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Load Models for Bridges: Statistical Analysis & Design Optimization

Understand dead, live, & extreme loads; explore bias factors, load distributions, & dynamic loads in bridge design. Learn load combinations using Turkstra's Rule. Examples & analyses included.

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Load Models for Bridges: Statistical Analysis & Design Optimization

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  1. Load Models for Bridges Andrzej S. Nowak University of Michigan Ann Arbor, Michigan Outline • Dead load • Live load • Extreme load events • Load combinations

  2. Load Models For each load component: • Bias factor, l = mean/nominal • Coefficient of variation, V = s/mean • Cumulative distribution function (CDF) • Time variation: return period, duration

  3. Statistical Data Base • Load surveys (e.g. weigh-in-motion truck measurement) • Load distribution (load effect per component) • Simulations (e.g. Monte Carlo) • Finite element analysis • Boundary conditions (field tests)

  4. Examples of Load Parameters • Dead load for bridges l = 1.03-1.05 V = 0.08-0.10 • Live load parameters for bridges (AASHTO LRFD Code) l = 1.25-1.35 V = 0.12

  5. No. 4 Stanley Road over I-75in Flint (S11-25032)

  6. Examples of Bias Factors Two bridge design codes are considered: • AASHTO Standard Specifications (1996) • AASHTO LRFD Code (1998) For the first one, denoted by HS20, bias factor is non-uniform, so design load in LRFD Code was changed, and the result is much better.

  7. Two trucks side-by-side

  8. Bias Factor for Load Effect • Bias factors shown previously were for lane load (bridge live load) • For components (bridge girders), bias factor can be very different

  9. Girder Distribution Factors • What is the percentage of lane load per girder? • Is the actual distribution the same as specified by the design code? • What are the maximum strains? • What is the load distribution factor for one lane traffic and for two lanes

  10. Code-Specified GDF -AASHTO Standard (1996) Steel and prestressed concrete girders One lane of traffic Two lanes of traffic S = girder spacing (m)

  11. Code-specified GDF -AASHTO LRFD (1998) One lane Two lanes

  12. Dynamic Load • Roughness of the road surface (pavement) • Bridge as a dynamic system (natural frequency of vibration) • Dynamic parameters of the vehicle (suspension system, shock absorbers)

  13. Dynamic Load Factor (DLF) • Static strain or deflection (at crawling speed) • Maximum strain or deflection (normal speed) • Dynamic strain or deflection = maximum - static • DLF = dynamic / static

  14. Code Specified Dynamic Load Factor • AASHTO Standard (1996) • AASHTO LRFD (1998) • 0.33 of truck effect, no dynamic load for the uniform loading

  15. Load Combinations • Load combination factors can be determined by considering the reduced probability for a simultaneous occurrence of time-varying load components • So called Turkstra’s rule can be applied

  16. Turkstra’s Rule • Consider a combination of uncorrelated, time-varying load components Q = A + B + C • For each load component consider two values: maximum and average. Then, Qmax = maximum of the following: (Amax + Bave + Cave) (Aave + Bmax + Cave) (Aave + Bave + Cmax)

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