probability based load rating -...
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Probability based Load RatingDennis R. Mertz, Ph.D., P.E. Center for Innovative Bridge Engineering
University of Delaware
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?
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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
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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
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Rating Factor
C = Capacity (bridge member/element)DL = Dead Load effectLL = Vehicular Live Load effect
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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
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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
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Bridge Evaluation Process1. Determine type of evaluation
2. Review bridge data
3. Perform load rating
4. Report results & make recommendations
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Data Requirementsfor Load Rating
• Geometric data
• Member and condition data
• Loading and traffic data
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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)
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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.
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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
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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
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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
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Elements of a Bridgeto be Load Rated
• ALL primary superstructure bridge components and connections shall be load rated
• Elements not typically load rated include:________________________________________________________________________________________________________________________
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Elements of a Bridgeto be Load Rated
Dead Load Considerations
Typical Stringer Bridge
Interior Stringer
Exterior Stringer
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Elements of a Bridgeto be Load Rated
Truss Member
Floorbeam
Truss Connection
Steel Pier Bent
Deck Truss BridgeStringer
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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.
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Quality Control• Quality control procedures:
– Checklists ensure uniformity/completeness
– Independent reviews of computation/load rating report
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Quality Assurance• Quality assurance measures:
– Overall review of the rating program
– Ascertain that the results meet or exceed the standards established by the owner
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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
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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
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Limit States Strength Limit on:
strength and stability
Service Limit on:stress, deformations, and cracks
Fatigue Limit on:stress range
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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
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Q
Q
Probabilistic Designand Evaluation
LOAD, Q
R,QPf
RESISTANCE, R
RESISTANCE MARGIN
LOAD MARGIN
CENTRAL SAFETY MARGIN
RRD
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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
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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)
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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
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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
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Uniform Reliability Predictors • Live load model
• Distribution factors
• Multiple presence of live loads
• Resistance formulations (LRFD)
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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
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What are Exclusion Loads?• Trucks exempted from Federal
weight laws
• Comply with state vehicle weight regulations
• Allowed to operate on non-interstate highways
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LRFD Live Load (HL-93)
Design TruckPLUS
Design Lane
8 kips 32 kips 32 kips
14’ Varies
or
(14’ to 30’)
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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
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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?
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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?
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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
Capacity, C
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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
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DC DW PDC DW P
• LRFD Values
• LRFR modifications
• = 1.25 if field measuredDW
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
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LRFR Live-Load LevelsDesign Load Rating Design(HL-93)
Legal Load Rating Posting(AASHTO and State Legal Loads)
Permit Load Rating Permits(Overweight Trucks)
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LRFR Load Rating Process
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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
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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
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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
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