Tacoma Narrows Bridge
The Tacoma Narrows Bridge was a mile-long suspension bridge (the third largest in the world when it was built) across the Tacoma Narrows of Puget Sound near Tacoma, Washington in the United States. Its spectacular self-destruction is often used an object lesson in the dangers of resonance effects in engineering. However, the term resonance usually implies forced resonance, while the vibrations in the bridge were self-induced.The bridge itself was solidly built, with girders of carbon steel anchored in huge blocks of concrete. However, shortly after its construction in July 1940 (opened to traffic on July 1), it was discovered that winds through the Tacoma Narrows caused vortex shedding on the bridge, which then induced resonance in the bridge, causing it to sway and buckle dangerously in windy conditions. This resonance was longitudinal, meaning the bridge buckled along its length. Drivers would see cars approaching from the other direction disappear into valleys which were dynamically appearing and disappearing. From this behavior the bridge gained the nickname, "Galloping Gertie."
However, the failure of the bridge was in a torsional rather than longitudinal mode. In fact, it was the second torsional mode, in which the centre of the bridge remained motionless and the two halves of the bridge twisted in opposite directions. This vibration was due to aeroelastic flutter. Flutter occurs when a torsional disturbance in the structure increases the angle of attack of the bridge (that is, the angle between the wind and the bridge). The structure responds by twisting further. Eventually, the angle of attack increases to the point of stall, and the bridge begins to twist in the opposite direction. In the case of the Tacoma Narrows bridge, this mode was negatively damped, meaning it increased in amplitude with each cycle. Eventually, the amplitude of the motion increased beyond the tolerance of the structure and the structure failed.
It is important to note that there was no periodic disturbance to cause this disaster. The wind was steady at 42 mph. The frequency of the destructive mode, 0.2 Hz, was neither a natural mode of the isolated structure nor the frequency of blunt-body vortex shedding of the bridge at that wind speed. The event can only be understood while considering the coupled structural and aerodynamic system.
The collapse occurred on November 7, 1940. From the account of a driver stranded on the bridge during this event:
- "Just as I drove past the towers, the bridge began to sway violently from side to side. Before I realized it, the tilt became so violent that I lost control of the car... I jammed on the brakes and got out, only to be thrown onto my face against the curb... Around me I could hear concrete cracking... The car itself began to slide from side to side of the roadway.
- "On hands and knees most of the time, I crawled 500 yards or more to the towers... My breath was coming in gasps; my knees were raw and bleeding, my hands bruised and swollen from gripping the concrete curb... Toward the last, I risked rising to my feet and running a few yards at a time... Safely back at the toll plaza, I saw the bridge in its final collapse and saw my car plunge into the Narrows."
The bridge has since been redesigned and rebuilt with stiffening struts and openings in the roadway to let wind through.
