Bridge Failures, Report

8/14/2019 Bridge Failures, Report

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Bridge failures

Analysis of Takoma Bridge failure

Inaam Lababibi & Elias Jamhour1/18/2010

Project summarized report.


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Definition:

A suspension bridge does just what the name implies. The deck, or roadway, is

suspended by large cables that are secured at each end and pass over the tops of

high towers.

The basic parts of a typical suspension bridge fall into two categories,

"superstructure" and "substructure." The superstructure is composed of a deck,

towers, and the main suspension cables. The substructure is composed of the piers

(caissons, or tower foundations) in the middle of the span that support the towers,

and the anchorages (anchors) for the cables at each end of the bridge.

The deck, or girder, is where we drive or walk. It is continuous and may be a truss,

or a box girder, or a plate girder.

Large anchors, or anchorages, at both ends of the bridge act as counter weights

that hold the ends of the main cables. The anchorages are normally either a mass of

concrete or solid rock. In the anchorage, the cables splay into separate strands to

distribute the tension load evenly and safely.

The main cables stretch from one anchor over the tops of the tower and attach tothe opposite anchorage. The cables are compacted strands of parallel wires carried

back and forth across the water. At the anchorage, each cable strand wraps around

a strand shoe. Each strand shoe connects to an eye-bar. The eye-bars are firmly

cemented in the anchorage.


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At the top of the towers each cable passes over a cable saddle. At

the cable saddle the cable transfers the load from the cables to the

tower.

The main cables are attached to the deckby suspender cables.

These are sometimes also called "suspender ropes" and "hanger

cables."

In a suspension bridge, the main cables suspend the deck

(girder, roadway). Most of the bridge's weight (and any vehicles

on the bridge) is suspended from the cables. The cables are held

up only by the towers, which mean that the towers support a

tremendous weight (load).

The steel cables are both strong and flexible.This makes long

span suspension bridges susceptible to wind forces. These days,

engineers take special measures to assure stability ("aerodynamic"

stability") to minimize vibration and swaying in a suspension bridge under heavy

winds.

The 1940 Tacoma Narrows Bridge is the world's most famous example of

aerodynamic instability in a suspension bridge.

Failure mechanism of the Tacoma Narrows :

The 1940 Narrows Bridge had relatively little resistance to torsional (twisting)

forces. That was because it had such a large depth-to-width ratio, 1 to 72. The

bridge's shallow stiffening girder made the structure extremely flexible.

On the morning of November 7, 1940 shortly after 10 am, at a wind speed around

42mph, the flexible bridge deck started a ''Vortex shedding''

Illustration

of tower andcable saddle


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Vortex-Induced vibratrion :

When fixed in a fluid stream. Bluff (nonstreamlined) bodies generate detached or

separated flow over substantial parts over their surfaces: that is, the flow lines do

not follow the contours of the body, but brake away at some points. At low

Reynolds number, when the separation first occurs, the flow around the body

remains steady. At some critical Reynolds number two thin layers often termed

the free shear layersfrom the lee of the body. These unstable layers interact

nonlinearly with each other in the body wake to produce a regular periodic array of

vortices (concentrations of rotating fluid particles) termed the Strouhal vortices.

Such wakes were symmetrically investigated for circular cylinders by Benard.

These vortex arrays arrange themselves in two rows, with opposite directions of

circulation. Each vortex is located opposite the midpoint of the interval between

the two vortices in the opposite row (fig. 2). The beauty of this "vortex street"

often termed theKarman vortex street long attracted attention.

The frequency of the shedding vortices over a fixed (restrained) body is often

termed the Strouhal frequency (fs) and follows the relation:

S

U

Dfs=

U

: is the cross-flow velocity.

D

: is the frontal dimension


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S

: is the Strouhal number (nearly constant) appropriate to the body in question.

In the original Takoma Narrows bridge

;8ftD = 11.0=S Hzfs 1=

As a result:

Wind separated as it struck the side of the bridge's deck, the 8-foot solid plate

girder. A small amount twisting occurred in the bridge deck;the twisting bridge

deck caused the wind flow separation to increase. This formed a vortex, or swirling

wind force, which further lifted and twisted the deck. The deck structure resistedthis lifting and twisting.

But, the external force of the wind alone was not sufficient to cause the severe

twisting that led the Narrows Bridge to fail.

Now the deck movement went into "torsional flutter."

"Torsional flutter" is a complex mechanism. "Flutter" is a self-induced harmonic

vibration pattern. This instability can grow to very large vibrations.

So, the flutter motion is an oscillating motion in which 2 or more modes of

oscillation usually bending and torsion are combined. As wind velocity increases, a

critical value is reached, which triggers the flutter motion. it is characterized by a

rapid buildup of amplitude with little or no flutter wind speed augmentation

Note: the flutter speed will be reduced if the wind velocity vector is inclined to the

plane or the bridge deck, which may occur as a result of turbulence and gustiness

of the wind.

5o change in the vertical wind angle reduction of critical speed from 100mph to50mph.


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A research by Scanlan and Tomko demonstrated that the catastrophic mode was a

single degree of freedom torsional flutter due to complex separated flow.

( )

,.22

FI =++

The excitation force was characterized as an aerodynamic self excitation effect that

caused a negative damping of the system.

I

: Moment of inertia

: damping ratio

: Angle of twist

: Natural frequency

( ) 32, AAF += (Linearly self excited form)


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Experiments:

( )

+=

*

3

2*

2

22

.)(2, AKUBkABUF

U: wind velocity

B: deck width

w: circular frequency of oscillation; (

U

BK

.=

)

*

2A

,*

3A

are aerodynamic (flutter) coefficients.


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The destructive oscillation of the Takoma bridge produced a flutter wake (not a

Karman vortex street).That action finally brought the bridge down, occurred in a

fundamental antisymetric torsion mode.

Design lessons from Takoma bridge failure:

Many lessons was taken from this particular bridge failure, and used in the design

of the new Takoma narrows bridge:

The wind effect more carefully studied, and models should be studied in

wind tunnels to assure aerodynamic stability.


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The deck system's prominent 33-foot deep steel Warren stiffening trusses:

These gave the bridge a depth-to-center span ratio of 1 to 85.

Double (top and bottom) lateral bracing of the stiffening trusses:This feature, combined with the 33-foot deep stiffening truss, gave the

bridge exceptional torsional rigidity.

Wind grates:

Three slots of open steel grating 33 inches wide separating all four traffic

lanes, and a strip 19 inches wide along each curb.

Hydraulic shock absorbers at three strategic points in the structure:

(1) at mid-span, at the main cable center tie, between the main suspension

cables and the top of the stiffening truss; 6 devices per cable (a "first" for along suspension bridge);

(2)between the top chords of the main span and side span stiffening trusses;and

(3) at each tower, where it joins the bottom of the deck truss.

In conclusion, the wind effect is a determinant factor for the long suspended

bridges, and should be studied with models in wind tunnels.

Documents

Bridge Failures, Report