Probability based Load RatingDennis R. Mertz, Ph.D., P.E. Center for Innovative Bridge Engineering

University of Delaware

Fundamentals of LRFRPart 1

Introduction to Load Rating of Highway

Bridges

1-2

How Did We Get Here?What do you know

about the collapse of the U.S. 35 Silver Bridge?

What bridge safety measures were introduced because of it?

1-3

Why Do We LoadRate Bridges?

1-4

???

Purposes of Load Rating• Ensure bridge safety

• Comply with federal regulations - National Bridge Inspection Standards (NBIS)

• Rehabilitation or replacement needs

• Posting needs

• Processing of overload permits

1-5

Definition of Load Rating • Live load capacity of a bridge

– Using as-built bridge plans– Using latest field inspection (NBIS)

• Expressed as a Rating Factor (RF) or in tonnage for a particular vehicle

1-6

Rating Factor

C = Capacity (bridge member/element)DL = Dead Load effectLL = Vehicular Live Load effect

1-7

C DLRFLL

Example Rating FactorC = 4391.5 kip-ftDL = 1694.1 kip-ftLL = 2111.4 kip-ft

C = 4391.5 kip-ftDL = 1694.1 kip-ftLL = 2815.2 kip-ft

Bridge in 1944 Bridge in 2008

1-8

4391.5 1694.1?

?

RF

RF

When Should a Load Rating be Performed?

• Design stage• Initial inventory inspection• Change in the live loading• Change in the dead load on the structure• Physical change in any structural

member of the bridge• Change in load rating method1-9

2008 AASHTO Manual for Bridge Evaluation (MBE)

• New single standard for bridge evaluation

• Replaces:– 2003 AASHTO Manual for Condition

Evaluation and Load and Resistance Factor Rating of Highway Bridges

– 1994 AASHTO Manual for Condition Evaluation

1-10

Bridge Evaluation Process1. Determine type of evaluation

2. Review bridge data

3. Perform load rating

4. Report results & make recommendations

1-11

Data Requirementsfor Load Rating

• Geometric data

• Member and condition data

• Loading and traffic data

1-12

Primary Types of Loads Used in Load Ratings

• Permanent loads or dead loads (DL)– Structure self weight– Superimposed dead loads (barriers,

overlays, utilities)– Construction induced forces

• Vehicular live load (LL)

1-13

Vehicular Live Loads• Design load (national)

• Legal loads (local)

• Permit loads (local)

1-14

Load Rating Methodsin the MBE

• Allowable Stress Rating (ASR)

• Load Factor Rating (LFR)

• Load & Resistance Factor Rating (LRFR)

FHWA considers LRFR to be thepreferred load rating methodologyfor existing bridges.

1-15

Allowable Stress Rating • Loads are at a working level

• Capacity is reduced by factors of safety

• Does not address variability in DL and LL

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

1-16

Load Factor Rating• Strength-based method using factored loads

• Uncalibrated code: load factors based on engineering judgment

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

• No guidance on permit loads

1-17

Load & ResistanceFactor Rating

• Reliability-based limit states philosophy

• Use probabilistic method to derive load & resistance factors

• Uniform reliability in load ratings

• Provides guidance on adjusting live load factors using site-specific traffic data

1-18

Elements of a Bridgeto be Load Rated

• ALL primary superstructure bridge components and connections shall be load rated

• Elements not typically load rated include:________________________________________________________________________________________________________________________

1-19

Elements of a Bridgeto be Load Rated

Dead Load Considerations

Typical Stringer Bridge

Interior Stringer

Exterior Stringer

1-20

Elements of a Bridgeto be Load Rated

Truss Member

Floorbeam

Truss Connection

Steel Pier Bent

Deck Truss BridgeStringer

1-21

MBE Requirements for Quality Measures

MBE Article 1.4

To maintain the accuracy and consistency of inspections and load ratings, bridge owners should implement appropriate QC/QA measures.

1-22

Quality Control• Quality control procedures:

– Checklists ensure uniformity/completeness

– Independent reviews of computation/load rating report

1-23

Quality Assurance• Quality assurance measures:

– Overall review of the rating program

– Ascertain that the results meet or exceed the standards established by the owner

1-24

Fundamentals of LRFR

Part2

Benefits of LRFR

2-25

LRFR Philosophy• Reliability-based, limit states approach

consistent with LRFD

• Rating done at strength limit state and checked for serviceability

• More easily adopts site-specific information while maintaining uniform reliability

2-26

DefinitionsLimit State -

Condition beyond which the bridge or component no longer satisfies the design or rating provisions

Resistance -Quantifiable value beyond which the particular limit state will be exceeded

2-27

Limit States Strength Limit on:

strength and stability

Service Limit on:stress, deformations, and cracks

Fatigue Limit on:stress range

2-28

Limit States andReliability Index

Strength Limit State has been calibrated to achieve uniform safety using structural reliability methods

Reliability Index ‘’ provides a new measure of safety that is statistically based

2-29

2-30

Q

Q

Probabilistic Designand Evaluation

LOAD, Q

R,QPf

RESISTANCE, R

RESISTANCE MARGIN

LOAD MARGIN

CENTRAL SAFETY MARGIN

RRD

2-31

As-built-Q

Probabilistic Designand Evaluation (cont.)

As-built-RIncrease over time-Q

Decrease over time-R

Reliability Index, ‘’

Design Level Reliability: = 3.5 or 1 in 5,000 notional probability of exceedence

Minimum for Evaluation: = 2.5or 1 in 1,200 notional probability of exceedence

2-32

Reliability IndicesReliability Indices

0

1

2

3

4

5

Span Length

LFD LRFD

β ~ 3.5

β ~ 2.5

LRFR (OP)

Bet

a

LRFR (INV)

2-33

Minimum Reliability for LRFR = 2.5

• Comparable to average reliability inherent in load factor ratings at Operating Level

• Shown to be an acceptable minimum level of safety for bridge evaluation

Exposure period for evaluation is 2-5 years vs. 75 years for design

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Reliability Index vs. LRFR and LFR

2-35

2.5

DESIGN LOAD OPERATING RATING FACTOR

RE

LIA

BIL

ITY

IND

EX

,

1.25 1.5 1.75 2.0 2.25

3.0

2.0

1.0

0

LRFRLFR

1.00.5

0.5

3.5

2.5

1.5

4.0

4.5

0.75

Study’s Key FindingsLRFR ratings correlate well with limit state exceedence rates

LFR ratings did not correlate well

2-36

Uniform Reliability Predictors • Live load model

• Distribution factors

• Multiple presence of live loads

• Resistance formulations (LRFD)

2-37

Live Load Effect on Reliability• Uniform reliability requires uniform bias

for load effects across all span lengths

• Force effects from HS20 load model to “exclusion vehicles” does not provide a uniform bias

• New live load model needed to achieve uniform reliability

2-38

What are Exclusion Loads?• Trucks exempted from Federal

weight laws

• Comply with state vehicle weight regulations

• Allowed to operate on non-interstate highways

2-39

What makes this an “Exclusion Truck?”

2-40

Michigan “Exclusion Truck”Load: 3-S3-5

Total weight = 77 ton Total length = 72.4 ft.

2-41

LRFD Live Load (HL-93)

Design TruckPLUS

Design Lane

8 kips 32 kips 32 kips

14’ Varies

or

(14’ to 30’)

2-42

Design TandemPLUS

Design Lane

25 kips 25 kips

4’

SPAN IN FEET 2-43

MOMEN

T RA

TIO

0 20 40 60 80 100 120 140 1600.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

EXCLUSION VEHICLESAASHTO HS‐20

EXCLUSION VEHICLESLRFD Load Model

Load & ResistanceFactor Rating Process

• Can it be used for the load rating of existing bridges designed using the Standard Specifications?

• If so, what are the benefits?

• If not, why not?

2-44

Potential LRFR Benefits?• What were the benefits of using the

LRFR rating for existing older bridges in YOUR state/region?

• How were these benefits realized?

• What changes, if any, would YOU implement for the rating process?

2-45

LRFR Ratings Benefits• Uniform reliability in load ratings and load

postings

• Promotes more confidence in rating and posting values

• Provides guidance for evaluation of overloads

• Introduces state-of-the-art technologies that could benefit existing bridges

• Evaluation of serviceability or service limit states2-46

Part 3

Overview of Load Rating Equation &

Rating Process

3-47

Fundamentals of LRFR

C DLRFLL

DC DW P

LL

C DC DW PRF

LL IM

LRFR Loading Rating Equation

3-48

c s n

R

C RC f

Capacity, C

3-49

c s n

R

C R

C f

0.85c s

• For the STRENGTH Limit States

• For the SERVICE or FATIGUE Limit States

Factored Permanent Loads

3-50

DC DW PDC DW P

• LRFD Values

• LRFR modifications

• = 1.25 if field measuredDW

Factored Live Loads

3-51

LL LL IM

LRFR calibrated values for load factors

LRFR Load-Rating Process• Performed for varied purposes using

different live-load models and evaluation criteria

• Three procedures with evaluation live-load models levels

• Results serve specific uses and guide the need for further evaluations

3-52

LRFR Live-Load LevelsDesign Load Rating Design(HL-93)

Legal Load Rating Posting(AASHTO and State Legal Loads)

Permit Load Rating Permits(Overweight Trucks)

3-53

LRFR Load Rating Process

3-54

Legal

Design (HL93)

Permit

• Load Posting• Strengthening

Post or Restrict For Routine Permits

RF 1

RF < 1RF < 1

NBI reporting

RF 1 RF < 1

HL 93 Design Load Rating• Screening level for identifying vulnerable

bridges

• Inventory Level: safe for state legal loads within federal weight laws and LRFD exclusion limits. Comparable to new design

• Operating Level: safe for state legal loads within federal weight laws

3-55

Legal Load Rating• Provides single level load rating• RF ≥ 1.0 Safe for unrestricted indefinite use• RF < 1.0 Need for posting or bridge

strengthening

3-56

Permit Load Rating• Single level rating

• Permits only allowed on bridges having RF ≥ 1.0 for legal loads or HL-93

• RF ≥ 1.0 safe for permit crossing

• Permit rating based on permit type:– Routine / Annual Permits– Special / Single-Trip Permits

3-57

Thank you for your attention.

Questions or comments?