Fundamentals of LRFR and Applications of LRFRFundamentals of LRFR and Applications of LRFR for Bridge Superstructures

Presented by:Sita Ram Pandey &Sreelatha Nandivada

AI E i IAI Engineers, Inc.919 Middle Street, Middletown, CT, 06457

From4 – day course by National highway Institute

How did we get Here? – Origin & History

• Two Major historical events • Tacoma Narrows bridge Collapse on Nov 7th

1940 • Silver Bridge ; from Point Pleasant WV, and

Gallipolis Ohio over Ohio river collapse inGallipolis Ohio , over Ohio river , collapse in 1967.

• Prompted National concern for Bridge safety conditions and to the establishment of the National Bridge Inspection Standards ( NBIS)Inspection Standards ( NBIS)

Tacoma Narrows Bridge - 1940

Tube - The Tacoma Narrows Bridge Collapse (1940

Purpose for Load Rating

• Ensure Public Safety

• Comply with federal standards / regulations –

• Ensure Public Safety

• Comply with federal standards / regulations –Comply with federal standards / regulations

NBIS

Comply with federal standards / regulations

NBIS

• Rehabilitation and replacement

• Posting needs

• Rehabilitation and replacement

• Posting needs

• Report to the NBI

Processing of Overload permits

• Report to the NBI

Processing of Overload permits• Processing of Overload permits• Processing of Overload permits

When should we Load Rate a bridge

• Design stage.

I iti l i t i ti

• Design stage.

I iti l i t i ti• Initial inventory inspection.

• Change in live loading.

• Initial inventory inspection.

• Change in live loading.

• Change in dead load on structure.

• Physical change in any structural member

• Change in dead load on structure.

• Physical change in any structural member• Physical change in any structural member.

• Change in load rating method.

• Physical change in any structural member.

• Change in load rating method.

Classification of Bridge ConditionsClassification of Bridge Conditions

BridgeCondition

Structurally Deficient

Functionally Obsolete

Not Deficient

id di iBridge Conditions 1991-2009

• 603 254 b id i• 603,254 bridges in the United States as of Decemberas of December 2009

• 71,179 were rated 7 , 79 w dstructurally deficient and 78,468 were rated functionally b lobsolete.

Wh t’ L d R ti ?What’s Load Rating?

• Live Load carrying capacity of the Bridge y g p y g

Using as-built bridge plans

Information gathered from latest field Inspection

• Expressed in Rating Factors or in tonnage for a particularvehicle instead of the design approach of ‘satisfying limitvehicle instead of the design approach of satisfying limitstates’

• Superstructure Spans, primary components of the bridge andconnections shall be load rated until the governing

t i t bli h dcomponent is established

Load Rating Standards and RequirementsStandards

• AASHTO – Manual for Bridge Evaluation (MBE) –single national standards for load rating of highway b idbridges.

• Load rating requirements and reporting are specified in NBISN S

Data

Geometric data

Member and condition data

Loading and traffic data

Load Rating Methods in the MBE

• Allowable Stress Rating ( ASR)

• Load Factor Rating ( LFR)

• Load and Resistance Factor Rating (LRFR)

Load Rating Method: ASR

• Loads are at a working level.

C it i d d b f t f f t• Capacity is reduced by a factor of safety.

• Live Load is the HS20 truck or lane load, whichever governs.

Load Rating Method: LFR

A S h b d l d i h d• A Strength-based load rating method

• Uncalibrated code. Load factors were established based on engineering judgment (Unknown reliability)

• No guidance on adjusting load and resistance factors for changed uncertainty in loadings or member resistance.member resistance.

• Live Load is the HS20 truck or lane load, whichever governswhichever governs.

Load Rating Method: LRFR

li bili b d li i hil h• Reliability- based limit states philosophy.

• Use probabilistic method to derive load & resistance factors

• Uniform reliability in load ratings and load postings.

• Provide guidance on adjusting live load g j gfactors using site-specific traffic data.

Overview Of LRFR

Benefits of LRFR

• Reliability-based, limit states approach consistent

• Rating done at strength limit state and check for serviceability

• More easily adopts site specific i f ti hil i t i i ifinformation while maintaining uniform reliability.

CALIBRATION OF LIMIT STATES

• Only the Strength Limit State was calibratedy gbased upon structural reliability theory. Otherlimit states were calibrated to current practice

• Reliability indices of bridges designed by theStandard Specs ranged from 1.5 to 4.5

T li bili i d f l d f• Target reliability index of 3.5 was selected for

new designs.

• Design Reliability β = 3.5 ; 1 in 10,000 notionalfailure probability.

• For evaluation β =2 5 or a 1 in 100 notional• For evaluation β =2.5 or a 1 in 100 notionalfailure Probability.

LRFR GOAL : UNIFORM RELIABILITYLRFR GOAL : UNIFORM RELIABILITY

Effect of LRFD and LRFR Specspon Bridges

• More Reliable and Safer Bridges

• Increased Bridge LifeIncreased Bridge Life

• Meaningful Load Ratings!

Methodology of LRFR

i i iLimit State Equation

FACTORED LOAD EFFECT < FACTORED RESISTANCE

ηDηRηIΣγiQi < φRnηDηRηI γiQi φ n

where:

ηD=ductility factor

ηR=redundancy factor

ηI=operational importance factor

l d fγi=load factor

Qi=force effect

φ=resistance factorφ=resistance factor

Rn=nominal resistance

i i

PDWDCCRF PDWDC ±−− γγγ

LRFR Rating Equation

)1( IMLLRF

L

PDWDC

+=

γC is the structural capacity

DC

DW

is the dead-load effect of structural components and attachments

is the dead-load effect of wearing surfaces and utilities

P

LL IMis the permanent loading other than dead loads

is the live-load effect is the dynamic load allowance

DCγDWγγ

is the load factor for structural components and attachments

is the LRFD load factor for wearing surfaces and utilities

is the load factor for permanent loads other than dead loadsPγLγ

is the load factor for permanent loads other than dead loads

is the evaluation live-load factor

iCapacity, C

C = φcφsφ Rn For the STRENGTH Limit StateC φcφsφ Rn For the STRENGTH Limit State

Where,φ = Condition Factorφc= Condition Factor

φs= System Factor

φφ = Resistance Factor

C fC = fR For the SERVICE or FATIGUE Limit States

fR= Allowable stress.

i ( d )Capacity, C (Contd.)

iLRFR Rating Process

i d lLRFR Live Load LevelDesign Load:

HL-93Legal Loads:

a) Routine Commercial Traffic• Type 3 Truck• Type 3 Truck• Type 3s2 Truck• Type 3-3 Truck• Lane Load model

b) Specialized Hauling Vehiclesb) Specialized Hauling Vehicles• NRL• SU4• SU5

SU6• SU6• SU7

Permit Loads:

• Permit > 80 kipsp• Routine/ Annual Permit < 150 kips• Special Permit > 150 kips

i dLRFD Design Load HL-93

or

Fatigue Truck

AASHTO Legal LoadsS O ega oads(Routine Commercial Traffic)

l dVDOT Legal Loads

VA Single= 54 kips

VA Truck & Semi Trailer = 80 kips

20’

20k

10’ 33’

17k17k17k17k12k

i kVDOT Permit Trucks

i i ( h)LRFR Limit States (Strength)

i i ( i / i )LRFR Limit States (Service/Fatigue)

dLRFR Load Factors

d ( d )LRFR Load Factors( Contd.)

d ( d )LRFR Load Factors( Contd.)

A l i M th dAnalysis Methods:

• Approximate Method

― Lever Rule.

―Distribution Formulas.

―Special Analysis for Exterior Girder.

• Refined Method

Refined method is used if the girders spacing are out of range of applicability ofLRFD, curved girders, NSG Vehicle and to improve load ratings of low ratedbridges.

T L d Di t ib tiTransverse Load Distribution

Distribution Factor (Contd )Distribution Factor (Contd.)

* The skew correction factor shall be applied for the skewed bridges.

Di t ib ti F tDistribution Factor

Distribution Factor for Exterior Members:Distribution Factor for Exterior Members:

• Distribution Factor for Moment, gm

• Distribution Factor for Shear, gvb , gv

Distribution Factor for Interior Members:

• Distribution Factor for Moment, gm

• Distribution Factor for Shear, gv

Version for each of :

• One lane loaded, and

• Two or more lane loaded• Two or more lane loaded

Distribution Factor (Contd )Distribution Factor (Contd.)

Distribution Factor (Contd )Distribution Factor (Contd.)

Distribution Factor (Contd )Distribution Factor (Contd.)

Distribution Factor (Contd )Distribution Factor (Contd.)

Distribution Factor (Contd )Distribution Factor (Contd.)

Distribution Factor (Contd )Distribution Factor (Contd.)

Load PostingLoad Posting

Load PostingLoad Posting

Load Rating ExampleLoad Rating Example

Load Rating ExampleLoad Rating Example

Load Rating ExampleLoad Rating Example

Load Rating ExampleLoad Rating Example

Load Rating ExampleLoad Rating Example

Load Rating ExampleLoad Rating Example

Load Rating ExampleLoad Rating Example

Load Rating ExampleLoad Rating Example

Load Rating ExampleLoad Rating Example

Load Rating ExampleLoad Rating Example

Interior Girder Rating Factor Summary:

h kThank You!!!

Questions????Questions????