# Introduction

In this project you will study models of the failure of the Tacoma Narrows Bridge, the first suspension bridge across the Narrows of Puget Sound in Washington State. It connected the Olympic Peninsula with the mainland of Washington. The bridge's main span was 853 meters.

These are uninteresting facts unless you know the fate of the Tacoma Narrows Bridge. The bridge is famous because on Nov. 7, 1940, four months after it opened, it collapsed in a 68 km per hour wind. Pictures of the bridges final moments have been shown many times, including on a recent television commercial for cassette tapes. Click here to see a
10-second video clip of the bridge collapse.

Immediately prior to the bridges failure, it was undergoing large twisting or torsional oscillations. This is shown in left-most figure below. When the twisting motion was at the maximum, shown in the middle figure, one side of the span was 8.5 meters higher than the other side. Shortly before 11 o'clock in the morning, a large piece of concrete dropped out of the roadway, and a few minutes later a 180 meter section of the bridge collapsed, shown in the right-most figure below.

Until the collapse of the Tacoma Narrows Bridge, suspension bridges were built with little theoretical understanding of their dynamics. These bridges exhibited interesting behavior:

• They were prone to large scale oscillations, both vertically and torsionally.
• Vertical oscillations were initiated and sustained by gusting winds.
• Large vertical oscillations could spawn large torsional oscillations.
The Golden Gate Bridge in San Francisco also exhibited these large oscillations, but the Brooklyn Bridge did not. The engineer of that bridge designed the truss stiffnesses six times larger than the normal standards of his day called for because he was aware of the oscillation problems of the bridges of his day, and didn't know how to estimate the stiffness that was required to keep the bridge from collapsing.

Your project is to study a sequence of models that incorporate more and more engineering analysis into this problem. We will see models that dissipate small oscillations, models that allow large oscillations and finally models that transform vertical oscillations into torsional oscillations.