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&ridge Failures &ridge FailuresdisastersisastersAnalysis of TAKOMA NAROWS bridge

failure.

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Objectives:Types of bridge failure.Suspension bridges (description).

TAKOMA NAROWS bridge failure.Solutions.

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Suspension bridges

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Used For Long Spans!Suspension bridges are amazing, wonderful structures. They appear almost fragile, viewed from a distance.Yet, they are very strong and nowadays are the world's longest bridge type.

Typical Lengths for spans of this type range from: 2,000 to 7,000 ft

Akashi Kaikyo 12,828'

Golden Gate 8,981'

Tacoma Narrows 5,979'

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They All Move!

Because they are relatively light and flexible, suspension bridges are all susceptible towind. They vibrate and move, both vertically (up and down) and laterally (sideways).The challenge for the bridge engineer is to keep this motion within safe limits.

The most vulnerable part of a suspension bridge is the suspended roadway, or deck.Do you have gephyrophobia?

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TAKOMA NARROWS

BridgeThe Damage.

Why Did Galloping Gertie Collapse???

Design Lessons of gerties failure.

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The DamageMain cables: During the collapse, the main suspension cables were thrown violentlyside to side, twisted, and tossed 100 feet into the air.

They slipped from their positions in the cable saddles atop each tower.And, they fell hard on the approach spans.

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The Damage

Suspender Cables: The violent collapse broke many suspender cables. Some were lost, some severely

damaged, and some undamaged. Their only value now was as scrap metal.

Deck-Floor System:

due to torsion and bending stresses, the floor system had sections that were bentand overstressed

and was destroyed.

View from below the deck atbuckled steel beams WSDOT

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The DamageSide Spans: The loss of the center section, followed by the dropping of the side spans, caused

substantial damage

Piers: The collapse of the center span caused partial sheering of rivets that attached the

towers to the tops of the piers.

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Why???How could the most "modern" suspension bridge,with the most advanced design, suffercatastrophic failure in a relatively light wind?

What was the weakness design points?

What was the failure mechanism?

Questions that need answers

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Why???Vortex induced vibration: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 notfollow the contours of the body, but brake away at some points. At some critical

Reynolds number two thin layers often termed the free shear layersfrom the lee ofthe body interact nonlinearly with each other in the body wake to produce a regularperiodic array ofvortices (concentrations of rotating fluid particles) termed theStrouhal vortices.

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Why???The frequency of the shedding vortices over a fixed (restrained) body is often termed the Strouhalfrequency (fs) and follows the relation:

SU

Dfs=

U: - .is the cross flow velocity

D:is the frontal dimension

S : ( )is the Strouhal number nearly constant appropriate to the body in.q u e stio n

In th e o rig in a l Ta ko m a N a rro w s b rid g e ftD 8=

11.0=S

Hzfs 1=

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Why???The destructive mechanism at the Tacoma Narrows:

The frequency observed for the final destructive oscillation is f=0.2Hz, the wind speed atthat time was 42mph.

sffit can be concluded that the "vortex shedding" was not thecause of collapse.

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Why???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=++

I

: Moment of inertia

: Damping ratio

: Natural frequency

: Angle of twist

The excitation force was characterized as an aerodynamic self excitation effect that caused anegative damping of the system.

( ) = ,F 32 AA + (linearly self excited form)

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Why???

+=

*

3

2*

2

22 .)(2),( AKU

BkABUF

The excitation force is written in this form:

U:wind velocityB :Deck width

:circular frequency of oscillation ).(U

BK

=

*

3

*

2 ,AA are aerodynamic (flutter) coefficient.

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Why???flutter motion:

it's an oscillating motion in which 2 or more modes of oscillation usually bending andtorsion are combined. As wind velocity increases, a critical value is reached, which triggersthe 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 thewind velocity vector is inclined to the planeor the bridge deck, which may occur as aresult of turbulence and gustiness of thewind.

5o change in the vertical wind angle reduction of critical speed from 100mph to 50mph.

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Why???

The destructive oscillation of the takoma bridge produced a flutter wake (not aKarman vortex street).That action finally brought the bridge down, occurred in afundamental antisymetric torsion mode.