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

Engineering Around Ignorance

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

How Design Codes Began

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.

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

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

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

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.

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.

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.

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.

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

Determinate Structures

• Forces distributed according to Newton’s laws of force and moment equilibrium.

• Fx = Fy = Fz = 0

• Mx = My = Mz = 0

Simple-Span Beams

Adding Hinges to Beams

Pont-Alexandre III, Paris 1890

End Hinge

Center Hinge

Determinacy vs. Redundancy

Déjà Vu

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.

2D Framed Element Analysis

• Each frame line is assumed to be an independent element.

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.

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.

Importance

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

Importance (cont.)

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.

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.

Capacity Load Live

LoadLiveApplied

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.

Calculating New Rating Factors

• Using a 3D computer model.

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.

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.

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Michael O’Rourke

– Of Rensselaer Polytechnical Institute

• “Nobody believes an analytical result except the analyst, and everybody believes an experimental result, except the experimenter...”

In Summary…