How Much Do I Need to Know to Design a Bridge?

1. How Much Do I Need to Know to Design a Bridge? Engineering Around Ignorance

2. Engineering • “Engineering is the art of molding materials we do not fully understand, into shapes we cannot fully analyze, while preventing the public from realizing the full extent of our ignorance.” • anonymous

3. How Design Codes Began

5. Design Codes • How we prevent the public from, “realizing the full extent of our ignorance.” • Factor of Safety or Factor of Ignorance? • However, as knowledge increases, the complexity of the codes increases.

6. Evolving Snow Loads • Pre-1975: uniform snow load specified by county building official • E.g. 45 pounds per square foot (psf). • Circa 1980: • Drift load calculations

7. Evolving Snow Loads (cont.) • Mid 1980’s: • Local terrain and exposure • Open expanse of water vs. hilly terrain • Alone on a hill vs. sheltered by trees. • Flat vs. sloped roof • Slope of roof • Temperature and insulation below roof • Slippery vs. rough roof surface • Roof obstructions

8. Evolving Snow Loads (concl.) • Mid 1980’s (cont.) • Partial loads • Drift loads • Windward vs. leeward drifts • Roof projections vs. adjacent structures • Snow sliding from adjacent roof. • Icicles and ice dams

9. The Increased Complexity is Due to • A better understanding of physical processes behind the loads. • Greater computational power available for modeling these physical processes. • Incorporation of probabilistic concepts. • We can’t eliminate the unknowns, but we can quantify their likelihood and provide a consistent level of risk for the various hazards.

10. But Are Structures Any Safer? • Probably not: • The older codes were reasonably successful. • The newer codes were typically calibrated to provide the same level of safety as the older codes.

11. However… • The level of safety should be more consistent, and • The code can provide the same level of safety for new materials and construction techniques that don’t have decades of experience behind them.

12. Evolution of Analysis • Proportions – as much art as science: • Height-to-thickness ratios for masonry walls. • Span-to-rise ratios for arches. • Span-to-depth ratios for beams.

13. Quantitative Methods • Cantilever beam • Galileo, 1638: Entire beam in tension. • Edme Mariotte, ca. 1688: Tension and compression • Jacob Bernoulli, ca 1700: Beam deflections • Leonard Euler, 1750: Large deflections

14. Determinate Structures • Forces distributed according to Newton’s laws of force and moment equilibrium. • SFx = SFy = SFz = 0 • SMx = SMy = SMz = 0

15. Simple-Span Beams

16. Adding Hinges to Beams

17. Pont-Alexandre III, Paris 1890

18. End Hinge

19. Center Hinge

22. Determinacy vs. Redundancy

23. Déjà Vu

24. Indeterminate Structures • Forces and displacements interact. • This interaction can be described as by a system of linear equations. • If we’re willing to make a few assumptions… • And computers are extremely efficient at analyzing systems of linear equations.

25. 2D Framed Element Analysis • Each frame line is assumed to be an independent element.

27. 2D vs 3D • 2D involves several assumptions or approximations. • Out-of-plane force distribution: • Tributary area or • (Semi-)Empirical distribution factors. • Ignoring torsion due to unbalanced loads.

29. Perrine Bridge • Location: US 93 north of Twin Falls • Span: 1485 ft: • Steel truss arch: 1000 ft • Steel plate girder approach spans on north and south. • Height: 486 ft.

31. Importance • The connection between US 93 from Nevada to the I-84 corridor.

33. Importance (cont.)

34. Permits • Most trucks are permitted under standard regulations for size, weight, number of axles, etc. • Over-weight or over-size trucks must apply to the Idaho Transportation Bridge Section for a special permit before crossing the bridge.

35. Rating Factors • Rating factors are a ratio: • A permit is denied if the rating factor > 1. • The Idaho Transportation Department has asked UI Civil Engineers to update their bridge rating factors.

36. Why a new rating? • The distribution factors used to calculate the rating factors are approximate and have some conservatism “built-in.” • A 3D model should appropriately distribute the transverse load without added conservatism. • We might be able to move larger loads across the bridge without compromising the safety of the bridge.

37. Calculating New Rating Factors • Using a 3D computer model.

40. Advantages of a 3D Computer Model • It eliminates the need for distribution factors. • It includes the effects of the concrete deck in the deformations of the longitudinal girders.

42. Shortcomings of the 3D Model • Connection behavior is greatly simplified. • Perfectly free to rotate with no friction , or • Completely fixed against rotation with no slip. • The effects of secondary items will still be simplified or ignored. • The transverse distribution will be tied to beams and girders instead of plates. • Sidewalks, barriers, etc. are ignored.

46. Michael O’Rourke • Of Rensselaer Polytechnical Institute • “Nobody believes an analytical result except the analyst, and everybody believes an experimental result, except the experimenter...”

47. In Summary…