Tandem-Tandem All OthersEvent Count 26846 65529 38245 1435

Mean All Events 20.250 28.137 35.959 52.836Std Dev All Events 3.797 7.918 10.593 14.560

CoV All Events 0.188 0.281 0.295 0.276

Mean Top 20% Events 25.502 39.453 51.242 72.742Std Dev Top 20% Events 2.466 3.589 4.796 7.242

CoV Top 20% Events 0.097 0.091 0.094 0.100

Mean Top 5% Events 28.747 44.419 57.927 82.833Std Dev Top 5% Events 2.315 3.100 3.749 6.593

CoV Top 5% Events 0.081 0.070 0.065 0.080

99th Percentile 28 44 58 86

WIM Site 9534 Two-Lane Multiple Presence Axle Load Statistics

WIM Site 9534Two-Lane MP Axle Loads

0

5

10

15

20

25

0 20 40 60 80 100 120 140 160 180 200

Axle Load (kips)

Freq

uenc

y %

Single-Single

Single-Tandem

Tandem-Tandem

AllOthers

A - 136

Implementation of Draft Protocols WIM Data Analysis

Indiana

WIM Site 9544

• GVW Histogram

• Single Truck Moment Histogram

• One-Lane and Two-Lane Moment Histogram

• One-Lane and Two-Lane Shear Histogram

• One-Lane and Two-lane Negative Moment Histogram

• Fatigue Adjustment Factor

• Axle Group Weight Histogram

A - 137

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 3777960 4010301

Mean All Trucks 48.512 46.565Std Dev All Trucks 16.127 13.388

CoV All Trucks 0.332 0.288

Mean Top 20% Trucks 70.797 64.240Std Dev Top 20% Trucks 9.048 4.645

CoV Top 20% Trucks 0.128 0.072

Mean Top 5% Trucks 83.024 69.887Std Dev Top 5% Trucks 9.238 5.582

CoV Top 5% Trucks 0.111 0.080

WIM Site 9544 Gross Vehicle Weight Statistics

WIM Site 9544Single Truck GVW Relative Frequencies

0

2

4

6

8

10

12

14

0 50 100 150 200

GVW (kips)

Freq

uenc

y %

Lanes 1 & 2Lanes 3 & 4

A - 138

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 3777960 4010301

Mean All Trucks 0.319 0.301Std Dev All Trucks 0.102 0.078

CoV All Trucks 0.319 0.258

Mean Top 20% Trucks 0.466 0.407Std Dev Top 20% Trucks 0.072 0.044

CoV Top 20% Trucks 0.154 0.108

Mean Top 5% Trucks 0.562 0.462Std Dev Top 5% Trucks 0.079 0.055

CoV Top 5% Trucks 0.140 0.120

WIM Site 9544 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 9544HL93 Single Truck Simple-Span Moment

60 ft Span

0

2

4

6

8

10

12

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Moment Ratio (Mtruck/MHL93)

Freq

uenc

y %

Lanes 1&2Lanes 3&4

A - 139

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 3860290 142839

Mean All Trucks 0.320 0.469Std Dev All Trucks 0.102 0.146

CoV All Trucks 0.319 0.311

Mean Top 20% Trucks 0.467 0.692Std Dev Top 20% Trucks 0.072 0.090

CoV Top 20% Trucks 0.153 0.130

Mean Top 5% Trucks 0.563 0.817Std Dev Top 5% Trucks 0.079 0.084

CoV Top 5% Trucks 0.140 0.102

WIM Site 9544 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 9544HL93 Simple-Span Moment Lanes 1&2

60 ft Span

0123456789

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 140

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 3860290 142839

Mean All Trucks 0.350 0.510Std Dev All Trucks 0.115 0.156

CoV All Trucks 0.328 0.306

Mean Top 20% Trucks 0.521 0.748Std Dev Top 20% Trucks 0.081 0.098

CoV Top 20% Trucks 0.156 0.130

Mean Top 5% Trucks 0.632 0.884Std Dev Top 5% Trucks 0.085 0.089

CoV Top 5% Trucks 0.134 0.101

WIM Site 9544 HL93 Simple-Span Shear Statistics - 60 ft Span

WIM Site 9544HL93 Simple-Span Shear Lanes 1&2

60 ft Span

012345678

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Shear Ratio (VWIM/VHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 141

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 3860290 142839

Mean All Trucks 0.316 0.478Std Dev All Trucks 0.107 0.138

CoV All Trucks 0.337 0.288

Mean Top 20% Trucks 0.463 0.684Std Dev Top 20% Trucks 0.059 0.084

CoV Top 20% Trucks 0.128 0.122

Mean Top 5% Trucks 0.544 0.802Std Dev Top 5% Trucks 0.060 0.073

CoV Top 5% Trucks 0.109 0.091

WIM Site 9544 HL93 Negative Moment Statistics - 60 ft Span

WIM Site 9544HL93 Negative Moment Lanes 1&2

60 ft Span

0123456789

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 142

WIM Site: 9544 Fatigue Adjustment Factor

Lanes 1 and 2LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7859 0.8626 0.9365 0.855 0.8871 0.9088 0.9333 0.9465K (pos.) 0.7693 0.8497 0.8714 0.8486 0.8793 0.8998 0.9247 0.939K (neg.) 1.0294 0.8755 1.0383 1.0358 0.9118 0.9299 0.9566 0.9688Modified LRFD Fatigue Truck GVW = 53.527 kips

Axle Weight: Steer = 5.947 kips Drive = 23.79 kips Trailer = 23.79 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7929 0.8703 0.9448 0.8625 0.895 0.9169 0.9415 0.9549K (pos.) 0.7761 0.8572 0.8791 0.8561 0.887 0.9078 0.9329 0.9473K (neg.) 1.0385 0.8832 1.0475 1.0449 0.9198 0.9381 0.965 0.9773Site-Specific Fatigue Truck GVW = 53.527 kips

Axle Weight: Steer = 11.776 kips Drive = 21.411 kips Trailer = 20.34 kipsAxle Spacing: 19 ft 37.5 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.881 1.0117 0.9901 1.0042 0.9953 0.995 0.9957 0.9963K (pos.) 0.8623 0.9647 0.9729 0.9853 0.9884 0.9907 0.9934 0.9948K (neg.) 0.9257 1.0179 0.9846 0.9821 1.0276 1.0108 1.0053 1.003

Lanes 3 and 4LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7016 0.7758 0.8546 0.7863 0.8216 0.8443 0.8694 0.8829K (pos.) 0.6868 0.7652 0.7939 0.7782 0.8118 0.8338 0.8599 0.8748K (neg.) 0.958 0.8069 0.9688 0.9695 0.848 0.8664 0.8934 0.9057Modified LRFD Fatigue Truck GVW = 50.13 kips

Axle Weight: Steer = 5.57 kips Drive = 22.28 kips Trailer = 22.28 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7558 0.8357 0.9206 0.8471 0.885 0.9094 0.9365 0.951K (pos.) 0.7398 0.8242 0.8552 0.8383 0.8745 0.8981 0.9263 0.9423K (neg.) 1.032 0.8692 1.0436 1.0444 0.9135 0.9333 0.9624 0.9756Site-Specific Fatigue Truck GVW = 50.13 kips

Axle Weight: Steer = 11.029 kips Drive = 20.052 kips Trailer = 19.049 kipsAxle Spacing: 19 ft 37.5 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8398 0.9715 0.9647 0.9861 0.9843 0.9869 0.9903 0.9923K (pos.) 0.822 0.9276 0.9464 0.9648 0.9744 0.9802 0.9864 0.9896K (neg.) 0.92 1.0018 0.981 0.9815 1.0205 1.0055 1.0025 1.0012

A - 143

Statistics Single Tandem Tridem QuadAxle Count 11326209 13379834 111155 4273

Mean All Axles 9.917 19.061 24.335 41.385Std Dev All Axles 2.941 6.974 11.476 10.210

CoV All Axles 0.297 0.366 0.472 0.247

Mean Top 20% Axles 13.522 28.591 41.048 52.806Std Dev Top 20% Axles 3.272 3.887 7.043 5.735

CoV Top 20% Axles 0.242 0.136 0.172 0.109

Mean Top 5% Axles 17.111 33.796 50.453 60.813Std Dev Top 5% Axles 4.626 4.266 7.920 5.951

CoV Top 5% Axles 0.270 0.126 0.157 0.098

99th Percentile 16 34 54 64

WIM Site 9544 Axle Group Weight Statistics

WIM Site 9544Axle Group Weight Relative Frequency

Histogram

05

1015202530354045

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

Axle Group Weight (kips)

Freq

uenc

y %

SingleTandemTridemQuad

A - 144

Statistics Single-Single Single-Tandem Tandem-Tandem All OthersEvent Count 52663 124160 70927 2951

Mean All Events 19.895 28.931 38.039 39.485Std Dev All Events 4.172 7.485 9.884 13.786

CoV All Events 0.210 0.259 0.260 0.349

Mean Top 20% Events 25.373 39.325 52.195 60.502Std Dev Top 20% Events 3.959 4.440 5.211 9.636

CoV Top 20% Events 0.156 0.113 0.100 0.159

Mean Top 5% Events 29.712 45.072 59.385 73.986Std Dev Top 5% Events 5.848 5.151 5.023 8.937

CoV Top 5% Events 0.197 0.114 0.085 0.121

99th Percentile 28 46 60 80

WIM Site 9544 Two-Lane Multiple Presence Axle Load Statistics

WIM Site 9544Two-Lane MP Axle Loads

0

5

10

15

20

25

30

0 20 40 60 80 100 120 140 160 180 200

Axle Load (kips)

Freq

uenc

y %

Single-Single

Single-Tandem

Tandem-Tandem

AllOthers

A - 145

Implementation of Draft Protocols WIM Data Analysis

Indiana

WIM Site 9552

• GVW Histogram

• Single Truck Moment Histogram

• One-Lane and Two-Lane Moment Histogram

• One-Lane and Two-Lane Shear Histogram

• One-Lane and Two-lane Negative Moment Histogram

• Fatigue Adjustment Factor

• Axle Group Weight Histogram

A - 146

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 95783 102130

Mean All Trucks 49.918 41.303Std Dev All Trucks 17.781 14.739

CoV All Trucks 0.356 0.357

Mean Top 20% Trucks 74.767 64.208Std Dev Top 20% Trucks 5.563 5.727

CoV Top 20% Trucks 0.074 0.089

Mean Top 5% Trucks 82.146 71.076Std Dev Top 5% Trucks 5.553 6.583

CoV Top 5% Trucks 0.068 0.093

WIM Site 9552 Gross Vehicle Weight Statistics

WIM Site 9552Single Truck GVW Relative Frequencies

02468

101214161820

0 50 100 150 200

GVW (kips)

Freq

uenc

y %

Lanes 1 & 2Lanes 3 & 4

A - 147

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 95783 102130

Mean All Trucks 0.337 0.282Std Dev All Trucks 0.113 0.091

CoV All Trucks 0.334 0.323

Mean Top 20% Trucks 0.500 0.424Std Dev Top 20% Trucks 0.065 0.059

CoV Top 20% Trucks 0.131 0.138

Mean Top 5% Trucks 0.588 0.497Std Dev Top 5% Trucks 0.074 0.075

CoV Top 5% Trucks 0.126 0.151

WIM Site 9552 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 9552HL93 Single Truck Simple-Span Moment

60 ft Span

02468

1012141618

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Moment Ratio (Mtruck/MHL93)

Freq

uenc

y %

Lanes 1&2Lanes 3&4

A - 148

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 95949 1109

Mean All Trucks 0.337 0.489Std Dev All Trucks 0.113 0.153

CoV All Trucks 0.334 0.314

Mean Top 20% Trucks 0.500 0.728Std Dev Top 20% Trucks 0.065 0.092

CoV Top 20% Trucks 0.131 0.127

Mean Top 5% Trucks 0.588 0.859Std Dev Top 5% Trucks 0.074 0.069

CoV Top 5% Trucks 0.126 0.080

WIM Site 9552 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 9552HL93 Simple-Span Moment Lanes 1&2

60 ft Span

0

2

4

6

8

10

12

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 149

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 95949 1109

Mean All Trucks 0.370 0.533Std Dev All Trucks 0.131 0.167

CoV All Trucks 0.354 0.314

Mean Top 20% Trucks 0.569 0.786Std Dev Top 20% Trucks 0.070 0.105

CoV Top 20% Trucks 0.123 0.133

Mean Top 5% Trucks 0.668 0.939Std Dev Top 5% Trucks 0.054 0.086

CoV Top 5% Trucks 0.081 0.092

WIM Site 9552 HL93 Simple-Span Shear Statistics - 60 ft Span

WIM Site 9552HL93 Simple-Span Shear Lanes 1&2

60 ft Span

0

2

4

6

8

10

12

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Shear Ratio (VWIM/VHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 150

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 95949 1109

Mean All Trucks 0.324 0.496Std Dev All Trucks 0.116 0.143

CoV All Trucks 0.358 0.288

Mean Top 20% Trucks 0.482 0.710Std Dev Top 20% Trucks 0.033 0.083

CoV Top 20% Trucks 0.069 0.117

Mean Top 5% Trucks 0.526 0.831Std Dev Top 5% Trucks 0.033 0.058

CoV Top 5% Trucks 0.063 0.070

WIM Site 9552 HL93 Negative Moment Statistics - 60 ft Span

WIM Site 9552HL93 Negative Moment Lanes 1&2

60 ft Span

0

2

4

6

8

10

12

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 151

WIM Site: 9552 Fatigue Adjustment Factor

Lanes 1 and 2LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8315 0.9213 0.9966 0.9156 0.9422 0.9604 0.981 0.9923K (pos.) 0.8115 0.906 0.9287 0.9086 0.9344 0.9518 0.9731 0.9855K (neg.) 1.0873 0.9294 1.0791 1.0734 0.9614 0.9778 1.0009 1.0115Modified LRFD Fatigue Truck GVW = 55.684 kips

Axle Weight: Steer = 6.187 kips Drive = 24.748 kips Trailer = 24.748 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8064 0.8934 0.9665 0.8879 0.9137 0.9313 0.9513 0.9623K (pos.) 0.787 0.8786 0.9006 0.8811 0.9061 0.923 0.9437 0.9557K (neg.) 1.0544 0.9013 1.0465 1.0409 0.9323 0.9482 0.9706 0.9809Site-Specific Fatigue Truck GVW = 55.684 kips

Axle Weight: Steer = 13.364 kips Drive = 22.274 kips Trailer = 20.046 kipsAxle Spacing: 19 ft 37.5 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.896 1.0361 0.9976 1.0163 1.0044 1.0017 1 0.9995K (pos.) 0.8744 0.9837 0.9822 1.0023 1.0003 0.9997 0.9993 0.9992K (neg.) 0.9109 1.053 0.9857 0.9748 1.0391 1.0204 1.0106 1.0065

Lanes 3 and 4LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.6732 0.7592 0.8318 0.7631 0.7839 0.7989 0.816 0.8253K (pos.) 0.6585 0.7466 0.7725 0.7544 0.776 0.7907 0.8087 0.8192K (neg.) 0.9258 0.7589 0.8956 0.8942 0.7968 0.8112 0.8311 0.8403Modified LRFD Fatigue Truck GVW = 46.318 kips

Axle Weight: Steer = 5.146 kips Drive = 20.586 kips Trailer = 20.586 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7848 0.8851 0.9698 0.8897 0.914 0.9314 0.9513 0.9622K (pos.) 0.7678 0.8705 0.9006 0.8795 0.9047 0.9218 0.9429 0.955K (neg.) 1.0794 0.8848 1.0441 1.0425 0.929 0.9458 0.9689 0.9797Site-Specific Fatigue Truck GVW = 46.318 kips

Axle Weight: Steer = 11.116 kips Drive = 18.527 kips Trailer = 16.675 kipsAxle Spacing: 19 ft 37.5 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.872 1.0264 1.001 1.0183 1.0047 1.0018 1 0.9995K (pos.) 0.8531 0.9746 0.9823 1.0005 0.9987 0.9984 0.9984 0.9985K (neg.) 0.9325 1.0337 0.9834 0.9763 1.0354 1.0178 1.0088 1.0053

A - 152

Statistics Single Tandem Tridem QuadAxle Count 266133 340190 3385 431

Mean All Axles 9.895 18.332 33.100 48.341Std Dev All Axles 2.866 8.006 13.048 7.442

CoV All Axles 0.290 0.437 0.394 0.154

Mean Top 20% Axles 13.682 30.321 49.287 56.977Std Dev Top 20% Axles 2.296 3.297 4.590 3.029

CoV Top 20% Axles 0.168 0.109 0.093 0.053

Mean Top 5% Axles 16.722 34.921 55.734 61.091Std Dev Top 5% Axles 1.919 2.815 4.144 2.860

CoV Top 5% Axles 0.115 0.081 0.074 0.047

99th Percentile 16 34 56 62

WIM Site 9552 Axle Group Weight Statistics

WIM Site 9552Axle Group Weight Relative Frequency

Histogram

0

5

10

15

20

25

30

35

40

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

Axle Group Weight (kips)

Freq

uenc

y %

SingleTandemTridemQuad

A - 153

Statistics Single-Single Single-Tandem Tandem-Tandem All OthersEvent Count 368 875 555 17

Mean All Events 19.989 27.731 37.879 49.588Std Dev All Events 4.110 8.517 11.669 15.277

CoV All Events 0.206 0.307 0.308 0.308

Mean Top 20% Events 25.486 40.806 55.505 67.667Std Dev Top 20% Events 2.383 4.145 5.550 4.163

CoV Top 20% Events 0.093 0.102 0.100 0.062

Mean Top 5% Events 28.889 46.455 63.286 71.000Std Dev Top 5% Events 1.875 3.091 3.558 0.000

CoV Top 5% Events 0.065 0.067 0.056 0.000

99th Percentile 28 46 64 70

WIM Site 9552 Two-Lane Multiple Presence Axle Load Statistics

WIM Site 9552Two-Lane MP Axle Loads

0

5

10

15

20

25

0 20 40 60 80 100 120 140 160 180 200

Axle Load (kips)

Freq

uenc

y %

Single-Single

Single-Tandem

Tandem-Tandem

AllOthers

A - 154

Implementation of Draft Protocols WIM Data Analysis

Mississippi

WIM Site 2606 – I-55

• GVW Histogram

• Single Truck Moment Histogram

• One-Lane and Two-Lane Moment Histogram

• One-Lane and Two-Lane Shear Histogram

• One-Lane and Two-lane Negative Moment Histogram

• Fatigue Adjustment Factor

• Axle Group Weight Histogram

A - 155

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 563952 604244

Mean All Trucks 66.466 63.146Std Dev All Trucks 22.518 13.922

CoV All Trucks 0.339 0.220

Mean Top 20% Trucks 99.718 79.706Std Dev Top 20% Trucks 12.403 5.895

CoV Top 20% Trucks 0.124 0.074

Mean Top 5% Trucks 117.545 86.881Std Dev Top 5% Trucks 10.917 7.069

CoV Top 5% Trucks 0.093 0.081

WIM Site 2606 Gross Vehicle Weight Statistics

WIM Site 2606Single Truck GVW Relative Frequencies

0

2

4

6

8

10

12

14

16

0 50 100 150 200

GVW (kips)

Freq

uenc

y %

Lanes 1 & 2Lanes 3 & 4

A - 156

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 563952 604244

Mean All Trucks 0.438 0.427Std Dev All Trucks 0.133 0.075

CoV All Trucks 0.302 0.175

Mean Top 20% Trucks 0.637 0.521Std Dev Top 20% Trucks 0.078 0.036

CoV Top 20% Trucks 0.122 0.069

Mean Top 5% Trucks 0.748 0.568Std Dev Top 5% Trucks 0.067 0.039

CoV Top 5% Trucks 0.089 0.069

WIM Site 2606 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 2606HL93 Single Truck Simple-Span Moment

60 ft Span

0

2

4

6

8

10

12

14

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Moment Ratio (Mtruck/MHL93)

Freq

uenc

y %

Lanes 1&2Lanes 3&4

A - 157

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 564956 13796

Mean All Trucks 0.438 0.643Std Dev All Trucks 0.133 0.196

CoV All Trucks 0.302 0.304

Mean Top 20% Trucks 0.637 0.944Std Dev Top 20% Trucks 0.078 0.112

CoV Top 20% Trucks 0.122 0.119

Mean Top 5% Trucks 0.748 1.103Std Dev Top 5% Trucks 0.067 0.090

CoV Top 5% Trucks 0.089 0.081

WIM Site 2606 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 2606HL93 Simple-Span Moment Lanes 1&2

60 ft Span

012345678

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 158

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 564956 13796

Mean All Trucks 0.481 0.704Std Dev All Trucks 0.151 0.209

CoV All Trucks 0.314 0.296

Mean Top 20% Trucks 0.708 1.024Std Dev Top 20% Trucks 0.084 0.120

CoV Top 20% Trucks 0.118 0.118

Mean Top 5% Trucks 0.827 1.192Std Dev Top 5% Trucks 0.074 0.100

CoV Top 5% Trucks 0.089 0.084

WIM Site 2606 HL93 Simple-Span Shear Statistics - 60 ft Span

WIM Site 2606HL93 Simple-Span Shear Lanes 1&2

60 ft Span

0

1

2

3

4

5

6

7

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Shear Ratio (VWIM/VHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 159

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 564956 13796

Mean All Trucks 0.430 0.656Std Dev All Trucks 0.149 0.192

CoV All Trucks 0.346 0.292

Mean Top 20% Trucks 0.651 0.948Std Dev Top 20% Trucks 0.081 0.116

CoV Top 20% Trucks 0.124 0.122

Mean Top 5% Trucks 0.767 1.112Std Dev Top 5% Trucks 0.070 0.093

CoV Top 5% Trucks 0.091 0.083

WIM Site 2606 HL93 Negative Moment Statistics - 60 ft Span

WIM Site 2606HL93 Negative Moment Lanes 1&2

60 ft Span

0

1

2

3

4

5

6

7

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 160

WIM Site: 2606 Fatigue Adjustment Factor

Lanes 1 and 2LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 1.0828 1.181 1.2731 1.1635 1.2129 1.2446 1.2803 1.2996K (pos.) 1.0575 1.1633 1.1857 1.1569 1.2019 1.2319 1.2682 1.289K (neg.) 1.3821 1.2065 1.4292 1.4209 1.2478 1.2772 1.3148 1.3324Modified LRFD Fatigue Truck GVW = 73.662 kips

Axle Weight: Steer = 8.185 kips Drive = 32.739 kips Trailer = 32.739 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7938 0.8657 0.9333 0.8529 0.8892 0.9124 0.9385 0.9527K (pos.) 0.7752 0.8528 0.8692 0.8481 0.8811 0.9031 0.9297 0.9449K (neg.) 1.0132 0.8845 1.0477 1.0416 0.9147 0.9363 0.9638 0.9768Site-Specific Fatigue Truck GVW = 73.662 kips

Axle Weight: Steer = 12.523 kips Drive = 31.675 kips Trailer = 29.465 kipsAxle Spacing: 19 ft 37.5 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8205 0.9433 0.9548 0.9838 0.9827 0.9854 0.9893 0.9916K (pos.) 0.8012 0.9073 0.9376 0.9573 0.9694 0.9765 0.984 0.9879K (neg.) 0.9321 0.9814 0.9819 0.9887 1.0103 1.0009 0.9996 0.9995

Lanes 3 and 4LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.9806 1.0806 1.1723 1.073 1.1083 1.1315 1.1581 1.1726K (pos.) 0.9567 1.0641 1.0912 1.0638 1.0975 1.1202 1.1478 1.1638K (neg.) 1.2732 1.0825 1.2735 1.2677 1.1261 1.1515 1.1819 1.1962Modified LRFD Fatigue Truck GVW = 65.973 kips

Axle Weight: Steer = 7.33 kips Drive = 29.321 kips Trailer = 29.321 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8027 0.8845 0.9596 0.8783 0.9071 0.9262 0.9479 0.9598K (pos.) 0.7831 0.871 0.8932 0.8708 0.8983 0.9169 0.9395 0.9526K (neg.) 1.0422 0.8861 1.0424 1.0376 0.9217 0.9425 0.9674 0.9791Site-Specific Fatigue Truck GVW = 65.973 kips

Axle Weight: Steer = 11.215 kips Drive = 28.368 kips Trailer = 26.389 kipsAxle Spacing: 19 ft 37.5 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8296 0.9637 0.9817 1.0131 1.0025 1.0002 0.9992 0.999K (pos.) 0.8094 0.9266 0.9634 0.9829 0.9883 0.9914 0.9945 0.9959K (neg.) 0.9588 0.9832 0.9769 0.985 1.018 1.0076 1.0033 1.0019

A - 161

Statistics Single Tandem Tridem QuadAxle Count 1817007 1878746 7075 321

Mean All Axles 12.126 28.423 38.642 27.623Std Dev All Axles 3.828 7.801 13.815 16.901

CoV All Axles 0.316 0.274 0.358 0.612

Mean Top 20% Axles 17.714 39.461 57.823 56.844Std Dev Top 20% Axles 2.531 5.248 9.226 12.222

CoV Top 20% Axles 0.143 0.133 0.160 0.215

Mean Top 5% Axles 21.101 46.880 70.955 73.875Std Dev Top 5% Axles 2.398 4.591 8.520 9.932

CoV Top 5% Axles 0.114 0.098 0.120 0.134

99th Percentile 20 48 76 78

WIM Site 2606 Axle Group Weight Statistics

WIM Site 2606Axle Group Weight Relative Frequency

Histogram

0

5

10

15

20

25

0 8 16 24 32 40 48 56 64 72 80 88 96

Axle Group Weight (kips)

Freq

uenc

y %

SingleTandemTridemQuad

A - 162

Statistics Single-Single Single-Tandem Tandem-Tandem All OthersEvent Count 5827 11967 6269 104

Mean All Events 24.182 40.490 56.660 56.135Std Dev All Events 5.287 8.504 11.145 15.589

CoV All Events 0.219 0.210 0.197 0.278

Mean Top 20% Events 31.776 52.398 72.397 79.000Std Dev Top 20% Events 3.330 5.395 7.340 8.718

CoV Top 20% Events 0.105 0.103 0.101 0.110

Mean Top 5% Events 36.285 60.040 83.006 91.400Std Dev Top 5% Events 3.393 4.747 5.971 7.127

CoV Top 5% Events 0.094 0.079 0.072 0.078

99th Percentile 36 62 86 92

WIM Site 2606 Two-Lane Multiple Presence Axle Load Statistics

WIM Site 2606Two-Lane MP Axle Loads

02468

1012141618

0 20 40 60 80 100 120 140 160 180 200

Axle Load (kips)

Freq

uenc

y %

Single-Single

Single-Tandem

Tandem-Tandem

AllOthers

A - 163

Implementation of Draft Protocols WIM Data Analysis

Mississippi

WIM Site 3015 – I-10

• GVW Histogram

• Single Truck Moment Histogram

• One-Lane and Two-Lane Moment Histogram

• One-Lane and Two-Lane Shear Histogram

• One-Lane and Two-lane Negative Moment Histogram

• Fatigue Adjustment Factor

• Axle Group Weight Histogram

A - 164

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 750128 666507

Mean All Trucks 53.344 59.575Std Dev All Trucks 14.222 11.667

CoV All Trucks 0.267 0.196

Mean Top 20% Trucks 73.095 73.238Std Dev Top 20% Trucks 6.152 5.528

CoV Top 20% Trucks 0.084 0.075

Mean Top 5% Trucks 81.245 78.320Std Dev Top 5% Trucks 4.965 8.742

CoV Top 5% Trucks 0.061 0.112

WIM Site 3015 Gross Vehicle Weight Statistics

WIM Site 3015Single Truck GVW Relative Frequencies

02468

1012141618

0 50 100 150 200

GVW (kips)

Freq

uenc

y %

Lanes 1 & 2Lanes 3 & 4

A - 165

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 750128 666507

Mean All Trucks 0.348 0.391Std Dev All Trucks 0.081 0.061

CoV All Trucks 0.232 0.155

Mean Top 20% Trucks 0.466 0.473Std Dev Top 20% Trucks 0.040 0.034

CoV Top 20% Trucks 0.086 0.072

Mean Top 5% Trucks 0.521 0.515Std Dev Top 5% Trucks 0.031 0.045

CoV Top 5% Trucks 0.060 0.087

WIM Site 3015 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 3015HL93 Single Truck Simple-Span Moment

60 ft Span

0

2

4

6

8

10

12

14

16

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Moment Ratio (Mtruck/MHL93)

Freq

uenc

y %

Lanes 1&2Lanes 3&4

A - 166

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 751492 18455

Mean All Trucks 0.348 0.508Std Dev All Trucks 0.081 0.142

CoV All Trucks 0.232 0.280

Mean Top 20% Trucks 0.466 0.724Std Dev Top 20% Trucks 0.040 0.067

CoV Top 20% Trucks 0.086 0.092

Mean Top 5% Trucks 0.521 0.819Std Dev Top 5% Trucks 0.031 0.049

CoV Top 5% Trucks 0.060 0.059

WIM Site 3015 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 3015HL93 Simple-Span Moment Lanes 1&2

60 ft Span

0

2

4

6

8

10

12

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 167

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 751492 18455

Mean All Trucks 0.393 0.564Std Dev All Trucks 0.101 0.150

CoV All Trucks 0.256 0.266

Mean Top 20% Trucks 0.539 0.792Std Dev Top 20% Trucks 0.045 0.078

CoV Top 20% Trucks 0.083 0.098

Mean Top 5% Trucks 0.601 0.902Std Dev Top 5% Trucks 0.031 0.058

CoV Top 5% Trucks 0.051 0.064

WIM Site 3015 HL93 Simple-Span Shear Statistics - 60 ft Span

WIM Site 3015HL93 Simple-Span Shear Lanes 1&2

60 ft Span

0123456789

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Shear Ratio (VWIM/VHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 168

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 751492 18455

Mean All Trucks 0.347 0.519Std Dev All Trucks 0.095 0.133

CoV All Trucks 0.274 0.256

Mean Top 20% Trucks 0.479 0.719Std Dev Top 20% Trucks 0.040 0.073

CoV Top 20% Trucks 0.084 0.102

Mean Top 5% Trucks 0.534 0.823Std Dev Top 5% Trucks 0.029 0.056

CoV Top 5% Trucks 0.054 0.069

WIM Site 3015 HL93 Negative Moment Statistics - 60 ft Span

WIM Site 3015HL93 Negative Moment Lanes 1&2

60 ft Span

0123456789

10

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 169

WIM Site: 3015 Fatigue Adjustment Factor

Lanes 1 and 2LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8712 0.9332 0.978 0.8937 0.9313 0.9567 0.9857 1.0014K (pos.) 0.8507 0.9182 0.9132 0.8935 0.9269 0.9498 0.9779 0.9942K (neg.) 1.0294 0.9545 1.1092 1.0932 0.9673 0.9906 1.018 1.0307Modified LRFD Fatigue Truck GVW = 56.888 kips

Axle Weight: Steer = 6.321 kips Drive = 25.283 kips Trailer = 25.283 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.827 0.8859 0.9283 0.8484 0.8841 0.9082 0.9357 0.9506K (pos.) 0.8075 0.8716 0.8668 0.8482 0.8798 0.9015 0.9282 0.9437K (neg.) 0.9771 0.906 1.0529 1.0378 0.9182 0.9403 0.9663 0.9784Site-Specific Fatigue Truck GVW = 56.888 kips

Axle Weight: Steer = 8.533 kips Drive = 24.462 kips Trailer = 23.893 kipsAxle Spacing: 19 ft 37 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8548 0.9674 0.9641 0.9858 0.982 0.9846 0.9889 0.9914K (pos.) 0.8347 0.9318 0.9486 0.9623 0.9718 0.9779 0.9847 0.9883K (neg.) 0.93 0.9854 0.9877 0.9949 1.0077 1.0006 0.9994 0.9995

Lanes 3 and 4LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.9231 1.0016 1.069 0.9814 1.0203 1.0457 1.0746 1.0904K (pos.) 0.8999 0.9858 0.9963 0.9772 1.0126 1.0364 1.0654 1.0822K (neg.) 1.1432 1.0253 1.197 1.1852 1.051 1.0751 1.1038 1.1179Modified LRFD Fatigue Truck GVW = 61.724 kips

Axle Weight: Steer = 6.858 kips Drive = 27.433 kips Trailer = 27.433 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8076 0.8763 0.9352 0.8586 0.8926 0.9148 0.9401 0.9539K (pos.) 0.7873 0.8625 0.8717 0.8549 0.8859 0.9067 0.9321 0.9468K (neg.) 1.0001 0.897 1.0472 1.0369 0.9195 0.9405 0.9657 0.978Site-Specific Fatigue Truck GVW = 61.724 kips

Axle Weight: Steer = 9.259 kips Drive = 26.541 kips Trailer = 25.924 kipsAxle Spacing: 19 ft 37 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8347 0.957 0.9713 0.9977 0.9915 0.9918 0.9936 0.9948K (pos.) 0.8137 0.922 0.9539 0.97 0.9785 0.9835 0.9888 0.9916K (neg.) 0.9519 0.9756 0.9824 0.9941 1.0091 1.0008 0.9988 0.9991

A - 170

Statistics Single Tandem Tridem QuadAxle Count 1996385 2440258 15219 83

Mean All Axles 9.354 24.884 34.024 35.217Std Dev All Axles 2.908 5.670 9.548 17.368

CoV All Axles 0.311 0.228 0.281 0.493

Mean Top 20% Axles 14.092 32.446 46.683 62.059Std Dev Top 20% Axles 2.090 2.260 3.466 3.944

CoV Top 20% Axles 0.148 0.070 0.074 0.064

Mean Top 5% Axles 16.753 35.552 51.557 67.000Std Dev Top 5% Axles 1.396 1.775 2.605 2.309

CoV Top 5% Axles 0.083 0.050 0.051 0.034

99th Percentile 16 36 52 68

WIM Site 3015 Axle Group Weight Statistics

WIM Site 3015Axle Group Weight Relative Frequency

Histogram

0

5

10

15

20

25

30

35

40

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

Axle Group Weight (kips)

Freq

uenc

y %

SingleTandemTridemQuad

A - 171

Statistics Single-Single Single-Tandem Tandem-Tandem All OthersEvent Count 5603 14159 8619 192

Mean All Events 18.645 34.113 49.724 54.219Std Dev All Events 4.280 6.514 8.197 12.042

CoV All Events 0.230 0.191 0.165 0.222

Mean Top 20% Events 25.180 42.921 60.520 70.842Std Dev Top 20% Events 2.386 2.770 3.289 5.016

CoV Top 20% Events 0.095 0.065 0.054 0.071

Mean Top 5% Events 28.586 46.771 65.181 77.600Std Dev Top 5% Events 1.893 2.316 2.661 2.836

CoV Top 5% Events 0.066 0.050 0.041 0.037

99th Percentile 28 46 66 78

WIM Site 3015 Two-Lane Multiple Presence Axle Load Statistics

WIM Site 3015Two-Lane MP Axle Loads

0

5

10

15

20

25

0 20 40 60 80 100 120 140 160 180 200

Axle Load (kips)

Freq

uenc

y %

Single-Single

Single-Tandem

Tandem-Tandem

AllOthers

A - 172

Implementation of Draft Protocols WIM Data Analysis

Mississippi

WIM Site 4506 – I-55

• GVW Histogram

• Single Truck Moment Histogram

• One-Lane and Two-Lane Moment Histogram

• One-Lane and Two-Lane Shear Histogram

• One-Lane and Two-lane Negative Moment Histogram

• Fatigue Adjustment Factor

• Axle Group Weight Histogram

A - 173

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 530152 477428

Mean All Trucks 62.557 52.169Std Dev All Trucks 17.810 16.210

CoV All Trucks 0.285 0.311

Mean Top 20% Trucks 85.398 75.869Std Dev Top 20% Trucks 7.629 7.882

CoV Top 20% Trucks 0.089 0.104

Mean Top 5% Trucks 95.928 86.934Std Dev Top 5% Trucks 7.113 6.359

CoV Top 5% Trucks 0.074 0.073

WIM Site 4506 Gross Vehicle Weight Statistics

WIM Site 4506Single Truck GVW Relative Frequencies

0

2

4

6

8

10

12

0 50 100 150 200

GVW (kips)

Freq

uenc

y %

Lanes 1 & 2Lanes 3 & 4

A - 174

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 530152 477428

Mean All Trucks 0.415 0.347Std Dev All Trucks 0.101 0.097

CoV All Trucks 0.244 0.279

Mean Top 20% Trucks 0.550 0.492Std Dev Top 20% Trucks 0.050 0.055

CoV Top 20% Trucks 0.090 0.111

Mean Top 5% Trucks 0.617 0.569Std Dev Top 5% Trucks 0.047 0.047

CoV Top 5% Trucks 0.076 0.082

WIM Site 4506 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 4506HL93 Single Truck Simple-Span Moment

60 ft Span

0

2

4

6

8

10

12

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Moment Ratio (Mtruck/MHL93)

Freq

uenc

y %

Lanes 1&2Lanes 3&4

A - 175

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 531051 12736

Mean All Trucks 0.415 0.604Std Dev All Trucks 0.101 0.167

CoV All Trucks 0.244 0.276

Mean Top 20% Trucks 0.550 0.859Std Dev Top 20% Trucks 0.050 0.079

CoV Top 20% Trucks 0.090 0.092

Mean Top 5% Trucks 0.618 0.970Std Dev Top 5% Trucks 0.047 0.064

CoV Top 5% Trucks 0.076 0.066

WIM Site 4506 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 4506HL93 Simple-Span Moment Lanes 1&2

60 ft Span

0

2

4

6

8

10

12

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 176

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 531051 12736

Mean All Trucks 0.456 0.662Std Dev All Trucks 0.117 0.175

CoV All Trucks 0.257 0.265

Mean Top 20% Trucks 0.613 0.928Std Dev Top 20% Trucks 0.058 0.086

CoV Top 20% Trucks 0.095 0.093

Mean Top 5% Trucks 0.696 1.048Std Dev Top 5% Trucks 0.049 0.070

CoV Top 5% Trucks 0.071 0.067

WIM Site 4506 HL93 Simple-Span Shear Statistics - 60 ft Span

WIM Site 4506HL93 Simple-Span Shear Lanes 1&2

60 ft Span

0123456789

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Shear Ratio (VWIM/VHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 177

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 531051 12736

Mean All Trucks 0.404 0.615Std Dev All Trucks 0.117 0.157

CoV All Trucks 0.290 0.256

Mean Top 20% Trucks 0.556 0.852Std Dev Top 20% Trucks 0.049 0.085

CoV Top 20% Trucks 0.088 0.100

Mean Top 5% Trucks 0.624 0.973Std Dev Top 5% Trucks 0.046 0.063

CoV Top 5% Trucks 0.073 0.065

WIM Site 4506 HL93 Negative Moment Statistics - 60 ft Span

WIM Site 4506HL93 Negative Moment Lanes 1&2

60 ft Span

0123456789

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 178

WIM Site: 4506 Fatigue Adjustment Factor

Lanes 1 and 2LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.989 1.085 1.1689 1.0724 1.1116 1.1386 1.1696 1.1865K (pos.) 0.9659 1.0677 1.0879 1.0615 1.1003 1.1265 1.1583 1.1767K (neg.) 1.2711 1.0969 1.2976 1.2925 1.1404 1.1671 1.2003 1.2156Modified LRFD Fatigue Truck GVW = 67.128 kips

Axle Weight: Steer = 7.459 kips Drive = 29.835 kips Trailer = 29.835 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7956 0.8728 0.9403 0.8627 0.8942 0.9159 0.9409 0.9544K (pos.) 0.777 0.8589 0.8751 0.8539 0.8851 0.9062 0.9318 0.9466K (neg.) 1.0225 0.8824 1.0438 1.0397 0.9173 0.9389 0.9655 0.9779Site-Specific Fatigue Truck GVW = 67.128 kips

Axle Weight: Steer = 12.083 kips Drive = 28.194 kips Trailer = 26.851 kipsAxle Spacing: 19 ft 37.5 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8419 0.972 0.9746 1.0038 0.9942 0.9937 0.9948 0.9957K (pos.) 0.8222 0.9323 0.9566 0.9738 0.9809 0.9854 0.9901 0.9925K (neg.) 0.941 0.9872 0.9787 0.985 1.0176 1.0064 1.0029 1.0017

Lanes 3 and 4LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8358 0.9197 0.997 0.9105 0.9438 0.9663 0.9921 1.0061K (pos.) 0.8157 0.9051 0.9275 0.9022 0.9343 0.9561 0.9826 0.9979K (neg.) 1.0863 0.9251 1.0992 1.0981 0.9661 0.988 1.0164 1.0297Modified LRFD Fatigue Truck GVW = 56.879 kips

Axle Weight: Steer = 6.32 kips Drive = 25.28 kips Trailer = 25.28 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7935 0.8732 0.9465 0.8644 0.896 0.9174 0.9419 0.9552K (pos.) 0.7744 0.8592 0.8806 0.8566 0.887 0.9077 0.9329 0.9474K (neg.) 1.0313 0.8783 1.0436 1.0425 0.9172 0.938 0.965 0.9776Site-Specific Fatigue Truck GVW = 56.879 kips

Axle Weight: Steer = 10.238 kips Drive = 23.889 kips Trailer = 22.752 kipsAxle Spacing: 19 ft 37.5 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8397 0.9725 0.981 1.0058 0.9962 0.9953 0.9959 0.9966K (pos.) 0.8195 0.9326 0.9626 0.9768 0.9831 0.987 0.9913 0.9934K (neg.) 0.9491 0.9827 0.9785 0.9877 1.0174 1.0055 1.0024 1.0014

A - 179

Statistics Single Tandem Tridem QuadAxle Count 1510996 1652907 10075 241

Mean All Axles 11.240 24.696 33.065 27.905Std Dev All Axles 3.398 7.585 11.494 19.482

CoV All Axles 0.302 0.307 0.348 0.698

Mean Top 20% Axles 16.320 35.095 49.531 59.458Std Dev Top 20% Axles 2.117 3.786 6.248 10.689

CoV Top 20% Axles 0.130 0.108 0.126 0.180

Mean Top 5% Axles 19.180 40.331 58.381 75.000Std Dev Top 5% Axles 1.969 3.316 5.620 5.721

CoV Top 5% Axles 0.103 0.082 0.096 0.076

99th Percentile 18 40 60 78

WIM Site 4506 Axle Group Weight Statistics

WIM Site 4506Axle Group Weight Relative Frequency

Histogram

0

5

10

15

20

25

30

0 8 16 24 32 40 48 56 64 72 80 88 96

Axle Group Weight (kips)

Freq

uenc

y %

SingleTandemTridemQuad

A - 180

Statistics Single-Single Single-Tandem Tandem-Tandem All OthersEvent Count 4679 10034 5668 175

Mean All Events 22.472 35.875 49.363 52.474Std Dev All Events 4.956 8.479 10.979 15.398

CoV All Events 0.221 0.236 0.222 0.293

Mean Top 20% Events 29.686 47.753 64.672 74.143Std Dev Top 20% Events 2.916 4.237 4.967 8.179

CoV Top 20% Events 0.098 0.089 0.077 0.110

Mean Top 5% Events 33.684 53.653 71.530 85.000Std Dev Top 5% Events 2.668 3.682 4.322 5.196

CoV Top 5% Events 0.079 0.069 0.060 0.061

99th Percentile 34 54 72 84

WIM Site 4506 Two-Lane Multiple Presence Axle Load Statistics

WIM Site 4506Two-Lane MP Axle Loads

02468

1012141618

0 20 40 60 80 100 120 140 160 180 200

Axle Load (kips)

Freq

uenc

y %

Single-Single

Single-Tandem

Tandem-Tandem

AllOthers

A - 181

Implementation of Draft Protocols WIM Data Analysis

Mississippi

WIM Site 6104 – US49

• GVW Histogram

• Single Truck Moment Histogram

• One-Lane and Two-Lane Moment Histogram

• One-Lane and Two-Lane Shear Histogram

• One-Lane and Two-lane Negative Moment Histogram

• Fatigue Adjustment Factor

• Axle Group Weight Histogram

A - 182

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 461697 497190

Mean All Trucks 62.134 62.734Std Dev All Trucks 15.347 15.075

CoV All Trucks 0.247 0.240

Mean Top 20% Trucks 79.324 79.269Std Dev Top 20% Trucks 5.021 3.438

CoV Top 20% Trucks 0.063 0.043

Mean Top 5% Trucks 85.213 83.408Std Dev Top 5% Trucks 5.946 4.812

CoV Top 5% Trucks 0.070 0.058

WIM Site 6104 Gross Vehicle Weight Statistics

WIM Site 6104Single Truck GVW Relative Frequencies

02468

1012141618

0 50 100 150 200

GVW (kips)

Freq

uenc

y %

Lanes 1 & 2Lanes 3 & 4

A - 183

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 461697 497190

Mean All Trucks 0.407 0.416Std Dev All Trucks 0.082 0.075

CoV All Trucks 0.201 0.180

Mean Top 20% Trucks 0.509 0.505Std Dev Top 20% Trucks 0.037 0.031

CoV Top 20% Trucks 0.072 0.061

Mean Top 5% Trucks 0.556 0.539Std Dev Top 5% Trucks 0.039 0.046

CoV Top 5% Trucks 0.071 0.085

WIM Site 6104 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 6104HL93 Single Truck Simple-Span Moment

60 ft Span

0

2

4

6

8

10

12

14

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Moment Ratio (Mtruck/MHL93)

Freq

uenc

y %

Lanes 1&2Lanes 3&4

A - 184

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 462477 11149

Mean All Trucks 0.407 0.591Std Dev All Trucks 0.082 0.161

CoV All Trucks 0.201 0.273

Mean Top 20% Trucks 0.509 0.835Std Dev Top 20% Trucks 0.037 0.060

CoV Top 20% Trucks 0.072 0.072

Mean Top 5% Trucks 0.556 0.920Std Dev Top 5% Trucks 0.039 0.043

CoV Top 5% Trucks 0.071 0.047

WIM Site 6104 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 6104HL93 Simple-Span Moment Lanes 1&2

60 ft Span

0

2

4

6

8

10

12

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 185

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 462477 11149

Mean All Trucks 0.458 0.657Std Dev All Trucks 0.103 0.169

CoV All Trucks 0.226 0.257

Mean Top 20% Trucks 0.587 0.916Std Dev Top 20% Trucks 0.037 0.073

CoV Top 20% Trucks 0.063 0.080

Mean Top 5% Trucks 0.637 1.020Std Dev Top 5% Trucks 0.035 0.052

CoV Top 5% Trucks 0.055 0.051

WIM Site 6104 HL93 Simple-Span Shear Statistics - 60 ft Span

WIM Site 6104HL93 Simple-Span Shear Lanes 1&2

60 ft Span

0123456789

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Shear Ratio (VWIM/VHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 186

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 462477 11149

Mean All Trucks 0.398 0.600Std Dev All Trucks 0.101 0.145

CoV All Trucks 0.255 0.242

Mean Top 20% Trucks 0.514 0.817Std Dev Top 20% Trucks 0.030 0.070

CoV Top 20% Trucks 0.058 0.086

Mean Top 5% Trucks 0.552 0.918Std Dev Top 5% Trucks 0.034 0.050

CoV Top 5% Trucks 0.062 0.054

WIM Site 6104 HL93 Negative Moment Statistics - 60 ft Span

WIM Site 6104HL93 Negative Moment Lanes 1&2

60 ft Span

0

2

4

6

8

10

12

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 187

WIM Site: 6104 Fatigue Adjustment Factor

Lanes 1 and 2LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.9653 1.0524 1.1266 1.056 1.0942 1.1188 1.1468 1.162K (pos.) 0.943 1.0347 1.0496 1.0449 1.0823 1.1068 1.1362 1.153K (neg.) 1.206 1.0904 1.2571 1.2402 1.1234 1.1473 1.1754 1.1888Modified LRFD Fatigue Truck GVW = 65.505 kips

Axle Weight: Steer = 7.278 kips Drive = 29.114 kips Trailer = 29.114 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7957 0.8675 0.9288 0.8706 0.902 0.9223 0.9454 0.9579K (pos.) 0.7774 0.853 0.8653 0.8614 0.8922 0.9124 0.9367 0.9505K (neg.) 0.9942 0.8989 1.0363 1.0224 0.926 0.9458 0.969 0.98Site-Specific Fatigue Truck GVW = 65.505 kips

Axle Weight: Steer = 10.481 kips Drive = 28.167 kips Trailer = 26.857 kipsAxle Spacing: 19 ft 33.5 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8225 0.9463 0.9573 0.9413 0.9532 0.9626 0.9736 0.9796K (pos.) 0.8035 0.9096 0.9401 0.9291 0.9454 0.956 0.9686 0.9756K (neg.) 0.9307 0.9613 1.001 1.0243 0.9834 0.9848 0.9905 0.9937

Lanes 3 and 4LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.9566 1.053 1.1428 1.0609 1.1007 1.1262 1.1548 1.1704K (pos.) 0.9345 1.0357 1.0634 1.0503 1.0887 1.1139 1.1439 1.1611K (neg.) 1.228 1.0858 1.2674 1.2569 1.1244 1.1508 1.182 1.1964Modified LRFD Fatigue Truck GVW = 65.972 kips

Axle Weight: Steer = 7.33 kips Drive = 29.321 kips Trailer = 29.321 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.783 0.8619 0.9354 0.8684 0.9009 0.9218 0.9453 0.958K (pos.) 0.7649 0.8478 0.8704 0.8597 0.8911 0.9117 0.9363 0.9504K (neg.) 1.0051 0.8887 1.0374 1.0288 0.9203 0.942 0.9675 0.9793Site-Specific Fatigue Truck GVW = 65.972 kips

Axle Weight: Steer = 10.556 kips Drive = 28.368 kips Trailer = 27.049 kipsAxle Spacing: 19 ft 33.5 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8093 0.9401 0.9642 0.9389 0.9521 0.962 0.9735 0.9797K (pos.) 0.7906 0.9041 0.9457 0.9273 0.9443 0.9553 0.9682 0.9755K (neg.) 0.9409 0.9504 1.0021 1.0307 0.9773 0.9808 0.9889 0.993

A - 188

Statistics Single Tandem Tridem QuadAxle Count 1598410 1490366 10044 437

Mean All Axles 11.405 27.725 37.358 39.403Std Dev All Axles 3.197 5.638 10.257 18.610

CoV All Axles 0.280 0.203 0.275 0.472

Mean Top 20% Axles 16.278 34.388 49.782 67.069Std Dev Top 20% Axles 1.162 1.509 2.463 5.251

CoV Top 20% Axles 0.071 0.044 0.049 0.078

Mean Top 5% Axles 17.405 36.128 53.016 74.182Std Dev Top 5% Axles 0.860 1.477 1.925 3.838

CoV Top 5% Axles 0.049 0.041 0.036 0.052

99th Percentile 16 36 52 74

WIM Site 6104 Axle Group Weight Statistics

WIM Site 6104Axle Group Weight Relative Frequency

Histogram

0

5

10

15

20

25

30

35

0 8 16 24 32 40 48 56 64 72 80 88 96

Axle Group Weight (kips)

Freq

uenc

y %

SingleTandemTridemQuad

A - 189

Statistics Single-Single Single-Tandem Tandem-Tandem All OthersEvent Count 5510 9970 4855 158

Mean All Events 22.804 39.159 55.303 56.734Std Dev All Events 4.506 6.437 8.038 16.140

CoV All Events 0.198 0.164 0.145 0.284

Mean Top 20% Events 29.261 47.346 65.573 79.000Std Dev Top 20% Events 2.299 2.340 2.454 7.687

CoV Top 20% Events 0.079 0.049 0.037 0.097

Mean Top 5% Events 32.522 50.554 68.844 89.500Std Dev Top 5% Events 1.458 1.620 1.948 8.332

CoV Top 5% Events 0.045 0.032 0.028 0.093

99th Percentile 32 50 68 90

WIM Site 6104 Two-Lane Multiple Presence Axle Load Statistics

WIM Site 6104Two-Lane MP Axle Loads

0

5

10

15

20

25

0 20 40 60 80 100 120 140 160 180 200

Axle Load (kips)

Freq

uenc

y %

Single-Single

Single-Tandem

Tandem-Tandem

AllOthers

A - 190

Implementation of Draft Protocols WIM Data Analysis

Mississippi

WIM Site 7900 – US61

• GVW Histogram

• Single Truck Moment Histogram

• One-Lane and Two-Lane Moment Histogram

• One-Lane and Two-Lane Shear Histogram

• One-Lane and Two-lane Negative Moment Histogram

• Fatigue Adjustment Factor

• Axle Group Weight Histogram

A - 191

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 69928 68069

Mean All Trucks 52.363 55.769Std Dev All Trucks 19.123 17.380

CoV All Trucks 0.365 0.312

Mean Top 20% Trucks 80.868 79.426Std Dev Top 20% Trucks 10.137 5.395

CoV Top 20% Trucks 0.125 0.068

Mean Top 5% Trucks 95.561 85.765Std Dev Top 5% Trucks 6.782 6.248

CoV Top 5% Trucks 0.071 0.073

WIM Site 7900 Gross Vehicle Weight Statistics

WIM Site 7900Single Truck GVW Relative Frequencies

0

2

4

6

8

10

12

0 50 100 150 200

GVW (kips)

Freq

uenc

y %

Lanes 1 & 2Lanes 3 & 4

A - 192

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 69928 68069

Mean All Trucks 0.354 0.377Std Dev All Trucks 0.116 0.103

CoV All Trucks 0.328 0.273

Mean Top 20% Trucks 0.528 0.521Std Dev Top 20% Trucks 0.069 0.039

CoV Top 20% Trucks 0.131 0.076

Mean Top 5% Trucks 0.626 0.572Std Dev Top 5% Trucks 0.055 0.042

CoV Top 5% Trucks 0.087 0.074

WIM Site 7900 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 7900HL93 Single Truck Simple-Span Moment

60 ft Span

0

1

2

3

4

5

6

7

8

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Moment Ratio (Mtruck/MHL93)

Freq

uenc

y %

Lanes 1&2Lanes 3&4

A - 193

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 70045 809

Mean All Trucks 0.354 0.513Std Dev All Trucks 0.116 0.159

CoV All Trucks 0.328 0.311

Mean Top 20% Trucks 0.528 0.753Std Dev Top 20% Trucks 0.069 0.094

CoV Top 20% Trucks 0.131 0.125

Mean Top 5% Trucks 0.626 0.888Std Dev Top 5% Trucks 0.055 0.079

CoV Top 5% Trucks 0.088 0.089

WIM Site 7900 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 7900HL93 Simple-Span Moment Lanes 1&2

60 ft Span

012345678

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 194

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 70045 809

Mean All Trucks 0.388 0.562Std Dev All Trucks 0.137 0.175

CoV All Trucks 0.354 0.311

Mean Top 20% Trucks 0.596 0.820Std Dev Top 20% Trucks 0.078 0.110

CoV Top 20% Trucks 0.131 0.134

Mean Top 5% Trucks 0.710 0.978Std Dev Top 5% Trucks 0.057 0.099

CoV Top 5% Trucks 0.081 0.101

WIM Site 7900 HL93 Simple-Span Shear Statistics - 60 ft Span

WIM Site 7900HL93 Simple-Span Shear Lanes 1&2

60 ft Span

012345678

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Shear Ratio (VWIM/VHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 195

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 70045 809

Mean All Trucks 0.337 0.517Std Dev All Trucks 0.126 0.153

CoV All Trucks 0.372 0.296

Mean Top 20% Trucks 0.525 0.738Std Dev Top 20% Trucks 0.065 0.097

CoV Top 20% Trucks 0.124 0.132

Mean Top 5% Trucks 0.619 0.875Std Dev Top 5% Trucks 0.045 0.094

CoV Top 5% Trucks 0.072 0.107

WIM Site 7900 HL93 Negative Moment Statistics - 60 ft Span

WIM Site 7900HL93 Negative Moment Lanes 1&2

60 ft Span

0123456789

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 196

WIM Site: 7900 Fatigue Adjustment Factor

Lanes 1 and 2LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8715 0.9631 1.0422 0.9701 1.0002 1.0192 1.0406 1.0522K (pos.) 0.8502 0.9481 0.9708 0.9611 0.9903 1.0093 1.032 1.0449K (neg.) 1.1372 0.9895 1.1383 1.1234 1.0163 1.0363 1.0604 1.0714Modified LRFD Fatigue Truck GVW = 58.917 kips

Axle Weight: Steer = 6.546 kips Drive = 26.185 kips Trailer = 26.185 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7987 0.8828 0.9552 0.8892 0.9168 0.9342 0.9538 0.9644K (pos.) 0.7793 0.869 0.8898 0.8809 0.9077 0.9251 0.9459 0.9577K (neg.) 1.0423 0.9069 1.0433 1.0296 0.9315 0.9499 0.9719 0.982Site-Specific Fatigue Truck GVW = 58.917 kips

Axle Weight: Steer = 11.194 kips Drive = 25.334 kips Trailer = 22.388 kipsAxle Spacing: 19 ft 33.5 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8256 0.9596 0.9629 0.9437 0.9563 0.9652 0.9755 0.9811K (pos.) 0.8054 0.92 0.9462 0.9381 0.9519 0.9611 0.972 0.9782K (neg.) 0.9294 0.9889 1.0085 1.0228 0.9909 0.9905 0.9944 0.9963

Lanes 3 and 4LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8965 0.9933 1.077 1.0125 1.0403 1.0578 1.0776 1.0884K (pos.) 0.8728 0.9779 1.0039 1.0004 1.0287 1.047 1.0687 1.081K (neg.) 1.1759 1.0211 1.1654 1.1487 1.0527 1.0724 1.0953 1.1058Modified LRFD Fatigue Truck GVW = 60.725 kips

Axle Weight: Steer = 6.747 kips Drive = 26.989 kips Trailer = 26.989 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7972 0.8833 0.9577 0.9004 0.9251 0.9406 0.9583 0.9679K (pos.) 0.7762 0.8696 0.8927 0.8896 0.9148 0.9311 0.9503 0.9613K (neg.) 1.0457 0.908 1.0363 1.0215 0.9361 0.9536 0.974 0.9833Site-Specific Fatigue Truck GVW = 60.725 kips

Axle Weight: Steer = 11.538 kips Drive = 26.112 kips Trailer = 23.075 kipsAxle Spacing: 19 ft 33.5 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.824 0.9602 0.9655 0.9556 0.965 0.9719 0.9801 0.9847K (pos.) 0.8023 0.9207 0.9493 0.9473 0.9594 0.9673 0.9766 0.9818K (neg.) 0.9324 0.99 1.0018 1.0148 0.9959 0.9944 0.9965 0.9977

A - 197

Statistics Single Tandem Tridem QuadAxle Count 179146 241958 2745 71

Mean All Axles 10.295 22.878 29.959 18.634Std Dev All Axles 2.998 8.423 12.419 14.640

CoV All Axles 0.291 0.368 0.415 0.786

Mean Top 20% Axles 14.778 34.689 48.275 36.714Std Dev Top 20% Axles 2.009 3.471 5.137 26.275

CoV Top 20% Axles 0.136 0.100 0.106 0.716

Mean Top 5% Axles 17.618 39.553 55.336 76.500Std Dev Top 5% Axles 1.572 3.001 4.177 4.123

CoV Top 5% Axles 0.089 0.076 0.075 0.054

99th Percentile 16 40 56 78

WIM Site 7900 Axle Group Weight Statistics

WIM Site 7900Axle Group Weight Relative Frequency

Histogram

0

5

10

15

20

25

30

35

40

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

Axle Group Weight (kips)

Freq

uenc

y %

SingleTandemTridemQuad

A - 198

Statistics Single-Single Single-Tandem Tandem-Tandem All OthersEvent Count 254 582 381 16

Mean All Events 20.362 32.725 44.654 42.750Std Dev All Events 4.354 9.372 11.278 16.731

CoV All Events 0.214 0.286 0.253 0.391

Mean Top 20% Events 26.725 46.172 60.684 69.000Std Dev Top 20% Events 2.714 4.188 4.954 12.166

CoV Top 20% Events 0.102 0.091 0.082 0.176

Mean Top 5% Events 30.385 51.966 67.526 77.000Std Dev Top 5% Events 2.755 4.093 4.101 0.000

CoV Top 5% Events 0.091 0.079 0.061 0.000

99th Percentile 32 52 68 76

WIM Site 7900 Two-Lane Multiple Presence Axle Load Statistics

WIM Site 7900Two-Lane MP Axle Loads

0

5

10

15

20

25

0 20 40 60 80 100 120 140 160 180 200

Axle Load (kips)

Freq

uenc

y %

Single-Single

Single-Tandem

Tandem-Tandem

AllOthers

A - 199

Implementation of Draft Protocols WIM Data Analysis

Texas

WIM Site 0506

• GVW Histogram

• Single Truck Moment Histogram

• One-Lane and Two-Lane Moment Histogram

• One-Lane and Two-Lane Shear Histogram

• One-Lane and Two-lane Negative Moment Histogram

• Fatigue Adjustment Factor

• Axle Group Weight Histogram

A - 200

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 558629 519230

Mean All Trucks 58.515 56.893Std Dev All Trucks 17.011 19.449

CoV All Trucks 0.291 0.342

Mean Top 20% Trucks 77.955 79.000Std Dev Top 20% Trucks 3.576 2.650

CoV Top 20% Trucks 0.046 0.034

Mean Top 5% Trucks 82.018 82.000Std Dev Top 5% Trucks 4.267 4.011

CoV Top 5% Trucks 0.052 0.049

WIM Site 0506 Gross Vehicle Weight Statistics

WIM Site 0506Single Truck GVW Relative Frequencies

02468

101214161820

0 50 100 150 200

GVW (kips)

Freq

uenc

y %

Lanes 1 & 2Lanes 3 & 4

A - 201

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 558629 519230

Mean All Trucks 0.381 0.377Std Dev All Trucks 0.098 0.110

CoV All Trucks 0.258 0.292

Mean Top 20% Trucks 0.499 0.506Std Dev Top 20% Trucks 0.032 0.025

CoV Top 20% Trucks 0.065 0.050

Mean Top 5% Trucks 0.540 0.535Std Dev Top 5% Trucks 0.039 0.033

CoV Top 5% Trucks 0.073 0.062

WIM Site 0506 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 0506HL93 Single Truck Simple-Span Moment

60 ft Span

0

2

4

6

8

10

12

14

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Moment Ratio (Mtruck/MHL93)

Freq

uenc

y %

Lanes 1&2Lanes 3&4

A - 202

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 559660 13864

Mean All Trucks 0.381 0.556Std Dev All Trucks 0.098 0.156

CoV All Trucks 0.258 0.281

Mean Top 20% Trucks 0.499 0.799Std Dev Top 20% Trucks 0.032 0.067

CoV Top 20% Trucks 0.065 0.084

Mean Top 5% Trucks 0.540 0.892Std Dev Top 5% Trucks 0.039 0.043

CoV Top 5% Trucks 0.073 0.048

WIM Site 0506 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 0506HL93 Simple-Span Moment Lanes 1&2

60 ft Span

0

2

4

6

8

10

12

14

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 203

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 559660 13864

Mean All Trucks 0.419 0.609Std Dev All Trucks 0.114 0.166

CoV All Trucks 0.272 0.272

Mean Top 20% Trucks 0.560 0.864Std Dev Top 20% Trucks 0.033 0.079

CoV Top 20% Trucks 0.059 0.091

Mean Top 5% Trucks 0.604 0.975Std Dev Top 5% Trucks 0.036 0.052

CoV Top 5% Trucks 0.059 0.053

WIM Site 0506 HL93 Simple-Span Shear Statistics - 60 ft Span

WIM Site 0506HL93 Simple-Span Shear Lanes 1&2

60 ft Span

0123456789

10

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Shear Ratio (VWIM/VHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 204

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 559660 13864

Mean All Trucks 0.378 0.570Std Dev All Trucks 0.113 0.148

CoV All Trucks 0.299 0.260

Mean Top 20% Trucks 0.511 0.794Std Dev Top 20% Trucks 0.025 0.075

CoV Top 20% Trucks 0.048 0.094

Mean Top 5% Trucks 0.543 0.901Std Dev Top 5% Trucks 0.028 0.053

CoV Top 5% Trucks 0.051 0.059

WIM Site 0506 HL93 Negative Moment Statistics - 60 ft Span

WIM Site 0506HL93 Negative Moment Lanes 1&2

60 ft Span

0

2

4

6

8

10

12

14

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 205

WIM Site: 0506 Fatigue Adjustment Factor

Lanes 1 and 2LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.9136 0.9931 1.0794 0.9889 1.0321 1.0608 1.093 1.1104K (pos.) 0.8939 0.9805 1.0054 0.9817 1.0223 1.0495 1.0822 1.1009K (neg.) 1.1794 1.0218 1.2198 1.2168 1.0654 1.089 1.1235 1.1396Modified LRFD Fatigue Truck GVW = 63.079 kips

Axle Weight: Steer = 7.009 kips Drive = 28.035 kips Trailer = 28.035 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7821 0.8502 0.9241 0.8466 0.8836 0.9081 0.9357 0.9506K (pos.) 0.7653 0.8394 0.8607 0.8404 0.8752 0.8984 0.9264 0.9424K (neg.) 1.0097 0.8747 1.0442 1.0417 0.912 0.9323 0.9618 0.9756Site-Specific Fatigue Truck GVW = 63.079 kips

Axle Weight: Steer = 12.616 kips Drive = 26.493 kips Trailer = 23.97 kipsAxle Spacing: 19 ft 37 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8276 0.9447 0.9435 0.9602 0.9652 0.9722 0.9805 0.985K (pos.) 0.8098 0.9066 0.9273 0.9419 0.9564 0.9656 0.976 0.9816K (neg.) 0.8997 0.9873 0.984 0.9884 1.0062 0.9962 0.9973 0.9983

Lanes 3 and 4LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.9121 0.9926 1.0841 0.9968 1.0377 1.0639 1.0932 1.109K (pos.) 0.8915 0.982 1.0098 0.9899 1.0278 1.0529 1.0829 1.1K (neg.) 1.1894 1.0224 1.212 1.2057 1.0607 1.0875 1.1201 1.135Modified LRFD Fatigue Truck GVW = 62.723 kips

Axle Weight: Steer = 6.969 kips Drive = 27.877 kips Trailer = 27.877 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7853 0.8546 0.9333 0.8582 0.8933 0.9159 0.9412 0.9548K (pos.) 0.7676 0.8454 0.8694 0.8522 0.8849 0.9065 0.9323 0.947K (neg.) 1.024 0.8802 1.0435 1.038 0.9132 0.9363 0.9643 0.9772Site-Specific Fatigue Truck GVW = 62.723 kips

Axle Weight: Steer = 12.545 kips Drive = 26.344 kips Trailer = 23.835 kipsAxle Spacing: 19 ft 37 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.831 0.9496 0.9529 0.9734 0.9759 0.9805 0.9862 0.9893K (pos.) 0.8122 0.9131 0.9367 0.9552 0.967 0.9742 0.9822 0.9864K (neg.) 0.9125 0.9936 0.9833 0.9849 1.0075 1.0004 0.9999 0.9999

A - 206

Statistics Single Tandem Tridem QuadAxle Count 1649570 1772433 12992 0

Mean All Axles 11.340 24.415 28.965 0.000Std Dev All Axles 3.008 8.599 12.513 0.000

CoV All Axles 0.265 0.352 0.432 0.000

Mean Top 20% Axles 15.955 34.173 46.105 0.000Std Dev Top 20% Axles 2.058 1.691 5.889 0.000

CoV Top 20% Axles 0.129 0.049 0.128 0.000

Mean Top 5% Axles 18.307 36.210 54.606 0.000Std Dev Top 5% Axles 1.484 1.917 4.325 0.000

CoV Top 5% Axles 0.081 0.053 0.079 0.000

99th Percentile 18 36 56 0

WIM Site 0506 Axle Group Weight Statistics

WIM Site 0506Axle Group Weight Relative Frequency

Histogram

0

10

20

30

40

50

60

0 8 16 24 32 40 48 56 64 72 80 88 96

Axle Group Weight (kips)

Freq

uenc

y %

SingleTandemTridemQuad

A - 207

Statistics Single-Single Single-Tandem Tandem-Tandem All OthersEvent Count 5092 11095 6025 188

Mean All Events 22.755 35.779 48.807 48.032Std Dev All Events 4.305 9.058 12.119 15.678

CoV All Events 0.189 0.253 0.248 0.326

Mean Top 20% Events 29.138 46.973 64.914 70.947Std Dev Top 20% Events 2.551 2.694 2.829 7.591

CoV Top 20% Events 0.088 0.057 0.044 0.107

Mean Top 5% Events 32.788 50.762 68.595 82.111Std Dev Top 5% Events 2.287 2.190 2.211 4.014

CoV Top 5% Events 0.070 0.043 0.032 0.049

99th Percentile 32 50 68 84

WIM Site 0506 Two-Lane Multiple Presence Axle Load Statistics

WIM Site 0506Two-Lane MP Axle Loads

0

5

10

15

20

25

30

35

0 20 40 60 80 100 120 140 160 180 200

Axle Load (kips)

Freq

uenc

y %

Single-Single

Single-Tandem

Tandem-Tandem

AllOthers

A - 208

Implementation of Draft Protocols WIM Data Analysis

Texas

WIM Site 0516

• GVW Histogram

• Single Truck Moment Histogram

• One-Lane and Two-Lane Moment Histogram

• One-Lane and Two-Lane Shear Histogram

• One-Lane and Two-lane Negative Moment Histogram

• Fatigue Adjustment Factor

• Axle Group Weight Histogram

A - 209

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 717135 707088

Mean All Trucks 50.782 54.060Std Dev All Trucks 16.469 16.099

CoV All Trucks 0.324 0.298

Mean Top 20% Trucks 73.507 75.145Std Dev Top 20% Trucks 4.388 4.066

CoV Top 20% Trucks 0.060 0.054

Mean Top 5% Trucks 79.592 80.283Std Dev Top 5% Trucks 3.364 3.507

CoV Top 5% Trucks 0.042 0.044

WIM Site 0516 Gross Vehicle Weight Statistics

WIM Site 0516Single Truck GVW Relative Frequencies

0123456789

10

0 50 100 150 200

GVW (kips)

Freq

uenc

y %

Lanes 1 & 2Lanes 3 & 4

A - 210

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 717135 707088

Mean All Trucks 0.339 0.361Std Dev All Trucks 0.097 0.096

CoV All Trucks 0.285 0.266

Mean Top 20% Trucks 0.471 0.486Std Dev Top 20% Trucks 0.033 0.030

CoV Top 20% Trucks 0.069 0.061

Mean Top 5% Trucks 0.514 0.527Std Dev Top 5% Trucks 0.031 0.027

CoV Top 5% Trucks 0.059 0.051

WIM Site 0516 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 0516HL93 Single Truck Simple-Span Moment

60 ft Span

0123456789

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Moment Ratio (Mtruck/MHL93)

Freq

uenc

y %

Lanes 1&2Lanes 3&4

A - 211

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 718382 17481

Mean All Trucks 0.339 0.497Std Dev All Trucks 0.097 0.143

CoV All Trucks 0.285 0.288

Mean Top 20% Trucks 0.471 0.718Std Dev Top 20% Trucks 0.033 0.074

CoV Top 20% Trucks 0.069 0.102

Mean Top 5% Trucks 0.514 0.824Std Dev Top 5% Trucks 0.031 0.048

CoV Top 5% Trucks 0.059 0.058

WIM Site 0516 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 0516HL93 Simple-Span Moment Lanes 1&2

60 ft Span

012345678

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 212

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 718382 17481

Mean All Trucks 0.369 0.540Std Dev All Trucks 0.108 0.153

CoV All Trucks 0.293 0.283

Mean Top 20% Trucks 0.523 0.773Std Dev Top 20% Trucks 0.039 0.082

CoV Top 20% Trucks 0.074 0.106

Mean Top 5% Trucks 0.575 0.889Std Dev Top 5% Trucks 0.033 0.056

CoV Top 5% Trucks 0.058 0.063

WIM Site 0516 HL93 Simple-Span Shear Statistics - 60 ft Span

WIM Site 0516HL93 Simple-Span Shear Lanes 1&2

60 ft Span

0

1

2

3

4

5

6

7

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Shear Ratio (VWIM/VHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 213

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 718382 17481

Mean All Trucks 0.331 0.505Std Dev All Trucks 0.110 0.138

CoV All Trucks 0.331 0.274

Mean Top 20% Trucks 0.482 0.712Std Dev Top 20% Trucks 0.029 0.074

CoV Top 20% Trucks 0.061 0.105

Mean Top 5% Trucks 0.523 0.818Std Dev Top 5% Trucks 0.023 0.059

CoV Top 5% Trucks 0.045 0.072

WIM Site 0516 HL93 Negative Moment Statistics - 60 ft Span

WIM Site 0516HL93 Negative Moment Lanes 1&2

60 ft Span

012345678

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 214

WIM Site: 0516 Fatigue Adjustment Factor

Lanes 1 and 2LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8412 0.9068 0.9729 0.8778 0.912 0.9361 0.9641 0.9793K (pos.) 0.8237 0.895 0.9076 0.8726 0.9049 0.9274 0.9551 0.9712K (neg.) 1.0679 0.902 1.0847 1.0844 0.9422 0.9603 0.9909 1.0049Modified LRFD Fatigue Truck GVW = 55.61 kips

Axle Weight: Steer = 6.179 kips Drive = 24.716 kips Trailer = 24.716 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8168 0.8806 0.9448 0.8524 0.8855 0.909 0.9362 0.9509K (pos.) 0.7999 0.8691 0.8813 0.8474 0.8787 0.9006 0.9275 0.9431K (neg.) 1.0369 0.8759 1.0533 1.053 0.9149 0.9325 0.9622 0.9758Site-Specific Fatigue Truck GVW = 55.61 kips

Axle Weight: Steer = 11.122 kips Drive = 22.8 kips Trailer = 21.688 kipsAxle Spacing: 19 ft 38 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8854 1.0017 0.9846 1.0011 0.9908 0.991 0.9931 0.9945K (pos.) 0.8671 0.9604 0.9693 0.9766 0.9813 0.9852 0.9896 0.9921K (neg.) 0.9393 1.0005 0.9862 0.9882 1.0239 1.006 1.0028 1.0017

Lanes 3 and 4LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8797 0.9536 1.0261 0.9267 0.9616 0.9862 1.0147 1.0302K (pos.) 0.8612 0.9406 0.9568 0.9207 0.9538 0.977 1.0054 1.0218K (neg.) 1.1201 0.9479 1.1374 1.138 0.9918 1.0098 1.0414 1.056Modified LRFD Fatigue Truck GVW = 58.422 kips

Axle Weight: Steer = 6.491 kips Drive = 25.966 kips Trailer = 25.966 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8131 0.8814 0.9484 0.8565 0.8888 0.9116 0.9379 0.9522K (pos.) 0.796 0.8694 0.8844 0.851 0.8816 0.903 0.9293 0.9445K (neg.) 1.0353 0.8761 1.0513 1.0518 0.9167 0.9334 0.9626 0.976Site-Specific Fatigue Truck GVW = 58.422 kips

Axle Weight: Steer = 11.684 kips Drive = 23.953 kips Trailer = 22.785 kipsAxle Spacing: 19 ft 38 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8814 1.0026 0.9884 1.006 0.9945 0.9937 0.9949 0.9959K (pos.) 0.8629 0.9607 0.9727 0.9807 0.9847 0.9879 0.9915 0.9935K (neg.) 0.9378 1.0007 0.9843 0.9871 1.026 1.0069 1.0032 1.0019

A - 215

Statistics Single Tandem Tridem QuadAxle Count 1998727 2359860 4022 0

Mean All Axles 10.822 22.481 28.529 0.000Std Dev All Axles 2.805 7.601 11.737 0.000

CoV All Axles 0.259 0.338 0.411 0.000

Mean Top 20% Axles 14.835 32.682 46.040 0.000Std Dev Top 20% Axles 2.171 2.212 6.458 0.000

CoV Top 20% Axles 0.146 0.068 0.140 0.000

Mean Top 5% Axles 17.989 35.708 55.169 0.000Std Dev Top 5% Axles 1.449 1.957 5.291 0.000

CoV Top 5% Axles 0.081 0.055 0.096 0.000

99th Percentile 18 36 56 0

WIM Site 0516 Axle Group Weight Statistics

WIM Site 0516Axle Group Weight Relative Frequency

Histogram

05

1015202530354045

0 8 16 24 32 40 48 56 64 72 80 88 96

Axle Group Weight (kips)

Freq

uenc

y %

SingleTandemTridemQuad

A - 216

Statistics Single-Single Single-Tandem Tandem-Tandem All OthersEvent Count 5757 13411 8176 69

Mean All Events 21.416 33.126 44.944 53.841Std Dev All Events 3.858 8.133 10.701 15.876

CoV All Events 0.180 0.246 0.238 0.295

Mean Top 20% Events 27.045 44.119 59.884 76.571Std Dev Top 20% Events 2.350 2.960 3.836 4.972

CoV Top 20% Events 0.087 0.067 0.064 0.065

Mean Top 5% Events 30.354 48.154 65.191 82.333Std Dev Top 5% Events 1.900 2.579 2.718 1.155

CoV Top 5% Events 0.063 0.054 0.042 0.014

99th Percentile 30 48 66 82

WIM Site 0516 Two-Lane Multiple Presence Axle Load Statistics

WIM Site 0516Two-Lane MP Axle Loads

0

5

10

15

20

25

30

0 20 40 60 80 100 120 140 160 180 200

Axle Load (kips)

Freq

uenc

y %

Single-Single

Single-Tandem

Tandem-Tandem

AllOthers

A - 217

Implementation of Draft Protocols WIM Data Analysis

Texas

WIM Site 0523

• GVW Histogram

• Single Truck Moment Histogram

• One-Lane and Two-Lane Moment Histogram

• One-Lane and Two-Lane Shear Histogram

• One-Lane and Two-lane Negative Moment Histogram

• Fatigue Adjustment Factor

• Axle Group Weight Histogram

A - 218

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 428669 392886

Mean All Trucks 53.961 56.205Std Dev All Trucks 20.240 19.016

CoV All Trucks 0.375 0.338

Mean Top 20% Trucks 81.205 80.139Std Dev Top 20% Trucks 3.933 4.006

CoV Top 20% Trucks 0.048 0.050

Mean Top 5% Trucks 85.452 84.562Std Dev Top 5% Trucks 5.097 5.610

CoV Top 5% Trucks 0.060 0.066

WIM Site 0523 Gross Vehicle Weight Statistics

WIM Site 0523Single Truck GVW Relative Frequencies

0

2

4

6

8

10

12

14

16

0 50 100 150 200

GVW (kips)

Freq

uenc

y %

Lanes 1 & 2Lanes 3 & 4

A - 219

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 428669 392886

Mean All Trucks 0.356 0.375Std Dev All Trucks 0.115 0.112

CoV All Trucks 0.324 0.299

Mean Top 20% Trucks 0.513 0.519Std Dev Top 20% Trucks 0.034 0.035

CoV Top 20% Trucks 0.066 0.068

Mean Top 5% Trucks 0.553 0.562Std Dev Top 5% Trucks 0.044 0.043

CoV Top 5% Trucks 0.080 0.077

WIM Site 0523 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 0523HL93 Single Truck Simple-Span Moment

60 ft Span

0

2

4

6

8

10

12

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Moment Ratio (Mtruck/MHL93)

Freq

uenc

y %

Lanes 1&2Lanes 3&4

A - 220

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 429398 10443

Mean All Trucks 0.356 0.528Std Dev All Trucks 0.115 0.165

CoV All Trucks 0.324 0.313

Mean Top 20% Trucks 0.513 0.782Std Dev Top 20% Trucks 0.034 0.091

CoV Top 20% Trucks 0.066 0.116

Mean Top 5% Trucks 0.553 0.912Std Dev Top 5% Trucks 0.044 0.052

CoV Top 5% Trucks 0.080 0.058

WIM Site 0523 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 0523HL93 Simple-Span Moment Lanes 1&2

60 ft Span

0

2

4

6

8

10

12

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 221

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 429398 10443

Mean All Trucks 0.396 0.581Std Dev All Trucks 0.138 0.181

CoV All Trucks 0.348 0.312

Mean Top 20% Trucks 0.591 0.854Std Dev Top 20% Trucks 0.040 0.104

CoV Top 20% Trucks 0.068 0.122

Mean Top 5% Trucks 0.642 1.004Std Dev Top 5% Trucks 0.046 0.064

CoV Top 5% Trucks 0.072 0.064

WIM Site 0523 HL93 Simple-Span Shear Statistics - 60 ft Span

WIM Site 0523HL93 Simple-Span Shear Lanes 1&2

60 ft Span

0123456789

10

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Shear Ratio (VWIM/VHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 222

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 429398 10443

Mean All Trucks 0.349 0.539Std Dev All Trucks 0.134 0.164

CoV All Trucks 0.383 0.304

Mean Top 20% Trucks 0.531 0.781Std Dev Top 20% Trucks 0.025 0.093

CoV Top 20% Trucks 0.047 0.119

Mean Top 5% Trucks 0.561 0.915Std Dev Top 5% Trucks 0.032 0.071

CoV Top 5% Trucks 0.056 0.077

WIM Site 0523 HL93 Negative Moment Statistics - 60 ft Span

WIM Site 0523HL93 Negative Moment Lanes 1&2

60 ft Span

0

2

4

6

8

10

12

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 223

WIM Site: 0523 Fatigue Adjustment Factor

Lanes 1 and 2LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8965 0.9699 1.0456 0.9633 1.0041 1.0304 1.0598 1.0756K (pos.) 0.8773 0.9569 0.975 0.957 0.9947 1.0197 1.0496 1.0668K (neg.) 1.1482 0.9998 1.1818 1.1742 1.0342 1.0572 1.0884 1.1027Modified LRFD Fatigue Truck GVW = 60.914 kips

Axle Weight: Steer = 6.768 kips Drive = 27.073 kips Trailer = 27.073 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7947 0.8598 0.9269 0.8539 0.8901 0.9134 0.9395 0.9535K (pos.) 0.7777 0.8483 0.8644 0.8484 0.8818 0.9039 0.9305 0.9457K (neg.) 1.0179 0.8863 1.0477 1.0409 0.9168 0.9372 0.9649 0.9775Site-Specific Fatigue Truck GVW = 60.914 kips

Axle Weight: Steer = 12.792 kips Drive = 25.584 kips Trailer = 22.538 kipsAxle Spacing: 19 ft 38 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8409 0.9543 0.9395 0.9769 0.9782 0.9823 0.9874 0.9903K (pos.) 0.823 0.9139 0.9247 0.9562 0.9683 0.9756 0.9834 0.9874K (neg.) 0.8929 1.0188 0.9827 0.9752 1.0207 1.0077 1.0041 1.0026

Lanes 3 and 4LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.9162 1.0051 1.0858 0.9994 1.0351 1.0593 1.0868 1.1018K (pos.) 0.8955 0.9903 1.0118 0.9916 1.026 1.0492 1.0772 1.0934K (neg.) 1.1828 1.0265 1.2047 1.1978 1.0636 1.0838 1.1134 1.1272Modified LRFD Fatigue Truck GVW = 62.199 kips

Axle Weight: Steer = 6.911 kips Drive = 27.644 kips Trailer = 27.644 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7954 0.8726 0.9427 0.8677 0.8987 0.9196 0.9435 0.9565K (pos.) 0.7775 0.8597 0.8785 0.8609 0.8908 0.9109 0.9352 0.9492K (neg.) 1.0269 0.8912 1.0459 1.0399 0.9234 0.941 0.9667 0.9786Site-Specific Fatigue Truck GVW = 62.199 kips

Axle Weight: Steer = 13.062 kips Drive = 26.124 kips Trailer = 23.014 kipsAxle Spacing: 19 ft 38 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8417 0.9685 0.9554 0.9927 0.9876 0.9889 0.9917 0.9934K (pos.) 0.8227 0.9262 0.9398 0.9703 0.9782 0.9831 0.9884 0.9912K (neg.) 0.9008 1.0244 0.9811 0.9743 1.028 1.0117 1.006 1.0037

A - 224

Statistics Single Tandem Tridem QuadAxle Count 1063777 1452822 9605 0

Mean All Axles 11.053 22.889 28.863 0.000Std Dev All Axles 2.791 9.518 14.753 0.000

CoV All Axles 0.252 0.416 0.511 0.000

Mean Top 20% Axles 15.013 35.046 51.821 0.000Std Dev Top 20% Axles 2.488 2.019 6.717 0.000

CoV Top 20% Axles 0.166 0.058 0.130 0.000

Mean Top 5% Axles 18.537 37.708 60.771 0.000Std Dev Top 5% Axles 1.634 1.984 4.676 0.000

CoV Top 5% Axles 0.088 0.053 0.077 0.000

99th Percentile 18 36 62 0

WIM Site 0523 Axle Group Weight Statistics

WIM Site 0523Axle Group Weight Relative Frequency

Histogram

0

10

20

30

40

50

60

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

Axle Group Weight (kips)

Freq

uenc

y %

SingleTandemTridemQuad

A - 225

Statistics Single-Single Single-Tandem Tandem-Tandem All OthersEvent Count 2732 7627 5216 157

Mean All Events 22.116 33.882 45.778 48.682Std Dev All Events 3.856 9.949 13.637 20.104

CoV All Events 0.174 0.294 0.298 0.413

Mean Top 20% Events 27.758 47.081 65.265 79.581Std Dev Top 20% Events 2.565 2.779 3.972 9.284

CoV Top 20% Events 0.092 0.059 0.061 0.117

Mean Top 5% Events 30.985 51.037 70.479 92.250Std Dev Top 5% Events 2.216 2.581 2.367 6.756

CoV Top 5% Events 0.072 0.051 0.034 0.073

99th Percentile 30 50 70 96

WIM Site 0523 Two-Lane Multiple Presence Axle Load Statistics

WIM Site 0523Two-Lane MP Axle Loads

0

5

10

15

20

25

30

35

0 20 40 60 80 100 120 140 160 180 200

Axle Load (kips)

Freq

uenc

y %

Single-Single

Single-Tandem

Tandem-Tandem

AllOthers

A - 226

Implementation of Draft Protocols WIM Data Analysis

Texas

WIM Site 0526

• GVW Histogram

• Single Truck Moment Histogram

• One-Lane and Two-Lane Moment Histogram

• One-Lane and Two-Lane Shear Histogram

• One-Lane and Two-lane Negative Moment Histogram

• Fatigue Adjustment Factor

• Axle Group Weight Histogram

A - 227

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 1328044 1171200

Mean All Trucks 55.512 56.592Std Dev All Trucks 18.027 18.103

CoV All Trucks 0.325 0.320

Mean Top 20% Trucks 78.403 78.089Std Dev Top 20% Trucks 3.925 4.772

CoV Top 20% Trucks 0.050 0.061

Mean Top 5% Trucks 82.773 83.577Std Dev Top 5% Trucks 5.181 6.256

CoV Top 5% Trucks 0.063 0.075

WIM Site 0526 Gross Vehicle Weight Statistics

WIM Site 0526Single Truck GVW Relative Frequencies

0

2

4

6

8

10

12

14

16

0 50 100 150 200

GVW (kips)

Freq

uenc

y %

Lanes 1 & 2Lanes 3 & 4

A - 228

Statistics Lanes 1 & 2 Lanes 3 & 4Truck Count 1328044 1171200

Mean All Trucks 0.363 0.370Std Dev All Trucks 0.105 0.106

CoV All Trucks 0.289 0.286

Mean Top 20% Trucks 0.500 0.501Std Dev Top 20% Trucks 0.035 0.045

CoV Top 20% Trucks 0.069 0.089

Mean Top 5% Trucks 0.540 0.554Std Dev Top 5% Trucks 0.045 0.062

CoV Top 5% Trucks 0.083 0.112

WIM Site 0526 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 0526HL93 Single Truck Simple-Span Moment

60 ft Span

0

2

4

6

8

10

12

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Moment Ratio (Mtruck/MHL93)

Freq

uenc

y %

Lanes 1&2Lanes 3&4

A - 229

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 1330594 53234

Mean All Trucks 0.363 0.529Std Dev All Trucks 0.105 0.155

CoV All Trucks 0.289 0.292

Mean Top 20% Trucks 0.500 0.769Std Dev Top 20% Trucks 0.035 0.079

CoV Top 20% Trucks 0.069 0.103

Mean Top 5% Trucks 0.540 0.880Std Dev Top 5% Trucks 0.045 0.053

CoV Top 5% Trucks 0.083 0.060

WIM Site 0526 HL93 Simple-Span Moment Statistics - 60 ft Span

WIM Site 0526HL93 Simple-Span Moment Lanes 1&2

60 ft Span

0123456789

10

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 230

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 1330594 53234

Mean All Trucks 0.399 0.578Std Dev All Trucks 0.121 0.165

CoV All Trucks 0.302 0.286

Mean Top 20% Trucks 0.562 0.832Std Dev Top 20% Trucks 0.040 0.089

CoV Top 20% Trucks 0.071 0.107

Mean Top 5% Trucks 0.610 0.957Std Dev Top 5% Trucks 0.051 0.058

CoV Top 5% Trucks 0.084 0.060

WIM Site 0526 HL93 Simple-Span Shear Statistics - 60 ft Span

WIM Site 0526HL93 Simple-Span Shear Lanes 1&2

60 ft Span

012345678

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Shear Ratio (VWIM/VHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 231

Statistics Lanes 1&2 - 1 Lane Event Lanes 1&2 - 2 Lane EventTruck Count 1330594 53234

Mean All Trucks 0.358 0.541Std Dev All Trucks 0.119 0.149

CoV All Trucks 0.332 0.276

Mean Top 20% Trucks 0.513 0.764Std Dev Top 20% Trucks 0.025 0.081

CoV Top 20% Trucks 0.049 0.105

Mean Top 5% Trucks 0.542 0.878Std Dev Top 5% Trucks 0.032 0.064

CoV Top 5% Trucks 0.058 0.072

WIM Site 0526 HL93 Negative Moment Statistics - 60 ft Span

WIM Site 0526HL93 Negative Moment Lanes 1&2

60 ft Span

0123456789

10

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Moment Ratio (MWIM/MHL93)

Rel

ativ

e Fr

eque

ncy

(%)

1-Lane Events2-Lane Events

A - 232

WIM Site: 0526 Fatigue Adjustment Factor

Lanes 1 and 2LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8813 0.962 1.0443 0.958 0.9991 1.0261 1.0563 1.0726K (pos.) 0.8624 0.9489 0.9725 0.9505 0.9892 1.0149 1.0458 1.0634K (neg.) 1.1455 0.9877 1.1771 1.1732 1.028 1.0524 1.0851 1.1Modified LRFD Fatigue Truck GVW = 60.836 kips

Axle Weight: Steer = 6.76 kips Drive = 27.038 kips Trailer = 27.038 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7823 0.8539 0.9269 0.8503 0.8869 0.9108 0.9376 0.9521K (pos.) 0.7655 0.8423 0.8632 0.8437 0.878 0.9009 0.9283 0.9439K (neg.) 1.0167 0.8767 1.0448 1.0414 0.9125 0.9341 0.9632 0.9764Site-Specific Fatigue Truck GVW = 60.836 kips

Axle Weight: Steer = 12.167 kips Drive = 25.551 kips Trailer = 23.118 kipsAxle Spacing: 19 ft 37.5 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.8278 0.9488 0.9464 0.9728 0.9746 0.9794 0.9855 0.9888K (pos.) 0.81 0.9097 0.9301 0.9511 0.9641 0.9721 0.9809 0.9855K (neg.) 0.9059 0.9949 0.9817 0.9827 1.0116 1.0015 1.0005 1.0003

Lanes 3 and 4LRFD Fatigue Truck GVW = 54 kips

Axle Weight: Steer = 6 kips Drive = 24 kips Trailer = 24 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.9166 0.9919 1.0648 0.9696 1.0099 1.0383 1.0707 1.0882K (pos.) 0.8961 0.9779 0.9924 0.9637 1.002 1.0284 1.0605 1.0791K (neg.) 1.1574 1.0054 1.2021 1.1996 1.0468 1.0688 1.1027 1.1185Modified LRFD Fatigue Truck GVW = 61.918 kips

Axle Weight: Steer = 6.88 kips Drive = 27.519 kips Trailer = 27.519 kipsAxle Spacing: 14 ft 30 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.7994 0.865 0.9287 0.8456 0.8808 0.9055 0.9338 0.9491K (pos.) 0.7815 0.8529 0.8655 0.8405 0.8739 0.8969 0.9249 0.9411K (neg.) 1.0094 0.8768 1.0484 1.0462 0.9129 0.9322 0.9617 0.9754Site-Specific Fatigue Truck GVW = 61.918 kips

Axle Weight: Steer = 12.384 kips Drive = 26.005 kips Trailer = 23.529 kipsAxle Spacing: 19 ft 37.5 ft

Span (ft) 20 40 60 80 100 120 160 200K (simple) 0.846 0.9612 0.9482 0.9674 0.9679 0.9737 0.9814 0.9857K (pos.) 0.827 0.9211 0.9325 0.9475 0.9596 0.9678 0.9773 0.9826K (neg.) 0.8993 0.995 0.985 0.9873 1.0121 0.9994 0.999 0.9993

A - 233

Statistics Single Tandem Tridem QuadAxle Count 3790839 4139191 29348 0

Mean All Axles 11.118 23.493 29.839 0.000Std Dev All Axles 3.071 8.627 13.915 0.000

CoV All Axles 0.276 0.367 0.466 0.000

Mean Top 20% Axles 15.610 34.270 50.718 0.000Std Dev Top 20% Axles 2.382 2.165 6.789 0.000

CoV Top 20% Axles 0.153 0.063 0.134 0.000

Mean Top 5% Axles 18.642 36.744 60.055 0.000Std Dev Top 5% Axles 1.782 2.916 4.486 0.000

CoV Top 5% Axles 0.096 0.079 0.075 0.000

99th Percentile 18 36 60 0

WIM Site 0526 Axle Group Weight Statistics

WIM Site 0526Axle Group Weight Relative Frequency

Histogram

05

101520253035404550

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

Axle Group Weight (kips)

Freq

uenc

y %

SingleTandemTridemQuad

A - 234

Statistics Single-Single Single-Tandem Tandem-Tandem All OthersEvent Count 18355 40071 21886 766

Mean All Events 22.196 34.532 47.017 48.572Std Dev All Events 4.333 9.102 12.294 17.604

CoV All Events 0.195 0.264 0.261 0.362

Mean Top 20% Events 28.566 46.217 63.981 73.980Std Dev Top 20% Events 2.560 3.035 3.944 9.879

CoV Top 20% Events 0.090 0.066 0.062 0.134

Mean Top 5% Events 32.004 50.330 69.174 87.684Std Dev Top 5% Events 2.361 2.851 3.603 10.052

CoV Top 5% Events 0.074 0.057 0.052 0.115

99th Percentile 32 50 68 96

WIM Site 0526 Two-Lane Multiple Presence Axle Load Statistics

WIM Site 0526Two-Lane MP Axle Loads

0

5

10

15

20

25

30

0 20 40 60 80 100 120 140 160 180 200

Axle Load (kips)

Freq

uenc

y %

Single-Single

Single-Tandem

Tandem-Tandem

AllOthers

A - 235

APPENDIX B Main Features of Selected Studies for Collecting and Using Traffic Data in Bridge Design The technical literature search resulted in the compilation of a reference list consisting of approximately 250 abstracts, research papers, journal articles, conference papers, and reports with applicability to the project research. Of the examined material, approximately 70 applicable documents were selected for further evaluation and possible summary preparation. A tabulated summary (given below) of approximately 40 documents was prepared from the reviewed material. Contained in each document summary is a brief study description, the study findings (if any), and recommendations for further research suggested by the authors (if any).

Reference

Study Description

Findings

Recommendations

Lui, Cornell and Imbsen Analysis of Bridge Truck Loads (1998)

Presents statistical analysis of truck loading variables including gross vehicle weight (GVW) data collected at several weigh-in-motion (WIM) sites on roadways of various functional classifications in Florida and Wisconsin. Discusses the application of WIM data and truck loading statistical analysis to site-specific load model development for bridge evaluation.

The upper tail of Florida GVW probability distribution data collected during this study is similar to the results of previous studies. The upper tail of collected Wisconsin GVW probability distribution data reveals two abnormalities in the data collected at several WIM sites: 1). Vehicles weighing in excess of 100 Kips, more than the 80 Kips legal limit, 2). Overloaded trucks weighing between 120 and 150 Kips.

Two distinct aspects of the site-specific load model for bridge rating are important: 1). Realistic assessment of the load level, 2). Uncertainty reduction associated with loads. To manage an aging infrastructure with limited available resources, site-specific load model development for bridge evaluation must critically assess the uncertainties of the random variables that make up the model.

Moses, Ghosn and Snyder Application of Load Spectra to Bridge Rating (1984)

Presents methods of acquiring and applying live load spectrum data at a bridge site for evaluation purposes. A reliability based model is described that can calibrate appropriate load factors, predict maximum expected truck loading, and incorporate the measured statistics of girder distribution and impact.

AASHTO girder distribution factors are generally conservative compared to measured values from WIM data when trucks are occupying two lanes. Design specification moments used in evaluation have a greater uncertainty than a measured load spectrum determined at the site.

Reduced load factors for permit loads may be warranted for permit loads if the loading is carefully controlled. Load and resistance factors in rating calculations need to differ from factors applied to design because of exposure period and available performance data.

B-1

Reference

Study Description

Findings

Recommendations

Miao and Chan Bridge Live Load Models from WIM Data (2002)

Hong Kong based study presents a new methodology for deriving highway bridge live load models for short span bridges using WIM data. Two methods are presented to obtain extreme daily bending moments using WIM data: 1). The lane loading model is derived based upon the equivalent base length concept, 2). The truck loading model is developed based upon a statistical approach. The developed lane and truck loadings are compared with other loading models adopted locally and overseas.

The developed Hong Kong Bridge Design Load (HKBDL) (per lane) was found to be best represented by the following: 1). For a span of 0 to 5 m – a single axle load of 15.0 t, 2). For a span of 5 to 23.5 m – a single axle load of 8.0 t plus a uniformly distributed load, 3). For a span greater than or equal to 23.5 m – a uniformly distributed load over 23.5 m. After studying five possible truck models, the developed HKBDL (standard truck) was determined to be best represented by a six axle vehicle with a total length of 14.0 m. Axle loads vary from 7.5 t to 11.0 t and axle spacings vary from 1.3 m to 4.0 m. The proposed design loadings for Hong Kong, developed assuming a probability of 0.98 of the heaviest vehicle in Hong Kong, induce forces that are less than the design loading standards of many other countries.

Additional work is necessary to consider shear effects and effects on continuous spans. Load factors need to be studied for various combinations of loadings.

Heywood and Nowak Bridge Live Load Models(1989)

Australian study presents the analysis of WIM data. The data is statistically analyzed and normalized by the National Association of Australian State Road Authorities (NAASRA) T44 design loading, and the results of analysis are compared to current Load and Resistance Factor Design (LRFD) loading limit states.

The ratio of ultimate limit state (ULS) to serviceability limit state (SLS) moments based on statistically analyzed WIM data is approximately constant for each distribution considered, however it varies from 1.1 to 1.4 for all of the distributions studied. The ratio of the largest ULS (recurrence interval distribution) to the smallest SLS (normal distribution) moments

Develop a new bridge design live load in place of the T44 loading in order to provide a more uniform prediction of the effects of traffic loads on a variety of bridge spans. Consider revising the recurrence interval for the serviceability limit state so that this condition does not control the bridge design.

B-2

Reference

Study Description

Findings

Recommendations

results in a value of 1.6. Similarly, the shear value varies from 1.4 to 1.5. Both the moment and shear values are less than the ultimate load factor of 2.0 that was proposed for the NAASRA Bridge Design Code.

Nowak and Hong Bridge Live-Load Models (1991)

Presents a statistical procedure for calculation of live-load moments and shears for highway girder bridges of various span lengths with one and two lane configurations and using truck survey data collected by the Ontario Ministry of Transportation. The maximum load effects for time periods from one day to 75 years are produced from extrapolations and simulations.

The maximum moment and shear for single lane bridges up to approximately 100 feet long result form the application of a single truck. The study shows that two trucks following each other produce the maximum moment and shear for longer single lane bridges. The simulation results indicate that that two side-by-side perfectly correlated truck or lane loads, depending upon bridge length, is the governing two lane bridge live load model.

None.

Nowak and Szerszen Bridge Load and Resistance Models (1998)

As a part of the development of rational codes (the AASHTO LRFD Bridge Design Specifications, Ontario Highway Bridge Design Code, and Eurocode) for the design of bridges and evaluation of existing structures, presents a procedure for statistically calculating the live-load moments and shears for highway girder bridges using truck survey data collected by the Ontario Ministry of Transportation. Resulting bias factors for live load from the analysis are presented with the corresponding changes to the design live loads for the national

The maximum moment and shear for single lane bridges up to approximately 30 to 40 m feet long result form the application of a single truck. The study shows that two fully correlated trucks following each other produce the maximum moment and shear for longer single lane bridges. The simulation results indicate that that two side-by-side perfectly correlated truck or lane loads, depending upon bridge length, is the governing two lane bridge live load model for interior girders. One truck may govern in some cases for exterior girders.

None.

B-3

Reference

Study Description

Findings

Recommendations

design codes.

The live load bias factors for moment and shear were found to be non-uniform for the span lengths investigated, necessitating a change in the live load model to produce a uniform factor. Current code girder distribution factors (GDF) were found to be inaccurate; long spans and large girder spacings result in conservative values, and short spans with small spacings result in non-conservative values.

Moses Calibration of Load Factors for Load and Resistance Factor Evaluation (1999)

Outlines the derivations of the live load factors in the proposed AASHTO Condition Evaluation Manual using truck weight spectra. The use of site specific traffic data is addressed.

Live load factor calibration, using similar data from the LRFD code development, was necessary to allow greater flexibility for evaluation as compared to design (varying site traffic and permits, and amount of site traffic data retrieved).

None.

Nowak and Grouni Calibration of the Ontario Highway Bridge Design Code 1991 Edition (1994)

Describes the calculation of load and resistance factors for the Ontario Highway Bridge Design Code (OHBDC) 1991 edition, including the development of load and resistance models utilizing available truck surveys from Ontario, the selection of the reliability analysis method, and the calculation of reliability indices for bridge design and evaluation.

An analysis of the reliability indices for girder bridge types designed per the OHBDC (1983) revealed that they are generally lower than the desired target for shorter spans. Therefore, the existing design truck tandem axle load was increased from 140 kN to 160 kN. For the evaluation of existing bridges, the time dependent load model results in shears and moments that are 3% to 5% lower than those used for design and lower reliability indices are generally used as compared to design.

The following are the results of this study: 1). For design, the live load was modified and the tandem axle load was increased to 160 kN. 2). Modified load and resistance factors should be used for the evaluation of existing bridges depending upon the frequency of inspection, if the components have single or multiple paths, and if the components are primary or secondary members.

Nowak Development of Bridge Load

Using truck surveys, weigh-in-motion measurements, and other

The values of live load moments and shear from truck survey data (number

Based upon the results of the two lane model simulation, the girder

B-4

Reference

Study Description

Findings

Recommendations

Model for LRFD Code (1993)

observations, this paper describes the development of the LRFD load model for static live load.

of axles and axle spacing, and axle loads and gross vehicle weight) are determined by extrapolation for a wide range of simple and continuous spans. Both one and two lane conditions are considered for time periods of 1 day to 75 years. For the one lane condition, the maximum lane moment or shear is caused by one truck, or two or more trucks following each other, depending upon span length. For the two lane condition, distribution of truck load to the girders is very important. Simulations reveal that for interior girders, the case of two fully correlated side-by-side trucks governs.

distribution factors specified by AASHTO (1992) are generally too conservative, particularly for larger girder spacing. The proposed LRFD live load is recommended as the following: 1). The superposition of an HS20 vehicle and a uniform load of 640 lb/ft. 2). For shorter spans a tandem is specified. 3). For negative moments, use two HS20 vehicles, however reduce the total effect by 10 percent.

Agarwal and Cheung Development of Loading-Truck Model and Live-Load Factor for the Canadian Standards Association CSA-S6 Code (1987)

Presents the methodology utilized to develop the CS-W loading design truck and uniform live load factor for the Canadian Standards Association CSA-S6 code. Truck survey data was collected in seven Canadian provinces and used in the development of the design load model and live load factor.

Using survey data from Newfoundland, Ontario, and Alberta, the study found that for spans up to 20m, the proposed CS-600 design truck requires a higher load factor, reflecting a deficiency in the live load model for short spans. The design load was revised to ensure a uniform live load factor. Using survey data from Nova Scotia, Quebec, Saskatchewan, and British Columbia, the study found that each province demonstrated live load factors of similar magnitude.

For all types of live-load effects and ranges of span lengths a uniform live-load factor of 1.60 should be adopted. The CS-600 loading should be adopted as the standard bridge design load for Canadian interprovincial truck routes. A load level different from the CS-600 loading may be adopted by provincial and local authorities.

Nowak and Nassif Live Load Models Based on WIM Data

Michigan bridge WIM study compares measurements taken on three instrumented US route and Interstate

Weigh station data greatly underestimates the gross vehicle weights of overloaded truck traffic in Michigan. Truck weigh

None.

B-5

Reference

Study Description

Findings

Recommendations

(1992) bridges to weigh station data.

station data is biased to less heavy vehicles due to trucker avoidance of the stationary scales. The study found that the gross weights collected at weigh stations were generally within the legal limits, however bridge WIM data shows that the structures are actually being significantly overloaded.

Heywood A Multiple Presence Load Model for Bridges (1992)

Australian study investigates the use of WIM data to simulate multi-lane traffic crossing short span multiple lane bridges. Two lane bridges with spans less than 30 m long are simulated in this study, as this model is representative of the majority of Australian bridges.

The multiple presence simulation models indicate that for low traffic volumes the serviceability recurrence interval is significantly less than the proposed AASHTO value considering that the ultimate limit state is far less sensitive to changing traffic volume.

None.

Jaeger and Bakht Multiple Presence Reduction Factors for Bridges (1987)

Paper reviews the multiple presence reduction factors specified in the AASHTO and Ontario codes and provides an alternate method for establishing these factors for short and medium span bridges in relation to traffic volume using truck survey data. Factors for design and evaluation are proposed.

The multiple presence reduction factors by the proposed method using traffic density and truck weight distribution data are not significantly different from those of the AASHTO and Ontario codes.

Traffic density should be one of the deciding factors in choosing a multiple presence reduction factor value for design and evaluation. The reduction factors used in evaluation should also consider the expected remaining bridge life, the number of loaded lanes, and the time interval for vehicle to cross the middle third of the bridge, using the procedure presented in the paper.

Fu and Hag-Elsafi New Safety-Based Checking Procedure for Overloads on Highway Bridges (1996)

Using WIM data from United States sites and NYSDOT overload permit data, this paper presents an evaluation method for nondivisible overload permit checking using the LRFD concept of uniform bridge safety.

The paper proposes live load factors to be used in the checking procedure for annual and trip permits for overloaded trucks.

Incorporation of this bridge evaluation method for overweight trucks into code may be considered.

Fujino and Ito Utilizing data from The study shows that the A revised design load is

B-6

Reference

Study Description

Findings

Recommendations

Probabilistic Analysis of Traffic Live Loading on Highway Bridges (1979)

surveys of traffic loads carried out on several Japanese highways, this paper summarizes the statistical analysis using computer simulation for the appraisal of the current design load and the development of a new design load.

current design load provides a safety reserve that is not constant for bridges of different span lengths, with a greater safety level provided for longer spans.

proposed, however the authors suggest analysis of continuous span bridges and further investigation of traffic flow on bridges.

Ghosn and Moses Reliability Calibration of Bridge Design Code (1986)

This study is the reliability calibration of the AASHTO bridge design code. The study incorporates two important concepts in bridge design load modeling: 1). The use of WIM to provide data on bridge loading and response for short and medium span bridges. 2). The use of reliability-based design to provide uniform reliability through a combined selection of nominal design loads and corresponding safety margins.

The reliability-based calibration of the AASHTO bridge design code revealed the following: 1). The AASHTO code provides high levels of reliability, but does not provide uniform reliability levels for all span lengths. 2). New safety factors and design loads are proposed to achieve uniform reliabilities or safety indices. 3). The target safety index was derived from average AASHTO performance. 4). The derived partial safety factors achieved more uniform safety indices. 5). Different live load factors are desirable for different loading intensities. 6). This approach to load modeling can be applied to bridge evaluation.

None.

Ghosn and Frangopol Site-Specific Live Load Models for Bridge Evaluation (1996)

Study focuses on the use of WIM to define site-specific bridge loads, and the differences in safety that result from applying site-specific values to evaluation rather than the national average (design loads).

For the bridge evaluation example presented, a safety index of 4.07 resulted from the use of the method presented in the Nowak (1993) model for design. Repeated with site-specific WIM data from two independent sites, the example resulted in safety indices of 3.69 and 3.03, displaying that the use of site-specific

The use of average live load data in the assessment of existing bridge reliability may not be representative of actual site conditions and actual site loading from WIM data should be utilized.

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Reference

Study Description

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Recommendations

load data provides results that are different than those obtained from typical data.

Laman and Nowak Site-Specific Truck Loads on Bridges and Roads (1997)

This study uses bridge WIM data to determine and compare site-specific bridge live loads at several locations on Interstate highways, state highways, US highways, and surface streets in Michigan. Weigh station data and truck citation data is utilized to verify the recorded truck loads by WIM.

The study shows that truck loads are strongly site specific and depends on factors such as traffic volume, local industry, and law enforcement effort. A negative correlation was found between law enforcement effort and the occurrence of overloaded trucks as overloaded trucks were found on roadways not controlled by truck weigh stations.

Additional truck data is needed to determine the site-specific load spectra for bridges. Rather than utilizing truck weigh station data, which is biased due to avoidance, unbiased WIM data is needed to determine accurate statistics for site-specific bridge live load models.

Nowak and Ferrand Truck Load Models for Bridges (2004)

Michigan bridge WIM study reviews some of the practical procedures used for field measurement of truck weights and uses this data to simulate site-specific truck loads.

The results of the WIM measurements show that truck traffic is strongly site specific and varies within a geographic area based on the number of trucks, gross vehicle weight, and axle weight. The study found that the shapes of the moment and shear distributions are almost identical, simplifying the bridge evaluation procedure since the same live load factors can be used for both moment and shear. Using the collected WIM data, maximum lane moments and shears were computed and compared to the AASHTO LRFD 1998 moments and shears. The maximum lane moments and shears due to the measured trucks vary between 0.6 and 2.0 times the AASHTO values.

None.

Frangopol, Goble and Tan Truck Loading Data for a Probabilistic

Study consists of a major bridge testing and analysis program for the FHWA. Thirty-five bridges in thirteen states

The study classified approximately 160,000 truck occurrences. Of these occurrences, approximately 6,881 fell

The data will be employed in the development of improved live load models for bridge design and

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Reference

Study Description

Findings

Recommendations

Bridge Live Load Model (1992)

were tested using WIM. into the multiple presence category, defined as a front axle-to-front axle spacing between vehicles of less than 120 feet. Side-by-side multiple presence was separated from same-line multiple presence. 5,516 side-by-side and 1,365 same-line multiple presence situations were recorded.

evaluation.

Fu and Hag-Elsafi Vehicular Overloads: Load Model, Bridge Safety, and Permit Checking (2000)

This study develops a live load model for truck traffic including overloads. The model is used to assess bridge safety subject to overloads and is designed to incorporate site-specific WIM data.

The paper proposes live load factors to be used in the checking procedure for annual and trip permits for overloaded trucks, consistent with the average bridge safety by the AASHTO code.

Consideration may be given to incorporating this bridge evaluation method for overloaded trucks into code.

Ghosn, Moses and Gabriel Truck Data for Bridge Load Modeling (1990)

Utilizing WIM data collected at several steel multi-girder Interstate bridges in Ohio, this study applies a simulation program that estimates the probabilistic distribution of maximum moment response of bridges. The study uses the model to develop a reliability-based truck weight formula that regulates the weight of trucks on US bridges. The developed truck weight formula is applicable to simply supported steel bridges designed for AASHTO’s WSD HS20 loading and will have a .25 safety index for a 50 year life.

In the calculation of the truck weight formula, H, the random variable that gives the overload factor due to the presence of closely spaced vehicles, was found to be sensitive to only very large changes in truck volumes.

None.

Nyman Calibration of Bridge Fatigue Design Model (1985)

This study consists of a structural reliability evaluation of the current AASHTO fatigue specification for steel bridges using field data obtained from a bridge-mounted WIM system. A fatigue life failure model

The study has determined the following: 1). The proposed fatigue vehicle model is more representative of the current truck traffic at sites examined in the US. 2). The current AASHTO code appears to lead to

The proposed revisions to the current specification include: 1). Replacement of the current AASHTO fatigue design load model with Pavia’s vehicle. 2). Modification of the allowable stress ranges to

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Reference

Study Description

Findings

Recommendations

is formulated in terms of a fatigue failure function.

safety indices that vary with the different stress categories. 3). Truck traffic including weight and volume vary too much from site to site to be covered by only two categories as currently done.

give a more uniform safety index for all stress categories. 3). Specification of different load factors for a range of volumes and loadometer values. 4). Refinement of the failure function variables to provide a more accurate safety index. The relationship between truck headway and volume also needs to be determined.

Caprani, Grave, O’Brien and O’Connor Critical Loading Events for the Assessment of Medium Span Bridges (2002)

Using WIM data from a French site, this study is the Monte-Carlo simulation of free-flowing traffic across bridges to determine the critical loading events and extreme load effects (bending moment and shear force).

The study shows that the two-truck event is the most important free-flowing event for short to medium span bridges with two opposing lanes of traffic. For longer spans, events involving three or more trucks can be significant.

Both two and three truck events should be modeled in the assessment of site-specific bridge loading for structure lengths up to 50 m and in free flowing situations.

Laman and Nowak Fatigue-Load Models for Girder Bridges (1996)

This paper focuses on the development of a new fatigue-load model for steel girder bridges using WIM data from five bridges. The data from the five structures consists of site-specific truck parameters and component-specific stress spectra.

The study findings indicate that the magnitude and frequency of truck loading are site-specific and component-specific. The results also reveal a significant variation in stress spectrum between girders. Generally, the girder that is located nearest to the left wheel track of vehicles traveling in the right lane experiences the highest stresses in the stress spectra and decreases as a function of the distance from this location. It was found that a vehicle that dominates the distribution of vehicle types does not necessarily dominate the fatigue damage of the particular component. Rather, a vehicle that dominates the distribution of the lane

A single truck model for fatigue loading is not recommended as the most accurate approach as a result of the site-specific nature of the distribution of vehicle types by axle. The paper recommends the use of an equivalent three axle fatigue truck with varying axle weight and spacings for sites with traffic consisting of two to nine axle trucks. Similarly, for sites with ten and eleven axle trucks, a four axle truck is recommended as an equivalent fatigue vehicle.

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Reference

Study Description

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Recommendations

moments will likely dominate the fatigue analysis.

Au, Lam, Agarwal and Tharmabala Bridge Evaluation by Mean Load Method per the Canadian Highway Bridge Design Code (2005)

This paper summarizes bridge evaluation by the Canadian Highway Bridge Design code (CHBDC) mean load method. The mean load method does not require the use of load or resistance factors. Instead, the uncertainties associated with the loads and resistances are considered by using default statistical parameters. The code also allows the use of parameters that are derived from collected site-specific WIM data. The paper compares the results of a steel box girder bridge evaluation using the mean load method default parameters, WIM derived parameters, and the LRFD method.

A comparison of the evaluation results shows that the LRFD method and the mean load method using the default statistical parameters provide similar results, with the mean load method offering a slightly higher live load capacity factor. The mean load method using live load statistics based on WIM data, provides the highest load carrying capacity. This is a result of the conservative statistical parameters provided in the CHBDC.

Mean load method evaluation results using WIM data may not be conclusive if the bridge’s most critical traffic loading periods are missed during field data collection. The season and measurement periods require thoughtful selection to capture the most critical live loading on the bridge.

van de Lindt, Fu, Zhou and Pablo Locality of Truck Loads and Adequacy of Bridge Design Load (2005)

This paper investigates the differences in live loading conditions between the national average as utilized in the AASHTO LRFD code and twenty site-specific Detroit, Michigan girder bridge locations. Resulting reliability indices are compared. WIM data is used to characterize the truck load effect in the bridges’ primary members for moment and shear at critical cross sections.

This study established the following: 1). In general, the local truck loading may vary significantly from the state or national average, resulting in inconsistent risk levels for highway bridges. 2). Based upon the study findings of the twenty subject bridges, the current Michigan HS25 design load does not consistently achieve a reliability index of 3.5 for the design-minimum strength of bridges in the Detroit area.

This WIM data used in this study did not include headroom information. Further study incorporating WIM data with headroom information should be performed to advance the study topic. Site-specific live load analyses are necessary, particularly for trunkline roadways with high ADTTs, in order to achieve a more uniform reliability index. Consideration should be given to performing a feasibility study at the national level.

Cohen, Fu, Dekelbab and Moses

Using WIM and truck survey data, this study presents a qualitative

This study has established the following: 1). The modeling is based

None.

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Reference

Study Description

Findings

Recommendations

Predicting Truck Load Spectra Under Weight Limit Changes and its Application to Steel Bridge Fatigue Assessment (2003)

method of predicting truck load spectra as a result of changing truck weight limits. This study utilizes historical and present truck weight data and can be used to estimate the impact of weight changes on bridges.

on freight transportation behavior, and it is flexible for both national and local changes. 2). Using measured truck data from Arkansas and Idaho, the paper shows that the proposed method can capture effects of truck weight-limit change on TWHs and on resulting steel bridge fatigue. 3). This method can be used to estimate possible impacts to bridges as a result of truck weight-limit changes, in developing rational policies for freight transportation.

Moses Probabilistic Load Modeling for Bridge Fatigue Studies (1982)

The author presents a reliability model to provide consistent levels of fatigue safety for steel girder bridges. Discussions of shortcomings with truck data collection systems are offered.

Since the fatigue model is considerably influenced by the heavy end of the weight spectra, a WIM system was developed as part of this study to collect truck data. It was found that weigh stations and temporary weigh scales are avoided by overloaded trucks, resulting in biased data. The study found that pavement weigh scales provide erroneous static truck weights due to adjacent pavement roughness and that their proposed bridge WIM system offers more accurate data.

The paper recommends that following for future consideration: 1). The allowable stress range for fatigue should be made a continuous function of truck volume instead of discrete volume categories. 2). The nominal loading should coincide with a representative vehicle with expected dimensions and axle load percentages instead of a variable wheelbase vehicle. 3). Safety indices for non-redundant structures should be based on risk models that integrate load probability occurrences over a range of damage. Models should be developed to produce consistent safety for redundant and non-redundant behavior. 4). Future tests should involve multi-lane measurements to monitor vehicle combinations.

Wang, Liu, Hwang and

Using data from a Florida WIM station, this study

This study has found the following:

None.

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Reference

Study Description

Findings

Recommendations

Shahawy Truck Loading and Fatigue Damage Analysis for Girder Bridges Based on Weigh-in-Motion Data (2005)

synthesizes the truck traffic data and establishes the live-load spectra, and performs a fatigue damage analysis for six typical steel multi-girder bridge models that were generated for this project.

1). Flexural stress and shear vary with bridge span length. 2). Truck loading on the bridges does not necessarily increase with GVW, but rather with axle weight. Tandem axles significantly exceed the loading of an HS20-44 vehicle. 3). The average impact factors are generally less than the values specified in AASHTO (1996). 4). The AASHTO fatigue truck and the actual truck-traffic flow based on with measurements have close effects.

Grundy and Boully Fatigue Design in the New Australian Bridge Design Code (2004)

This paper presents an overview of the work performed in developing the fatigue provisions for the new Australian Bridge Design Code AS5100. Calibration of the fatigue loading model against Culway WIM data is described. The projected growth in traffic volume and magnitude of vehicle and axle mass is incorporated in the fatigue loading model.

The following was noted: 1). Span has a great effect on the fatigue damage per truck. For short steel bridges, fatigue can become the governing limit state for structures on heavily traveled roadways. For longer spans, fatigue is not as great an issue due to the effect of dead load. 2). Multiple presence of trucks in the same or adjacent lanes occurs infrequently per the WIM data.

None.

Jamera et al FHWA Study Tour for European Traffic-Monitoring Programs and Technologies (1997)

This FHWA-sponsored study is a scanning tour of the Netherlands, Switzerland, Germany, France, and the United Kingdom. The tour was conducted in order to learn how European countries perform traffic monitoring and if and how these concepts can be applied in the United States. Several areas of specific interest regarding WIM system and data collection were reviewed

The study found the following: 1). Fewer and less detailed data are collected on trucks than in the US. 2). Standardization of data collection equipment is common. The Europeans are working to coordinate WIM research and development to produce better, more reliable WIM equipment (DIVINE, COST 323, and WAVE projects). 3). WIM systems require

The study recommends that there are two areas in which US transportation experts should pay attention to European WIM systems and activities: 1). The Europeans employ limited classification schemes, allowing the use of less sophisticated and less costly collection equipment. An analysis of cost savings versus loss of detailed

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Reference

Study Description

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Recommendations

and summarized. calibration at least twice a year. 4). Only France and the United Kingdom have extensive WIM system installations.

information requires analysis. 2). The COST and WAVE WIM tests should be monitored by US researchers to eliminate duplicate efforts in this county.

O’Brien and Caprani Headway Modelling for Traffic Load Assessment of Short to Medium Span Bridges (2005)

The assumed headways of successive trucks on bridges have a great impact on the critical loading events from which the characteristic effects are derived. This paper presents a new approach that uses measured headway statistical distributions generated from French WIM data.

The following has been established from this study: 1). Headways of less than 1.5 sec. were found to be insensitive to traffic flow and are influenced by driver behavior. Headways between 1.5 sec. And 4.0 sec. were found to be considerably influenced by traffic flow. 2). Assumptions related to headways and gaps have a great impact on load effects and characteristic values.

The authors recommend a statistical (HeDS) approach for site-specific assessment of bridge loading.

van de Lindt, Fu, Pablo and Zhou Investigation of the Adequacy of Current Design Loads in the State of Michigan (2002)

This report presents the process and results of a research effort to examine the adequacy of current vehicle loads used to design bridges in the State of Michigan. The target reliability index used in the AASHTO LRFD code was utilized in the study as the criterion for evaluating the adequacy. Reliability indices were calculated for twenty different bridges selected from the Michigan inventory of new bridges. Existing WIM data was processed to statistically characterize the truck load effect.

The following conclusions were made by the report: 1). The reliability indices were found to vary among bridge types. 2). The 50th and 90th percentile of traffic volume do not noticeably influence the reliability indices. 3). The current design load, HS25, could be modified to achieve, on average, a reliability index of 3.5, which was used as a target index for the AASHTO LRFD code. 4). The deck design load of HS20 is adequate for reinforced concrete decks.

The authors recommend that a new design load level be considered for bridge beam design in the Detroit Metro Region.

Nichols and Bullock Quality Control Procedures for Weigh-in-Motion Data

This study consists of the development of a quality control program for the Indiana Department of Transportation to improve the accuracy of

The study found the following: 1). The WIM applications at static weigh stations were effective for identifying safety

The study recommended the following: 1). The drive tandem axle spacing metric should be applied to all WIM systems to monitor the

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Reference

Study Description

Findings

Recommendations

(2004) the data produced from their WIM sites. The quality control program is based on the Six Sigma quality control program DMAIC performance improvement model and provides a mechanism for assessing the accuracy of vehicle classification, weight, speed, and axle spacing data and monitoring it over time.

violations, but ineffective for identifying overweight vehicles. Virtual weigh stations in Indiana were found to be approximately 55 times more effective than the static weigh stations for overweight truck identification. 2). Robust metrics for speed and axle spacing accuracy, weight accuracy, and sensor error rates are necessary in a quality control program that can be continuously monitored using statistical process control procedures. 3). Data mining of these metrics revealed variations in the data caused by incorrect calibration, sensor failure, temperature, and precipitation.

speed calibration and prioritize maintenance on a lane basis. 2). The bending plate and single load cell WIM systems should be configured to log the left and right wheel data to compute the left-right residual metric. Use the left-right residual for detecting weight calibration drift and to prioritize maintenance on a lane basis. 3). The error proportion metric should be applied to all WIM systems to identify lanes that experience high error rates to prioritize maintenance on a lane basis. 4). The WIM data should be continuously monitored for errors and drifts to establish and maintain accurate data. 5). The WIM system algorithms should consider variations in the climate to account for temperature and precipitation or flag data that is collected during days of climatic anomalies when the accuracy is questionable. 6). To apply the recommended quality control procedures, the WIM data must be uploaded to a relational database that supports free-form queries. Analysis cubes are recommended for data mining. 7). A test bed should be constructed of various types of WIM sensor for long-term evaluation of performance, accuracy, and maintenance costs for

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Reference

Study Description

Findings

Recommendations each type. Installation of equipment to collect continuous climate data would allow further exploration of the climatic impacts on the WIM sensors.

Hwang and Koh Simulation of Bridge Live Load Effects (2000)

The current design load in Korea, which is not based on any research or actual data, was adopted in 1978. This paper presents the research for the new live load model for the reliability-based design code that is based on collected bridge WIM data and video recording. The new model is compared to the design live load model from several countries.

The study has determined the following: 1). The new live load model should consist of a combination of truck load and distributed load with a varying magnitude based on span length. 2). Weight distributions differ for each WIM site and direction, highlighting the importance of accurate data for the live load model. 3). The maximum moment ratio is variable based on span length. A single truck controls for shorter span lengths and two fully correlated trucks govern for longer spans.

The paper suggests that additional data should be collected to better represent truck load effects.

O’Connor and O’Brien Traffic Load Modelling and Factors Influencing the Accuracy of Predicted Extremes (2005)

This paper describes traffic simulation (direct and Monte Carlo method) using European WIM statistics for the assessment of existing bridges. The implications of the accuracy of the recorded data and the duration of recording and of the sensitivity of the extreme to the method of prediction are investigated. Traffic evolution with time is also explored.

The paper offers the following findings: 1). The accuracy of the extreme load effects by Monte Carlo simulation increases with increasing span length in inverse proportion to the variance in the extreme. 2). A comparison of extrapolation techniques shows the importance of appropriate selection of an extreme value distribution. 3). The accuracy of WIM data is more critical for shorter span lengths. The effects of increasing inaccuracy were seen to attenuate with span. 4). The time-dependent and seasonal analyses do not provide any clear

None.

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Reference

Study Description

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Recommendations

proof of a seasonal trend. 5). When considering future growth, it is found that the factor that could have major influence on predicted extremes in the future is a change allowable gross vehicle weight. 6). The sensitivity of characteristic extremes to the duration of recording and the amount of available data is a function of the effect and span under consideration.

Lu, Harvey, Le, Lea, Quinley, Redo and Avis Truck Traffic Analysis Using Weigh-In-Motion (WIM) Data in California (2002)

This report is based on truck traffic data collected from all of the WIM stations on the California State highway network. Two objectives of the study were to determine truck traffic volume and load growth trends using regression methods and to check the possibility of extrapolating available truck traffic data to sites where WIM stations are not installed.

The report concluded the following: 1). Axle load spectra are heavier at night than during the daytime, possibly due to more efficient operation without car traffic or avoidance due to closure of more weigh stations. 2). Axle load spectra shows little seasonal variation. 3). Axle load spectra are much higher at rural WIM stations compared to urban stations, likely due to the presence of more long-haul trucking at rural WIM stations, and more short-haul, less-than-full-load trucking in urban areas. 4). The proportion of larger truck types, which would more typically be used for long-haul trucking, increases at night. 5). The analysis of six representative WIM sites shows that GVW generally did not grow across the six sites. Although the number of trucks using the highways increased, the trucks were

The following recommendations were made: 1). Further research should be conducted to improve methods of estimation for locations that are not equipped with WIM systems. 2) Several recommendations were made regarding improvement to the capability of the WIM data collection system including regular quality assurance checks and maintenance at all WIM stations.

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Reference

Study Description

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Recommendations

generally not carrying heavier loads. 6). Axle load spectra can generally be extrapolated for steering and single axles to adjacent sites.

O’Brien and Znidaric Report of Work Package 1.2 – Bridge WIM Systems (B-WIM) (2001)

This work package 1.2 report is part of the Weigh-in-motion of Road Vehicles for Europe (WAVE) study and focuses on bridge WIM systems. The objectives of the study are to understand the dynamics of a truck crossing event, to develop a bridge WIM system, to develop new approaches and algorithms, to investigate the possibility of systems that are free of axle detectors, and to test the accuracy of bridge WIM systems.

The study has shown that major difficulties observed with bridge WIM systems in the past can be avoided when using new and updated algorithms and more powerful computers and data-acquisition systems. The study results indicate that bridge WIM systems have an accuracy comparable to other types of WIM systems. Several advantages of the bridge WIM system include portability, durability, and the lack of influence of the pavement on the weighing accuracy. One issue that has not been addressed by this study is the multiple presence of more than one heavy vehicle on the bridge at the time of weighing.

The further development of free of axle detector systems is necessary as there are many potential improvements in accuracy and in the range of bridge types to which it can be applied.

Chotickai and Bowman Truck Models for Improved Fatigue Life Predictions of Steel Bridges (2006)

This paper presents the development of a new fatigue model based on WIM data collected from three different sites in Indiana. The recorded truck traffic was simulated over analytical bridge models to investigate moment range responses of bridge structures under truck traffic loadings. The bridge models include simple and two equally continuous spans. Based on Miner’s hypothesis, fatigue damage accumulations were computed for details at

Based on the analysis of the WIM database, the paper shows that the effective fatigue stress range is site-specific and can be significantly different from the gross weight specified for the AASHTO fatigue truck. The simulation results indicate that the use of the studied fatigue trucks in a fatigue evaluation of bridge structures subjected to different truck traffic loadings can result in a considerable underestimation or overestimation of the extent of the actual

The paper recommends the use of the newly developed fatigue trucks. The three-axle fatigue truck can be used to represent truck traffic on typical highways with a majority of the fatigue damage dominated by two- to five-axle trucks. The new four-axle truck can better estimate the fatigue damage on heavy duty highways with more than 10% of the truck traffic dominated by eight- to eleven-axle trucks.

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Reference

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Recommendations

various locations on the bridge models and compared with the damage predicted for the AASHTO fatigue truck, a modified AASHTO fatigue truck with an equivalent gross weight, and other fatigue truck models.

fatigue damage when compared to the damage predicted using the WIM database.

Tallin and Petreshock Modeling Fatigue Loads for Steel Bridges (1990)

Using WIM data from seven states, histograms of truck GVW are analyzed. These histograms are modeled by two bimodal distributions. Fatigue lifetimes for AASHTO categories A, B, C, and E details are calculated from these distribution of GVW models by approximating the Miner’s stress as a linear function of the mth root of the mth expected moment of the GVW. The lifetimes based on the two models are compared with each other and with the results obtained by assuming a single lognormal distribution.

The study results show that the fatigue lifetimes for AASHTO categories A, B, C, and E details estimated using the bimodal distributions differ little from each other but are significantly shorter than the lifetimes estimated from the single lognormal distribution. It was also noted that there are large differences between the estimated lifetimes of different AASHTO fatigue categories.

None.

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APPENDIX C NCHRP 12-76 SURVEY QUESTIONNAIRE AND RESPONSES

General Information A new vehicular live-load model was developed for the AASHTO LRFD Bridge Design Specifications because the HS20 truck from AASHTO's Standard Specifications for Highway Bridges did not accurately represent service-level truck traffic. The HL-93, a combination of the HS20 truck and lane loads, was developed using 1975 truck data from the Ontario Ministry of Transportation to project a 75-year live-load occurrence. Because truck traffic volume and weight have increased and truck configurations have become more complex, the 1975 Ontario data do not represent present U.S traffic loadings. Other design live loads were based on past practice and did not consider actual or projected truck traffic. Although the quality and quantity of traffic data has improved in recent years, it has not been used to update the bridge design loads. The objective of this project is to develop and demonstrate the application of protocols for collecting and processing traffic data to calibrate national bridge live-load models. Project Objectives The goal of this project is to develop a set of protocols and methodologies for using available truck traffic data collected at different US high-speed WIM sites and recommend a step-by-step procedure that can be followed to develop and calibrate vehicular loads for superstructure design, fatigue design, deck design, and overload permitting. The models will be applicable for the design of bridge members, for both ultimate capacity and cyclic fatigue. The models will be applicable for both main structural members as well as the design of bridge decks. Purpose of Survey High quality WIM data obtained from a network of mainline WIM sites is necessary for using WIM data in bridge design application. The purpose of this questionnaire is to obtain information and document practices on issues central to this research, such as: types of WIM equipment in use in each state and the locations of WIM sites; WIM equipment maintenance and calibration procedures; the types of data being collected and how it is used; ability of state’s WIM system to capture and save accurate truck arrival time stamps; etc. Reports on past traffic studies of truck weight trends and bridge design loads using WIM data are also of particular interest. The responses to this questionnaire will guide the development of the recommended protocols. If you wish to discuss any items related to the questionnaire please contact Bala Sivakumar, P.E., Principal Investigator at 201-368-0400. You may also communicate with us by e-mail at bsivakumar @ lce.us. Fax: 201-368-3955.

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The completed questionnaire should be returned to bsivakumar@lce.us, or mailed to:

Bala Sivakumar, P.E. Lichtenstein Engineering Associates, Inc. 45 Eisenhower Drive Paramus, New Jersey 07652

We ask that you return the completed questionnaire to us by June 1, 2006 On behalf of the NRC/TRB-NCHRP programs and the AASHTO Subcommittee on Bridges and Structures, and the Research Team, we thank you for your cooperation.

Respondent Information Please provide the name, address and telephone number of the person completing this questionnaire: Name: Title: Agency: Address: Telephone No.: Fax No. E-Mail:

Weigh-in-Motion Representative

We are interested in recent truck weight data collected using high-speed weigh-in-motion techniques within your state. Please provide the following information on the contact person in your agency who coordinates such data acquisition and maintenance: Name: Title: Agency: Address: _____________________________

Telephone No.: E-Mail:

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SECTION 1.0 Weigh-In-Motion (WIM) Program 1.1 Do you have a Weigh-In-Motion (WIM) program? Yes _______ No _____ If yes please answer the following questions. If not, please just respond with no and

send the questionnaire back. 1.2 How long have high-speed WIM sites been in use for traffic data collection in your

state? ________ Years. SECTION 2 – WIM Sites 2.1 Please provide the following information:

Total number of high speed WIM sites --------------------

Number of WIM sites on Interstates ---------------------

Number of weigh stations --------------------- 2.2 How do you select WIM sites (Interstates, NHS, rural arterials, functional

classification, etc.). Is there an overall strategy in your site selection?

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

__________________________________________________________________

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1.4 Please fill out the following table providing information for each mainline WIM site. Use additional sheets as required.

WIM Site ID

Route ADTT Sensor Type

Vendor Date Installed

Date Last Calibrated

# of Traffic lanes

# of WIM Lanes

WIM in both Travel Directions? (Yes/No)

Near a Weigh Station (Yes/No)

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SECTION 3 – WIM Data 3.1 How frequent are WIM system breakdowns? In your opinion, what percentage of the

time is data being collected at the above sites?

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

3.2 How often and how is your WIM data captured?

_______________________________________________________________________________________________________________________________________________________________________________________________________________

3.3 What types of traffic data are typically stored and used (axle weights, gross weights,

axle spacings, truck type, etc)? ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

___________________________________________________________________ 3.4 What is the accuracy of truck arrival time stamps reported in the data set (1 sec, 0.01

sec, etc)? Are time stamps available for more than one lane at a site? What is the highest resolution possible for truck arrival times? Please explain. ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

3.5 Do you archive your WIM data? In what format and for how long is the data

archived? Please explain.

_________________________________________________________________________________________________________________________________________________________________________________________________________

3.6 Do you archive the binary WIM data files from the data collector? If so, how much binary data do you have archived? Please explain. _______________________________________________________________________________________________________________________________________________________________________________________________________________

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3.7 Do you have traffic data for a whole year (or close to a year) at a WIM site that can be made available for our statistical analyses of seasonal variations of truck weights? Yes _______ No _____

3.5 Do you have traffic data of similar quality for a number of years at the same site that

may be helpful in estimating trends in truck loadings? Yes _______ No _____ SECTION 4 – WIM Data Validation and WIM System Calibration 4.1 Do you do WIM data quality testing or validation to ensure data accuracy? Please

explain. ________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________________________________________________________

4.2 How often do you recalibrate WIM systems? Do you have a procedure to decide if a

recalibration is required? Please explain. ________________________________________________________________________________________________________________________________________ ________________________________________________________________________________________________________________________________________

4.2 Who does the recalibration of WIM systems? ________________________________________________________________________________________________________________________________________

4.3 Please describe the recalibration techniques (Test trucks, AVI, Auto-calibration)? ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

___________________________________________________________________ ___________________________________________________________________

4.4 Do you have a Quality Assurance Program in place for your WIM systems to check data accuracy? Yes _______ No _____. .

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SECTION 5 – WIM Data Analysis & Applications 5.1 What specialized software do you use for data handling and processing of WIM data?

________________________________________________________________________________________________________________________________________

5.2 Do you analyze your WIM data? What factors do you analyze? To whom do you

distribute the results? ________________________________________________________________________________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________

5.3 Is your WIM data currently used for the following?

Pavement Design __________ Bridge Design __________ Enforcement __________

Planning & Programming __________ 5.4 Have you used WIM data to investigate truck weight trends in your state? Yes

_______ No _____. If yes, please explain (please also include references to any reports). ________________________________________________________________________________________________________________________________________ ____________________________________________________________________

5.5 Has your state used WIM data for bridge design applications / bridge live load

modeling? Yes _______ No _____. If yes, please explain (please also include references to any reports). ________________________________________________________________________________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________

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TABULATED RESPONSES Question 1.1 Do you have a WIM program? Question

1.2 If yes, how long

State Yes No Alaska Department of Transportation X 10+ years California Department of Transportation X 15 years Arkansas Department of Transportation X Connecticut Department of Transportation X 9 years Florida Department of Transportation X 32 years Georgia Department of Transportation X 10 years Hawaii Department of Transportation X 18 years Idaho Department of Transportation X 12 years Indiana Department of Transportation X 15 years Iowa Department of Transportation X 15 years Kansas Department of Transportation X 14 years Louisiana Department of Transportation X 7 years Michigan Department of Transportation X 14 years Minnesota Department of Transportation X 22 years Mississippi Department of Transportation X 14 years Missouri Department of Transportation X 10 years Nevada Department of Transportation X 20 years New Jersey Department of Transportation X 13 years New Mexico Department of Transportation X 17 years New York Department of Transportation X 10+ years North Dakota Department of Transportation X 3 years Ohio Department of Transportation X 15 years Oregon Department of Transportation X 8 years South Dakota Department of Transportation X 15 years Virginia Department of Transportation X Washington Department of Transportation X 16 years Wyoming Department of Transportation X 8 years NR - No Response

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Question 2.1 Please provide the following information

Total number of high speed

WIM Sites

Number of WIM sites on Interstates

Number of weigh stations

State Alaska Department of Transportation 7 4 5 California Department of Transportation 137 58 36 Arkansas Department of Transportation NR Connecticut Department of Transportation 36 bi-

directional +4 LTPP

21 bi-directional +2 LTPP

5

Delaware Department of Transportation NR Florida Department of Transportation 40 14 20 Georgia Department of Transportation 90 30 14 Hawaii Department of Transportation 7 2 1 Idaho Department of Transportation 16 6 10 Illinois Department of Transportation NR Indiana Department of Transportation 52 24 10 Iowa Department of Transportation 28 9 ? Kansas Department of Transportation 9 Perm

70 Portable 3 Perm

25 Portable 4 (not DOT, Hiway Patrol

Louisiana Department of Transportation 3 3 7 Maine Department of Transportation NR Maryland Department of Transportation NR Massachusetts Department of Transportation NR Michigan Department of Transportation 41 21 13 Minnesota Department of Transportation 6 2 7 Mississippi Department of Transportation 15 7 30 Missouri Department of Transportation 13 7 1 Nebraska Department of Transportation NR Nevada Department of Transportation 4 4 2 New Jersey Department of Transportation 64 14 New Mexico Department of Transportation 18 7 N/A New York Department of Transportation 21 11 North Dakota Department of Transportation 12 4 7 Ohio Department of Transportation 49 proposed

44 built 23 proposed

21 built 19 proposed

19 built Oklahoma Department of Transportation NR Oregon Department of Transportation 22 18 56 fixed

27 portables 28 mes

Pennsylvania Department of Transportation NR South Dakota Department of Transportation 14 6 0 Texas Department of Transportation NR Vermont Department of Transportation NR Virginia Department of Transportation 3 2 0 Washington Department of Transportation 37 10 8 Wisconsin Department of Transportation NR Wyoming Department of Transportation 5 3 NR - No Response

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Question 2.2 How do you select WIM sites (interstates, NHS, rural arterials, functional classification, etc.). Is there an overall strategy in your site selection?

State Alaska Department of Transportation WIM sites are placed in areas of high truck traffic

along truck routes. Arkansas Department of Transportation California Department of Transportation NR Connecticut Department of Transportation Interstates, functional classification. We use

existing permanent class 1 sensor locations providing there is free flowing traffic. LTPP data collection sites based on program need for pavement site specific data.

Delaware Department of Transportation Florida Department of Transportation We try to select our WIM sites so that we have all

functional class highways sampled (as long as those roads carry trucks).

Georgia Department of Transportation We are undergoing a total count reengineering process to determine where we count, what we count, how often we count and what equipment we use at each location. This is due to be completed in October 2006. We currently we collect weigh in motion data at 90 sites on a three year rotation. 30 sites per year using portable piezo equipment and collect for only 48 hours per location, ten of these sites are on the interstate system. We are however looking to have permanent sites in the near future.

Hawaii Department of Transportation WIM sites are selected according to the guidelines in the TMG.

Idaho Department of Transportation Site selection is based on required coverage and available resources. We try to add WIM sites when possible in areas of the state that need addition traffic data collection facilities to round out our overall statewide coverage. We also consider traffic trends and current characteristics.

Illinois Department of Transportation NR Indiana Department of Transportation Many of the original sites were selected to comply

with the Traffic Monitoring Guide (TMG) and the Highway Performance Monitoring System (HPMS) requirements. Other sites were selected as Long Term Pavement Performance (LTPP) sites. Still others were selected due to pavement warranty projects. At one time there was an emphasis to have WIM at all Interstate Port of Entries. Currently there is an effort underway combine WIM activities with the Weigh Station./Enforcement in an overall strategic plan

Iowa Department of Transportation We try to get a mix of different functional classes. Currently we are trying to select sites that are on routes entering/exiting the state (near the borders if possible) and routes on new highways or highways that we know that are about to be expanded to from 2 to 4 lanes.

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Kansas Department of Transportation FHWA-DOT Traffic Monitoring Guide outlines a selection procedure based on the HPMS. Our samples are selected by Functional Class and stratified by volume group. Portable weighing is based on this sample. The permanent sites were selected to support the Long-Term Pavement Performance program of the Strategic Highway Research Program in 1990-2000. These sites are still collecting for this program, and used as appropriate to collect for the HPMS.

Louisiana Department of Transportation High volume interstates Maine Department of Transportation Maryland Department of Transportation NR Massachusetts Department of Transportation NR Michigan Department of Transportation At the current time and in the past there was no

overall strategy. Initially SHRP drove the installation of WIM. Some of those sites are still in service. Others were installed per requests of State Police Motor Carrier and Pavement Design engineers to monitor activity on pavement test areas. We install our sites mostly at existing Permanent Traffic Recorder sites.

Minnesota Department of Transportation Truck volumes, geographic locations and dispersion.

Mississippi Department of Transportation In previous years the sites were selected randomly using statistical analysis with the intent that the randomly selected roadway had to be sufficient to collect WIM data. The sites were selected for each functional classification group. You have to have a smooth, flat, and straight roadway.

Missouri Department of Transportation We select a small number of locations designed to be representative of much larger groups of roads. For accurate WIM operations, we locate WIM sites on flat, strong pavement in good condition with constant vehicle speeds. We also take in consideration truck load factors and freight movement.

Nebraska Department of Transportation Nevada Department of Transportation WIM sites are selected according to traffic

segments. Selection of WIM sites is prioritized as a hierarchy of significant truck routes assuming that the roadway meets physical characteristic specifications for effective WIM data collection. The highest priority is to have coverage on the Interstate system. These sites are used for planning purposes and to a lesser degree for weight enforcement screening with the permanent WIM sites, which are located upstream from an inspection facility.

New Jersey Department of Transportation New Jersey’s initial 9 WIM systems were selected as part of the SHRP/LTPP Program. New sites are being installed as part of construction projects and are based on geographical location within the state and functional classification.

New Mexico Department of Transportation On routes with high volume truck traffic, mostly interstate and NHS.

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New York Department of Transportation The following factors are included: program area need, design need, geometry of location, minimum pavement condition to support sensor accuracy, minimum truck traffic to support auto-calibration of system, funding, ability to integrate into statewide traf mon (continuous count) program.

North Dakota Department of Transportation Near weigh stations and on major truck routes. Ohio Department of Transportation We group the WIM sites by FC. We try to have

WIM’s by % of AADTT for each of those FC’s. Due to budget limitations we have capped our program of 50 WIM’s. We strive to have WIM’s on all major NHS routes and roads that contain specialized commodities. Known coal, steel, logging, land fill & quarry roads have been and will be part of our WIM site plan.

Oklahoma Department of Transportation Oregon Department of Transportation Based on truck volume. Pennsylvania Department of Transportation South Dakota Department of Transportation Mixture of all functional classifications Texas Department of Transportation Vermont Department of Transportation Virginia Department of Transportation We look for new, smooth pavement. We plan to

eventually have 6 sites in each of 3 groups: 1) high volume interstate and arterials, 2) low volume interstate and arterials, and 3) minor arterials and major collectors

Washington Department of Transportation The WIM sites were selected in 1991 to address the needs of the Strategic Highway Research Program (SHRP). This program needed traffic and weight data on selected section of highway. Since then we have added several sites based on customer needs (the last installation was to determine if trucks were trying to bypass a point of entry and if so were they overweight.

Wisconsin Department of Transportation Wyoming Department of Transportation The priority has been placed on interstates. A

representative sample of all functional classifications has been a goal and secondary strategy.

NR - No Response

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Question 3.1 How frequent are WIM system breakdowns? In your opinion, what percentage of the time is data being collected at the above site?

State Alaska Department of Transportation Our WIM sites breakdown infrequently. With the

exception of the Chulitna and Glenn OB site, our sites are collecting useable data 90% of the time.

Arkansas Department of Transportation California Department of Transportation Variable. Some every 4-6 months others operate

for years. Average once a year. 90% Connecticut Department of Transportation Most breakdowns are failure of sensors imbedded

in the roadway. Data is only collected for 48 hours once every three years. Varies by site and age of the equipment. We have had lightening strikes, software changes etc. that involve breakdowns. Currently we have had systems running a couple of years continuously without breakdowns. Overall it is expected that ¾ of a year on continuous collection devices is a reasonable expectation. Vehicle tracking during snowstorms, etc. can cause data to be erroneous.

Delaware Department of Transportation Florida Department of Transportation Not very. Usually the problem lies with

communications or piezo failures. The WIM electronics are very reliable. Last year, 20 of 40 WIM systems collected a full year of data. The systems operate 85 – 90% of the time.

Georgia Department of Transportation Since we only have portable sites, I am unable to respond to this question.

Hawaii Department of Transportation WIM breakdowns do not occur that often, but they can last for long periods. It varies from site to site, however, on average they are fully operational at least 75% of the time.

Idaho Department of Transportation We have had very good luck with our WIM system dependability. Systems are down a very small percentage of the time - no more than a few days a year on average.

Illinois Department of Transportation NR Indiana Department of Transportation Approximately 20% of our WIM sites are down due

to equipment failures, connection problems or road construction. This varies tremendously from month to month.

Iowa Department of Transportation System breakdowns are infrequent. Occasionally have a data collector malfunction. If a sensor goes bad might be months before it is replaced due to the season. At 90% of the sites data is being collected 100% of the time unless.

Kansas Department of Transportation The data is frequently unusable. System breakdowns are part of the problem. A greater limitation is that some sites were chosen in locations that are not ideal for data collection, but were necessary for LTPP test site proximity. Portable provides a better data sample.

Louisiana Department of Transportation Major breakdowns are fairly rare. There are occasional software and camera adjustments and maintenance needs.

Maine Department of Transportation Maryland Department of Transportation NR Massachusetts Department of Transportation NR

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Michigan Department of Transportation Not very often. Our estimate is that about 95% of the time the systems are up and running. If sites do not respond during polling, we go to the site and correct the problem. When sensors fail we replace them as soon as weather permits.

Minnesota Department of Transportation Very few breakdowns, mostly in electronic cabinets, power outages. 95% of the time - data is collected.

Mississippi Department of Transportation The WIM system usually does not breakdown. The loops and sensors are what usually go bad. As far as the WIM board goes…they typically last awhile unless something happens that you can’t control like lightning. To answer your question I would say 85 to 90% of the time they are collecting data, but it may not always be good data.

Missouri Department of Transportation Very infrequent, 98% of the time Nebraska Department of Transportation Nevada Department of Transportation 95% New Jersey Department of Transportation The frequency of breakdowns depends on the age

of the system -- both roadway sensors and electronics. Average percentage of data being collected for 1 to 3 year old systems is 95%; over 3 years old and sensors still intact in the pavement and in working condition, 60 to 75%; and over 5 years old, 50%.

New Mexico Department of Transportation Breakdowns are not that frequent (mostly the piezos go bad), our problem is road deterioration. 80 percent.

New York Department of Transportation Sites are fully operational approximately 90% of the time. Sites typically go down due to sensor failure but sensors are replaced under performance based maintenance contracts.

North Dakota Department of Transportation 95% of the time, data is available Ohio Department of Transportation This varies by type of system. The high end load

cells and bending plates are more reliable. You can get 2 years or more before they break. Our load cell systems require year PM’s. Prezo sites last 2-3 years. Our BL’s don’t seem to hold up very well. On we have about 5 sites breakdown a month. (10%)

Oklahoma Department of Transportation Oregon Department of Transportation Less than 3% downtime Annually at any given

site, otherwise data is collected 100% of the time. Pennsylvania Department of Transportation South Dakota Department of Transportation Breakdown is not very often, 99% of time data is

collected Texas Department of Transportation Vermont Department of Transportation Virginia Department of Transportation 99.7% uptime Washington Department of Transportation This depends on construction. The site maybe

working but due to construction, it’s down. About 98% working

Wisconsin Department of Transportation Wyoming Department of Transportation Frequency varies from site to site. Data is being

collected 80-90% on average from these sites. NR - No Response

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Question 3.2 How of and how is your WIM data captured?

State Alaska Department of Transportation Our WIM data is captured through remote site

telemetry and dial up phone connections on a daily basis. However, during communication breakdowns manual downloads may be required.

Arkansas Department of Transportation California Department of Transportation Daily at some weekly at others Connecticut Department of Transportation Data collected for 48 hours once every three

years. Data is collected in IMG format. The LTPP sites in Connecticut are set-up for continuous data collection and storage. Currently, FHWA Classes 1-3 vehicle records are filtered from the stored records.

Delaware Department of Transportation Florida Department of Transportation All WIM sites operate continuously and save data

in daily files. The daily files are downloaded automatically every night.

Georgia Department of Transportation We collect 48 hours of data annually at 30 sites. Contractor collects data processes the data through VTRIS and submits to us at the end of the year. It is all bundled and ready for submission to FHWA.

Hawaii Department of Transportation The data is polled on the next work day. Idaho Department of Transportation We autopoll all WIM systems nightly. Illinois Department of Transportation NR Indiana Department of Transportation We utilize Chaparral Systems “TRADAS 3”

program to auto poll all WIM sites nightly. Iowa Department of Transportation The WIM data is captured and saved on an hourly

basis with Peek Automatic Data Recorders (ADR). Kansas Department of Transportation Permanent sites are downloaded

daily/weekly/monthly as appropriate. Louisiana Department of Transportation It’s not Maine Department of Transportation Maryland Department of Transportation NR Massachusetts Department of Transportation NR Michigan Department of Transportation Our Permanent Traffic Recorders are polled every

night. The data is uploaded to our database once per week.

Minnesota Department of Transportation Polled daily - except weekends Mississippi Department of Transportation Each vehicle is captured in one record and then

the data is stored on the server by day by hour. Missouri Department of Transportation Data is extracted from WIM units bi-weekly via

phone/modem connection with our central traffic monitoring section.

Nebraska Department of Transportation Nevada Department of Transportation Our WIM data is downloaded daily to a remote

computer in our home office New Jersey Department of Transportation Data is downloaded from the office through dial up

modem daily, covering each of the WIM sites about once weekly.

New Mexico Department of Transportation Polled and downloaded weekly. New York Department of Transportation Sites are polled every 2-3 days North Dakota Department of Transportation 7 24 365 captured and downloaded daily. Ohio Department of Transportation We collect WIM data every day from every site.

The Traffic Monitoring Guide (TMG) format is produced along with the vendor raw data files.

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Oklahoma Department of Transportation Oregon Department of Transportation Crescent (streaming) data captured “real time” in a

DB2 format. Report data downloaded monthly (notepad – text)

Pennsylvania Department of Transportation South Dakota Department of Transportation Every day Texas Department of Transportation Vermont Department of Transportation Virginia Department of Transportation a PC modem polls each site daily Washington Department of Transportation The data is collected hourly and polled weekly. Wisconsin Department of Transportation Wyoming Department of Transportation Sites are polled daily via telemetry. NR - No Response

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Question 3.3 What types of traffic data are typically stored and used (axle weights, gross weights, axle spacings, truck type, etc.)?

State Alaska Department of Transportation All data collected by the WIM sites is stored in an

in house Oracle database. Arkansas Department of Transportation California Department of Transportation Axle WT, spacing. Classification, length. Connecticut Department of Transportation Axle weights, gross weights, axle spacing and

truck type. Data are stored to create the FHWA C and W cards. These data include axle weights, gross weights, axle spacings and vehicle length.

Delaware Department of Transportation Florida Department of Transportation Per vehicle records are saved for all vehicles with

classifications of 04 and higher. The data consists of date, time, vehicle number, lane, class, gross vehicle weight, speed, overall length, left and right wheelpath weights of each axle, and spacings between each axle.

Georgia Department of Transportation We store on disk all the raw files and FHWA VTRIS reports. Which includes the axle weights, gross weights, axle spacings, truck types, etc.

Hawaii Department of Transportation Axle weight, spacing, gross weight vehicle class, speed, and overall length

Idaho Department of Transportation We collect all variables possible on each system. This includes each of the ones you mention plus everything else the system allows us to collect.

Illinois Department of Transportation NR Indiana Department of Transportation We have daily, monthly, and annual WIM

summaries going back to 2000. The TRADAS 2 versions were converted to TRADAS 3. These summaries include axle load distributions by lane, direction, and roadway, and for daily, monthly, and annual time periods. Beginning with TRADAS 3, we store the above plus the raw data files, plus a binary version of the individual vehicle records. We have those for 2005 through the present.

Iowa Department of Transportation Traffic data stored is record type, FIPS state code, station ID, direction and lane of travel, date and hour, vehicle class, total weight of vehicle, individual axle weights and axle spacings.

Kansas Department of Transportation Axle weights and spacings, truck classification, time, date, speed

Louisiana Department of Transportation Axle, GVW, Bridge Formula, Truck Type—Not kept for longer than is needed to deal with truck loads real time. Historical WIM data is non-existent at this point.

Maine Department of Transportation Maryland Department of Transportation NR Massachusetts Department of Transportation NR Michigan Department of Transportation We store all data gathered – individual axle

weights, total gross weight, axle spacing, total length, number of axles, Federal Scheme F vehicle code, speed of the truck

Minnesota Department of Transportation Vehicle class, axle wt., gross wt., axle configuration wt. ESALs

Mississippi Department of Transportation Vehicle type, axle weights, total weight, axle spacings are stored. To a certain degree all data is used for calculating ESAL factors.

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Missouri Department of Transportation Total Vehicle Weight – Gross Vehicle Weight Number of Axles Axle Weight Axle Spacing Vehicle Classification

Nebraska Department of Transportation Nevada Department of Transportation All planning data items have been archived in a

database until recently we have transitioned into using a canned processing software known as Tradas which does not have the capability to write individual truck weight records with such information as axle weights, gross weights etc. It does write the federally required “W” card which could be appended to a data base but at that this time it is written in metric and at this point we do not have the capability to produce customized reports.

New Jersey Department of Transportation Raw data in binary format from each of the sites is saved for future use. Various reports are generated monthly from each of the sites. Classification data in C-record format are all saved monthly. Weight or W-record format data are only saved one week each quarter. Average vehicle speed data is saved in a Microsoft Office worksheet format. Special reports can always be generated from the raw-binary data.

New Mexico Department of Transportation 4 and 7 cards. New York Department of Transportation Truck data is captured and stored using the

FHWA ‘w’ card format with the addition of vehicle speed to 0.1 mph and vehicle time stamp to 0.01 seconds.

North Dakota Department of Transportation Axle weights & spacings, GVW, Time, date Ohio Department of Transportation For 2006 and beyond all load cell sites will store

per vehicle records for all vehicles - not just trucks. For every WIM we collect and store spacings, time, date, GVW, and axle weights. We are working at having speed in the TMG W-card format from each of our vendors.

Oklahoma Department of Transportation Oregon Department of Transportation Axle weights, axle spacing, GVW, classification,

length, speed, lane, time/date Pennsylvania Department of Transportation South Dakota Department of Transportation weights, gross weights, axle spacings, truck type

(Federal Classification Scheme F) Texas Department of Transportation Vermont Department of Transportation Virginia Department of Transportation time, lane, speed, class, length, gross wt., ESAL,

axle spacings, axle weights Washington Department of Transportation All of the above is collected at most sites. Axle

spacing not always used other to determine class of vehicle.

Wisconsin Department of Transportation Wyoming Department of Transportation Station ID, direction of travel, lane of travel, year,

month, day, hour, FHWA classification, number of axles, GVW, axle weights and spacings.

NR - No Response

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Question 3.4 What is the accuracy of truck arrive time stamps reported in the data set (1 sec, 0.01 sec, etc.)? Are time stamps available for more than one lane at a site? What is the highest resolution possible for truck arrival times? Please explain.

State Alaska Department of Transportation The accuracy of the truck time arrival is .01 for all

lanes of data. The time stamp is on each vehicle record (PVR). This was an Alaska requirement to ensure that duplicate records were not loaded to the data base. This is the highest resolution possible for truck arrival times.

Arkansas Department of Transportation California Department of Transportation 0.01 sec. Yes. Connecticut Department of Transportation Truck arrival time stamps are reported for each

lane at a site and are recorded by 1 second. The IRD software shows the data time stamp recorded to one hundredth of a second (0.01) in the individual vehicle viewing software. Additional work would be needed to determine the resolution of the data that is reported in the output file formats.

Delaware Department of Transportation Florida Department of Transportation Times are recorded to the nearest full second, for

all lanes. Georgia Department of Transportation Accurate to the .01 second and we weight in one

lane of the roadway. At 10 locations we collect truck traffic in the two outside lanes.

Hawaii Department of Transportation Time stamps are not checked for minute/second accuracy. We check them for date accuracy, and we check the WIM system clock at least once per month. Observed accuracy for those can range from within 1-2 seconds to 1-2 minutes.

Idaho Department of Transportation ECM WIM system equipment has a time resolution of one tenth of a second. The IRD/Diamond WIM systems have a “scientific” mode setting which allows for data collection with a time stamp of one hundred thousands of a second. We have used this mode to collected WIM data for use by Dr. Gong Fu of Wayne State University in his bridge design modeling. Call me at 208-334-8207 if you want to discuss this further.

Illinois Department of Transportation NR Indiana Department of Transportation The timestamps for the vehicle records are to the

1/100 of a second. The ASCII report, however, will alone show the timestamp to the nearest second. This is a shortcoming that has been identified and will be corrected in future versions of the software.

Iowa Department of Transportation They are stored by the hour. We can view the info real time to the second and can be viewed for all lanes at the site.

Kansas Department of Transportation Accuracy varies because the on-site clock is not externally synchronized. Precision of the arrival time is 1 second, which is the finest resolution available from the equipment. Time stamps are available for each truck, regardless of lane.

Louisiana Department of Transportation N/A Maine Department of Transportation Maryland Department of Transportation NR

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Massachusetts Department of Transportation NR Michigan Department of Transportation The time stamp is down to the second for each

lane of travel. So we have the hour, minute and second the vehicle started to cross the sensor.

Minnesota Department of Transportation whole second Mississippi Department of Transportation We store the data on an hourly basis in the cardw,

but the img file has a time stamp associated with each vehicle. We collect WIM data on all lanes at a permanent site.

Missouri Department of Transportation Year, month, day, hour Nebraska Department of Transportation Nevada Department of Transportation We have never had the need to investigate this

but from my experience it is within a second New Jersey Department of Transportation Truck arrival time stamps using the “View Vehicle”

menu of the IRD office software shows a time stamp of up to 0.01 of a second; processed weight data from the W-record cards only up to one minute.

New Mexico Department of Transportation Hourly, for all lanes. New York Department of Transportation All lanes are monitored and trucks are time

stamped to 0.01 seconds. North Dakota Department of Transportation 1 second resolution – Yes, time stamps available

on all lanes at all times Ohio Department of Transportation Mettler-Toledo’s time stamp is now sub second at

.01 sec. The TMG does not have this resolution and needs to be changed. The time stamp is on each vehicle so it would be by lane. Peek or Pat/IRD do not provide time stamps to the .01 second level.

Oklahoma Department of Transportation Oregon Department of Transportation Time stamp accuracy is within .01 seconds. Time

stamps are available for each lane in multi-lane systems.

Pennsylvania Department of Transportation South Dakota Department of Transportation unknown on accuracy of arrival time and are by

lane Texas Department of Transportation Vermont Department of Transportation Virginia Department of Transportation time stamps are to the nearest second, and are

available for all lanes Washington Department of Transportation 12:00:00:00 Wisconsin Department of Transportation Wyoming Department of Transportation Time stamps are to the second and are by lane. NR - No Response

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Question 3.5 Do you archive your WIM data? In what format and for how long is the data archived? Please explain.

State Alaska Department of Transportation All WIM data is saved into an Oracle database for

future use and analysis. Arkansas Department of Transportation California Department of Transportation Yes, indefinite Connecticut Department of Transportation WIM data is collected in IMG format and

converted to STA, CLA and WGT. Data is archived and stored on a floppy disk. Data are stored to create the FHWA C and W cards. These data include axle weights, gross weights, axle spacings and vehicle length.

Delaware Department of Transportation Florida Department of Transportation Yes. Binary data is archived forever. We have

the most recent 2 years of ASCII data online. Georgia Department of Transportation We maintain our WIM data on CDs and we have

only 3 years of data. It is maintained in raw formats and VTRIS formats

Hawaii Department of Transportation We maintain an archive of the raw data files, TMG format files, and processed report files (as Adobe PDFs) starting from 2003.

Idaho Department of Transportation We have WIM data archived back to original installation date for each system.

Illinois Department of Transportation NR Indiana Department of Transportation INDOT has processed WIM data from 2000 to the

present. The processed data includes ESAL and GVW statistics, vehicle classification distributions, and axle load distributions. These exist for each lane, direction, and for the roadway, and for daily, monthly, and annual time periods. Beginning in 2005, we have the above plus the binary raw data files (stored as zipped BLOBs in the database) and a binary version of the individual vehicle records. Our analysis program will convert the binary versions to FHWA W-records.

Iowa Department of Transportation We archive our WIM data in FHWA 7-card format. We have data back to 1996.

Kansas Department of Transportation 14 years, so far. The oldest data is stored in the FHWA Card-7 format, newer data is stored in the FHWA Card-W (since 1995.) Some data is also available in the vendor formats provided by the field equipment.

Louisiana Department of Transportation Not at this time, though it is planned for the future. Maine Department of Transportation Maryland Department of Transportation NR Massachusetts Department of Transportation NR Michigan Department of Transportation Yes we archive the WIM data. We have an Oracle

database table that the data is imported into. We have 3 years of data in that database. Data before that is stored in the original output format and there is a fair amount in FHWA format.

Minnesota Department of Transportation Proprietary binary in zipped files stored indefinitely.

Mississippi Department of Transportation The data is archived in a text file…cardw format. We have archived WIM data from 1993.

Missouri Department of Transportation Yes, tabular format, 5 years Nebraska Department of Transportation

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Nevada Department of Transportation Up to this point we have archived all data items in a foxpro database format and have archived our federally submitted files for a period of ten years.

New Jersey Department of Transportation Raw data (bin format) collected from each site are saved in a CD-ROM monthly. Classification and speed data are summarized in Excel format and published on NJDOT’s website. Reporting requirement by FHWA is on a VTRIS data base and copy is also saved.

New Mexico Department of Transportation Yes 4card and 7card formats. Seven years as specified by TMG.

New York Department of Transportation Yes, See 3.3 North Dakota Department of Transportation Data is currently stored on PC, - No long term

storage plan has been developed yet. Ohio Department of Transportation We archive all WIM data forever and we store it in

the current TMG W & C card formats. We also store speed for each site.

Oklahoma Department of Transportation Oregon Department of Transportation Crescent data is stored on a mainframe –

indefinitely. Report data (text format) is kept for one year.

Pennsylvania Department of Transportation South Dakota Department of Transportation Processed TMG Card 4 and 7 Format. Forever Texas Department of Transportation Vermont Department of Transportation Virginia Department of Transportation WIM Data is archived in its original format on a

server. Washington Department of Transportation We do archive our data. We have data back to

1994 Wisconsin Department of Transportation Wyoming Department of Transportation WIM data is archived in the FHWA “traffic

monitoring data formats” and the WIM instruments unique text format.

NR - No Response

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Question 3.6 Do you archive the binary WIM data files from the data collector? If so, how much binary data do you have archived? Please explain.

State Alaska Department of Transportation All AK WIM data files are archived in binary

format. In 2000, the WIM program was centralized in the Statewide Program Development office. Since that time, WIM sites have been added and existing systems rebuilt. Also, the State contracted out on-site WIM maintenance and the biannual calibration to IRD. Under the States IT Task Order system, a new WIM Oracle Database and web interface reporting system was developed by Wostmann & Associates, Inc. for use by DOT&PF staff.

Arkansas Department of Transportation California Department of Transportation Yes Connecticut Department of Transportation Data is collected in ASCII format. Data are stored

to create the FHWA C and W cards. These data include axle weights, gross weights, axle spacings and vehicle length.

Delaware Department of Transportation Florida Department of Transportation Yes. WIM binary files are available for systems

installed since 1988. Georgia Department of Transportation No we do not maintain the binary files at this time. Hawaii Department of Transportation Yes. Binary data back to March of 2003 is

available. Idaho Department of Transportation Same as above – archived back to original

installation date for each system. Illinois Department of Transportation NR Indiana Department of Transportation See answer to 3.4 Iowa Department of Transportation We do not archive binary WIM data. Kansas Department of Transportation binary data, but the final data reported for FHWA

is the official archive. Louisiana Department of Transportation No Maine Department of Transportation Maryland Department of Transportation NR Massachusetts Department of Transportation NR Michigan Department of Transportation Yes we do and we have up to 10 years of data

backed up on DVD/CD Minnesota Department of Transportation All recent data is stored, also some from 1990’s Mississippi Department of Transportation Yes, that would be the img file as mentioned

above. Missouri Department of Transportation Yes, 5 years of data Nebraska Department of Transportation Nevada Department of Transportation Yes we do and we have from three to ten years of

data archived New Jersey Department of Transportation Yes, see above section 3.5. New Mexico Department of Transportation Current year only. New York Department of Transportation No North Dakota Department of Transportation Same as above Ohio Department of Transportation Yes - class & speed files from all of our peek sites.

At some point we will store all per vehicle records at these sites so we won’t need to bin the data. From what we see, as soon as data is summarized (binned), it isn’t what a customer wants.

Oklahoma Department of Transportation

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Oregon Department of Transportation The “binary” data (Crescent) appears as “text.” Archived to the beginning of WIM data collection

Pennsylvania Department of Transportation South Dakota Department of Transportation None Texas Department of Transportation Vermont Department of Transportation Virginia Department of Transportation We have all binary WIM data files archived on a

server. Washington Department of Transportation We archive the binary data - see above Wisconsin Department of Transportation Wyoming Department of Transportation No NR - No Response

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Question 3.7 Do you have traffic data for a whole year (or close to a year) at a WIM site that can be made available for our statistical analyses of seasonal variations of truck weights?

State Alaska Department of Transportation Yes Arkansas Department of Transportation California Department of Transportation Yes Connecticut Department of Transportation Yes Delaware Department of Transportation Florida Department of Transportation Yes Georgia Department of Transportation No Hawaii Department of Transportation Yes Idaho Department of Transportation Yes. Lots of available WIM data. Illinois Department of Transportation NR Indiana Department of Transportation Yes Iowa Department of Transportation Yes Kansas Department of Transportation Yes Louisiana Department of Transportation No Maine Department of Transportation Maryland Department of Transportation NR Massachusetts Department of Transportation NR Michigan Department of Transportation Yes Minnesota Department of Transportation Yes Mississippi Department of Transportation Yes Missouri Department of Transportation Yes Nebraska Department of Transportation Nevada Department of Transportation Yes New Jersey Department of Transportation Yes New Mexico Department of Transportation Yes New York Department of Transportation Yes North Dakota Department of Transportation Yes. Possibly. Ohio Department of Transportation Yes Oklahoma Department of Transportation Oregon Department of Transportation Yes. In a text format Pennsylvania Department of Transportation South Dakota Department of Transportation Yes Texas Department of Transportation Vermont Department of Transportation Virginia Department of Transportation Yes Washington Department of Transportation Yes Wisconsin Department of Transportation Wyoming Department of Transportation Yes NR - No Response

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*Question 3.8 Do you have traffic data of similar quality for a number of years at the same site that may be helpful in estimating trends in truck loadings?

State Alaska Department of Transportation Yes Arkansas Department of Transportation California Department of Transportation Yes Connecticut Department of Transportation No. See answer for previous question. Delaware Department of Transportation Florida Department of Transportation Yes Georgia Department of Transportation No Hawaii Department of Transportation Yes Idaho Department of Transportation Yes Illinois Department of Transportation No Indiana Department of Transportation Yes Iowa Department of Transportation Yes Kansas Department of Transportation Yes Louisiana Department of Transportation No Maine Department of Transportation Maryland Department of Transportation NR Massachusetts Department of Transportation NR Michigan Department of Transportation Yes Minnesota Department of Transportation Yes Mississippi Department of Transportation No Missouri Department of Transportation Yes Nebraska Department of Transportation Nevada Department of Transportation Yes New Jersey Department of Transportation Yes New Mexico Department of Transportation Yes New York Department of Transportation Yes North Dakota Department of Transportation Yes. Possibly. Ohio Department of Transportation Yes Oklahoma Department of Transportation Oregon Department of Transportation Yes. From “official” state weigh records. These

are available from every weigh station location, not just WIM sites.

Pennsylvania Department of Transportation South Dakota Department of Transportation Yes Texas Department of Transportation Vermont Department of Transportation Virginia Department of Transportation No Washington Department of Transportation Yes Wisconsin Department of Transportation Wyoming Department of Transportation Possibly NR - No Response

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Question 4.1 Do you do WIM data quality testing or validation to ensure data accuracy? Please explain.

State Alaska Department of Transportation Currently we use only IRD’s software to determine

the accuracy of the data. The quality of the data is suspect at this stage in WIM development.

Arkansas Department of Transportation California Department of Transportation Yes. Validation done with Infotek validation pro.

Custom software designed to validate California data.

Connecticut Department of Transportation Yes. Calibration is done using known vehicles from the traffic stream and typically known weight ranges. When data is processed the volume, speed, classification, and weights collected are checked and compared to the last time data was collected at that specific site. All the data submitted to FHWA is run through a series of validation checks to target common errors. In addition, the data is graphed to determine if vehicle distributions are consistent and appropriate for FHWA Class 9 and FHWA Class 9 front axle loadings. In the past we have run a series of checks including FHWA Class 9 vehicle distributions on the data after collection and prior to submittal.

Delaware Department of Transportation Florida Department of Transportation All WIM systems are calibrated shortly after

construction is completed. The data is then monitored to ensure it adheres to the standard established when it was first installed. If the data deviates from the standard, technicians find and correct the problem, and a new calibration is performed.

Georgia Department of Transportation We only run our data through the quality checks that are contained within VTRIS. We rely on the contractor to validate the data at this time.

Hawaii Department of Transportation Only basic comparison with historic ADTs, and truck percentages.

Idaho Department of Transportation We perform routine monitoring of WIM systems to verify data validity and accuracy.

Illinois Department of Transportation NR Indiana Department of Transportation Yes. Through the use of TRADAS software we

have thresholds set that look at vehicle characteristics, vehicle stream characteristics. We are also implementing a system where we capture all class 9 vehicle and monitor front axle weight, tandem axle weights and other characteristics to see if through trend data we can determine the failing of sensors before total failure occurs.

Iowa Department of Transportation We do validation of each site by using the Vehicle Travel Information System on a weekly basis.

Kansas Department of Transportation We use the front-axle average weight and bi-modal graph to indicate that a site may be out of calibration.

Louisiana Department of Transportation Compare WIM measurements to static scale readings on a daily basis.

Maine Department of Transportation Maryland Department of Transportation NR Massachusetts Department of Transportation NR

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Michigan Department of Transportation For data preceding 2004 there was not any validation or quality testing with the exception of SHRP/LTPP locations. Since then our data is passed through gross validity checks when uploaded to our Truck Weight Information System(TWIS) databases. Individual sites have been scrutinized better and has resulted in site upgrade from piezo to quartz piezo or other auto-calibration tweaking.

Minnesota Department of Transportation Visual observation. Mississippi Department of Transportation We just started Quality Control measures to

ensure that our sites are calibrated and not malfunctioning on a daily basis.

Missouri Department of Transportation Yes, With the assistance the CVE division within the Missouri State Highway Patrol, a sampling of the weights of combination vehicles is taken and compared the weights collected by the WIM unit being calibrated.

Nebraska Department of Transportation Nevada Department of Transportation We do several analyses on the data, which we

collect. We check the average ESALS as compared to historical data. We also graph the average front axle and gross weight distribution for type”9” vehicles. We also check the vehicle class distribution and total volume as compared to historical data.

New Jersey Department of Transportation Monthly, data is summarized at each site and we look at vehicle classification information, comparing the numbers from prior months and years. We check the average front axle weights of class 9 vehicles, the peak number, and average empty and loaded weights, which are analyzed whether they fall within expected ranges.

New Mexico Department of Transportation Yes, when all piezo’s are good, we hire a truck with a known weight 75k and calibrate all lanes.

New York Department of Transportation Please contact us for further information. It is more detailed than what can fit here. Our checks are in line with the FHWA’s ‘TDQ’ program procedures.

North Dakota Department of Transportation WIM sites and data are monitored daily for calibration drift – Highway patrol uses data and WIM site real time data to monitor truck traffic weights against static/portable weights

Ohio Department of Transportation Yes - we now have software called Traffic Keeper Ohio (TKO) that does QC checks on all of our volume, length class, axle class and weight data. TKO uses GVW curves and detects the peaks. It reports shifts in the weight peaks based on a “n” number of week average.

Oklahoma Department of Transportation Oregon Department of Transportation Only when an error appears. Pennsylvania Department of Transportation South Dakota Department of Transportation Yes, many internal programs to watch daily files

for reasonable values Texas Department of Transportation Vermont Department of Transportation Virginia Department of Transportation The front axle weights and GVW distribution of

class 9 vehicles are tracked to detect calibration drift. The number and type of vehicle errors are also monitored.

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Washington Department of Transportation The Electronics Section visits each of the WIM sites and performs a field check of all the equipment and sensors. Once this check is completed a truck (Class 9) with a known weight is rented and the driver makes 10 passes per lane to calibrate the sensors and counter. The data is then polled weekly and placed into a file. At month end the data is evaluated and graphs are produced that show the trend for trucks over the month based on total weight and front axle weight.

Wisconsin Department of Transportation Wyoming Department of Transportation Weekly GVW graphs for FHWA class 9’s are

utilized to validate weight accuracy. Weekly vehicle classification graphs are used to validate classification and volume.

NR - No Response

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Question 4.2 How often do you recalibrate WIM systems? Do you have a procedure to decide if a recalibration is required? Please explain.

State Alaska Department of Transportation Currently, we have a maintenance contract with

IRD. The sites are calibrated in the spring and fall. Arkansas Department of Transportation California Department of Transportation LTPP/SHRP sites typically annually. Office

calibrations are done first then field calibrations. Connecticut Department of Transportation Calibration is conducted each time data is

collected. We conduct calibrations and field validations using the FHWA LTPP procedures. These include use of two Class 9 vehicles in good shape, one with air-ride suspension that are fully loaded, statically weighted, and run at least 20 passes by the WIM scale. When possible, it has also been found necessary to use the same truck from one field calibration to the next, as there can be variability between vehicles. This is done at least once a year, sometimes twice. In addition, field calibrations are scheduled if the issues are detected from office review of the data or observed in the field.

Delaware Department of Transportation Florida Department of Transportation Two SHRP WIM at SPS test sites are

calibrated/validated annually. Bending plate and Quartz piezo systems are calibrated initially upon installation, and whenever system components (sensors, CPU) are changed. Regular piezo WIM systems will not stay in calibration—they are too temperature dependent.

Georgia Department of Transportation All our sites use portable machines which have auto calibration features.

Hawaii Department of Transportation At least once or twice per year. Idaho Department of Transportation We monitor systems and compare results to

vehicles of known weight. If sensors show problems, we make necessary system adjustments.

Illinois Department of Transportation NR Indiana Department of Transportation All sites are calibrated annually. Obviously if data

validation indicated calibration error then that can change the priority of site calibrations.

Iowa Department of Transportation We have an auto calibrate feature on our data collectors that calibrates the sensors by using front axle weights of class 9(truck/tractor 5 axle combos) and is set to recalibrate approximately 6 times a day.

Kansas Department of Transportation Portables are recalibrated to a test truck at every site. The permanents are supposed to be calibrated every year.

Louisiana Department of Transportation As needed-if weight measurements are determined to be somewhat inaccurate (consistently more than plus or minus 5 percent) then recalibration is done.

Maine Department of Transportation Maryland Department of Transportation NR Massachusetts Department of Transportation NR

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Michigan Department of Transportation The sites are initially calibrated but not in great detail. All sites have auto-calibration running. We have just implemented a calibration procedure for our bending plate and quartz locations. These are sites used by Motor Carrier and newly installed sites caused by road reconstruction. We are going to monitor the sites to determine when to recalibrate.

Minnesota Department of Transportation When system results seems erroneous Mississippi Department of Transportation We calibrate annually and sometimes more often if

the site falls out of tolerance. We check the steering weights and spacings on a VC 9 because these attributes usually remain constant.

Missouri Department of Transportation We try to do the calibration at least once a year sometime between October and December. If a site is re-installed throughout the year a calibration is done with a vehicle of known weight until it can be re-calibrated during the time the remainder of the sites are calibrated.

Nebraska Department of Transportation Nevada Department of Transportation We check the calibration values once a year by

collecting observations of a type “9” vehicle at all the permanent sites. We collect seventy-seven observations at each lane being verified which yield the statistical reliability required for 95% accuracy +-5%

New Jersey Department of Transportation We calibrate only once every 2 years. We go through the listing and try to cover each WIM site. Also, at least once a month, the classification is checked, comparing types of vehicles from the traffic stream to the classes recorded by the WIM computer. During the validation process, system calibration factors are also adjusted if found to be over- or under-calibrated.

New Mexico Department of Transportation We calibrate when all piezo’s are good, over 3V output. Below three 3V output we calibrate with front axle factor with trucks on the road.

New York Department of Transportation We use the calibration methods outlined in the ASTM WIM Spec. Sites are calibrated with the method annually. The sites also auto-calibrate using the steering axle of a Class 9 (352) truck.

North Dakota Department of Transportation Once our warranty period expires we plan on calibrating once a year or if calibration drift is detected – Currently, no plan has been initiated yet

Ohio Department of Transportation We try to do an annual calibration at each WIM site. Our high end systems are calibrated using 2 trucks. Prezo sites are calibrated using 1 truck. If a site has a problem we will delay calibrating it until the problem is fixed.

Oklahoma Department of Transportation Oregon Department of Transportation WIM’s are calibrated twice annually, or when

weight discrepancies between WIM and static scales are recognized

Pennsylvania Department of Transportation South Dakota Department of Transportation Try to calibrate on a 2 to 3 year cycle and if

internal program see unreasonable data then will calibrate

Texas Department of Transportation Vermont Department of Transportation

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Virginia Department of Transportation Recalibrations are done when data quality testing indicates excessive calibration drift. Also, DMV mobile weight enforcement crews do periodic spot checks which could trigger a recalibration.

Washington Department of Transportation Sites are being calibrated once a year. We just restarted our calibration program 2 years ago so not all of our sites have received calibration (some have been rendered useless due to construction programs where the project is lasting 2 – 3 years – HOV lanes additions would be one example in the urban area). We monitor the WIM data and if we have front axle weights or total weights outside of an expected range our WIM technician will perform a trouble call to the site. Also if any of the sensors are replaced the site will be recalibrated.

Wisconsin Department of Transportation Wyoming Department of Transportation Annually if needed and only if test truck results

warrant adjustments. NR - No Response

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*Question 4.3 Who does the recalibration of WIM systems?

State Alaska Department of Transportation IRD Arkansas Department of Transportation California Department of Transportation Caltrans or IRD, for field calibrations. Caltrans only

for office calibrations. Connecticut Department of Transportation The person who collects the WIM data.

Recalibration is conducted in-house with ConnDOT staff and hiring with rented vehicles and operators.

Delaware Department of Transportation Florida Department of Transportation In-house staff or consultants. Georgia Department of Transportation NR Hawaii Department of Transportation The manufacturer’s own technicians (usually IRD)

or an authorized representative thereof. Idaho Department of Transportation Our staff does all system installation, maintenance

and calibration. Illinois Department of Transportation NR Indiana Department of Transportation We have a maintenance contract with International

Road Dynamics (IRD) who does our site calibrations.

Iowa Department of Transportation I am responsible for recalibration. Kansas Department of Transportation KDOT personnel responsible for portable scales. Louisiana Department of Transportation International Road Dynamics can do it remotely. Maine Department of Transportation Maryland Department of Transportation NR Massachusetts Department of Transportation NR Michigan Department of Transportation We do our own calibration. Minnesota Department of Transportation Internal staff Mississippi Department of Transportation Mississippi DOT Planning Division’s Traffic

Section Missouri Department of Transportation MoDOT Field Personnel along with assistance a

personnel from the MSHP - CVE section. Nebraska Department of Transportation Nevada Department of Transportation Our Traffic Information division New Jersey Department of Transportation Bureau (DOT) staff with help from the Department

of Treasury’s truck and driver. New Mexico Department of Transportation NMDOT/Contractor New York Department of Transportation In-house staff. North Dakota Department of Transportation NDDOT personnel plan to do this Ohio Department of Transportation I do most of the calibrations. One field technician

calibrates the 8 WIM’s in his area. Oklahoma Department of Transportation Oregon Department of Transportation ITS Specialist – through remote access Pennsylvania Department of Transportation South Dakota Department of Transportation US with assistance from Motor Carrier Division Texas Department of Transportation Vermont Department of Transportation Virginia Department of Transportation This is done in-house Washington Department of Transportation Our WIM Technician – Hoang Nguyen. Wisconsin Department of Transportation Wyoming Department of Transportation Planning WIM personnel. NR - No Response

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*Question 4.4 Please describe the recalibration techniques (Test trucks, AVI, Auto-calibration)?

State Alaska Department of Transportation Test truck Arkansas Department of Transportation California Department of Transportation Test trucks driven at various speeds. Limits set at

+/-5% error. Office calibration’s using weights from Class 9 vehicles using 10.5 kips as base and historical data.

Connecticut Department of Transportation Calibration is conducted using known vehicles from the traffic stream and typically known weight ranges. Through the office checks and the LTPP checks conducted by the FHWA Regional contractors.

Delaware Department of Transportation Florida Department of Transportation We calibrate our WIM systems to a class 09 truck

with air suspension that is loaded between 70,000 and 80,000 pounds gvwt. As many runs as needed to dial in the system, and then a minimum of 20 runs with no changes to any parameters to validate the calibration. The validation runs consist of a minimum of 3 runs at each speed calibration point (there are 3 such points) and each intermediate 5mph speed. If the truck can make quick turnarounds, we’ll make 4 runs at each speed point.

Georgia Department of Transportation NR Hawaii Department of Transportation Recalibration is performed as per ASTM 1318

using pre-weighed test trucks. Idaho Department of Transportation Primarily auto-calibration, but also adjustment of

gain and control based on system software provided by the vendor. We can also control the type and number of characteristic vehicles used by each WIM system for auto-calibration.

Illinois Department of Transportation NR Indiana Department of Transportation When we do our annual calibrations at the WIM

sites, we typically have a class 9 semi, 5 axle, loaded between 70K – 80K with a static load and make 10 passes. Auto-calibration is only used at piezo sites, it is disabled at our Single Load Cell sites.

Iowa Department of Transportation As mentioned before we do recalibration using the auto-calibrate feature on data collector. We have also done validation by using test trucks.

Kansas Department of Transportation Autocalibration full-time, with annual test trucks. The load-cell scale was calibrated using the ASTM calibration specification initially, but it became far too expensive and time-consuming to continue.

Louisiana Department of Transportation Calibrated against static scale using vehicle of known weight.

Maine Department of Transportation Maryland Department of Transportation NR Massachusetts Department of Transportation NR Michigan Department of Transportation Sites with Piezo sensors are on auto-calibration.

The calibration process we are implementing is accomplished using test trucks.

Minnesota Department of Transportation Auto-calibration, test trucks

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Mississippi Department of Transportation We use the test truck method for calibration. We have a test truck (VC 9) with a known static weight. We make 3 runs…if the dynamic weights are in tolerance we make 4 more consecutive runs. If the dynamic weights fall out of tolerance we start over. You can refer to AASHTO guidelines for the tolerance levels.

Missouri Department of Transportation Along with the assistance of MSHP -CVE personnel, combination vehicles are randomly pulled over and weighed along the roadside. The weights taken from the scales are radioed to the attending technician at the permanent WIM installation after the vehicle passes over the piezos at the site location.

Nebraska Department of Transportation Nevada Department of Transportation We perform the analyses described previously

and do an annual on-site verification of calibration factors with a test vehicle.

New Jersey Department of Transportation A five axle tractor-trailer combination truck with a good suspension and a non-shifting load (approximately symmetric side to side load) of between 75,000 and 80,000 pounds gross vehicle weight (GVW) is used. The weight (front axle and GVW) is recorded at a certified static scale. The test vehicle makes multiple runs over the WIM-system sensors in each lane at prescribed speeds. At least 10 runs per lane are made before adjustments to the calibration factors followed by 3 more runs after the adjustment with value within about +/- 5 of the GVW. Each sensor is calibrated independently from each other in each lane. The system’s auto calibration parameters are also set up to self-adjust at various temperatures and specified times.

New Mexico Department of Transportation Test trucks, front axle factor 10K to 12K when piezo’s are 3V and under.

New York Department of Transportation See 4.2 North Dakota Department of Transportation Calibration truck used to provided several runs to

calibrate front axle as well as GVW and axle spacing

Ohio Department of Transportation At prezo sites we have auto cal. turned on. Prezo sites are calibrated using 1 test truck of known weight. Bending plate & load cell sites are calibrated using 2 trucks. We normally make enough passes to verify the WIM is accurate and functioning properly. This could be as few as 5 & as many of 15 passes per lane.

Oklahoma Department of Transportation Oregon Department of Transportation We use samples from the normal stream of traffic.

Most often weights from the WIM are compared to weights from in-station static scale for 20 consecutive trucks. The % difference is calculated, and adjustments made accordingly.

Pennsylvania Department of Transportation South Dakota Department of Transportation During installation use test trucks and then later

calibration weigh all truck on road with motor carries static scale and compare each truck weight to WIM scale

Texas Department of Transportation Vermont Department of Transportation

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Virginia Department of Transportation At sites near a weigh station, we use trucks selected from the traffic stream. At other sites, test trucks are used.

Washington Department of Transportation A class 9 truck makes several passes (minimum of 5) over a lane to establish a baseline. From that baseline a recalibration factor is established. Then a minimum of 5 more passes are done. A final calibration number is established from those passes.

Wisconsin Department of Transportation Wyoming Department of Transportation A test truck (FHWA classification 9 loaded to

greater than 67k lbs) makes 10 passes over each lanes sensors at average site speed. The trucks static GVM is compared to the 10 pass average WIM GVM and adjustments are performed from these results.

NR - No Response

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*Question 4.5 Do you have a Quality Assurance Program in place for your WIM systems to check data accuracy?

State Alaska Department of Transportation No Arkansas Department of Transportation California Department of Transportation No Connecticut Department of Transportation Yes. Through the office checks and the LTPP

checks conducted by the FHWA Regional contractors.

Delaware Department of Transportation Florida Department of Transportation Yes Georgia Department of Transportation No Hawaii Department of Transportation No Idaho Department of Transportation Yes. This is a daily ongoing part of our WIM

maintenance and processing program. Illinois Department of Transportation NR Indiana Department of Transportation Yes Iowa Department of Transportation Yes Kansas Department of Transportation No Louisiana Department of Transportation Yes Maine Department of Transportation Maryland Department of Transportation NR Massachusetts Department of Transportation NR Michigan Department of Transportation Yes Minnesota Department of Transportation Yes Mississippi Department of Transportation Yes Missouri Department of Transportation Yes Nebraska Department of Transportation Nevada Department of Transportation Yes New Jersey Department of Transportation Yes New Mexico Department of Transportation Yes New York Department of Transportation Yes North Dakota Department of Transportation No. Still under development. Ohio Department of Transportation Yes. TKO Oklahoma Department of Transportation Oregon Department of Transportation Yes. A trouble Report system. Pennsylvania Department of Transportation South Dakota Department of Transportation Yes Texas Department of Transportation Vermont Department of Transportation Virginia Department of Transportation Yes Washington Department of Transportation Yes Wisconsin Department of Transportation Wyoming Department of Transportation The procedures explained in Section 4.1 assure

data quality. NR - No Response

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Question 5.1 What specialized software do you use for data handling and processing of WIM data?

State Alaska Department of Transportation We use the provided software from IRD to test the

validity of the data and then the data is uploaded into a “homegrown” Oracle database where it is then available to other Alaska Department of Transportation officials and offices.

Arkansas Department of Transportation California Department of Transportation IRD office/CT WIM/Infotek Validation Pro Connecticut Department of Transportation Vendor software – Mikros. IRD (International

Road Dynamics) software the comes with the purchased systems. The LTPP data processing/flagging software is run by after our data is submitted to the FHWA Regional contractor.

Delaware Department of Transportation Florida Department of Transportation Polling and processing use custom written

software. The California CTWIM software is used for analysis.

Georgia Department of Transportation VTRIS Hawaii Department of Transportation IRD Data Analysis Software Rev.C, IRD Office

Rev. 7.5.0, PAT Reporter 100, PAT Reporter 200, TVT, VTRIS, in house developed data processing macros

Idaho Department of Transportation Currently installing the TrafLab Software system for traffic data management and processing – which includes WIM data. TrafLab is provided by Trancite Systems of Boise, Idaho.

Illinois Department of Transportation NR Indiana Department of Transportation We predominately utilize the Chaparral System’s

TRADAS 3 Software data management. We will also utilize IRD’s Office software to validate data to create summary reports and data exports.

Iowa Department of Transportation We use Peek TOPS software for data handling and processing.

Kansas Department of Transportation Vendor software, TRADAS, VTRIS, several in-house programs

Louisiana Department of Transportation International Road Dynamics proprietary software. Maine Department of Transportation Maryland Department of Transportation NR Massachusetts Department of Transportation NR Michigan Department of Transportation MDOT developed software – Truck Weight

Information System (TWIS). This program imports, conducts gross validity checks, and reports how much data did not pass those validity checks.

Minnesota Department of Transportation IRD proprietary software Mississippi Department of Transportation For QA\QC we have an in-house program that was

written to do some basic checks as mentioned above. As of this moment…for data reporting we use VTRIS. We are moving toward a commercial software called WIM NET for QA\QC and data reporting.

Missouri Department of Transportation WIM data is processed through our Traffic Data Analysis Software where it is factored and made available to our transportation community via our Transportation Management System.

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Nebraska Department of Transportation Nevada Department of Transportation Tradas New Jersey Department of Transportation IRD Office software is used for generating various

reports; Vehicle Travel Information System (VTRIS) is used for processing, editing, and storing processed data for submission to the FHWA and generating the various W-Tables; K-Edit is used for viewing and editing huge ASCII files; and Microsoft Office is used for tabulating different summary tables.

New Mexico Department of Transportation TRADAS 3 (Traffic Data System) by Chaparral. New York Department of Transportation ‘Trafman’, in-house software (TCE (CC)). North Dakota Department of Transportation Vendors software (IRD/PAT) along with in-house

programs in Access, Excel Ohio Department of Transportation Vendor software to download, report, and

generate TMG files. TKO to QC all data & reports for customer data requests.

Oklahoma Department of Transportation Oregon Department of Transportation Unix Pennsylvania Department of Transportation South Dakota Department of Transportation In house developed Client server software Texas Department of Transportation Vermont Department of Transportation Virginia Department of Transportation 1) Oracle database, 2) an in-house developed

application which loads the data into the database, 3) MS Excel spreadsheet for the data quality graphs, 4) MS Access front end which produces TMG-W files.

Washington Department of Transportation SAS, SPF/SE, Microsoft excel, Brio, Access Wisconsin Department of Transportation Wyoming Department of Transportation Software provided by the WIM vendor. FHWA

“VTRIS” program. NR - No Response

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Question 5.2 Do you analyze your WIM data? What factors do you analyze? To whom do you distribute the results?

State Alaska Department of Transportation We analyze the data for errors and equipment

failures. The data is then put on the Oracle database and can be viewed and used by any employee of DOT&PF

Arkansas Department of Transportation California Department of Transportation Yes/Analysis of errors and class/wt percentages,

internal distribution. Connecticut Department of Transportation Yes – check volume, classification and weight.

Provide data to FHWA, CT-DOT Pavement Management, and CT-DOT Systems Inventory.

Delaware Department of Transportation Florida Department of Transportation Yes. We look at gross vehicle weight distributions,

steering axle weight, and tandem axle spacing for Class 09 vehicles. This information is kept in-house.

Georgia Department of Transportation We do not currently analyze the data on a regular basis. We have done one special study for our Bridge Office regarding posted bridges.

Hawaii Department of Transportation WIM data is analyzed for overweight vehicles, with the results being distributed to HDOT’s design, lab, and bridge design sections.

Idaho Department of Transportation Results are compared to previous months and years for the same site. Our software also has a broad range of data editing parameters. Weights and spacings are both analyzed. We provide WIM data based reports to a broad range of data clients including maintenance and design people, as well as private retailers and vendors.

Illinois Department of Transportation NR Indiana Department of Transportation Not internally. We provide a monthly download of

WIM data to Purdue University and to our research section. They perform their own analysis.

Iowa Department of Transportation We analyze our WIM data using Vehicle Travel Information System(VTRIS). Factors we use when analyzing data are vehicle weights, ESAL’s, percentage of errors in the data and gross vehicle weight distribution. We distribute the data to other departments with the Iowa Dept. of Transportation, FHWA and LTPP.

Kansas Department of Transportation ESAL rates for Pavement Design. Overweight rates for Enforcement

Louisiana Department of Transportation No Maine Department of Transportation Maryland Department of Transportation NR Massachusetts Department of Transportation NR

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Michigan Department of Transportation We review overweight trucks to determine percentage overweight by single axle, tandem and gross weights. Motor Carrier Division of the State Police have direct access to this data and the reports. We calculate ESAL values for the existing pavement. We can also perform ESAL estimates for a site using various pavement types and thickness. Planners responsible for traffic forecasting and working with Pavement Design engineers have direct access to this information and the “what if” ESAL calculations.

Minnesota Department of Transportation Damage from overweight vehicles, ESALs that are over design limits and ESALs by vehicle class. FHWA, traffic forecasting, pavement design, pavement management.

Mississippi Department of Transportation Yes. We use WIM data to derive our ESAL factors, and we will be using our WIM data to implement the new Pavement Design Guide. We report WIM data to FHWA on a monthly basis. Some of our customers for WIM data are roadway design, bridge division, research division, and enforcement.

Missouri Department of Transportation We utilize our WIM data for mechanistic pavement design and for the calculation of ESALS relating to our pavement warranty program. We also utilize the data to determine tonnage hauled. We regularly provide data to the Missouri State Highway Patrol in the enforcement of overweight hauling as well. We also work with FHWA to have sites assessed for LTPP. And, we send all our WIM and class data to ERSI to be included in the ‘New Pavement Design Program’.

Nebraska Department of Transportation Nevada Department of Transportation This was described previously New Jersey Department of Transportation Yes -- Classification, Weight, Speed and Volume

information are all analyzed for integrity of data. Results are not distributed and used internally in deciding if information is good or not, or if equipments needs maintenance.

New Mexico Department of Transportation Yes, Volume and Classification Data,. WIM Data sent to TWS and LTPP. Front axle factor 10K -12K, FHWA.

New York Department of Transportation Minimal. Our biggest customer is the FHWA and that consists of reporting required by and detailed in the FHWA ‘Traffic Monitoring Guide’

North Dakota Department of Transportation Currently only overweight vehicles and time of day – day of week information is shared with North Dakota Highway Patrol

Ohio Department of Transportation Yes-front axle weights, average ESAL’s, load spectrum, GVW by class curves, over weight by vehicle type. Pavement design, the public, planning & programming sections use our data regularly.

Oklahoma Department of Transportation

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Oregon Department of Transportation Yes – for my purpose I look specifically at axle weight/spacing, classification, GVW. In addition, WIM data is currently distributed to; ODOT – Highway Division ODOT – Bridge Section ODOT – Engineering Section Oregon State University School of Engineering Portland State University Scholl of Engineering

Pennsylvania Department of Transportation South Dakota Department of Transportation Yes we analyze data, __ weights, gross weights,

axle spacings, truck type( Federal Classification Scheme F), ESAL’s, see below

Texas Department of Transportation Vermont Department of Transportation Virginia Department of Transportation We look for calibration drift and other errors in the

WIM data. This information is shared with our installation and maintenance contractor and hardware vendors.

Washington Department of Transportation Yes, 4 vs 7card, high volume hours, peak periods, lane info, Truck % increase/Decrease, Lane info, Zero hours, shift in patterns, site history compare of trends from other sites.

Wisconsin Department of Transportation Wyoming Department of Transportation FHWA vehicle type classification and ESAL

calculations are reported to WYDOT’s traffic analysis section.

NR - No Response

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Question 5.3 Is your WIM data currently used for the following?

State Alaska Department of Transportation Arkansas Department of Transportation California Department of Transportation Connecticut Department of Transportation Delaware Department of Transportation Florida Department of Transportation Georgia Department of Transportation Hawaii Department of Transportation Idaho Department of Transportation Illinois Department of Transportation Indiana Department of Transportation Iowa Department of Transportation Kansas Department of Transportation Louisiana Department of Transportation Maine Department of Transportation Maryland Department of Transportation Massachusetts Department of Transportation Michigan Department of Transportation Minnesota Department of Transportation Mississippi Department of Transportation Missouri Department of Transportation Nebraska Department of Transportation Nevada Department of Transportation New Jersey Department of Transportation New Mexico Department of Transportation New York Department of Transportation North Dakota Department of Transportation Ohio Department of Transportation Oklahoma Department of Transportation Oregon Department of Transportation Pennsylvania Department of Transportation South Dakota Department of Transportation Texas Department of Transportation Vermont Department of Transportation Virginia Department of Transportation Washington Department of Transportation Wisconsin Department of Transportation Wyoming Department of Transportation NR - No Response

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Question 5.4 Have you used WIM data to investigate truck weight trends in your state? If yes, please explain (please also include references to any reports).

State Alaska Department of Transportation No Arkansas Department of Transportation California Department of Transportation NR Connecticut Department of Transportation Yes. For pavement, management purposes. Delaware Department of Transportation Florida Department of Transportation No Georgia Department of Transportation No Hawaii Department of Transportation No Idaho Department of Transportation Yes. We use both monthly and annual reports to

track truck weight trends in Idaho. Illinois Department of Transportation NR Indiana Department of Transportation No. Our research Section is currently performing

this analysis on our data. Iowa Department of Transportation No Kansas Department of Transportation Yes. Annual truck weight data publication has

trend analysis Louisiana Department of Transportation No Maine Department of Transportation Maryland Department of Transportation NR Massachusetts Department of Transportation NR Michigan Department of Transportation No. Not yet. We are starting to develop some site

reports to monitor trends and data quality. We have one Pavement Performance Warranty project where we have tracked the accumulated ESAL’s and truck volumes for a little over a year.

Minnesota Department of Transportation No Mississippi Department of Transportation No Missouri Department of Transportation Yes. Tons hauled Nebraska Department of Transportation Nevada Department of Transportation No New Jersey Department of Transportation Yes. Classification reports by site are available on

the NJDOT’s website. We have also provided information for various studies to Rutgers University and the New Jersey Institute of Technology (NJIT) and to other traffic professionals.

New Mexico Department of Transportation No New York Department of Transportation Yes. Minimal and typically for a specific location

and time period to satisfy a particular program area need.

North Dakota Department of Transportation No Ohio Department of Transportation Yes. GVW by functional class, loading by industry,

loadings that change by year. Oklahoma Department of Transportation Oregon Department of Transportation Yes. Truck trend data is considered for pending

highway overlay or bridge work. Pennsylvania Department of Transportation South Dakota Department of Transportation No Texas Department of Transportation Vermont Department of Transportation Virginia Department of Transportation No

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Washington Department of Transportation Yes. The weigh data that is collected is used in the development of the state freight and goods report

Wisconsin Department of Transportation Wyoming Department of Transportation No NR - No Response

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Question 5.5 Has your state used WIM data for bridge design applications / bridge live load modeling? If yes, please explain (please also include references to any reports).

State Alaska Department of Transportation No Arkansas Department of Transportation California Department of Transportation Yes. Caltrans has started using WIM data for

bridge design recently. Connecticut Department of Transportation No. Based loads permitted through the state. Delaware Department of Transportation Florida Department of Transportation No Georgia Department of Transportation No Hawaii Department of Transportation No Idaho Department of Transportation Yes. We provide some commercial vehicle weight

data and reports to our bridge design people. Illinois Department of Transportation NR Indiana Department of Transportation No. The data is not provided directly to them.

However through Purdue University or our research section they maybe utilizing the data.

Iowa Department of Transportation No Kansas Department of Transportation No Louisiana Department of Transportation No Maine Department of Transportation Maryland Department of Transportation NR Massachusetts Department of Transportation NR Michigan Department of Transportation No. Not to my knowledge. Minnesota Department of Transportation No Mississippi Department of Transportation No Missouri Department of Transportation No Nebraska Department of Transportation Nevada Department of Transportation No New Jersey Department of Transportation No New Mexico Department of Transportation No New York Department of Transportation North Dakota Department of Transportation No Ohio Department of Transportation Yes. Maumee River crossing design & I think for a

few other applications a few years back. Oklahoma Department of Transportation Oregon Department of Transportation Yes – currently the ODOT Bridge Section is

conducting an analysis for Bridge re-design, and engineering standards.

Pennsylvania Department of Transportation South Dakota Department of Transportation Unknown Texas Department of Transportation Vermont Department of Transportation Virginia Department of Transportation No Washington Department of Transportation No at least not to our knowledge Wisconsin Department of Transportation Wyoming Department of Transportation Not to my knowledge NR - No Response

C-47

Question 1.4 Please fill out the following table providing information for each mainline WIM site. Use additional sheets as required. Alaska Department of Transportation

WIM Site ID Route AADT Sensor Type

Vendor Date Installed

Date Last Calibrated

# of Traffic lanes

# of WIM Lanes

WIM in both Travel Directions? (Yes/No)

Near a Weigh Station (Yes/No)

Seward Seward Hwy 5000 Bending Plate

IRD September 2003

Fall 05 4 4 Yes No

Tudor Tudor Road

2000

Bending Plate

IRD August 2003

Fall 05 4 4 Yes

No

Glenn Glenn Hwy 6000

Bending Plate

IRD July 2003

Fall 05 6 1 No Yes

Port of Anchorage

Ocean Dock Road

950 Bending Plate

IRD June 2001

Fall 05 2 2 Yes No

Minnesota Minnesota Drive

2000 Bending Plate

IRD June 2001

Fall 05 5 5 Yes No

Fox Steese Hwy 500 Bending Plate

IRD August 2005

Fall 05 2 2 Yes Yes

Tok Alaska Hwy 120 Bending Plate

IRD August 2005

Fall 05 2 2 Yes Yes

Chulitna Parks Hwy 300 Piezo IRD TC540W

Fall 2004 Aug 05 2 2 Yes No

C-48

California Department of Transportation At the time of publication of this report, the compilation of this table was still in-progress by Caltrans.

C-49

Connecticut Department of Transportation

YEAR 2003:

WIM Site ID (Town) Route

Combined Directional

ADTT Sensor Type Vendor Date

Installed Date Last Calibrated

Number of

Traffic Lanes

Number of WIM Lanes

WIM in both Travel

Directions? (Yes/No)

Near a Weigh Station

(Yes/No) Glastonbury 2 46500 MSI(Portable) IRD 10/6/2003 10/6/2003 4 4 Yes No Winchester 8 13000 Phillips Phillips 8/25/2003 8/25/2003 4 4 Yes No Windsor 20 45200 MSI IRD 6/30/2003 6/30/2003 4 4 Yes No Montville 32 12700 MSI IRD 7/28/2003 7/28/2003 2 2 Yes No New Britain 72 62400 MSI IRD 8/25/2003 8/25/2003 6 6 Yes No Middlebury 84 62500 MSI IRD 12/10/2003 12/10/2003 4 4 Yes No Farmington 84 85900 MSI IRD 5/13/2003 5/13/2003 6 6 Yes No Manchester 84 113500 MSI IRD 12/1/2003 12/1/2003 8 8 Yes No Wallingford 91 82300 MSI IRD 8/27/2003 8/27/2003 6 6 Yes No Wethersfield 91 147900 MSI IRD 11/18/2003 11/18/2003 8 8 Yes No Windsor 91 130900 MSI IRD 7/7/2003 7/7/2003 8 8 Yes No Windsor 91 88800 MSI IRD 7/9/2003 7/9/2003 7 7 Yes No Madison 95 62000 MSI IRD 11/18/2003 11/18/2003 4 4 Yes No Cheshire 691 47300 Phillips Phillips 9/10/2003 9/10/2003 4 4 Yes No Killingly 695 3900 Phillips Phillips 9/3/2003 9/3/2003 4 4 Yes No Danbury(State Line) 84 76000 MSI IRD 8/20/2003 8/20/2003 4 4 Yes Yes Union(State Line) 84 33200 MSI IRD 12/1/2003 12/1/2003 6 6 Yes Yes Enfield(State Line) 91 94400 MSI IRD 8/27/2003 8/27/2003 6 6 Yes No Thompson(State Line) 395 23400 MSI IRD 9/3/2003 9/3/2003 4 4 Yes No

Weigh-In-Motion data collection is conducted on a rotating basis throughout the state. Equipment is used to collect data for a period of 48 hours once every three years with the exception being state lines which are collected for a period of 48 hours every year. Calibration is conducted using known typical vehicles

from the traffic stream and typically known weight ranges.

C-50

YEAR 2004:

WIM Site ID (Town) Route

Combined Directional

ADTT Sensor Type Vendor

Date Installed

Date Last Calibrated

Number of

Traffic Lanes

Number of WIM Lanes

WIM in both Travel

Directions? (Yes/No)

Near a Weigh Station

(Yes/No) Colchester 2 32500 MSI IRD 9/27/2004 9/27/2004 4 4 Yes No Mansfield 6 22300 MSI IRD 8/30/2004 8/30/2004 4 4 Yes No Harwinton 8 24100 MSI IRD 6/7/2004 6/7/2004 4 4 Yes No Waterford 85 26900 MSI IRD 6/21/2004 6/21/2004 4 4 Yes No Manchester 384 57600 MSI IRD 9/27/2004 9/27/2004 8 8 Yes No Bolton 384 26500 MSI IRD 9/14/2004 9/14/2004 4 4 Yes No Montville 395 58400 MSI IRD 8/30/2004 8/30/2004 4 4 Yes No Danbury(State Line) 84 70600 MSI IRD 6/14/2004 6/14/2004 4 4 Yes Yes Union(State Line) 84 45600 MSI IRD 11/16/2004 11/16/2004 6 6 Yes Yes Greenwich(State Line) 95 130800 MSI IRD 5/17/2004 5/17/2004 6 6 Yes Yes Thompson(State Line) 395 22800 MSI IRD 7/12/2004 7/12/2004 4 4 Yes No

Weigh-In-Motion data collection is conducted on a rotating basis throughout the state. Equipment is used to collect data for a period of 48 hours once every three years with the exception being state lines which are collected for a period of 48 hours every year. Calibration is conducted using known typical

vehicles from the traffic stream and typically known weight ranges.

C-51

YEAR 2005:

WIM Site ID (Town) Route

Combined Directional

ADTT Sensor Type Vendor

Date Installed

Date Last Calibrated

Number of

Traffic Lanes

Number of WIM Lanes

WIM in both Travel

Directions? (Yes/No)

Near a Weigh Station

(Yes/No) Brideport 8 84400 MSI IRD 8/9/2005 8/9/2005 6 6 Yes No Shelton 8 67000 MSI IRD 10/26/2005 10/26/2005 4 4 Yes No Berlin 15 28000 MSI IRD 11/14/2005 11/15/2005 4 4 Yes No Windsor Locks 20 49500 MSI IRD 7/19/2005 7/20/2005 4 4 Yes No Danbury(Exits 6-7) 84 123400 MSI IRD 11/1/2005 11/1/2005 6 6 Yes No North Haven 91 121200 MSI IRD 9/19/2005 9/19/2005 8 8 Yes No Wethersfield 91 151400 MSI IRD 11/30/2005 11/30/2005 8 8 Yes No Darien 95 152300 MSI IRD 7/25/2005 7/25/2005 7 7 Yes No Norwalk 95 129900 MSI IRD 9/19/2005 9/19/2005 6 6 Yes No Plainfield 95 28000 MSI IRD 10/18/2005 10/18/2005 4 4 Yes No Danbury(State Line) 84 65200 MSI IRD 11/8/2005 11/8/2005 4 4 Yes Yes Greenwich(State Line) 95 130100 MSI IRD 7/25/2005 7/25/2005 6 6 Yes Yes Thompson(State Line) 395 24400 MSI IRD 7/11/2005 7/11/2005 4 4 Yes No

Weigh-In-Motion data collection is conducted on a rotating basis throughout the state. Equipment is used to collect data for a period of 48 hours once every three years with the exception being state lines which are collected for a period of 48 hours every year. Calibration is conducted using known typical

vehicles from the traffic stream and typically known weight ranges.

C-52

WIM Site ID

Route ADTT Sensor Type

Vendor Date Installed

Date Last Calibrated

# of Traffic lanes

# of WIM Lanes

WIM in both Travel Directions? (Yes/No)

Near a Weigh Station (Yes/No)

LTPP 090600

CT 2 23900 Quartz-Piezo

Kistler/ IRD

Fall 1997 June 2005 4 (2-DIR)

4 Y No

LTPP 095001

I-84 90700 Quartz-Piezo

Kistler/ IRD

July 2003 June 2005 3 1 N WB only

No (20 mi)

LTPP 094008

I-84 111500 Quartz-Piezo

Kistler/ IRD

July 2003 June 2005 3 1 N WB only

No

LTPP 091803

CT 117 9900 Quartz-Piezo

Kistler/ IRD

July 2003 June 2005

1 1 N NB only

No

C-53

Florida Department of Transportation

WIM SITE ID ROUTE ADTT

SENSORTYPE VENDOR

DATEINSTALLED

DATE LASTCALIBRATED

# OF TRAFFICLANES

# OF WIM

LANES

WIM IN BOTHTRAVEL

DIRECTIONS ?(YES/NO)

NEAR A WEIGH

STATION ?(YES/NO)

128 US-27 23487 KISTLER IRD/PAT 12/3/2004 12/21/2004 4 1 NO NO192 SR-20 1852 KISTLER IRD/PAT 12/10/2004 2/25/2005 2 1 NO NO194 I-75 8500 KISTLER IRD/PAT ************ ************ 6 1 NO NO217 I-95 89303 KISTLER IRD/PAT 1/20/2005 4/6/2005 6 1 NO NO219 SR-85 14232 KISTLER IRD/PAT 2/10/2005 2/24/2005 4 1 NO NO220 I-10 29128 KISTLER IRD/PAT 6/8/2005 9/14/2005 4 1 NO YES223 SR-407 6662 KISTLER IRD/PAT 3/28/2005 4/7/2005 2 1 NO NO224 I-75 72500 KISTLER IRD/PAT 1/4/2005 2/22/2005 6 1 NO NO9901 I-10 26373 KISTLER IRD/PAT 5/30/2001 1/23/2003 4 4 YES YES9904 I-75 63375 KISTLER IRD/PAT 10/20/2005 1/11/2006 6 4 YES YES9905 I-95 71310 KISTLER IRD/PAT 11/10/2005 12/20/2005 6 4 YES YES9907 US-231 14996 BL IRD/PAT 6/10/1998 1/22/2003 4 4 YES NO9909 US-19 13192 BL IRD/PAT 11/2/2001 8/11/1997 4 4 YES NO9913 TPK 37093 KISTLER IRD/PAT 12/6/1994 10/22/2002 4 4 YES NO9914 I-295 64390 KISTLER IRD/PAT 11/14/2003 ************* 4 4 YES NO9916 US-29 33438 BL IRD/PAT 5/7/2002 ************** 4 4 YES NO9917 US-41 16554 B.PLATE IRD/PAT 5/2/2002 8/5/1997 4 2 NO NO9918 US-27 15802 BL IRD/PAT 1/12/2001 ************** 4 4 YES NO9919 I-95 38059 BL IRD/PAT 1/30/2003 10/31/2003 4 4 YES NO9920 I-75 44109 KISTLER IRD/PAT 5/14/2003 9/11/2003 4 4 YES YES9921 US-1 17837 KISTLER IRD/PAT 3/21/2003 7/10/2003 4 2 YES NO9922 I-275 78282 BL IRD/PAT 12/10/2002 12/19/2002 6 6 YES NO9923 I-95 75139 B.PLATE IRD/PAT 3/29/2004 5/20/2004 4 2 YES NO9925 US-92 16429 B.PLATE IRD/PAT 7/1/1990 7/15/2004 4 2 YES NO9926 I-75 126547 B.PLATE IRD/PAT 6/1/1990 10/31/2002 6 4 YES NO9927 SR-546 14064 B.PLATE IRD/PAT 9/28/1990 6/5/1997 4 4 YES NO9928 I-10 20112 KISTLER IRD/PAT 12/7/1994 5/15/2002 4 4 YES YES9929 US-1 13105 B.PLATE IRD/PAT 4/11/2003 7/14/2004 4 2 NO NO9930 US-1 53300 BL IRD/PAT 3/21/2003 *************** 6 6 YES NO9931 TPK 36301 KISTLER IRD/PAT 10/4/1996 ************** 4 2 YES NO9934 SR-821 81727 BL IRD/PAT 6/3/2002 ************** 7 7 YES NO9935 US-27 8220 KISTLER IRD/PAT 3/20/2003 7/9/2003 4 2 YES NO9936 I-10 20838 BL IRD/PAT 1/30/2003 2/24/2003 4 4 YES NO9937 SR-87 12690 B.PLATE IRD/PAT 5/16/1996 ************** 4 4 YES NO9939 US-331 2161 B.PLATE IRD/PAT 10/25/1996 ************** 2 2 YES NO9940 SR-267 8453 B.PLATE IRD/PAT 3/25/1998 ************** 4 4 YES NO9942 SR-85 4278 B.PLATE IRD/PAT 6/9/1998 ************** 2 2 YES NO9943 US-90 4943 B.PLATE IRD/PAT 6/10/1998 ************** 2 2 YES NO9944 SR-69 1589 B.PLATE IRD/PAT 8/14/1998 ************** 2 2 YES NO9946 SR-363 2161 B.PLATE IRD/PAT 8/18/1998 ************** 2 2 YES NO

C-54

Hawaii Department of Transportation

WIM Site ID

Route ADTT Sensor Type

Vendor Date Installed

Date Last Calibrated

# of Traffic lanes

# of WIM Lanes

WIM in both Travel Directions? (Yes/No)

Near a Weigh Station (Yes/No)

C12E 30 598 Piezo / Loop

IRD 1994 11/2005 2 2 Y N

S8R 19 1455 Piezo / Loop

IRD 1994 11/2005 2 2 Y N

S9 11 2652 Piezo / Loop

IRD 1994 11/2005 2 2 Y N

C202B 64 2272 Bending Plate

PAT 1988 11/2005 6 5 N Y

H41W H-3 1577 Bending Plate

PAT 1996 11/2005 4 4 Y N

10W 95 5759 Bending Plate

IRD 1/2003 11/2005 4 4 Y N

C7L H-1 11,000 Piezo / Loop

IRD 2/2006 2/2006 13 12 Y N

C-55

Idaho Department of Transportation WIM Site

ID Route ADTT Sensor

Type Vendor Date

Installed Date Last Calibrated

# of Traffic lanes

# of WIM Lanes

WIM in both Travel Directions? (Yes/No)

Near a Weigh Station (Yes/No)

Downey I-15 7900 Piezzo &loop

ECM June, 1996 ongoing 4 All lanes

Yes No

Mass Rocks I-86 6300 Piezzo &loop

ECM June, 1995 ongoing 4 All lanes

Yes No

Rigby US-20 18000 Piezzo &loop

ECM June, 1996 ongoing 4 All lanes

Yes No

Wolf Lodge I-90 13000 Piezzo &loop

ECM Sept, 1997 ongoing 4 All lanes

Yes No

Cotteral I-84 6600 Piezzo &loop

ECM July, 1994 ongoing 4 All lanes

Yes Yes

Mica US-95 10000 Piezzo &loop

ECM Sept, 1995 ongoing 2 All lanes

Yes No

Samuels US-95 8800 Piezzo &loop

ECM Sept, 1995 ongoing 2 All lanes

Yes No

Black Canyon

I-84 18000 Piezzo &loop

ECM June, 1995 ongoing 4 All lanes

Yes No

Flattop US-93 5300 Piezzo &loop

ECM July, 1995 ongoing 2 All lanes

Yes No

Filer US-30 6100 Piezzo &loop

ECM July, 1995 ongoing 2 All lanes

Yes No

GTown US-30 4000 Piezzo &loop

ECM July, 1995 ongoing 2 All lanes

Yes No

Mesa US-95 2100 Piezzo &loop

ECM May, 1995 ongoing 2 All lanes

Yes No

Parma US-95 6100 Piezzo &loop

IRD Aug, 2005 ongoing 4 All lanes

Yes No

Hammett I-84 13500 Piezzo &loop

IRD July, 2005 ongoing 4 All lanes

Yes No

Dubois I-15 2800 Piezzo &loop

IRD July, 2003 ongoing 4 All lanes

Yes No

Alpine US-95 17000 Piezzo &loop

IRD June, 2004 ongoing 2 All lanes

Yes No

C-56

Indiana Department of Transportation

Station Route/Location ADTT Sensors Vendor Date Installed Date Last Calibrated

Traffic Lanes

WIM Lanes

WIM Both Dir

Near Weigh Station

1000 US 41 SB RM 199.9 769 2P, 1 D IRD Not readily Available 2006 4 2 N

Not readily Available

1100 I 65 NB MM 175.9 11186 4P IRD Not readily Available 2006 4 4 Y

Not readily Available

1200 I 74 EB MM 5.2 6016 8SLC IRD Not readily Available 2006 4 4 Y

Not readily Available

1300 I 70 WB MM 7.5 n/a 4P,2D IRD Not readily Available 2006 4 4 Y

Not readily Available

2000 I 69 SB MM 137.9 n/a 8SLC IRD Not readily Available 2006 4 4 Y

Not readily Available

2100 US 24 WB RM 87.6 1542 8P IRD Not readily Available 2006 4 4 Y

Not readily Available

2200 US 27 SB RM 100.2 1928 1BP IRD Not readily Available 2006 4 4 Y

Not readily Available

2300 I 69 SB MM 68.3 15424 2P IRD Not readily Available 2006 4 4 Y

Not readily Available

2400 US 24 WB RM 158.1 3643 4SLC IRD

Not readily Available 2006 2 2 Y

Not readily Available

3000 SR 332 WB RM 0.5 1279 2P,1D IRD Not readily Available 2006 4 1 N

Not readily Available

3100 SR 37 SB RM 172.25 4117 1VBP IRD

Not readily Available 2006 4 1 N

Not readily Available

3200 US 31 NB RM 125.7 2774 8P IRD Not readily Available 2006 4 4 Y

Not readily Available

3300 I 465 SB MM 10.0 n/a 12P IRD Not readily Available 2006 6 6 Y

Not readily Available

3400 I 65 NB MM 102.5 15025 12P IRD Not readily Available 2006 6 6 Y

Not readily Available

C-57

3500, 3510, 3520, 3530 I 465 NB MM 42.4 n/a 24SLC IRD

Not readily Available 2006 12 12 Y

Not readily Available

3600 I 70 EB MM 108.0 13875 8SLC IRD Not readily Available 2006 4 4 Y

Not readily Available

3700 I 70 EB MM 155.5 n/a 6P IRD Not readily Available 2006 4 4 Y

Not readily Available

4000, 4010, 4020, 4030

I 80 / I 94 EB MM 6.0 n/a 20SLC IRD

Not readily Available 2006 10 10 Y

Not readily Available

4100 I 65 NB MM 218.4 n/a 4P IRD Not readily Available 2006 4 2 Y

Not readily Available

4200, 4210 I 65 NB MM 253.7 n/a 12SLC IRD

Not readily Available 2006 6 6 Y

Not readily Available

4300 I 94 EB MM 38.0 134118SLC / 4P IRD

Not readily Available 2006 6 6 Y

Not readily Available

4400 I 80 / 94 WB MM 13.4 18791 12P IRD

Not readily Available 2006 6 6 Y

Not readily Available

4500 SR 2 WB RM 65.2 995 8P IRD Not readily Available 2006 4 4 Y

Not readily Available

4600 US 31 NB RM 217.0 n/a 2P IRD Not readily Available 2006 4 1 N

Not readily Available

4700 SR 49 NB RM 35.3 3969 8P IRD Not readily Available 2006 4 4 Y

Not readily Available

5000 SR 37 SB RM 96.7 2791 2P IRD Not readily Available 2006 4 1 Y

Not readily Available

5100 I 65 SB MM 79.1 n/a 8SLC IRD Not readily Available 2006 4 4 Y

Not readily Available

5200 US 50 WB RM 137.4 1173 4P IRD

Not readily Available 2006 2 2 Y

Not readily Available

5300 I 74 EB MM 169.8 8161 4P IRD Not readily Available 2006 4 2 Y

Not readily Available

C-58

5400 I 64 EB MM 117.0 7437 4P IRD Not readily Available 2006 4 2 Y

Not readily Available

5500, 5510 I 65 NB MM 13569 16SLC IRD

Not readily Available 2006 8 8 Y

Not readily Available

5600, 5610 I 65 NB MM 12694 12SLC IRD

Not readily Available 2006 6 6 Y

Not readily Available

6000 US 50 EB RM 24.1 2118 2P IRD Not readily Available 2006 2 2 Y

Not readily Available

6100 I 64 EB MM 27.9 5318 4P IRD Not readily Available 2006 4 2 Y

Not readily Available

6200 I 64 EB MM 54.8 2308 2P IRD Not readily Available 2006 4 1 N

Not readily Available

6300 SR 62 WB RM 12.5 1365 1BP IRD Not readily Available 2006 4 1 N

Not readily Available

6400 SR 66 EB RM 18.7 492 8P IRD Not readily Available 2006 4 4 Y

Not readily Available

6500 I 164 WB MM 2.2 2434 1BP / 2P IRD Not readily Available 2006 4 2 Y

Not readily Available

6600 SR 66 WB RM 47.7 947 12P IRD Not readily Available 2006 6 6 Y

Not readily Available

7300 I 80/90 WB MM 32.0 10947 8P IRD

Not readily Available 2006 4 4 Y

Not readily Available

7320 I 80/90 WB MM 71.6 n/a 8P IRD

Not readily Available 2006 4 4 Y

Not readily Available

7340 I 80/90 WB MM 79.4 n/a 8P IRD

Not readily Available 2006 4 4 Y

Not readily Available

P=Piezo BP= Bending Plate VBP= Vaulted Bending Plate SLC= Single Load Cell D= Dynax

C-59

Iowa Department of Transportation

ADTT is based on 2004 data. WIM

Site ID Route ADTT Sensor

Type Vendor Date

Installed Date Last Calibrated

# of Traffic lanes

# of WIM Lanes

WIM in both Travel Directions? (Yes/No)

Near a Weigh Station (Yes/No)

190100 US 61 864 B/L

Measurement Specialist

1992 4 1 No No

190200 US 65 3229 B/L

Measurement Specialist

1995 4 4 Yes No

190600 I 35 5947 B/L

Measurement Specialist

1990 4 4 Yes Yes

190700 I 35 4635 B/L

Measurement Specialist

1992 4 4 Yes No

191044 US 20 4458 B/L

Measurement Specialist

1990 4 1 No No

193006 US 30 1229 B/L

Measurement Specialist

1991 4 1 No No

193009 I 380 6199 B/L

Measurement Specialist

1990 6 1 No No

193028 US 218 2948 B/L

Measurement Specialist

1991 4 1 No No

193033 US 218 2246 B/L

Measurement Specialist

1990 4 4 Yes No

193055 US 20 1616 B/L

Measurement Specialist

1991 4 1 No No

195042 I 35 3871 B/L

Measurement Specialist

1991 4 4 Yes No

196049 I 80 11260 B/L

Measurement Specialist

1991 4 4 Yes No

196150 IA 196 249 B/L

Measurement Specialist

1990 2 2 Yes No

C-60

WIM Site ID

Route ADTT Sensor Type

Vendor Date Installed

Date Last Calibrated

# of Traffic lanes

# of WIM Lanes

WIM in both Travel Directions? (Yes/No)

Near a Weigh Station (Yes/No)

199116 I 35 4864 B/L

Measurement Specialist

1991 4 4 Yes No

199126 I 80 9134 B/L

Measurement Specialist

1991 4 4 Yes No

Agency US 34 832 B/L

Measurement Specialist

2004 2 2 Yes No

Benton I 380 3261 B/L

Measurement Specialist

1990’s 4 4 Yes No

Brchnl US 18 1825 B/L

Measurement Specialist

2004 4 4 Yes No

Charles US 218 1350 B/L

Measurement Specialist

2004 4 4 Yes No

Dundee IA 13 261 B/L

Measurement Specialist

2002 2 2 Yes No

Eldrdg US 61 2049 B/L

Measurement Specialist

1992 4 4 Yes No

Iafall US 20 1117 B/L

Measurement Specialist

2004 4 4 Yes No

Iowa21 IA 21 141 B/L

Measurement Specialist

1990’s 2 2 Yes No

Mville I 80 9371 B/L

Measurement Specialist

2001 4 4 Yes Yes

Newham US 18 844 B/L

Measurement Specialist

2004 4 4 Yes No

Sibley IA 60 749 B/L

Measurement Specialist

2004 2 2 Yes No

Swedes US 218 1657 B/L

Measurement Specialist

1190’s 4 4 Yes No

Wmburg I 80 9817 B/L

Measurement Specialist

1991 4 4 Yes No

C-61

Kansas Department of Transportation

WIM Site ID

Route ADTT Sensor Type

Vendor Date Installed

Date Last Calibrated

# of Traffic lanes

# of WIM Lanes

WIM in both Travel Directions? (Yes/No)

Near a Weigh Station (Yes/No)

201005 K-68 830 Piezo ITC 4 2 No No 201006 US-166 435 Piezo ECM 4 2 No No 203013 I-435 5810 Piezo ECM 6 3 No No 203015 US-50 2240 Piezo ECM 2 2 Yes No 204016 US-24 800 Piezo ITC 4 2 No No 204052 US-36 1270 Piezo ITC 4 2 No No 204053 I-70 6615 Piezo ECM 6 3 No No 206026 K-96 860 Piezo ECM 4 2 No No 0USKI5 K-27 400 Kistler IRD 2 2 Yes No 200200 I-70 4010 Load Cell Toledo 4 2 No No 200100 US-54 1580 Bending

Plate IRD 2 2 No No

Portable Various Capacitance Mat

AVIAR Each set 1 No

C-62

Louisiana Department of Transportation

WIM Site ID

Route ADTT Sensor Type

Vendor Date Installed

Date Last Calibrated

# of Traffic lanes

# of WIM Lanes

WIM in both Travel Directions? (Yes/No)

Near a Weigh Station (Yes/No)

I-12 Load Cell IRD 1999 As needed 2 1 Y Y I-10 Load Cell IRD 2004 “ 2 1 Y Y I-20 Load Cell IRD 1999 “ 2 1 N N

C-63

Michigan Department of Transportation

WIM Site ID

Route ADTT Sensor Type

Vendor Date Installed

Date Last Calibrated

# of Traffic lanes

# of WIM Lanes

WIM in both Travel Directions? (Yes/No)

Near a Weigh Station (Yes/No)

011 M-6 Bending PAT 2004 2004 6 6 Yes No 016 US-23 Piezo PAT 1995 AutoCal 2 2 Yes No 020 US-127 Piezo PAT 1999 AutoCal 4 4 Yes No 022 I-96 Piezo PAT 1998 AutoCal 6 6 Yes No 023 US-23 Piezo PAT 1998 AutoCal 4 4 Yes No 026 I-75 Piezo PAT 2001 AutoCal 4 4 Yes No 028 I-75 Piezo PAT 1999 AutoCal 4 4 Yes No 032 US-23 Quartz PAT 1991 AutoCal 4 4 Yes No 034 I-75 Quartz PAT 2005 2006 8 6 Yes No 036 US-131 Piezo PAT 1999 AutoCal 4 4 Yes No 040 US-127 Piezo PAT 2001 AutoCal 4 4 Yes No 044 I-69 Quartz PAT 2003 2006 4 4 Yes Yes 052 I-96 Piezo PAT 1999 AutoCal 4 4 Yes Yes 054 I-94 Quartz PAT 1997 2006 4 4 Yes Yes 058 US-12 Quartz PAT 2001 2001 2 2 Yes No 071 I-94 Piezo PAT 1997 AutoCal 6 6 Yes No 075 I-75 Piezo PAT 1998 AutoCal 4 4 Yes No 079 US-31 Quartz PAT 2000 2001 4 4 Yes No 084 I-75 Piezo PAT 1999 AutoCal 6 6 Yes Yes 090 US-2 Piezo PAT 1997 AutoCal 2 2 Yes No 093 US-2 Piezo PAT 1999 AutoCal 2 2 Yes No 102 M-46 Bending PAT 1999 1999 2 2 Yes No 107 I-275 Piezo PAT 1997 AutoCal 6 6 Yes No 119 US-10 Piezo PAT 1990 AutoCal 4 4 Yes No 122 US-131 Piezo PAT 1990 AutoCal 4 4 Yes No 126 M-57 Piezo PAT 1990 AutoCal 2 2 Yes No 131 I-196 Quartz PAT 1997 1997 4 4 Yes No

C-64

141 I-275 Piezo PAT 1997 AutoCal 6 6 Yes No 143 I-96 Piezo PAT 1999 AutoCal 6 6 Yes No 144 I-75 Piezo PAT 2000 AutoCal 6 6 Yes No 145 I-275 Piezo PAT 2000 AutoCal 6 6 Yes No 149 I-94 Piezo PAT 1996 AutoCal 4 4 Yes No 150 I-94 Piezo PAT 1996 AutoCal 4 4 Yes No 152 I-94 Piezo PAT 1995 AutoCal 6 6 Yes No 155 US-2 Piezo PAT 1997 AutoCal 4 4 Yes No 167 US-23 Bending PAT 2000 2001 4 4 Yes No 173 US-24 Quartz PAT 2002 2002 4 4 No No 308 I-69 Piezo PAT 1990 AutoCal 4 4 Yes No 312 I-96 Quartz PAT 1990 2002 4 4 Yes Yes 315 US-23 Quartz PAT 1994 2006 4 4 Yes No 317 US-127 Quartz PAT 2005 2006 4 4 Yes No

C-65

Minnesota Department of Transportation WIM Site

ID Route ADTT Sensor

Type Vendor Date

Installed Date Last Calibrated

# of Traffic lanes

# of WIM Lanes

WIM in both

Travel Directions?

(Yes/No)

Near a Weigh Station

(Yes/No)

25 I94 7000 Quartz Kistler 2000 2006 4 2 No No 26 I35 3600 Quartz Kistler 2003 2003 4 4 Yes No 27 TH60 800 Quartz Kistler 2004 2004 4 2 No No 29 TH53 900 Quartz Kistler 2004 2004 4 4 Yes No 30 TH61 530 Quartz Kistler 2004 2004 4 4 Yes No 31 TH7 500 Quartz Kistler 2005 2005 4 2 No No

C-66

Mississippi Department of Transportation

WIM Site ID

Route ADTT Sensor Type

Vendor Date Installed

Date Last Calibrated

# of Traffic lanes

# of WIM Lanes

WIM in both Travel Directions? (Yes/No)

Near a Weigh Station (Yes/No)

18 US 61 BL ITC 3/22/2005 4 4 Y N 46 I-55 BL ITC 2/27/2006 4 4 Y N 77 I-55 BL ITC 1/19/2006 4 4 Y Y

115 US 82 BL ITC 1/26/2006 4 4 Y N 121 I-55 Bending

Plates ITC 2/7/2006 4 4 Y N

123 US 61 BL ITC 4/29/2005 4 4 Y N 124 US 49 BL ITC 1/20/2006 4 4 Y N 125 US 82 BL ITC 4/28/2005 4 4 Y N 126 US 49 BL ITC 4/28/2005 2 2 Y Y 127 US 78 BL ITC 4/27/2005 4 4 Y N 128 I-59 BL ITC 5/5/2005 4 4 Y N 129 I-10 BL ITC 5/5/2005 4 4 Y N 130 I-10 BL ITC 5/4/2005 4 4 Y N 131 I-55 BL ITC 1/25/2006 4 4 Y N 132 SR 27 BL ITC 5/10/2005 2 2 Y N

C-67

Missouri Department of Transportation

WIM Site ID

Route AADT Sensor Type

Vendor Date Installed

Date Last Calibrated

# of Traffic lanes

# of WIM Lanes

WIM in both Travel Directions? (Yes/No)

Near a Weigh Station (Yes/No)

182 IS29 12980 LP/PIEZO IRD 09/1999 12/2005 4 2 YES NO 188 IS35 13740 LP/PIEZO IRD 09/1992 10/27/2004 4 2 YES NO 200 US63 6289 LP/PIEZO IRD 10/2005 10/2005 4 4 YES NO 202 US63 6835 LP/PIEZO IRD 03/1939 10/2005 4 4 YES NO 302 US61 5459 LP/PIEZO IRD 06/1946 12/2005 4 2 YES NO 420 IS435 11144* LP/PIEZO IRD 07/1992 12/01/2004 2 1 NO NO 441 US65 4679* LP/PIEZO IRD 07/1995 12/03/2004 2 1 NO NO 500 IS70 32998 LP/PIEZO IRD 07/1992 01/26/2004 4 2 YES NO 610 IS55 18285 LP/PIEZO IRD 03/1946 12/13/2005 4 2 YES NO 740 US71 6812* LP/PIEZO IRD 07/1992 11/16/2004 2 1 NO NO 760 IS44 11674* LP/PIEZO IRD 07/1991 11/17/2004 2 1 NO YES 920 US60 2551* LP/PIEZO IRD 11/1990 12/2005 2 1 NO NO 930 IS44 14647* LP/PIEZO IRD 10/1992 11/23/2004 2 1 NO NO

* = AADT for WIM direction only

C-68

Nevada Department of Transportation

WIM Site ID

Route ADTT Sensor Type

Vendor Date Installed

Date Last Calibrated

# of Traffic lanes

# of WIM Lanes

WIM in both Travel Directions? (Yes/No)

Near a Weigh Station (Yes/No)

008009 IR-015 4500 Kistler IRD/PAT 08-01-03 05-26-05 4 4 Y N 018019 IR-080 2300 B. Plate PAT 04-05-95 07-06-03 4 2 Y N 022023 IR-080 2200 Kistler IRD/PAT 10-21-03 08-25-05 4 4 Y Y 034035 IR-215 3000 Kistler IRD/PAT 02-03-06 02-03-06 8 8 Y N

C-69

New Jersey Department of Transportation

WIM Site ID

Route ADTT Sensor Type

Vendor Date Installed

Date Last Calibrated

# of Traffic lanes

# of WIM Lanes

WIM in both Travel Directions? (Yes/No)

Near a Weigh Station (Yes/No)

001 US-1 57089 BL IRD Sep 2005 Sep 2005 6 6 YES NO

01A US-1 53436 NB-PHILIPPS SB - BL

IRD 1999 Jun 2005

4 4 YES NO

01D US-1&9 77442

BL IRD 2003 May 2003 7 7 NO NO

09A US-9 47411 PHILIPPS IRD 1997 AUG 2002

4 4 YES NO

015 NJ-15 42574 PHILIPPS IRD 1993 DEC 2004

4 4 YES NO

017 NJ-17 32768 BENDING PLATE

IRD 1995 OOC -1998 6 3 NO YES

18B NJ-18 35941 BL IRD 2002 APR 2005 4 4 YES NO

018 NJ-18 44894 PHILIPPS IRD 2001

AUG 2003 4 4 YES NO

18D NJ-18 32503 BL IRD 2005

APR 2005 5 5 YES NO

022 US-22 29555 PHILIPPS IRD

1996 JUL 2004 4 4 YES NO

22B US-22 38361 PHILIIPS IRD 2001

AUG 2004 4 4 YES NO

023 NJ-23 28232 BL IRD 1993 APR 2005 4 4 YES NO 31B NJ-31 13253 BL IRD 1997 JUN 2004 2 2 YES NO 31D NJ-31 20801 BL IRD 2004 SEP 2004 4 4 YES NO 031 NJ-31 23876 PHILIPPS IRD 1994 00C- 2003 4 4 YES NO 31C NJ-31 18722 PHILIPPS IRD 1998 SEP 2002 2 2 YES NO

C-70

033 NJ-33 25292 BL IRD 1997 SEP 2004 5 4 YES NO 034 NJ-34 34389 BL IRD 2001 SEP 2005 4 4 YES NO 34B NJ-34 262863 PHILIPPS IRD 2001 SEP 2005 4 4 YES NO 40A US-40 14005 BL IRD 1997 OCT 2005 4 4 YES YES 040 US-40 9538 PHILIPPS IRD 1995 OCT 2004 2 2 YES NO 40B US-

40/322 31343 PHILIPPS IRD 2002 OCT 2005 4 4 YES NO

046 US-46 24054 BL IRD 2001 APR 2004 4 4 YES NO 052 NJ-52 23937 PHILIPPS IRD 2002 APR 2005 4 4 YES NO 55C NJ-55 13600 PHILIPPS IRD 2003 OCT 2005 4 2 NO NO 551 NJ-55 29045 PHILIPPS IRD 1993 OOC -1999 4 4 YES NO 552 NJ-55 64245 PHILIPPS IRD 1993 OCT 2005 4 4 YES NO 068 NJ-68 5034 PHILIPPS IRD 1997 JUL 2005 2 2 YES NO 68A NJ-68 12807 PHILIPPS IRD 2002 MAY 2005 4 4 YES NO 072 NJ-72 9425 PHILIPPS IRD 1997 MAY 2005 2 2 YES NO 72B NJ-72 19926 PHILIPPS IRD 2003 MAY 2005 4 4 YES NO 073 NJ-73 19963 PHILIPPS IRD 2003 OCT 2004 4 4 YES NO 78A I-78 76009 PHILIPPS IRD 1994 OOC- 2000 6 6 YES NO 78D I-78 101485 BL IRD 2003 OCT 2004 6 6 YES NO 78B I78 35540 BL IRD 2000 OOC-2003 6 3 NO NO 80A I-80 54525 PHILIPPS IRD 1995 OOC-2002 7 7 YES YES 80B I-80 111046 PHILIPPS IRD 1994 OOC-2003 6 6 YES NO 80C I-80 136740 PHILIPPS IRD 1995 OOC-1997 8 8 YES NO 80D I-80 163773 BL IRD 1997 JUN 2004 12 12 YES NO 095 I-95 53766 PHILIPPS IRD 1993 OOC-2001 6 4 YES NO 124 NJ-124 13327 BL IRD 2004 JUN 2004 4 2 NO NO 130 US-130 12658 BENDING

PLATES IRD 1997 OOC-2003 2 2 YES YES

13B US-130 13933 BL IRD 1999 JUL 2005 4 2 NO YES 13A US-130 31977 PHILIPPS IRD 1999 AUG 2005 4 4 YES NO 138 NJ-138 23411 BL IRD 2003 AUG 2005 4 4 YES NO 168 NJ-168 11539 PHILIIPS IRD 1997 JUN 2004 3 2 YES NO 169 NJ-440 26974 BENDING IRD 1997 OOC-1999 4 4 YES NO

C-71

PLATES 195 I-195 48909 PHILIPPS IRD 1993 JUN 2005 4 4 YES NO 202 US-202 12657 PHILIPPS IRD 1993 JUL 2004 4 4 YES NO 206 US-206 14351 PHILIPPS IRD 1997 OOC-2002 2 2 YES NO 280 I-280 50274 PHILIPPS IRD 1999 JUL 2005 6 3 NO NO A87 I-287 49554 PHILIPPS IRD 1998 JUL 2005 6 3 NO NO 287 I-287 56614 BL IRD 1993 OOC-2004 4 4 YES NO I2S I-295 30775 BENDING

PLATES IRD 1997 OOC-2004 4 4 YES YES

I2D I-295 112769 BL IRD 1997 JUL 2005 6 6 YES NO 295 I-295 93815 BL IRD 1993 JUL 2005 6 6 YES NO 322 US-322 17811 BL IRD 1997 JUN 2005 4 4 YES NO 700 NJTPK 22123 PHILIPPS IRD 1997 SEP 1997 4 2 NO YES CO0539 CO-539 10530 PHILIPPS IRD 2000 MAY 2002 2 2 YES NO CO0551 CO-551 1293 PHILIPPS IRD 1997 JUN 2002 2 2 YES YES CO0653 CO-653 8705 PHILIPPS IRD 1997 JAN 1997 4 2 NO NO DRM DOREM

US AVE 8906 BL IRD 2004 AUG 2004 2 2 YES NO

C-72

New Mexico Department of Transportation

WIM Site ID

Route ADTT Sensor Type

Vendor Date Installed

Date Last Calibrated

# of Traffic lanes

# of WIM Lanes

WIM in both Travel Directions? (Yes/No)

Near a Weigh Station (Yes/No)

004 I-10 12821 Piezo / L MS 1998 2005 4 4 Yes Yes 300 I-25 6874 Piezo / L MS 1998 2005 4 4 Yes Yes 252 I-25 11034 Piezo / L MS 2001 2004 4 4 Yes No B28 I-25 5889 Piezo / L MS 1998 4 4 Yes Yes 101 I-40 20020 Piezo / L MS 2002 2003 4 4 Yes Yes 201 I-40 18384 Piezo / L MS 1998 4 4 Yes No B20 I-40 13124 Piezo / L MS 1998 4 4 Yes Yes 918 US 54 7592 Piezo / L MS 2004 4 4 Yes No 100 US 54 2312 Piezo / L MS 2002 2004 2 2 Yes Yes 202 US 62 2958 Piezo / L MS 1998 4 4 Yes No 919 US 70 6738 Piezo / L MS 2003 4 4 Yes No 921 US 70 5114 Piezo / L MS 1991 4 4 Yes No 916 US 70 2184 Piezo / L MS 2003 4 4 Yes No 007 US 84 31721 Piezo / L MS 2005 2005 4 4 Yes No 915 US 380 1404 Piezo / L MS 2005 2 2 Yes No 103 US 550 4825 IRD BP IRD 2002 2002 4 4 Yes No 102 US 550 4236 IRD BP IRD 2002 2002 4 4 Yes No 155 US 550 4990 IRD BP IRD 2001 2001 4 4 Yes No

C-73

New York Department of Transportation WIM Site

ID Route ADTT Sensor

Type Vendor Date

Installed Date Last Calibrated

# of Traffic lanes

# of WIM Lanes

WIM in both

Travel Directions?

(Yes/No)

Near a Weigh Station

(Yes/No)

1800 4 Piezo IRD/MSI 2002 2005 2 2 Yes No 12841 9106 Piezo IRD/MSI 2005 2005 2 2 Yes No 7181 2 Piezo IRD/MSI 2001 2005 2 2 Yes No 7100 I-87 Piezo IRD/MSI 2001 2005 4 4 Yes Yes 7381 I-81 Piezo IRD/MSI 2005 2005 4 4 Yes Yes 2680 8 Piezo IRD/MSI 2001 2005 4 4 Yes No 9580 I-88 Piezo IRD/MSI 2001 2005 5 5 Yes No 8382 I-84 Piezo IRD/MSI 2001 2005 4 4 Yes No 8280 I-84 Piezo IRD/MSI 2001 2005 4 4 Yes No 0199 I-95 Piezo IRD/MSI 2003 N/A 6 6 Yes No 0280 McGuiness

Blvd Piezo IRD/MSI 2004 2005 4 4 Yes No

580 I-495 Piezo IRD/MSI 2003 2005 6 6 Yes No 0797 25 Piezo IRD/MSI 2003 2005 2 2 Yes No 3382 I-690 Piezo IRD/MSI 2001 2005 2 2 Yes No 3311 I-81 Piezo IRD/MSI 2005 2005 2 2 Yes No 9121 I-81 Piezo IRD/MSI 2004 2005 2 2 Yes No 4483 5 Piezo IRD/MSI 2001 2005 4 4 Yes No 6282 328 Piezo IRD/MSI 2001 2005 4 4 Yes No 4342 590 Piezo IRD/MSI 2004 2005 6 6 Yes No 5384 219 Piezo IRD/MSI 2005 2005 4 4 Yes No 5280 I-86 Piezo IRD/MSI 2001 2005 4 4 Yes No

C-74

North Dakota Department of Transportation

WIM Site ID

Route ADTT Sensor Type

Vendor Date Installed

Date Last Calibrated

# of Traffic lanes

# of WIM Lanes

WIM in both Travel Directions? (Yes/No)

Near a Weigh Station (Yes/No)

1 I-94 2000 Kistler Quartz

Kistler Corp.

2003 2003 2 2 NO NO

2 US 85 600 “ “ 2003 2003 1 1 NO NO 3 US 281 1250 “ “ 2003 2003 2 2 YES YES 4 I-29 2600 “ “ 2003 2003 2 2 NO YES 5 US 2 950 “ “ 2004 2004 2 2 NO YES 6 I-29 1400 “ “ 2004 “ 2 2 NO YES 7 I-94 7500 “ “ “ “ 2 2 NO YES 8 US 52 400 “ “ “ “ 1 1 NO NO 9 US 83 4500 “ “ “ “ 4 4 YES NO 10 US 2 1475 “ “ “ “ 2 2 NO NO 11 US 85 2075 “ “ “ “ 2 2 YES NO 12 US 52 1675 “ “ “ “ 2 2 YES NO

C-75

Ohio Department of Transportation WIM Site

ID Route ADTT Sensor

Type Vendor Date

Installed Date Last Calibrated

# of Traffic lanes

# of WIM Lanes

WIM in both

Travel Directions?

(Yes/No)

Near a Weigh Station

(Yes/No)

056 SR47 900 Prezo Peek Summer 06

N/A 2 2 Y N

065 IR75 20,510 Prezo Peek 10/05 Spring 06 6 6 Y N 535 IR75 9,631 Prezo Peek 1999 04/04 6 6 Y N 706 US20 819 Bending

Plate Pat/IRD 1997 06/05 4 2 Y N

707 IR70 6,644 Prezo Peek 1993 09/03 4 4 Y N 708 IR270 12,751 Load Cell MT 1994 04/04 6 4 Y N 709 SR7 1,010 Load Cell MT 1994 08/04 4 2 Y N 710 US68 690 Load Cell MT 1994 06/05 2 2 Y N 711 IR675 7,420 Load Cell MT 1994 05/05 4 2 Y N 714 US33 1,556 Prezo Peek 1995 07/03 4 2 N N 715 IR71 11,470 Load Cell MT 1995 05/05 4 2 Y y 716 US33 1,520 Load Cell MT 1995 10/04 4 2 Y N 717 IR75 16,530 Load Cell MT 1995 03/05 4 1 N Y 718 IR75 17,870 Load Cell MT 1995 03/05 6 4 Y N 719 IR 75 18,430 Load Cell MT 1995 03/05 4 1 Y Y 721 US23 5,480 Load Cell MT 1996 04/05 4 4 Y N 722 SR 126 1,090 Load Cell MT 1998 11/04 4 1 N N 723 IR 270 3,179 Bending

Plate Pat/IRD 1999 06/05 7 4 Y N

724 US20 5,110 Prezo Peek 1999 04/02 2 2 Y N 725 US68 4,555 Prezo Peek 1999 11/03 4 4 Y N 726 US 24 3,907 Prezo Peek 1999 03/05 2 2 Y N 727 US 23 4,318 Prezo Peek 1999 03/05 4 4 Y N 732 IR 475 6,750 Prezo Peek 1999 03/05 4 4 Y N

C-76

736 IR 75 12,538 Prezo Peek 1999 11/03 4 4 Y N 737 IR 75 14,375 Prezo Peek 1999 11/03 4 4 Y N 738 US 127 2,470 Prezo Peek 1999 07/03 4 4 Y N 740 County

Road 8 Prezo Peek 1996 07/03 4 4 Y N

743 IR 70 17,360 Prezo Peek 2002 07/03 4 4 Y N 745 IR 70 20,967 Prezo Peek 2000 07/03 4 4 Y N 752 IR 7-0 9,303 Prezo Peek 2004 07/04 6 6 Y N 754 IR 76 8,150 Prezo Peek 2000 05/05 4 4 Y N 755 IR 77 3,958 Prezo Peek 2000 05/05 4 4 Y N 757 IR 76 6,956 Prezo Peek 2000 05/05 4 4 Y N 760 SR 18 1,551 Prezo Peek 2000 05/05 4 4 Y N 762 IR 80 13,639 Prezo Peek 2000 05/05 4 4 Y N 763 SR 11 3,251 Prezo Peek 2000 05/05 4 4 Y N 764 SR 82 2,699 Prezo Peek 2000 05/05 4 4 Y N 766 IR 480 2,551 Prezo Peek 2000 05/05 4 4 Y N 768 US 62 490 Prezo Peek 2003 07/05 2 2 Y N 769 SR 104 750 Prezo Peek Summer

06 N/A 2 2 Y N

770 IR 77 3,598 Prezo Peek 2003 05/05 4 4 Y N 771 SR 78 182 Prezo Peek 2003 05/05 2 2 Y N 772 SR 683 175 Prezo Peek 2003 05/05 2 2 Y N 773 SR 821 627 Prezo Peek 2003 05/05 2 2 Y N 774 SR 14 521 Prezo Peek 2004 05/05 2 2 Y N 775 IR 70 12,896 Prezo Peek 2004 05/05 4 4 Y N 776 SR 183 377 Prezo Peek 2004 05/05 2 2 Y N 777 IR 71 9,157 Prezo Peek 2005 10/05 6 6 Y N 778 US 30 3,609 Prezo Peek 2005 10/05 4 4 Y N 779 US 30 2,869 Load Cell MT 2006 01/06 4 2 Y N

C-77

Oregon Department of Transportation

WIM Site ID

Route ADTT Sensor Type

Vendor Date Installed

Date Last Calibrated

# of Traffic lanes

# of WIM Lanes

WIM in both Travel Directions? (Yes/No)

Near a Weigh Station (Yes/No)

Wdbn S SB I-5 5200 Single-load cell

IRD Oct 97 Jan 06 3 2 Same direction Yes

Wdbn N NB I-5 4900 SLC IRD June 98 Jan 06 3 2 Same direction Yes Wilbur SB I-5 3200 SLC IRD June 00 Oct 05 2 1 Same direction Yes Booth Ranch

NB I-5 2900 SLC IRD June 00 May 06 2 1 Same direction Yes

Ashl POE NB I-5 3800 SLC IRD Aug 99 Apr 06 2 1 Same direction Yes Ashl SB SB I-5 3200 SLC IRD Aug 99 Apr 06 2 1 Same direction Yes K Falls N NB

I-97 1600 SLC IRD June 00 Apr 06 2 1 Same direction Yes

K Falls S SB I-97

1200 SLC IRD June 00 Apr 06 2 1 Same direction Yes

Bend NB I-97

700 SLC IRD July 05 Feb 06 2 1 Same direction Yes

J Butte N NB I-97

700 SLC IRD June 00 Nov 05 2 1 Same direction Yes

J Butte S SB I-97

650 SLC IRD June 00

Nov 05 2 1 Same direction Yes

CCL EB I-84

3500 SLC IRD July 01 Mar 06 2 1 Same direction Yes

Wyeth WB I-84

3200 SLC IRD July 01 Mar 06 2 1 Same direction Yes

E. Hill WB I-84

1800 SLC IRD July 01 Apr 06 2 1 Same direction Yes

LaGrande EB I-84

1800 SLC IRD Oct 99 Apr 06 2 1 Same direction Yes

Farewell Bend

WB I-84

2400 SLC IRD Aug 99 Apr 06 2 1 Same direction Yes

C-78

Olds Ferry EB I-84

2100 SLC IRD Aug 99 Apr 06 2 1 Same direction Yes

Umatilla SB I-82

2600 SLC IRD Oct 99 May 06 2 1 Same direction Yes

Lowell WB US-58

1100 SLC IRD Aug 00 May 06 2 2 Same direction Yes

Rocky Point WB US-30

850 SLC IRD Jan 01 Nov 05 2 1 Same direction Yes

EB Brightwood

EB US-26

180 SLC IRD Nov 00 Mar 06 2 1 Same direction Yes

WB Brightwood

WB US-26

200 SLC IRD Nov 00 Mar 06 2 1 Same direction Yes

C-79

South Dakota Department of Transportation

WIM Site ID

Route ADTT Sensor Type

Vendor Date Installed

Date Last Calibrated

# of Traffic lanes

# of WIM Lanes

WIM in both Travel Directions? (Yes/No)

Near a Weigh Station (Yes/No)

801 SD 37 166 Blending Plate

PAT 10/23/2001 7/16/2003 2 2 Y n

802 US 18 68 Blending Plate

PAT 10/01/1996 6/06/2002 2 2 Y n

803 US 14 127 Blending Plate

PAT 10/15/1996 7/19/2005 2 2 Y n

804 US 83 110 Blending Plate

PAT 09/01/1999 6/21/2005 2 2 Y n

805 I 90 834 Blending Plate

PAT 10/15/1999 11/4/2004 4 4 Y n

806 I 29 1143 Blending Plate

PAT 9/01/1999 7/7/2005 4 4 Y n

807 I 90 1079 Blending Plate

PAT 9/16/2002 11/7/2005 4 4 Y Y

808 SD 79 353 Blending Plate

PAT 11/2/2004 11/2/2004 4 2 N N

809 I 29 2763 Blending Plate

IRD 2002 2002 4 2 N y

810 US 212 75 Kistler Quartz

IRD 6/14/2005 6/14/2005 2 2 Y n

901 I 90 1194 Blending Plate

PAT 9/19/1991 8/7/2003 4 2 N y

903 US 12 440 Blending PAT 7/22/1992 7/20/2004 4 2 N n 909 US 14 134 Blending

Plate PAT 10/1/1996 6/17/2002 2 2 Y N

910 I 29 503 Blending Plate

PAT 9/1/1999 7/27/2004 4 4 Y y

C-80

Virginia Department of Transportation

WIM Site ID

Route ADTT Sensor Type

Vendor Date Installed

Date Last Calibrated

# of Traffic lanes

# of WIM Lanes

WIM in both Travel Directions? (Yes/No)

Near a Weigh Station (Yes/No)

190050 I66 WB 17000 Quartz Piezo

Kistler/ Peek

4/14/2005 1/18/2006 2 2 No No

140318 I95 NB 17000 Quartz Piezo

Kistler/ Peek

6/15/2005 1/10/2006 2 2 No Yes

040289 SR288 30000 Quartz Peizo

Kistler/ Peek

9/7/2005 11/17/2005 4 4 Yes No

C-81

Washington Department of Transportation

WIM Site ID

Route ADTT (2005)

Sensor Type

Vendor Date Installed

Date Last Calibrated

# of Traffic lanes

# of WIM Lanes

WIM in both Travel Directions? (Yes/No)

Near a Weigh Station (Yes/No)

B02 SR 012 20,677 PIEZO IRD 12/90 4 4 YES YES B03 SR 395 13,301 PIEZO IRD 12/90 5/24/05 4 4 YES B04 I-90 27,300 PIEZO IRD 6/91 4 4 YES YES D1 I-405 141,573 PIEZO IRD 11/91 7/27/05 6 4 YES D3 SR 512 90,949 PIEZO IRD 8/92 7/25/05 6 6 YES P01 SR 002 20,619 PIEZO IRD 3/92 7/19/05 4 4 YES P03 SR 097 11,372 PIEZO IRD 4/93 4 4 YES P04 I-5 43,690 PIEZO IRD 12/91 11/16/05 4 4 YES P05 SR 012 2,072 PIEZO IRD 12/91 5/25/05 2 2 YES P06 SR 014 36,897 PIEZO IRD 7/91 6/7/05 4 4 YES P07 SR 014 6,033 PIEZO IRD 8/91 6/7/05 2 2 YES P08 I-082 23,448 PIEZO IRD 8/91 4 4 YES P09 I-082 15,377 PIEZO IRD 9/91 4 4 YES P10 I-090 9,823 PIEZO IRD 9/91 5/5/05 4 4 YES YES P13 SR 195 4,758 PIEZO IRD 4/92 6/6/06 2 2 YES P14 SR 195 3,119 PIEZO IRD 4/92 6/6/06 2 2 YES P15 SR 195 8,738 PIEZO IRD 4/92 5/5/04 4 4 YES P17 SR 221 1,945 PIEZO IRD 6/92 5/24/05 2 2 YES P18 SR 101 2,627 PIEZO IRD 12/92 9/15/05 2 2 YES P19 SR 522 41,957 PIEZO IRD 12/91 4 4 YES P20 SR 018 52,611 PIEZO IRD 3/92 7/26/05 4 4 YES P21 SR 009 11,427 PIEZO IRD 10/92 9/14/05 2 2 YES P22 SR 097 2,036 PIEZO IRD 3/93 7/20/05 2 2 YES P23 SR 097 3,927 PIEZO IRD 3/93 7/20/05 2 2 YES P24 I-090 45,458 PIEZO IRD 6/94 5/03/05 4 4 YES YES P28 SR 002 17,444 PIEZO IRD 3/93 5/4/05 4 4 YES P29 I-082 43,334 PIEZO IRD 9/93 7/19/05 4 4 YES

C-82

P30 SR 027 6,412 PIEZO IRD 8/95 2 2 YES P33 SR 290 7,834 PIEZO IRD 7/03 5/3/05 2 2 YES P1 I-005 179,752 PIEZO IRD 6/95 11/15/05 8 6 YES P3 I-005 189,529 PIEZO IRD 8/91 9 7 YES P4 I-005 140,253 PIEZO IRD 8/91 9/15/05 8 6 YES P6 SR-167 118,764 PIEZO IRD 5/95 7/27/05 6 4 YES

P7C SR-395 6,953 KISTLER IRD 3/98 1/18/06 4 4 YES P8 I-005 50,092 PIEZO IRD 9/01 6 6 YES

C-83

Wyoming Department of Transportation WIM Site

ID Route ADTT Sensor

Type Vendor Date

Installed Date Last Calibrated

# of Traffic lanes

# of WIM Lanes

WIM in both

Travel Directions?

(Yes/No)

Near a Weigh Station

(Yes/No)

LA0176 I80 8800 Piezo ECM 2001 2005 4 4 Yes Yes UI0177 I80 13340 Piezo ECM 2001 2005 4 4 Yes Yes BH0173 WY310 1320 Piezo ECM 1999 2006 2 2 Yes No 160 I25 6060 Piezo ECM 1997 2005 4 2 Yes No 156 WY59 5030 Piezo ECM 1998 2006 2 2 Yes No

APPENDIX D

POTENTIAL PROCESSES TO DEVELOP AND CALIBRATE VEHICULAR DESIGN LOADS

Background Task 2 of this research project was focused on existing and potential processes to develop and calibrate vehicular loads for superstructure design, fatigue design, deck design, and overload permitting. WIM data should be used to obtain accurate nationwide statistics on truck headway (multiple presences) and overload (above legal levels) occurrences. Characterization of the live load effect requires the quantification of the expected or mean maximum value, uncertainty expressed by the standard deviation (or coefficient of variation equal to standard deviation divided by mean) and the determination of the probability distribution type (Normal, Lognormal, Gumbel etc.). Depending on the application, the live loading must be characterized as the maximum lifetime event (strength) or in terms of a histogram of repetitive loads (fatigue). Maximum live loading depends on the weights of the individual trucks on the span. Typically traffic conditions cause a large number of vehicle multiple presences on the span, especially those due to side by side moving trucks. These multiple presence events will often control the distribution of the maximum loading event. With multiple-presence, the maximum bridge loading depends on the weight and axle configuration of each truck on the span and their relative spacing or headway (nose-to-nose separation of trucks).

This data is analyzed using processes discussed herein to project a maximum bridge-loading event (Lmax) defined over a period of 75 years for design. One simplified calibration approach recommended for this project is to focus on the expected or mean maximum live load variable, Lmax but update the load model or the load factor for current traffic conditions in a manner consistent with the LRFD calibration approach. The most direct way of using the new WIM data reflecting current truck loads in the various jurisdictions is to focus on Lmax and compare it to the value utilized during the calibration of the existing LRFD code, as described in NCHRP Report 368. This assumes that the overall LRFD calibration and safety indices are adequate for the strength and load data then available. Another key assumption in this regard is that the site-to-site variability in Lmax as measured by the COV is the same as that used during the AASHTO LRFD calibration. In AASHTO LRFD calibration, the overall live load COV was taken as 20%.

The maximum loading, Lmax, is defined for a suite of representative bridge configurations and should be normalized by the maximum allowed loading in the jurisdiction where the WIM data is taken. Lmax reflects both the multiple presence, which is input to any load model and the degree of weight overloading for various types of truck classifications and jurisdictions. The HL-93, and in fact all bridge loading models, are driven by the degree that truck weights exceed their allowable legal limits. In LRFD, a load model has been used in which 8% of trucks are overweight and the average of the top 20% of trucks is 95% of the legal limiting value with a 25% COV. This overweight value has a very important influence on the live load factors selected for bridge designs. With additional WIM data now available and consistent examination of the tails of these distributions the research team will expand the basis for truck weight modeling.

The availability of new WIM data should be used to check the fatigue truck developed in the 1980’s and determine if the stress ranges under newer truck configuration and current traffic conditions typically exceed the ranges found from the 1980’s WIM data. Fatigue is an averaging process, so small numbers of extreme loads are not relatively significant. Rather, the average fatigue “damage” per truck determines the design and assessment criteria. In this case, data from many WIM sites should be combined and compared to the data from the 1980’s to determine the

D-1

adequacy of the present AASHTO fatigue truck configuration and weight for current applications. The increasing presence of multi-axle trucks in the traffic stream, investigated in NCHRP 12-63, must also be accounted for in the fatigue load model. Also, the live load modeling in LRFD did not specifically address the increasing load effects on bridge decks from the heavier and more complex axle configurations of current truck traffic. Recent WIM data should be analyzed to ascertain overweight statistics specific to axle loads, just as it was done for truckloads. It is likely that axle overload probabilities may be significantly higher than the overload probabilities for truck gross weights.

Several procedures exist to estimate the maximum expected load effect on a highway bridge. These procedures, of various levels of complexity, explain how site-specific truck weight and traffic data can be used to obtain estimates of the maximum live load for the design life of a bridge, specified to be 75 years as per the AASHTO LRFD code, or the two-year return period to be used for the load capacity evaluation of existing bridges. The models require as input the WIM data collected at a site after being “scrubbed” and processed for quality assurance as described in the following chapter. The models described in this section include: 1) a probability convolution approach, 2) a Monte Carlo simulation approach, and 3) simplified methods. The convolution method uses numerical integrations of the collected WIM data histograms to obtain projections of the expected maximum load effect within a given return period (e.g. 2-years or 75-years). The Monte Carlo simulation uses random sampling from the collected data to obtain the maximum load effect. Potential Processes for Estimating Maximum Lifetime Loading Lmax from Traffic Statistics Convolution Approach This section presents a convolution (numerical integration) procedure for modeling the maximum live load effect on a highway bridge. 1. Assemble histogram for truck load effect

In this step, using the WIM data files, the moment effect of each truck in the WIM record is calculated by passing the trucks through the proper influence line. The moment of each truck is then normalized by dividing the calculated value by the moment of the HL-93 load model. The data is collected into a percent frequency histogram. This histogram will provide a discretized form of the probability density function (pdf) of the moment effects for the site. The histogram is designated as Hx(X) while the pdf is designated as fx(X). The relation between Hx(X) and fx(X) is given by:

∫=uX

lXxx dx)x(f)X(H (D-1)

where Xl and Xu give the upper and lower bounds of the bin within which X lies. If the bin size is small, then fx(X) can be assumed to be constant within the range of Xl to Xu and Equation D-1 becomes:

( )luxxx XX)X(fX)X(f)X(H −=Δ= (D-2)

where ΔX is the bin size.

D-2

Assemble histogram for the moment effects of side-by-side trucks.

The total moment effect when two side-by-side trucks are on a bridge is obtained from xs=x1+x2 where x1 is the effect of the truck in the drive lane and x2 is the effect of the truck in the passing lane. Assuming independence between truck moments, the probability density function of the effect of side-by-side trucks fs(S) can be calculated using a convolution approach. The convolution equation is presented as:

( ) ( ) ( )∫+∞

∞−

−= 111x1s2xssx dxxfxXfXf (D-3)

where: fxs (…) is the probability distribution of the side-by-side effects fx1(…) is the probability distribution of the effects of trucks in lane 1 fx2(…) is the probability distribution of the effects of trucks in lane 2

Equation D-3 can be interpreted as follows: Given that the effect of the truck in lane 1 is equal to x1, then the probability that the effects of two side-by-side trucks will take a value Xs, is equal to the probability that the effect of the truck in lane 1 is x1, times the probability that the effect of the truck in lane 2 is equal to X2=XS-x1. This will lead to the following expression: . The integration is executed to cover all possible values of x1. Equation D-3 gives the probability density function (pdf) for one particular value of Xs. Thus, Equation D-3 must be repeated for each possible value of Xs. Equation D-2 is used to convert the pdf’s into equivalent histograms.

( ) ( 11x1s2x xfxXf − )

2. Assemble cumulative distribution functions.

Use the histograms and the probability density functions fx1(…), fx2(…), fxs(…) and fz(…) assembled above to obtain the cumulative distributions for the moment effects of single trucks in the drive lane and moment effects of two trucks side-by-side. Note, that the moment effect for the passing lane is not considered independently since it does not govern for the data collected at this site. The cumulative distribution is assembled from the pdf using the equation:

( ) ∫∞−

=Z

zz dy)y(fZF (D-4)

In essence, Equation D-4 assembles all the bins of the histogram below a certain value Z into a single bin at Z. This is repeated for all possible values of Z. Thus, Fz(Z) will give the probability that a loading event will produce a load effect less or equal to Z.

3. Calculate the cumulative probability function for the maximum load effect over

a return period of time, treturn.

A bridge structure should be designed to withstand the maximum load effect expected over the design life of the bridge. The AASHTO LRFD code specifies a design life of 75 years. The LRFR bridge load rating also requires checking the capacity to resist the maximum load effects for a two-year return period. It is simply impossible to get enough data to determine the maximum load effect expected over 75 years of loading. Even getting sufficient data for the two-year return period would require several cycles of two-year data. Therefore, some form of statistical projection should be performed. The proposed calculation procedure calculates the cumulative distribution function for the loading event over a short return period

D-3

typically less than 75 years (in some cases even less than two years) and then using statistical projections to obtain the information required for the longer two-year and 75-year return periods.

To find the cumulative distribution for the maximum loading event in a period of time t we have to start by assuming that N loading events occur during this period of time t. These events are designated as S1, S2, … SN. The maximum of these N events, call it smax,N, is defined as:

smax,N = max (s1, s2, … sN) (D-5)

We are interested in finding the cumulative probability distribution of Smax,N. This cumulative probability distribution, Fs max N(S), gives the probability that smax,N is less than or equal to a value S. If smax,N is less than S, this implies that s1 is less than s, and s2 is less than s, … and SN is less than s. Hence, assuming that the loading events are independent, the probability that smax,N≤S can be calculated from:

( ) )S(F)...S(F).S(FSF

Ns2s1sNmaxs = (D-6)

If s1, s2, ... sN are independent random variables but they are drawn from the same probability distribution, then:

)S(F)S(F...)S(F)S(F sNs2s1s==== (D-7)

and Equation (D-6) reduces to ( ) [ ]NsNmaxs )S(FSF = (D-8) Note that Equation D-8 assumes that the number of events is a deterministic value. Sensitivity analysis, however, demonstrates that the results of Equation D-8 will not be highly sensitive to variations in N as N becomes large. One way to project the results is by using the Normal fit of the tail of the histogram and substitute the Normal distribution into Equation D-8 rather than the WIM data cumulative distribution.

4. Determine the probability density function of maximum load effect in a return

period treturn.

The probability density function and the histogram for the load effect of the maximum loading in different return periods can be calculated from:

( ) ( )S

NmaxsNmaxS |

dssdF

Sf = (D-9)

D-4

5. tatistical projection of maximum load effects using Extreme Value probability

escribed in this section lies in the fact that it wou

M istogram is consistent with the extreme value fit of the projected data but the extreme value

for non-normal distributions as well.

The cumulative Gumbel distribution has th

Sprinciples. Since it is not possible to collect enough data to estimate the maximum load effect for long return periods, statistical methods need to be used to obtain such estimates. Although statistical projections are based on some basic assumptions that should be justified by physical evidence and mathematical reasoning, there is no guarantee that the projections will exactly forecast the future. Statistical estimates of the confidence limits can only give some assurance that the projections are reasonable within the constraints of the assumptions. In the previous section, the statistical projection was executed assuming that the tail of the WIM data histogram approaches that of a Normal distribution whose mean and standard deviation are obtained from the regression fit of the data plotted on Normal curves. Another method described in this section, executes the statistical projection based on the principles of extreme value theory. The advantage of the approach d

ld be valid even if the tail of the WIM histogram does not approach that of a Normal distribution.

The largest value for N loading repetitions approaches the double exponential distribution as the value of N increases (Ang & Tang (2007)). The double exponential distribution, also known as the Extreme Value Type I distribution or the Gumbel distribution, is the asymptotic distribution for the largest value if the original distribution, Fs (S), has an exponentially decaying tail. Thus, this approach is valid if the tail of the WIM histogram can be fitted by a Normal distribution but would also be valid if the tail can be fitted by any other exponentially decaying distribution. If the tail end of the WIM histogram can be fitted by a Lognormal distribution, then the Frechet Type II extreme value distribution can be used for the statistical projection. If the tail end of the WIM histogram has an upper limit, then the Type III Weibull distribution may be used. In this section, the process of using Extreme value distributions is illustrated using the Gumbel Type I distribution although the process is applicable for the other types as well. It should be noted that the Normal fit of the tail end of the WIhfit of the projected data is more general as it applies

e form:

( ) ( )kuSkekmax,s eSF

−α−−= (D-10) where Fsmax k (S) is the cumulative distribution of the maximum of k events, uk is the most

robable value of Smax, k and αk is an inverse measure of the dispersion in smax, k. The rr pondi probability density function of the Gum

pco es ng bel distribution is then: ( ) ( ) ( )kuSk −α−ekuSk

kkmax,s eeSf −−α−α= (D-11)

The mean value for x k can be calc

sma ulated as:

k

ksk uαγ

+=μ (D-12)

in which γ is the Euler number γ=0.577216. The standard deviation, σs,k of smax k can be calculated from:

D-5

2k

22

k,S 6απ

=σ (D-13)

To verify that the distribution of the maximum load effect for a return period treturn approaches the Gumbel distribution, one can use some form of probability plot. In this case, the plot is executed by taking the double natural logarithm of both sides of Equation D-10 so that:

( )( ) kkkkmax,s usFnlognlog α+α−=− (D-14) which has the linear form:

y = m s + n (D-15)

This indicates that if Fsmax,k follows a Gumbel distribution, the plot of the double log should follows a straight line with a slope = -αk and an intercept at αkuk

6. Projection of results to longer return periods

The design and safety evaluation of bridges requires the estimation of the maximum load effect over periods of 75 years and 2 years respectively. However, it is clear that the WIM data collected cannot reasonably be accurate enough in the tail of the distributions to obtain good estimates of the parameters for such extend return periods. Hence, the only possible means to obtain the parameters of the distributions of the maximum two-year and 75-year maximum load effect is by using statistical projections. As mentioned earlier, the probability distribution of the maximum value of a random variable will asymptotically approach an extreme value distribution as the number of repetition increases.

Although the Gumbel fit was executed on the tail of the one-week maximum, the properties of the Gumbel distribution allows for the projection of the results for any return period. For example, given the mean and standard deviation of the one week maximum for which the number of events is k=19x7 for the side-by-side events, we can calculate the mean and standard deviation for any return period during which a total of N events take place using the relationships:

σN=σk (D-16)

⎟⎠⎞

⎜⎝⎛σ

π+μ=μ

kNnlog6

kkN (D-17)

Equation D-16 indicates that the standard deviation of the Gumbel distribution is independent of the return period or the number of repetitions, while the mean value of the Gumbel is a linear function of the natural logarithm of the number of repetitions.

7. Summary of convolution approach

The convolution approach presented in this section shows a procedure that can be used to obtain the maximum load effect over different return periods. When the approach was applied using the original raw data, it was found to be insufficient for projecting the maximum load for the drive lane for large return periods. Hence, two statistical projections techniques were compared. The first statistical projection fitted a Normal distribution to the

D-6

tail end of the raw WIM data histogram while the second approach fitted an extreme value distribution to the tail end of the projected one-week maximum load effect. The assumptions made in this section are:

• The WIM data can be used to generate histograms for the load effects of the trucks that are in the drive and passing lanes with good accuracy in the tail end of the histograms. Since it is not possible to gather sufficient data to have exact results for the maximum 2-year and 75-year return periods, statistical projection techniques must be used.

• The average number of loading events including single lane loadings and side-by-side cases is reasonably well known from the WIM data or other headway data available for the site. A sensitivity analysis to be performed in the next chapter will demonstrate that the results are not very sensitive to small errors in these values. However, a good estimate is still required.

• The trucks in the passing lane are independent and uncorrelated from those in the drive lane. This assumption has been verified by the analysis of the WIM data obtained for this project.

• The probability distribution of the maximum load effect approximately approaches an extreme value distribution as the return period increases. If the tail end of the original raw data has an exponential form (including a Normal distribution shape) then the Gumbel Type I extreme value distribution is adequate.

• If the tail end of the raw WIM data approaches the tail end of a known probability distribution (e.g. a Normal distribution), this known distribution can be directly used to obtain the maximum load effect for any projection period.

The next section of this chapter describes how Monte Carlo simulations can be executed to obtain the projections for the maximum load effect. Another section describes a number of simplified approximate procedures that would lead to similar results as those obtained from the convolution method and the Monte Carlo simulations. Monte Carlo Simulation An alternative to the convolution approach described above consists of using a Monte Carlo simulation to obtain the maximum load effect. In this approach, results of WIM data observed over a short period can be used as a basis for projections over longer periods of time. A Monte Carlo simulation requires the performance of an analysis a large number of times and then assembling the results of the analysis into a histogram that will describe the scatter in the final results. Each iteration is often referred to as a cycle. The process can be executed for the single lane-loading situation or the side-by-side loading. A step-by-step procedure for Monte Carlo Simulation is described in Step 12.3 of the Draft protocols, in the next chapter.

Like the convolution approach, the Monte Carlo simulation will not be accurate for large projections periods because of the limitations in the originally collected data. Also, the Monte Carlo simulation will be extremely slow when the number of repetitions K is very high. Furthermore, one should make sure not to exceed the random number generation limits of the software used, otherwise the generated numbers will not be independent and the final results will be erroneous. Hence, statistical projections must be made to estimate the maximum load effects for long return periods. For example, the same steps 7 through 9 used in the convolution approach can be used to fit the one-week data into cumulative distribution functions that are plotted on Gumbel scales from which the dispersion coefficients are extracted and used to find the mean values and standard deviations for different return periods. Alternatively, one can used a smoothed tail end of the WIM histogram by fitting the tail with a known probability distribution

D-7

function (such as the Normal distribution) and use that fitted distribution with the Monte Carlo simulation. It should be emphasized however, that the Monte Carlo simulation would still be very inefficient for projections over long return periods. Simplified Procedures for Estimating Maximum Load Effects

The advantages of accurate convolution and simulation approaches for Lmax is that it allows a more accurate calculation of failure probability in those applications where target risks should be known in quantitative form. For most applications, such as code calibration and comparative risk assessments, simplified models for Lmax may be acceptable. Several reasons support this approach:

1. There may never be sufficient data to fully support an actuarial approach to risk calculation for a bridge structure.

2. Specifications by their very nature represent simplification and compromises that allow

designers to perform calculations in a deterministic manner which is transparent to the risk analysis process.

3. There are many variables affecting risk which are beyond the control of designers for

which accurate statistics are not available. These variables include growth in future traffic, human errors which are the cause of most structural failures and limitations in the data base of variables other than the external live load including structural analysis uncertainties, fabrication variabilities, costs of failure which affect the optimal target risk, future changes in truck types and horsepower which affect multiple presence probabilities, etc.

Two simplified procedures are proposed for estimating the maximum load effect in a given return period. The two approaches are based on the assumption that the tail end of the moment load effect for the original population of trucks as assembled from the WIM data approaches a Normal distribution. The first method uses the properties of the extreme value distribution and the second is based on the properties of the Normal distribution. Simplified Extreme Value Model

Let us assume that the tail end of the parent moment effect histogram approaches a Normal distribution. If this assumption is accepted, it will provide a powerful tool to use the results of the Normal probability fit to obtain projections of the maximum load effect for different return periods without the need to execute the convolution or the Monte Carlo simulation. The approach is based on the following known concepts as provided by Ang and Tang (2006) and stated earlier in this section but repeated herein for emphasis: “if the parent distribution of the initial variable x has a general Normal distribution with mean μx and standard deviation σx, then the maximum value of x after K repetitions approaches asymptotically an Extreme Value Type I (Gumbel) distribution with a dispersion αK given by:

( )X

K

Kln2σ

=α (D-18)

and a most probable value uK given by:

D-8

( ) ( )( ) ( )( ) ⎟

⎟⎠

⎞⎜⎜⎝

⎛ π+−σ+μ=

Klog224logKloglogKln2u xxK (D-19)

These values for αK and uK can then be used in Equation D-10 and D-11 to find the probability density functions and the histogram for any return period with K load repetitions. Also, αK and uK can be used in Equations D-12 and D-13 to find the mean and standard deviation for the maximum load effect for any return period having K repetitions. Simplified Normal Distribution Model

A final comparison is performed between the projected results obtained using the procedures described above and the simplified method used by Fred Moses in previous NCHRP projects on load modeling and LRFR code calibration. This procedure starts by fitting a Normal distribution through the tail end of the moment histogram (Fig D-1). The approach can be used for trucks in the drive lane and for side-by-side trucks. The expected maximum two-year side-by-side event can be estimated to be:

μ2year= μs’ + t σs’ (D-20) where t = standard deviate corresponding to a probability of exceedance

It is noted that the results of this simplified Normal approach and the simplified Gumbel approach are less than 7.5% for the worst case scenario. The reason for the larger differences for short return periods is due to the fact that the maximum loading approaches the Gumbel distributions (i.e. Equations D-18 and D-19) are exact only in an asymptotic sense i.e. only as the number of repetitions becomes very high (approaches infinity). Unlike the simplified Gumbel approach and the Convolution and Monet Carlo simulation methods that provide the whole probability distribution of the maximum load effect as well as the mean values and the standard deviations, the simplified Normal approach only gives the expected value but cannot calculate the standard deviation of the maximum load effect.

D-9

Probability of Exceedance

X

XtX σ.+

Figure D -1 Illustration of the Simplified Normal distribution approach

D-10

Summary This chapter presented several methods for projecting the data from load effect histograms to obtain the maximum load effect for different return periods. The projections assume that the collected WIM data histogram extends beyond the largest value observed during the data collection period. The methods are illustrated for two cases: 1) the tail end of the parent histogram follows a Normal distribution or 2) the tail of the maximum load effect for a short return period follows a Gumbel distribution. The two assumptions are not necessarily contradictory since assumption 1 leads to assumption 2. But, assumption 2 is more general because it is valid when the tail of the parent histogram follows any type of exponentially decaying distribution. For whichever assumption is used, the results show that all the proposed methods asymptotically approach the same values as the number of loading repetitions increases. The convolution and Monte Carlo approaches are however valid even if the tail of the original WIM histogram was found to fit other than Normal distributions. If the fitted distribution is not exponentially decaying, then the Gumbel may not be valid and other types of extreme value distributions such as the Frechet or the Weibull distributions may be more adequate. In any case, the general steps for the analysis process remain the same.

APPENDIX E

Implementation of WIM Error Filtration Algorithm on Load Effect Histogram

The procedure is presented through an example based on the WIM data collected at the I-81 site in NY. To verify the validity of the proposed approach for filtering out the WIM errors, the WIM histogram for the moment effect of a simply support 60-ft bridge span is used. The histogram of the moment effect on a 60-ft simple span for the I-81 WIM data as collected on site is shown in Figure E-1. The moments are normalized to the moment of the HL-93 design truck. The frequencies are also normalized and presented in percent.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

1

2

3

4

5

6

7Histogram of Measured Data

Moment/HL-93

Freq

uenc

y in

per

cent

Figure E-1 Histogram of load effect of I-81 data on a simple 60-ft span.

In this example, because of the lack of site-specific calibration data, we are assuming that the WIM calibration error data of the I-87 site as provided in Chapter 3, Tables 16 and 17 are valid for this I-81 site also. This assumption is only used to illustrate the procedure and should not be made for actual calculations of maximum load effect Lmax because the WIM calibration errors are highly site dependent.

A simulated histogram of a random sample of 10,000 values of the error, ε, with mean=1.04 and standard deviation =0.078 is obtained as shown in Figure E-2 and plotted against the histogram obtained from the Normal distribution function. This comparison serves to illustrate that the random sample of the error is consistent with the assumption of a Normal probability distribution.

E-1

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.50

100

200

300

400

500

600Distribution of calibration factor

Calibration factor

frequ

ency

histogramNormal distribution

Figure E-2 Histogram of simulated WIM error distribution.

The application of the WIM error algorithm produces the results that are shown in black + signs in Figure E-3. These + signs give the frequency in percent for each of the bins for the histogram of the actual 60-ft simple span moment effects of the trucks that crossed this bridge after filtering out the WIM errors. The results of the filtration are compared to those obtained through a Monte Carlo simulation assembled into the red histogram of Figure E-3. The Monte Carlo simulation consisted of randomly generating 10,000 samples of truck moment effects, xm, from the measured WIM data histogram of Figure E-1. Also, a random sample of 10,000 errors, ε, was generated from the calibration error histogram of Figure E-2. By taking a value of xm and dividing by one value of ε, we obtain a single value of xr. Repeating the process 10,000 times, a sample of 10,000 xr values is obtained and assembled into the red histogram of Figure E-3.

A visual comparison between the values indicated by the symbol + and the red histogram show overall good agreement. In order to obtain an objective measure of the differences, a normalized error function is used that has been defined as:

( )2i

N

1i

2ii

e

neE

∑=

−= (E-1)

Where N is the total number of bins, ni is the number of samples that fall in bin i from the simulation where the total number of simulated samples is 10,000, ei is the total number of samples in bin i obtained from the filtered histogram re-normalized for a total number of 10,000 samples. The error E was found to be equal to E=46.55 when comparing the simulated no-error histogram to the filtered histogram. However, when ni represents the number of samples of measured WIM data that fall in bin i, the error was calculated to be E=91.70 confirming the improved accuracy of the filtered histogram in representing the actual load effect of the trucks when compared to the measured WIM data histogram. In all cases, the number of samples in each bin is re-normalized to provide an overall total number of 10,000 samples in all the bins.

E-2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

1

2

3

4

5

6

7

8

9

10Comparison of filtered histogram to simulated true histogram

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Figure E-3 Histogram of simulated WIM error distribution. The results of the filtration and those of the originally measured data are plotted on Normal probability curves in Figure E-4. For the regression fit of the tail end, the highest values are not considered to reduce the effect of the numerical errors introduced when the bins are very lightly populated. The plots show that the tail end of the original histogram representing the upper 5% of the data as collected from the original WIM data may be represented on the Normal probability plot by a straight line represented by the equation:

0784.0x0159.3y −= (E-2) This indicates that the tail end of the WIM data matches that of normal distribution with a mean

eventμ =0.026 and a standard deviation σevent=0.332. Similarly, the filtered histogram’s upper tail can be modeled by a Normal distribution with mean eventμ =0.089 and a standard deviation σevent=0.326. The tail end of the histogram obtained from simulation matches that of Normal distribution with mean eventμ =0.020 and a standard deviation σevent=0.326.

The above calculated means and standard deviations are then implemented into the equations for calculating the maximum load effect in a 75-year return period, Lmax which are given by applying the following steps:

• Set the number of events in 75 years given nday=2000 truck loading events/day to be: N= nday*365*75 (E-3)

• Find the most probable value, u, for the Gumbel distribution that models the

maximum value in 75 years Lmax given by:

E-3

( ) ( ) (( )

)⎥⎥⎦

⎤

⎢⎢⎣

⎡ +−×+=

Nln224ln)Nln(lnNln2u eventeventN

πσμ (E-4)

• Find the dispersion coefficient for the Gumbel distribution that models the maximum

load effect Lmax as:

( )event

N

Nln2σ

α = (E-5)

• The mean value of Lmax is given as:

NNmax

577216.0uLα

+= (E-6)

• The standard deviation of the Gumbel distribution that best models the maximum 75-

year load effect is given as:

N

max 6απσ = (E-7)

The application of the above equations lead to Lmax=1.887 and σmax=0.071 for the original WIM data, Lmax=1.920 and σmax=0.001 for the filtered data, and Lmax=1.853 and σmax=0.070 for the simulated data, where the differences in Lmax are less than 2%. This small difference in the estimated Lmax values is due to the small standard deviation of 0.078 in the WIM error as observed during the calibration of the WIM system. A sensitivity analysis is performed in the next section to study the effect of the WIM errors on the estimated Lmax values.

Normal Probability Plot y = 3.0159x - 0.0784R2 = 0.9975

y = 3.0642x - 0.2731R2 = 0.9973

y = 3.0628x - 0.0621R2 = 0.9853

0

0.51

1.52

2.53

3.54

4.5

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Moment/HL-93

Nor

mal

Dev

iate

measured histogram

histogram after WIM errorfilteringsimulation histogram

Linear ( measured histogram)

Linear ( histogram after WIMerror filtering)Linear (simulation histogram)

Figure E-4 Normal Probability plots of upper 5% of original and filtered histograms

E-4

Sensitivity Analysis

The analysis performed above uses a mean value for the calibration error ε, with mean=1.04 and a standard deviation =0.078. A comparison between the filtered histogram and the original measured histogram is provided in Figure E-5a and Figure E-5b where the latter shows the tail end of the histogram. The comparison between the filtered histogram and the one obtained from a Monte Carlo simulation of a histogram without measurement errors is provided in Figure E-5c and Figure E-5d where the latter gives a comparison of the tail ends of the histograms. The visual comparison shows little difference between all three histograms (measured, filtered and simulated with no WIM errors). However, the application of the error function of Equation E-2 confirms that the simulated histogram with no error and the filtered histogram are compatible as evidenced by a reduction of the error obtained when comparing the measured histogram to the simulated no-error histogram.

When the standard deviation of the WIM calibration error is assumed to increase from 0.078 to 0.10, 0.15 and 0.20, the application of the filtration algorithm will result in a large improvement in the match between the filtered histogram and the simulated no-error histogram. This comparison is presented in Figures E-6, E-7 and E-8 for the assumed higher standard deviations. The figures show a large improvement in the match between the filtered histogram and the simulated histogram as opposed to the comparison between filtered histogram and the measured histogram. The fourth and fifth columns of Table E-1 also provide the error function confirming that the filtered histogram and the simulated no-error histogram are compatible. Table E-1 Sensitivity Analysis Cases for 60-ft moment. Mean of WIM

calib. error ε Standard deviation σε

E (filtered vs simulated)

E (filtered vs measured)

Lmax (% difference from Measured data Lmax =1.887)

Case 1 1.04 0.078 46.55 91.68 1.920 (1.75%) Case 2 1.00 0.10 62.21 84.54 2.015 (6.78%) Case 3 1.00 0.15 80.39 95.79 2.134 (13.1% Case 4 1.00 0.20 73.39 105.9 2.340 (24.0%)

E-5

0 0.5 1 1.5 2 2.5 30

2

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6

Comparison of measured histogram to estimated filtered histogram

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measured histogramhistogram after WIM error filtering

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0.2

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0.8

1Comparison of measured histogram to estimated filtered histogram

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measured histogramhistogram after WIM error filtering

0 0.5 1 1.50

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Comparison of filtered histogram to simulated true histogram

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0.2

0.4

0.6

0.8

1Comparison of filtered histogram to simulated true histogram: tail end

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Figure E-5 Comparison of Filtered histogram to measured and simulated no-error histogram

for ε =1.04 and σε=0.078 a) Comparison between measured histogram and filtered histogram. b) Zoom on tail ends of filtered and measured histograms. c) Comparison between simulated true histogram and filtered histogram. d) Zoom on tail ends of filtered and simulated true histograms

0 0.5 1 1.5 2 2.5 30

2

4

6

Comparison of measured histogram to estimated filtered histogram

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measured histogramhistogram after WIM error filtering

0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1Comparison of measured histogram to estimated filtered histogram

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measured histogramhistogram after WIM error filtering

0 0.5 1 1.50

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Comparison of filtered histogram to simulated true histogram

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0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1Comparison of filtered histogram to simulated true histogram: tail end

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Figure E-6 Comparison of Filtered histogram to measured and simulated no-error histogram

for ε =1.0 and σε=0.10 a) Comparison between measured histogram and filtered histogram. b) Zoom on tail ends of filtered and measured histograms. c) Comparison between simulated true histogram and filtered histogram. d) Zoom on tail ends of filtered and simulated true histograms

E-6

0 0.5 1 1.5 2 2.5 30

2

4

6

Comparison of measured histogram to estimated filtered histogram

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measured histogramhistogram after WIM error filtering

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0.2

0.4

0.6

0.8

1Comparison of measured histogram to estimated filtered histogram

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measured histogramhistogram after WIM error filtering

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Comparison of filtered histogram to simulated true histogram

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0.2

0.4

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0.8

1Comparison of filtered histogram to simulated true histogram: tail end

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Figure E-7 Comparison of Filtered histogram to measured and simulated no-error histogram

for ε =1.0 and σε=0.15 a) Comparison between measured histogram and filtered histogram. b) Zoom on tail ends of filtered and measured histograms. c) Comparison between simulated true histogram and filtered histogram. d) Zoom on tail ends of filtered and simulated true histograms

0 0.5 1 1.5 2 2.5 30

2

4

6

Comparison of measured histogram to estimated filtered histogram

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measured histogramhistogram after WIM error filtering

0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

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1Comparison of measured histogram to estimated filtered histogram

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Figure E-8 Comparison of Filtered histogram to measured and simulated no-error histogram

for ε =1.0 and σε=0.20 a) Comparison between measured histogram and filtered histogram. b) Zoom on tail ends of filtered and measured histograms. c) Comparison between simulated true histogram and filtered histogram. d) Zoom on tail ends of filtered and simulated true histograms

E-7

Implementation of WIM Error Filtration Algorithm on Axle Weight Histogram The Coefficient of Variation (COV) in the WIM errors for the moment load effect may sometimes be reduced due to the random nature of the errors that may be higher on some of the axles and lower on some other axles. However, this compensating effect would not be triggered when dealing with deck design for which the axle weight is the controlling loading parameter. For this reason, it may be more important to filter out the WIM errors when analyzing the axle weight histograms as compared to load effect histograms. In this section, the filtration algorithm is further tested by analyzing the axle weight histograms collected at three sites in New York State. These sites are site 0580 (over I-495), 2680 (over Rt. 12) and 9121 (over I-81). Each site is analyzed for four difference cases:

1. WIM calibration error with mean =ε =0.97 and standard deviation σε=0.10 corresponding to the WIM error for axle weights as listed in Chapter 3 Table 17.

2. An assumed WIM calibration error with mean =ε =1.0 and standard deviation σε=0.15.

3. An assumed WIM calibration error with mean =ε =1.0 and standard deviation σε=0.20.

4. An assumed WIM calibration error with mean =ε =1.0 and standard deviation σε=0.40.

Cases 2–4 are used as a sensitivity analysis to determine at which level of the WIM calibration error the filtration become necessary. The filtered histogram for each of the cases studied is first compared to the measured histogram, which includes the WIM errors and a simulated histogram where the WIM errors are filtered out using a Monte Carlo simulation procedure. In all the cases studied, the filtered histogram shows good agreement with the simulated histogram. For low standard deviations of the WIM errors, the filtered histogram is reasonably close to the measured histogram. When the Lmax value calculated from the measured data is compared to the Lmax value calculated from the filtered data, the difference is on the order of 7% to 13% when the standard deviation of the WIM calibration error is 10% as shown in the summary of results given in Tables E-2 thru E-4. The difference increases dramatically as the standard deviation of the WIM error increases beyond 10%. These results illustrate the importance of filtering out the WIM errors if the standard deviation of the WIM error is high on the order of 0.10 or higher. For low standard deviations, there is little difference between the filtered histogram and the originally measured histogram. Conclusion This report presented a procedure to filter out the WIM calibration errors from the measured WIM histograms of gross weights or load effects. A comparison between the Lmax values obtained from the filtered histograms to those obtained from the measured histograms show the importance of filtering out the errors when the WIM calibration error has a standard deviation higher than 0.10.

E-8

Table E-2. Sensitivity Analysis Cases for axle weights of I-495 site Case Mean of

WIM calib. error ε

Standard deviation σε

E (filtered vs simulated)

E (filtered vs measured)

Lmax (% difference from Measured data Lmax =97.88)

Case 1 0.97 0.10 14.08 69.77 104.73 (7.0%) Case 2 1.00 0.15 36.24 71.20 108.16 (10.5%) Case 3 1.00 0.20 30.08 76.69 119.67 (22.3%) Case 4 1.00 0.40 77.34 85.00 213.87 (118%) Table E-3 Sensitivity Analysis Cases for axle weights of Route 12 site Case Mean of

WIM calib. error ε

Standard deviation σε

E (filtered vs simulated)

E (filtered vs measured)

Lmax (% difference from Measured data Lmax=61.52)

Case 1 0.97 0.10 3.79 12.96 69.98 (13.8%) Case 2 1.00 0.15 12.96 79.26 75.99 (23.5%) Case 3 1.00 0.20 5.11 85.03 89.07 (44.8%) Case 4 1.00 0.40 52.45 87.63 168.15 (173%) Table E-4 Sensitivity Analysis Cases for axle weights of I-81 site Case Mean of

WIM calib. error ε

Standard deviation σε

E (filtered vs simulated)

E (filtered vs measured)

Lmax (% difference from Measured data Lmax=72.37)

Case 1 0.97 0.10 7.98 76.76 81.76 (13.0%) Case 2 1.00 0.15 8.72 80.06 89.06 (23.1%) Case 3 1.00 0.20 19.77 84.94 106.26 (46.8%) Case 4 1.00 0.40 65.54 90.08 209.49 (189%)

E-9