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

shrubflattenUrban and Civil

Nov 25, 2013 (3 years and 8 months ago)

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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.



S
F
x

=
S
F
y

=
S
F
z

= 0



S
M
x

=
S
M
y

=
S
M
z

= 0



Simple
-
Span Beams

Adding Hinges to Beams

Pont
-
Alexandre III, Paris 1890


End Hinge

Center Hinge



Determinacy vs. Redundancy


D
éjà 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
Load
Live
Applied
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.





-10
0
10
20
30
40
0
50
100
150
200
250
300
350
400
Distance from North Approach Abutment (ft)
Column C
'
o Axial Force (kip) (+ comp./ -
tens.)
finite element
model
field test
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…