REDUNDANCY OF TWIN

STEEL BOX GIRDER

BRIDGES

C. Tony Hunley, PE, SE

Dr. Issam E. Harik, Ph.D.

BIOGRAPHY C. Tony Hunley, PE, SE is the Deputy Structural Engineering Manager for the Lexington, KY office of ENTRAN. He has over ten years of experience in Structural Engineering, including prestressed concrete, steel plate girder, and steel box girder bridges, seismic design and retrofits, and bridge erection engineering for large steel bridges. Tony has also taught a graduate-level course in prestressed concrete at the University of Kentucky. Additionally, he is a doctoral candidate at the University of Kentucky, where his research is focusing on the redundancy evaluation of twin steel box girder bridges. Dr. Issam Harik is the Raymond-Blythe Professor of Civil Engineering, and Program Manager of the Structures and Coatings Section at the Kentucky Transportation Center, University of Kentucky, Lexington, KY. His research interests are in the areas of fiber reinforced polymer composites, seismic analysis and retrofit of bridges, vessel impact on bridges, and hazard management of highway structures. He currently serves as a member of eleven societies, and holds offices in four of them. He has authored and co-authored more than 240 technical publications. He has directed the research of more than 100 students and 25 visiting professors and scholars.

SUMMARY Non-redundant steel bridges are designated as fracture critical, which results in stringent fatigue design considerations, a substantial testing program during fabrication, and more involved periodic inspections at a higher frequency than for redundant bridges. This results in higher construction and maintenance costs for fracture critical bridges. NCHRP Report 406 investigated and quantified structural redundancy in highway bridges. That research did not, however, explicitly investigate steel box girder superstructures. Steel box girders are increasingly more common for curved highway bridges because they offer superior aesthetics and torsional rigidity. Current practice considers twin steel box girder bridges as non-redundant and fracture critical. However, their torsional rigidity results in considerable ability to redistribute loads. The current paper is a preliminary report on ongoing research into the redundancy evaluation of twin steel box girder bridges. The parametric study examines the effects of simple and continuous span bridges, span length, curvature, and external diaphragm spacing and stiffness.

REDUNDANCY OF TWIN STEEL BOX GIRDER BRIDGES C. Tony Hunley, PE, SE and Issam E. Harik, PhD

Introduction A recent advancement in the field of bridge engineering is the increased use of steel box girder superstructures. Construction and re-construction of urban highway interchanges throughout the country have resulted in more and more single- and two-lane ramp bridges (generally on curved alignments) being constructed. This increase in the construction of continuous, curved bridges has led to several construction-related problems with the traditional bridge framing, curved steel I-girders, due to local and global rotation of the girders during construction. As a result of construction problems with curved I-girders, increased box girder research, and improved fabrication techniques, twin steel box girder superstructures are increasingly more common for curved highway ramps and other bridge structures up to a width of around 40-ft. These bridges offer superior torsional rigidity, aesthetic value, and ease of in-service inspection. Historically, however, choosing a twin box girder bridge instead of a bridge composed of three or four I-girders has resulted in a nonredundant, or “Fracture Critical”, designation for the bridge.

Although there is no clear, objective, and quantifiable definition of redundancy in published bridge design or inspection standards (6), the structural redundancy of a highway bridge can be generally defined as the ability of the bridge to resist a general failure or collapse of the structure after failure of one critical tension element. Structural redundancy is critically important in highway bridges due to the classification of non-redundant bridges as fracture critical. The major drawback to the use of twin steel box girder superstructures is that, historically, they have been considered non-redundant. This designation leads to more stringent fatigue considerations during design, a substantial testing program during fabrication, and more involved periodic maintenance inspections at a higher frequency than redundant bridges. All of these factors result in higher construction costs and increased maintenance costs for fracture critical bridges.

This paper presents preliminary results from an analytic investigation of the redundancy of twin steel box girder bridges. Parametric non-linear finite element method (FEM) studies of representative steel box girder bridges are used to determine the collapse mechanisms for a damaged bridge, and evaluate minimum guidelines for design and detailing that result in redundant bridges. The role of different bridge components in developing sufficient load transfer from the damaged girder to the undamaged girder is being investigated. The key parameters are span length, bridge continuity, curvature, location of girder damage, girder flange sizing methodology, concrete deck, type and spacing of external diaphragms, and connection of the external diaphragms to the box girders.

Redundancy Research Several investigations attempting to develop a definition of redundancy, and to provide a tool to measure the level of redundancy in structural systems, were undertaken between the late 1970’s and the late 1990’s. This research focused on two types of redundancy measures: deterministic and probabilistic. Deterministic measurements of redundancy focus on the indeterminacy of the structural system and strength calculations of the intact and damaged system. Alternatively, probabilistic measurements of redundancy focus on the probability and uncertainties of loads and structural capacity using structural reliability analysis techniques. Definitions of redundancy include:

• Degree of static indeterminancy, • Ability of a structure to withstand the failure of any main member without collapse (AASHTO

definition), and • Ability of a structure to maintain serviceability (collapse or excessive deflection) through

alternate load paths and load redistribution after failure of any main member.

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The above definitions of redundancy are intuitive to most structural engineers, and, perhaps for that reason, design codes contain ambiguous and subjective definitions of bridge redundancy. For example, it is commonly agreed that two-girder bridges are nonredundant (some agencies even include three-girder bridges). Historically, tied arch bridges have been generally considered nonredundant due to the importance of the single tension tie. However, research and several bridge design and rehabilitation projects have explored the gray area between bridges that are generally accepted as redundant and nonredundant. For example, post-tensioning the ties of tied arch bridges has gained wide acceptance as a measure to increase redundancy. Investigations of two-girder/sub-stringer bridges (7, 13, 14) have shown that redundancy can be enhanced by providing additional load plates in tension areas and by strengthening bracing systems. Connor et al. (5) note that many bridges have had full-depth fracture of “nonredundant” girders and did not collapse, citing alternative-load-carrying mechanisms as preventing collapse. Furthermore, research (6) has shown that four-girder bridges can exhibit a live load capacity, after fracture of one girder, as low as 28 percent of the undamaged capacity. This illustrates the need for a quantitative measurement of redundancy when evaluating bridges that fall in the gray area between clearly nonredundant and acceptably redundant.

Although the concept of redundancy is vague yet intuitive, the real source of confusion lies in its measurement. Following the publication of the AASHTO Guide Specification for Fracture Critical Nonredundant Steel Bridge Members in 1978 (1), the concept of redundancy, and the introduction of lower allowable stress ranges for nonredundant steel bridges, was first introduced into the AASHTO Standard Specifications for Highway Bridges in 1979 (3). However, these design standards only included subjective definitions of redundancy, and no rules for measuring the level of redundancy. In 1985, a joint ASCE-AASHTO Task Committee (16) concluded that little work had been done on quantifying necessary levels of redundancy in highway bridges and called for more research into structural redundancy of bridge systems.

NCHRP Report 406 A study to investigate and quantify structural redundancy in highway bridges was performed and resulted in NCHRP Report 406 [Redundancy in Highway Bridge Superstructures (9)]. The goal of the study was to develop a method to account for redundancy during the design and safety evaluation of highway bridges. The research proposed objective, quantifiable minimum criteria for redundancy classification of a bridge, and presented guidelines for the redundancy analysis and evaluation of any bridge system. Redundant steel I-girder, prestressed concrete I-beam, and prestressed concrete box beam bridge superstructures were used to develop the proposed redundancy criteria. Therefore asserting that if any bridge type could be shown to meet the redundancy criteria measurements of “redundant” bridges, then that bridge type can safely be classified as redundant.

The proposed redundancy measures compare four critical limit states:

• Member failure based on individual member safety using elastic analysis and member capacity, LF1, • Ultimate limit sate based on the ultimate capacity of the bridge, or formation of a collapse mechanism,

LFu, • Functionality limit state based on the capacity of the intact bridge at a live load displacement limit equal

to the span length/100, LFf, and • Damaged condition limit state based on the ultimate capacity of the bridge after removal of one main

load-carrying component, LFd.

And, three calibrated redundancy measures were proposed:

Damaged Condition Redundancy Measure = Ru = LFu / LF1 ≥ 1.30 Functional Condition Redundancy Measure = Rf = LFf / LF1 ≥ 1.10 Ultimate Condition Redundancy Measure = Rd = LFd / LF1 ≥ 0.50

The primary benefits of the redundancy measures proposed in the NCHRP Report 406 are: logically direct, define quantitative limits, do not depend on the choice of live load model, and are based on system reliability evaluations of bridges whose redundancy is generally agreed upon. The ultimate, Ru, and functional, Rf, limit

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state requirements listed above insure post-yield ductility in the bridge. And, as such, should be satisfied by any bridge that is designed in accordance with current design specifications. The Damaged Condition, Rd, limit state requirement is therefore the critical measure of a bridge’s redundancy. It requires that a bridge’s damaged condition capacity must be at least 50 percent of the load which would result in first member failure.

The approach proposed in NCHRP Report 406 has gained acceptance from agencies and bridge designers on several projects. However, it has not been adopted into bridge design standards. The 2005 Interims to the AASHTO LRFD Specifications (2) allows the engineer to determine if any component of a bridge should be classified as a Fracture Critical Member(FCM) by utilizing a “rigorous analysis with assumed hypothetical cracked components” to “confirm the strength and stability of the hypothetically damaged structure.” However, the commentary states

“The criteria for refined analysis used to demonstrate that part of a structure is not fracture critical has not yet been codified. Therefore, the loading cases to be studied, location of potential cracks, degree to which the dynamic effects associated with a fracture are included in the analysis, and fineness of the models and choice of element type should all be agreed upon by the owner and the engineer.”

Previous Studies of Twin Steel Box Girders The torsional rigidity provided by curved steel box girders suggests that they will not respond to girder damage in the same way as other two-girder bridge types. Furthermore, two recent investigations (10, 11) have proposed that, with proper design and detailing, it could be shown that twin steel box girder superstructures can be designed to meet the minimum criteria of NCHRP Report 406. The Marquette Interchange redundancy study (11) was the first investigation of the redundancy of twin steel box girders. The Wisconsin DOT and FHWA accepted the results of the study, and consider the twin steel box girder bridges on this project to be redundant. Also, current research at the University of Texas at Austin is investigating methods of evaluating the redundancy of steel bridges. As part of this work, a 120 foot long full-size twin steel box girder bridge was tested to evaluate its ability to remain intact if one of the girders suffers a brittle fracture, simulated by cutting the bottom flange. (17)

The preliminary study into the redundancy of twin steel box girder bridges by Kumarasena, et al., (10) investigated a 225 foot long simple span bridge at four curvature levels (straight, 1150-ft radius, 750-ft, and 400-ft). The bridge models included four full-depth intermediate external steel diaphragms. The finite element models included the nonlinear material response of the steel box girders. However, the concrete deck of the bridge was modeled as a linear elastic material. Not surprisingly, the results indicated that cracking of the concrete deck would occur prior to collapse of the bridge. The results of the study suggest that the Damaged Condition limit state redundancy measure (Rd) varies from 0.62 to 0.89 for the four curvature levels modeled, indicating that the bridges meet the redundancy requirements of NCHRP Report 406.

Current Study The current study, with preliminary results presented herein, is an analytic investigation of the redundancy of twin steel box girder bridges. The parametric investigation is performed utilizing non-linear FEM studies of steel box girder bridges. Four steel box girder bridge superstructures have been design in accordance with the AASHTO LRFD bridge design code (2). Non-linear FEM models are then developed for each bridge to measure the Damaged Condition redundancy measure, Rd, and determine the effect of various parameters on the redundancy measure. The key parameters are span length, bridge continuity, curvature, location of girder damage, concrete deck, and type and spacing of external diaphragms.

Study Bridges The typical bridge section utilized in this study is a 38-ft wide reinforced concrete bridge deck supported on two steel box girders spaced at 19-ft between the centerline of the girders (Figure 1). The box girders utilize a 1H:4V web slope, and AASHTO M270-Grade 50W steel throughout. Four bridge configurations are presented in this preliminary report.

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• 150-ft simple span bridge with no curvature, and 60-in deep steel box girders. (Figure 2a) • 225-ft simple span bridge with no curvature, and 90-in deep steel box girders. (Figure 2b) • 225-ft simple span bridge on a 1000-ft radius. (Figure 2c) • 450-ft two-span bridge on a 1000-ft radius. (Figure 3)

(a) 150-ft Spans (b) 225-ft Spans

Figure 1: Typical Sections

(c) 225-ft Simple Span Bridge (1000-ft Radius) Figure 2: Simple Span Bridge Layouts

(b) 225-ft Simple Span Bridge (Straight)

(a) 150-ft Simple Span Bridge (Straight)

Figure 3: 450-ft Two Span Bridge (1000-ft Radius)

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These initial bridge configurations allow a comparison of three key components of the redundancy of twin steel box girder bridges; span length, curvature, and continuity. The span lengths of curved steel ramp bridges typically range from 150-ft to 300-ft. Curvature is critically important to redundancy because of the load shedding that occurs from the inner girder to the outer girder. Therefore, a failure of the outer girder in a curved two girder bridge will have a greater impact on the failure of the bridge.

Simple span bridges were included in a previous study because they are more critical and approximate the end spans of continuous bridges (10). It was also suggested that continuity provides additional redundancy and, therefore, any redundancy design requirements could be relaxed for interior spans. There are several characteristics of continuous bridges, however, that suggest that continuity be included in a comprehensive evaluation. First, flange sizes in positive moment regions of continuous girders are generally smaller than those of a simple span bridge of the same span length. Also, in a well-proportioned girder design, the flange sizes near the moment contraflexure regions are smaller than in the positive and negative moment areas. This “fuse” area could lead to a lower bridge failure load, depending on the location of the initial damage. Another critical factor for continuous bridges is the location of the initial girder damage.

Simulated Girder Damage The damage state considered in this study is a fracture of the bottom flange and webs of one of the box girders. For the curved bridges, the outside girder is damaged. Damage of the girder could result from several factors. In the classic sense for Fracture Critical bridges, it would initiate as a crack at a fatigue prone detail, such as a connection plate-to-flange weld. Damage could also result from an overload condition, or deterioration due to poor drainage details.

The damage is affected in the FEM model by reducing the element stiffness of a line of flange and web shell elements at the critical location to a near-zero value. The top flange element stiffnesses are not reduced to enhance FEM model convergence. This is acceptable because the longitudinal stress in the top flanges reaches the plastic material response region at a small live load level, and thus contributes little to the overall stiffness of the damaged bridge.

The response of a bridge superstructure to the sudden fracture of a flange includes a dynamic effect and a continuing propagation of the crack into the web. This dynamic effect may be more significant in longer span bridges where the dead load is a higher percentage of the total load and could release significant levels of “stress energy.” These responses do not typically, however, result in failure of the bridge. This has been illustrated by the many bridges that have had cracks detected during routine bridge inspections, while still supporting daily vehicular loading. Potential reasons include energy dissipation through load redistribution, and the fact that the daily vehicular loading is less than the design loading for the bridge. Thus, the approach used in this analysis does not address the “impact” effects and dynamics of crack propagation for the damaged girder. Rather, the post-damage load carrying capacity of the bridge is determined for comparison with the undamaged capacity. This approach is further justified by the results of the University of Texas at Austin bridge fracture test (17), in which the bridge deflection did not increase significantly after an explosive fracture of the full bottom flange of one box girder.

The critical location for girder damage of simple span bridges is at mid-span. In order to fully evaluate the effect of bridge continuity on redundancy, however, additional damage locations must be investigated. These areas of damage include near the continuous pier support and near the moment contraflexure regions.

External Girder Bracing Load redistribution from the damaged girder to the adjacent intact girder must occur to prevent the collapse of a bridge. The distinct advantage of steel box girders in this area is their superior torsional stiffness. However, a lateral load transfer mechanism must remain intact to redistribute live load from the damaged girder to the intact girder. The two lateral load transfer mechanisms are the concrete deck and any external crossframes or diaphragms between the girders. The need for permanent external crossframes in steel box girder bridges is a controversial topic. Many twin steel box girder bridges have been built in the United States with the external

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crossframes removed after slab construction. These bridges rely on the concrete deck for lateral load distribution between the box girders. No subsequent problems have been published on bridges built with this construction technique. This technique is not desirable, however, in regards to redundancy. Although sufficient as a lateral load distribution mechanism, the concrete deck will not fully support the damaged girder and sufficient levels of live load over the damaged girder to classify the bridge as redundant. Permanent external crossframes or diaphragms provide a significant lateral load transfer mechanism that may prove essential in the classification of these bridges as redundant.

The connections of external crossframes or diaphragms in curved steel bridges are generally designed for the real forces, which are typically less than the crossframe member capacities. Therefore, utilizing external bracing to ensure redundancy must be evaluated thoroughly with respect to the force levels generated. For permanent external crossframes or diaphragms to provide the necessary lateral load transfer mechanism, the connection design is critical.

Two types of external bracing are typically used for steel box girders, K-type crossframes and solid diaphragms. Typically, solid diaphragms have only been used at support areas, on heavily skewed bridges, or where the combination of box girder spacing and depth are not suited for K-type crossframes. The use of full-depth solid diaphragms with a moment connection to the box girder offer distinct advantages for the lateral load transfer mechanism needed to enhance redundancy. In this study three external bracing configurations are investigated (Figure 4). They include:

• Two external K-type crossframes (Figure 4a) at approximately the L/3 points of the span. • Three external K-type crossframes (Figure 4a) at approximately the L/4 points of the span. • Two external full-depth solid diaphragms with moment connection (Figure 4b) at approximately the

L/3 points of the span.

Figure 4: External Bracing Types

Bridge Design ted in this study were first designed in accordance with the AASHTO LRFD bridge

The finite element software package, ANSYS/CivilFEM, was utilized in this study. ANSYS/CivilFEM incorporates the Full Newton-Raphson Method to perform the incremental nonlinear analysis.

(a) K-Type Crossframe (b) Full-Depth Diaphragm

The bridges investigadesign code (2) using the grid analysis method. The AASHTO LRFD code recommends box girder depths of L/25 as a good starting point. However, tangent steel tub girders with span-to-depth ratios of nearly 35 have been designed (12). A span-to-depth ratio of 30 was used for this study. One key aspect of the design of any curved steel bridge is the approach to the load shedding that occurs from the inner girder to the outer girder. Traditionally, this can be taken advantage of in the design of the bridge by using smaller flange sizes on the inner girder. This results in a design where both girders are optimized, and less total steel weight. However, another option would be to use the same flange sizes on both girders. This could reduce fabrication costs by limiting the number of plate thicknesses, and simplify connection details by using consistent flange widths. Another major benefit to utilizing the same flange sizes on both girders is improved redundancy levels. If girder damage occurs to the outer girder, the overall capacity of the bridge will be lower if the intact inner girder has smaller flange sizes. Therefore, in the current study, the girder designs were performed utilizing consistent flange sizes between the inner and outer girders.

Finite Element Modeling

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Steel Girders and Bracing The response of the bridge after damage of the girder results in yielding of the intact girder and significant load in the lateral load transfer elements. The structural stthe box girder webs and flan

eel material model (15) used for ges included post-yield strain

ant. Although less demanding computationally, material for the concrete deck would be inconsistent with the goal of the analysis, and

servative redundancy measurements. The concrete deck was modeled with 4-node layered

modes of nonlinear response, including linear elastic, mbrane action of the rebar. This variation of response is

an “effective” thickness of the concrete deck, and reducing the element o a near-zero value when they reach the crushing strain

hardening, Figure 5. Fracture is assumed to occur at a steel strain level of 19%. All internal and external bracing, including external full-depth solid diaphragms, assume an elastic-perfectly plastic material model. The primary reason for not including the strain-hardening response in the bracing members is their connection design. If sufficient redundancy levels can be shown while limiting the forces in the bracing to the yield strength of the member, then the bracing connections will be more straightforward to design and fabricate. K-type external crossframes are modeled as trusses. The interface between the full-depth external steel diaphragms and the steel box girders is assumed to be a full moment connection. This is affected by the bolted splices that connect these members.

Concrete Deck The reinforced concrete deck is a critical element in the post-damagnonlinear response of the deck after girder damage is signific

e evaluation of a two-girder bridge. The

utilizing a linear-elastic may result in unconshell elements overlaid with a layered reinforcing element. The reinforcing element utilizes a smeared approach with the reinforcing located in the correct location and orientation in the shell element. The concrete material model (8) is shown in Figure 6. The steel reinforcement material model (4) is shown in Figure 7.

The reinforced concrete deck undergoes several cracking, yielding of the rebar, crushing, and mereplicated in the study by utilizing stiffness of the individual concrete finite elements t . The steel reinforcement then continues in membrane action until its failure.

0

10

20

30

40

50

60

70

0.00 0.02 0.04 0.06 0.08 0.10 0.12

Strain, εs

Stre

ss, f

s (ks

i)

(0.015, 68 ksi)

80

90

100

Figure 7: Steel Reinforcement Stress-Strain Model

(0.09, 95 ksi)

0

1

2

3

0.000 0.001 0.002 0.003

Strain, εc

Stre

ss, f

' c (ks

i)

40.95f ' c

Ref . (8)

ANSYS/ CivilFEM

Figure 6: Concrete Stress-Strain Model

Figure 5: Grade 50W Structural Steel Stress-Strain Model

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Proposed Definition Of “Collapse” In evaluating bridge redundancy at the Damaged Condition limit state, the term “ultimate capacity” must be

apacity is defined as the maximum live load that can be her defined as the formation of a collapse mechanism, for

yielding throughout the damaged structure. Collapse was defined as the point at

of

h to be uncomfortable to the bridge user or significant to an observer, providing

ve load capacity of a damaged bridge (LFd) to the live load capacity of the intact bridge based on current design guidelines (LF1). LF1 is determined by incrementing the truck portion of the HL-93 live load in a linear-elastic FEM analysis and determining the live load increment that corresponds to the initiation of yielding in the

Fi

defined. In the NCHRP Report 406, the ultimate capplied before the bridge collapses. Collapse is furtbridges with high member ductility, or the point at which the structure is inadequate for use, for less ductile bridges. One problem with highly ductile structures, however, is that significant deflections can occur prior to formation of a collapse mechanism. Therefore, using the load level at formation of a collapse mechanism will result in a higher redundancy measure, even though the structure is rendered useless at this load level because it is impassable to traffic.

Kumarasena et al. (10) noted rather large deflections prior to reaching bridge failure. However, the rate of increase in deflection with increased live load was observed to increase beyond a certain load level. Bridge stiffness decreased during which the rate of change in bridge stiffness increases, indicating strain hardening in the undamaged girder.

One feature of redundant bridges that should not be overlooked is their ability to give sufficient notice of damage prior to collapse. Many redundant bridges have withstood significant damage while maintaining nearly full functionality, allowing for observation and repair prior to collapse. Similarly, some level functionality of the damaged bridge would be desirable for the classification of a questionable bridge type as redundant. This would provide time after member damage and before collapse for detection and reporting of the damage by the traveling public or an agency’s representative during the next scheduled bridge maintenance inspection.

A functionality limit, or deflection limit, is herein recommended to define the ultimate capacity, LFd, of the damaged bridge. A value equal to the span length/100 is also herein recommended. This level of displacement is considered high enougsufficient indication of damage to the bridge. One concern, however, with utilizing a deflection limit to define the damaged condition limit state is that the progressive response of the bridge is not necessarily captured. For this reason, the load level at which progressive failure initiates should be greater than the load level at span length/100 of the damaged structure. A proposed correlation between bridge stiffness (defined as the ratio of

the total applied live load to the maximum girder live load deflection) and increasing live load on a damaged two girder bridge can be approximated as in Figure 8, modeled after Kumarasena et al. (10). At high load levels, the stiffness approaches asymptotically the horizontal axis. This is assumed to be at the initiation of strain hardening in the undamaged girder, indicating it is nearing fracture. It also signals extensive damage or crushing of the concrete deck and/or “unzipping” of the external diaphragms between the damaged and undamaged girders. To insure sufficient additional live load carrying capacity of the damaged bridge, the functionality limit load used in redundancy evaluation should be less than the load corresponding to progressive failure of the bridge (point X in Figure 8).

t, or redundancy factor, is defined as the ratio of the li

gure 8: Bridge stiffness vs. increasing live load (damaged two girder bridge)

Redundancy Evaluation The Damaged Condition, Rd, limit state requiremen

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girders. LFd is determined by incremThe limiting value of LF is selected

enting the truck load on a nonlinear FEM model of the damaged bridge. by evaluating the following criteria:

ges

tates

d

1. Damaged condition failure load. 2. Damaged bridge functionality limit, i.e. deflection exceeding L/100.

Using the above criteria, the redundancy factors were calculated for each of the four bridge models in Figures 1 to 3. The results are listed in Tables 1 and 2 for the simple-span and continuous bridge models respectively.

Table 1: Redundancy Factors for Simple Span Brid

Limit SSpan / Radius

Number of External Braces

External Brace Type LF1 LF Rd d

2 K-type 5.5 4.5 0.82 2 Diaphragm 5.6 4.0 0.71 150-ft

Tangent 3 K-type 4.9 4.1 0.84 2 K-type 6.7 2.9 0.43 2 Diaphragm 6.6 3.1 0.47 225

Tan-ft gent 3 K-type 6.5 5.5 0.83

2 K-type 5.0 3.3 0.66 2 Diaphragm 4.9 3.8 0.78 225-ft

1000-ft Radius 3 K-type 4.9 4.1 0.84

Table 2: Redundancy Fac s for 45 an dg

L S

tor 0-ft, Two-Sp Bri e

imit tates Damage Numb of External Braces

EBLocation

er xternal race Type LF1 LFd Rd

2 D i aphragm 8.0 14.3 1.79Mid-Span 3 K-ty 7.9 pe 15.9 2.01 2 Diaphragm 8.5 15.6 1.84 Near

Contraflexure 3 K-type 9.6 18.9 1.97

Based on the values presented in Tables 1 and 2, the p u idg n be nsidered redundant by the NCHRP Report 406

The redundancy factors for the two-span continuous bridg neral gh ple span bridges. For a mid-span damage location, this could be the fact that the intact girder has a shorter effective span length than for a simple span bridge of th pan th. d location near the

ly a lower redundancy factor.

e load level, or ultimate capacity of the he alternate definition presented herein leads to a conservative evaluation of bridge

ng sufficient notice of bridge damage prior to collapse.

reliminary st dy br es ca cocriteria.

e are ge ly hi er than those for the simexplained by

e same s leng For a amagemoment contraflexure location, the loading was placed near the damage location. However, the maximum flexural stresses in the intact girder were closer to mid-span, indicating that a different live load location may produce higher stresses and potential

Conclusions A universally accepted, clear, and quantifiable definition of redundancy continues to elude the structural engineering community. However, the approach proposed by the NCHRP Report 406 has gained acceptance from agencies and bridge designers on several projects. The key aspect of implementing a Damaged Condition limit state redundancy measure is defining the collapsdamaged bridge. Tredundancy, while providi

A reasonable functionality limit for the damaged condition, span length/100, is proposed. This level of displacement is considered high enough to be uncomfortable to the bridge user or significant to an observer, providing sufficient indication of damage to the bridge. Further research, however, is needed to verify this limit. For example, would bridge types that are considered inherently redundant still result in a damaged

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condition system reserve ratio, Rd, greater than 0.50? If not, a higher limit, based on evaluation of redundant bridge types, could be allowed.

External bracing on steel box girder bridges is generally only required for construction purposes, and not required after the concrete deck reaches full strength. However, with particular attention to the design of the connections, the presence of external bracing may prove essential in providing a sufficient load transfer mechanism to enable the classification of twin steel box girder bridges as redundant.

The preliminary results presented herein suggest that twin steel box girder bridges can be classified as redundant, with certain minimum design provisions. Results were included in this paper for two levels of

mparable levels of bridge redundancy to

Association of State Highway and Transportation Officials (AASHTO), (1979), Standard ions for Highway Bridges, 12th Ed.,Washington, DC.

undancy Design and Rating of Two-

1

1

11

bracing: two external crossframes/diaphragms, and three external crossframes. The redundancy factors were very close for all three external bracing configurations for a give bridge. Subsequent investigations will include additional bracing to determine an effective level of external bracing, and to further define the role of the reinforced concrete slab in the lateral load transfer mechanism.

The preliminary results presented herein also suggest that continuous bridges have higher redundancy factors. However, the live load placement for maximum effect on a continuous bridge with damage at locations other than mid-span requires additional investigation.

Additional bridge models further investigating the effects of curvature, span length, external bracing spacing and stiffness, and continuity are ongoing. It is clear, however, that twin steel box girder bridges, although historically considered Fracture Critical, can be shown to provide coother bridge types which have been historically considered redundant.

References 1. American Association of State Highway and Transportation Officials (AASHTO), (1978), Guide

Specification for Fracture Critical Nonredundant Steel Bridge Members, Washington, DC. 2. American Association of State Highway and Transportation Officials (AASHTO), (2004), LRFD

Bridge Design Specifications, 3rd Ed.,Washington, DC. 3. American

Specificat4. 5.

CALTRANS, (2006), “Seismic Design Criteria,” Connor, R.J., et al., (2005), “Inspection and Management of Bridges with Fracture-Critical Details,” NCHRP Synthesis 354, National Cooperative Highway Research Program. Crampton, D.D., et al., (2007), “Improving Redundancy of Two-Girder Bridges,” Paper No. 07-2573

th6.

Presented at the Transportation Research Board’s 86 Annual Meeting, Washington D.C., January 2007.

elines for Red7. Daniels, J.H., et al., (1989), “Recommended GuidGirder Steel Bridges,” NCHRP Report 319, National Cooperative Highway Research Program. Ford, J.S., et al., (1981), “Behavior of Concrete Columns under Controlled Lateral Deformation,” 8. ACI Journal, ACI, Vol. 78, No. 1, pp. 3-20. Ghosn, M., and Moses, F., (1998), “Redundancy in Highway Bridge Superstructures,” NCHRP Report 406, National Cooperative Highway Research Program.

9.

0. Kumarasena, S., et al., (2004), “Structural Redundancy of Steel Box Girder Bridges,” Proceedings of the 2004 FHWA Steel Bridge Conference, San Antonio, Texas, pp. 57-68.

1. Milwaukee Transportation Partners, (2005), “Redundancy of Box Girder Steel Bridges – A Study For the Marquette Interchange HPS Twin Box Girder Structures,” Project I.D. 1060-05-1222.

2. 3.

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