Narrows bridge was not felled by resonance.
This has been a common misstatement, even in engineering text books, as to the reason the bridge failed.
According to the Washington State DOT, it was caused by aerodynamics:
(1) The principal cause of the 1940 Narrows Bridge's failure was its "excessive flexibility;"
(2) the solid plate girder and deck acted like an aerofoil, creating "drag" and "lift;"
(3) aerodynamic forces were little understood, and engineers needed to test suspension bridge designs using models in a wind tunnel.
The primary explanation of Galloping Gertie's failure is described as "torsional flutter." It will help to break this complicated series of events into several stages.
Here is a summary of the key points in the explanation.
1. In general, 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. Gertie's long, narrow, and shallow stiffening girder made the structure extremely flexible.
2. On the morning of November 7, 1940 shortly after 10 a.m., a critical event occurred. The cable band at mid-span on the north cable slipped. This allowed the cable to separate into two unequal segments. That contributed to the change from vertical (up-and-down) to torsional (twisting) movement of the bridge deck.
3. Also contributing to the torsional motion of the bridge deck was "vortex shedding." In brief, vortex shedding occurred in the Narrows Bridge as follows:
(1) Wind separated as it struck the side of Galloping Gertie's deck, the 8-foot solid plate girder. A small amount twisting occurred in the bridge deck, because even steel is elastic and changes form under high stress.
(2) 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.
(3) The deck structure resisted this lifting and twisting. It had a natural tendency to return to its previous position. As it returned, its speed and direction matched the lifting force. In other words, it moved " in phase" with the vortex. Then, the wind reinforced that motion. This produced a "lock-on" event.
4. But, the external force of the wind alone was not sufficient to cause the severe twisting that led the Narrows Bridge to fail.
5. 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.
When the bridge movement changed from vertical to torsional oscillation, the structure absorbed more wind energy. The bridge deck's twisting motion began to control the wind vortex so the two were synchronized. The structure's twisting movements became self-generating. In other words, the forces acting on the bridge were no longer caused by wind. The bridge deck's own motion produced the forces. Engineers call this "self-excited" motion.
It was critical that the two types of instability, vortex shedding and torsional flutter, both occurred at relatively low wind speeds. Usually, vortex shedding occurs at relatively low wind speeds, like 25 to 35 mph, and torsional flutter at high wind speeds, like 100 mph. Because of Gertie's design, and relatively weak resistance to torsional forces, from the vortex shedding instability the bridge went right into "torsional flutter."
Now the bridge was beyond its natural ability to "damp out" the motion. Once the twisting movements began, they controlled the vortex forces. The torsional motion began small and built upon its own self-induced energy.
In other words, Galloping Gertie's twisting induced more twisting, then greater and greater twisting.
This increased beyond the bridge structure's strength to resist. Failure resulted.