The Torsional Flutter of Puget Sound

Aeroelastic Self-Excitation and the Collapse of Tacoma Narrows

Four months after opening to traffic across Puget Sound in Washington State, the 2,800-foot central suspension span of the Tacoma Narrows Bridge twisted itself to pieces on November 7, 1940, in a steady 42-mile-per-hour wind. Designed by New York consulting engineer Leon Moisseiff using elastic deflection theory, the bridge was the third-longest suspension span in the world, yet by far the narrowest and most flexible. To reduce structural dead weight and cut steel fabrication costs to $6.4 million, Moisseiff narrowed the two-lane roadway to just 39 feet. That geometry gave the main span an extreme width-to-length ratio of 1:72. Even more critically, Moisseiff replaced traditional 25-foot-deep open steel stiffening trusses with solid 8-foot-deep carbon-steel plate girders running along both edges of the deck.

From the day the deck was planked in the spring of 1940, construction workers nicknamed the crossing "Galloping Gertie" because winds as light as four miles per hour excited benign vertical ripple waves along the roadway. On the morning of November 7, the bridge initially bounced in a vertical nine-node wave at 36 cycles per minute. At 10:00 AM, after a steel cable band slipped on the north main cable at mid-span, the vertical bouncing abruptly stopped. In its place, the roadway entered a violent two-node antisymmetric torsional oscillation at $0.2\text{ Hz}$ (12 cycles per minute). The deck twisted 28 degrees to either side while the mid-span nodal point remained stationary, until the suspender cables snapped and dropped the central roadway into the sound at 11:10 AM.

In the immediate aftermath, aerodynamicist Theodore von Kármán attributed the disaster to resonant Kármán vortex shedding—the periodic alternation of swirling vortices shed behind a bluff obstacle at a frequency $f_s = \text{St} \cdot U / D$. Here $\text{St} \approx 0.11$ is the Strouhal number, $U$ is wind velocity, and $D = 8\text{ feet}$ is the girder depth. Yet subsequent wind-tunnel measurements conducted by Frederick Farquharson at the University of Washington exposed a decisive mismatch. In a 42 mph ($61.6\text{ ft/s}$) wind, natural Kármán vortex shedding behind an 8-foot plate girder occurs near $0.85\text{ to }1.0\text{ Hz}$—nearly five times faster than the fatal $0.2\text{ Hz}$ torsional twist that destroyed the bridge.

In the 1970s, Princeton civil engineering professor Robert Scanlan resolved the paradox by measuring the aeroelastic flutter derivatives of bluff bridge decks. Scanlan proved that Tacoma Narrows was destroyed not by external forced resonance, but by single-degree-of-freedom aeroelastic torsional flutter, governed by the torsional equation of motion for deck twist angle $\alpha$:

Here $I$ is the deck polar moment of inertia, $c_\alpha$ is mechanical damping, and $k_\alpha$ is torsional stiffness. In the aerodynamic term, $\rho$ is air density, $B = 39\text{ feet}$ is deck width, and $A_2^*$ is Scanlan's dimensionless torsional flutter derivative.

On an open truss bridge, wind passes cleanly through the steel lattice. The coefficient $A_2^$ remains negative, so aerodynamic forces damp out twisting motions. On Tacoma Narrows, the solid 8-foot plate girders acted as impermeable bluff walls. Whenever the deck twisted through a small angle $\alpha$, the sharp windward girder lip tripped a large leading-edge vortex. That vortex rolled across the roadway at a phase delay synchronized with the deck's angular velocity $\dot{\alpha}$. Above 35 miles per hour, the aeroelastic coefficient $A_2^$ turned strongly positive and overwhelmed the bridge's small structural damping $c_\alpha$. Total effective damping became negative. The bridge became a self-excited aerodynamic engine where every twist extracted energy from the steady wind to amplify the next cycle.