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Risk Mitigation for Highway and Railway Bridges


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Bridges are vulnerable to extreme events such as natural disasters in addition to hazards stemming from negligence and improper maintenance, overloading, collisions, intentional acts of vandalism, and terrorist attacks. These structures must be protected but the current approach to risk is not always rational. Sensitivity analysis will be performed to relate the reliability of bridges and reliability of the transportation network.

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Risk Mitigation for Highway and Railway Bridges

  1. 1. Risk Analysis and Target Reliability for Bridges Andrzej S. Nowak, Ph.D. University of Nebraska-Lincoln
  2. 2. DisclaimerThe contents of this report reflect the views of theauthors, who are responsible for the facts and theaccuracy of the information presented herein. Thisdocument is disseminated under the sponsorship of theU.S. Department of Transportation’s UniversityTransportation Centers Program, in the interest ofinformation exchange. The U.S. Government assumes noliability for the contents or use thereof.
  3. 3. Outline Problem Statement Load and Resistance Models Reliability Analysis Procedure Selection of the Target Reliability Load and Resistance Factors
  4. 4. Problem Statement 585,000 highway bridges in USA 30-35% are inadequate 10-15% are structurally deficient How to use the available limited resources?
  5. 5. Needs New design – how to design with optimum life cycle costs? Existing structures – how to assess the actual loads and capacity? How to predict the remaining life? Select a rational safety margin
  6. 6. Uncertainties Loads (natural and created) Material properties Load carrying capacity (resistance) Basic requirement: Load effect (Q) < Resistance (R) Safety margin R–Q>0
  7. 7. Reliability Index, β
  8. 8. Basic Questions:• How can we measure safety of a structure?• How safe is safe enough? What is the target reliability?• How can we implement the optimum safety level?
  9. 9. Safety Factors• Allowable stress• Load factors• Load combination factors• Resistance factors
  10. 10. Load Factor
  11. 11. Resistance Factor
  12. 12. Code Calibration Procedure• Select representative structures• Develop statistical models for loads• Develop statistical models for resistance• Develop/select reliability analysis procedure• Determine the target reliability index• Determine load and resistance factors
  13. 13. Bridge Loads• Dead load• Live load (static and dynamic)• Environmental loads (wind, snow, earthquake, temperature, ice)• Special loads (vehicle and vessel collision, fire, explosion)
  14. 14. Two Trucks Side by Side
  15. 15. Video Recordings of Traffic Jam Situations FHWA Data • Multiple-presence of trucks occupying three lanes • One lane is almost exclusively occupied by trucks Video 1, time: 00:18:36
  16. 16. Resistance (Load Carrying Capacity)• Material tests• Component tests• Diagnostic tests• Analytical simulations• Proof load tests
  17. 17. Reliability Index, βFor a linear limit state function, g = R – Q = 0, and R and Q both being normal random variables β= (µ R − µQ ) σ +σ 2 R 2 Q µR = mean resistance µQ = mean load σR = standard deviation of resistance σQ = standard deviation of load
  18. 18. Reliability Index and Probability of Failure PF β 10-1 1.28 10-2 2.33 10-3 3.09 10-4 3.71 10-5 4.26 10-6 4.75 10-7 5.19 10-8 5.62 10-9 5.99
  19. 19. Reliability Analysis Procedures• Closed-form equations – accurate results only for special cases• First Order Reliability Methods (FORM), reliability index is calculated by iterations• Second Order Reliability Methods (SORM), and other advanced procedures• Monte Carlo method - values of random variables are simulated (generated by computer), accuracy depends on the number of computer simulations
  20. 20. What is Optimum Reliability?• If reliability index is too small – there are problems, even structural failures• If reliability index is too large – the structures are too expensive
  21. 21. Selection Criteria for the Target Reliability • Consequences of failure • Economic analysis • Past practice • Human perception • Social/political decisions
  22. 22. Target Reliability Index – Major Considerations • Primary and secondary components • Multiple and single load paths (redundancy) • Element and system reliability • New design and existing structure • Ductile and brittle materials and components • Important, historical and ordinary structures
  23. 23. Types of Components• Primary component – its failure causes failure of other components (or total collapse)• Secondary component – its failure does not affect performance of other components
  24. 24. Examples of the Target Reliability Indices for Bridge ComponentsPrimary component (multiple load path) βT = 3.5Primary component (single load path) βT = 5.0Secondary component βT = 2.0
  25. 25. β T for Strength vs. Service Limit States• Consequences of exceeding the limit state are different• For decompression, βT = 1• For deflection, βT = 0• For fatigue, βT = 1-2
  26. 26. System vs. Component• Structures are systems made of components• Failure of a component may not mean failure of the system• Ductile and brittle components• Correlation between components
  27. 27. Structural Systems• Series systems – weakest link systems, to be avoided• Parallel systems – components share the load, preferred systems• Avoid brittle materials and elements, use ductile materials and elements
  28. 28. The weakest linkdetermines the strength
  29. 29. 37
  30. 30. 38
  31. 31. Parallel system
  32. 32. Golden Gate Bridge, San Franciscobuilt in 1933-1935, span of 1280 m
  33. 33. Examples of the Target Reliability Indices for Bridges - MaterialsFor steel, reinforced concrete, prestressedconcrete girders, βT = 3.5For sawn wood bridge components, βT = 2.0For girder bridge as a system (all materials), βT = 5.5-6.5
  34. 34. Operational Importance• Regional and national economy• Emergency situations (floods, earthquakes, fires, hurricanes)
  35. 35. Historical Value• Historical structures can have a special value for the society• Preservation of the general features
  36. 36. New Design vs. Existing Structure• For a new design, reliability can be increased with little extra cost• For an existing structure, any strengthening can be prohibitively expensive• Current practice accepts lower reliability levels for existing structures
  37. 37. Reliability of Connections• For a bolted connection, the reliability can be increased with negligible extra cost (extra bolts)• For a steel component, the increase of reliability is much more costly (heavier section)• Target reliability index for bolts is βT = 5-6, while for beams, βT = 3-4
  38. 38. How can we implement the target reliability?• Design and evaluation of existing bridges – by load and resistance factors, safety margins in the design, fool-proof design• Construction – quality control of materials and work skill, fool-proof construction• Proper use and operation, maintenance, preventive repairs
  39. 39. Recommended β T TIME PRIMARY COMPONENTS SECONDARYPERIOD COMPONENTS Single Path Multiple Path5 years 3.50 3.00 2.2510 years 3.75 3.25 2.5050 years 4.00 3.50 2.75
  40. 40. Conclusions• Target reliability index varies depending on consequences of failure, costs, and other considerations• For new design, bT can be significantly higher than for evaluation of existing structures• For historical structures, in addition, bT depends on social and political considerations
  41. 41. CREDITS Thank You!Slide design © 2009, Mid-America Transportation Center. All rights reserved.
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