DRIVEN HARMONIC OSCILLATIONS.

Film Loop: Tacoma Narrows Bridge Collapse

Length: 4:40 Min., Black and White, No Sound

Note: This is also available in 16 mm Film in color, 4 Min.

The main span of the bridge near Tacoma, Washington was 2800 ft long, 39 ft wide, and the steel stiffening girders (shown during construction) were 8 ft tall. The bridge was opened for traffic on July 1, 1940. In the four months of active life of the bridge before failure, many transverse (vertical) modes of vibration were observed before November 7, 1940. The main towers were nodes, of course, and between them there were from 0 to 8 additional nodes. Maximum double amplitude (crest to trough) was about 5 ft in a mode with 2 nodes between the towers; the frequency of vibration at that time was 12 vib/min.

Measurements made before failure indicated that higher wind velocities favored modes with higher frequency. This correlation may be explained by the fact that turbulent velocity fluctuations of winds can be considered as composed of a superposition of many periodic fluctuations, and the fluctuations of higher frequency are preponderant at higher wind velocities. There was no correlation between wind velocity and amplitude of vibration. Early on the morning of November 7 the wind velocity was 40 to 45 mi/hr, perhaps larger than any previously encountered by the bridge. Traffic was shut down. By 9:30 a.m. the span was vibrating in 8 or 9 segments with frequency 36 vib/min and double amplitude about 3 ft. While measurements were under way, at about 10:00 a.m., the main span abruptly began to vibrate torsionally in 2 segments with frequency 14 vib/min. The amplitude of torsional vibration quickly built up to about 35degrees each direction from horizontal. The main span broke up shortly after 11:00 a.m. During most of the catastrophic torsional vibration there was a transverse nodal line at mid-span, and a longitudinal nodal line down the center of the roadway (the yellow center stripe!). Note that Prof. Farquharson sensibly strides (?) down the nodal line as he leaves the bridge after making observations.

The crucial event at 10 a.m. which directly led to the catastrophic torsional vibration was apparently the loosening in its collar of the north cable by which the roadway was suspended. The center of the cable was moving back and forth relative to the center of the suspended span. This allowed the structure to twist. The wind velocity was close enough to the critical velocity for the torsional mode observed, and the vibration built up by resonance and was maintained until collapse inevitably took place.

The bridge was rebuilt using the original anchorages and tower foundations. Studies at the University of Washington Engineering Experiment Station resulted in a design for the new bridge which used deep stiffening trusses instead of girders. The new bridge is entirely successful.