Probability based Load Rating

Transcription

1 Probability based Load Rating Dennis R. Mertz, Ph.D., P.E. Center for Innovative Bridge Engineering University of Delaware

2 Fundamentals of LRFR Part 1 Introduction to Load Rating of Highway Bridges 1-2

3 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

4 Why Do We Load??? Rate Bridges? 1-4

5 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

6 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

7 Rating Factor RF C LL DL C = Capacity (bridge member/element) DL = Dead Load effect LL = Vehicular Live Load effect 1-7

8 Example Rating Factor Bridge in 1944 Bridge in 2008 C = kip-ft C = kip-ft DL = kip-ft LL = kip-ft DL = kip-ft LL = kip-ft RF ? RF? 1-8

9 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 1-9 Change in load rating method

10 2008 AASHTO Manual for Bridge Evaluation (MBE) New single standard for bridge evaluation Replaces: AASHTO Manual for Condition Evaluation and Load and Resistance Factor Rating of Highway Bridges 1994 AASHTO Manual for Condition Evaluation

11 Bridge Evaluation Process 1. Determine type of evaluation 2. Review bridge data 3. Perform load rating 4. Report results & make recommendations 1-11

12 Data Requirements for Load Rating Geometric data Member and condition data Loading and traffic data 1-12

13 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

14 Vehicular Live Loads Design load (national) Legal loads (local) Permit loads (local) 1-14

15 Load Rating Methods in the MBE Allowable Stress Rating (ASR) Load Factor Rating (LFR) Load & Resistance Factor Rating (LRFR) FHWA considers LRFR to be the preferred load rating methodology for existing bridges. 1-15

16 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

17 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

18 Load & Resistance Factor 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

19 1-19 Elements of a Bridge to be Load Rated ALL primary superstructure bridge components and connections shall be load rated Elements not typically load rated include:

20 Elements of a Bridge to be Load Rated Typical Stringer Bridge Interior Stringer Dead Load Considerations Exterior Stringer 1-20

21 Elements of a Bridge to be Load Rated Deck Truss Bridge Stringer Floorbeam Truss Member Truss Connection Steel Pier Bent 1-21

22 MBE Requirements for Quality Measures MBE Article To maintain the accuracy and consistency of inspections and load ratings, bridge owners should implement appropriate QC/QA measures.

23 Quality Control Quality control procedures: Checklists ensure uniformity/completeness Independent reviews of computation/load rating report 1-23

24 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

25 Fundamentals of LRFR Part2 Benefits of LRFR 2-25

26 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

27 Definitions Limit 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

28 Limit States Strength Limit on: strength and stability Service Limit on: stress, deformations, and cracks Fatigue Limit on: stress range 2-28

29 Limit States and Reliability 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

30 Probabilistic Design and Evaluation CENTRAL SAFETY MARGIN Q R D R LOAD MARGIN RESISTANCE MARGIN LOAD, Q Q RESISTANCE, R P f R,Q 2-30

31 Probabilistic Design and Evaluation (cont.) As-built-Q Increase over time-q As-built-R Decrease over time-r 2-31

32 Reliability Index, Design Level Reliability: = 3.5 or 1 in 5,000 notional probability of exceedence Minimum for Evaluation: = 2.5 or 1 in 1,200 notional probability of exceedence 2-32

33 5 4 β ~ β ~ Beta Reliability Indices Reliability Indices LFD LRFD LRFR (INV) LRFR (OP) 0 Span Length 2-33

34 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 2-34

35 RELIABILITY INDEX, Reliability Index vs. LRFR and LFR LFR LRFR DESIGN LOAD OPERATING RATING FACTOR 2-35

36 Study s Key Findings LRFR ratings correlate well with limit state exceedence rates LFR ratings did not correlate well 2-36

37 Uniform Reliability Predictors Live load model Distribution factors Multiple presence of live loads Resistance formulations (LRFD) 2-37

38 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

39 What are Exclusion Loads? Trucks exempted from Federal weight laws Comply with state vehicle weight regulations Allowed to operate on noninterstate highways 2-39

40 What makes this an Exclusion Truck? 2-40

41 Michigan Exclusion Truck Load: 3-S3-5 Total weight = 77 ton Total length = 72.4 ft. 2-41

42 LRFD Live Load (HL-93) 8 kips 32 kips 32 kips 14 Varies 25 kips 25 kips 4 (14 to 30 ) Design Truck PLUS Design Lane or Design Tandem PLUS Design Lane 2-42

43 MOMENT RATIO EXCLUSION VEHICLES AASHTO HS 20 EXCLUSION VEHICLES LRFD Load Model SPAN IN FEET 2-43

44 Load & Resistance Factor 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

45 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

46 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 states 2-46

47 Fundamentals of LRFR Part 3 Overview of Load Rating Equation & Rating Process 3-47

48 LRFR Loading Rating Equation RF C LL DL RF C C DC DW P DC DW P R c s n LL IM LL 3-48 C f R

49 Capacity, C C R c s n For the STRENGTH Limit States C f R For the SERVICE or FATIGUE Limit States 0.85 c s 3-49

50 Factored Permanent Loads DC DW P DC DW P LRFD Values LRFR modifications DW = 1.25 if field measured 3-50

51 Factored Live Loads LL IM LL LRFR calibrated values for load factors 3-51

52 LRFR Load-Rating Process Performed for varied purposes using different live-load models and evaluation criteria Three procedures with evaluation liveload models levels Results serve specific uses and guide the need for further evaluations 3-52

53 LRFR Live-Load Levels Design Load Rating (HL-93) Design Legal Load Rating (AASHTO and State Legal Loads) Posting 3-53 Permit Load Rating (Overweight Trucks) Permits

54 LRFR Load Rating Process RF 1 Design (HL93) NBI reporting RF < 1 Legal RF 1 Permit RF < 1 RF < 1 Load Posting Strengthening Post or Restrict For Routine Permits 3-54

55 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

56 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

57 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

58 Thank you for your attention. Questions or comments?