The Start of the Torsional Oscillations

The start of the torsional oscillations was due to the loosening of a cable band on the northern end of the mid-span of the bridge.  Prior to the cable loosening, the hanger ties on the bridge were alternating between being slack and taut due to the oscillations already occuring on the bridge.  This was causing snap loads to be put on the cable that it was not designed to handle, which caused it to fail by fraying and loosening and led to the start of the torsional oscillations.  Now, normally suspension bridges undergo very limited torsional movement; however, when symmetry around the bridge's center line is lost, which is what happened to the Tacoma Narrows Bridge, then torsional oscillations are expected to initiate, and, if circumstances allow, increase in magnitude.

In this specific case, it is clear that the driving force behind the oscillations was the wind, which, on the day of the collapse, was approximately 40 mph.  While this is clear, there are two theories on the exact way that the wind drove the oscillations.  In the first, a phenomenon known as vortex shedding caused alternating low and high pressures which matched the natural frequency of the bridge to drive the oscillations.  In the second, a phenomenon called aeroelastic flutter acted on the bridge in such a way that it caused negative damping to occur and increase the magnitude of the oscillations.

Vortex Shedding and Resonance

This theory was originally put forth by the lead engineer who investigated the collapse on commission of the DOT (Department of Transportation), he outlined this theory in his autobiography in which he stated that this was the reason for the collapse.  This however completely contradicted his original report which explicitly stated that it was not vortex shedding that caused the collapse of the bridge.  This has become the popular theory among the general public and has been used as a classic example of the extreme results that resonance can produce. 

Vortex shedding occurs when wind hits an object and alternating low and high pressure areas form behind the object.  In this theory the vortexes that occurred from the wind hitting the bridge had a period that matched the natural frequency of the bridge and drove the magnitude of the oscillations to increase until the collapse of the bridge.  This theory has a number of flaws for which it has received criticism for however.  Resonance models are limited to linear equations with no damping present, which is not common in a structure so large. In addition, the calculated periods of the wind and the bridge do not match as the wind was found to have a period of one Hertz, while the bridge had a period of approximately 0.2 Hertz.

Aeroelastic Flutter and Negative Damping

The alternative model of the bridge's collapse is based on aeroelastic flutter, causing a negative damping situation to occur in the bridge. This theory also has changed the model to a non-linear equation, and much better reflected the bridge's behavior before, and during, its collapse.  Their inherent unpredictability matched up well with the fact that at time smaller wind speeds would produce larger magnitude oscillations in the bridge than higher wind speeds would.

In aeroelastic flutter, the wind would blow on the side of the bridge and cause a clockwise or counterclockwise torque to act on the bridge, depending on the section's current orientation.  This torque acts on the bridge in such a way that it is always amplifying the current motion of that section of the bridge and causing the magnitudes of the oscillations to increase in size. The force caused by the aeroelastic flutter in this model causes a situation to occur known as negative damping.



Negative damping refers to a situation in harmonic equations in which the damping coefficient is negative.  This causes the magnitude of the oscillations to increase over time instead of the typical situation where the magnitude decreases.  Negative damping actually occurs in many real life situations, most notably: in a number of musical instruments.
This model actually correlates very well with the initial cause of the torsional oscillations when the cable band started to fail.  When this occurred, the bridge started to twist, and this was amplified by the torque that would have been applied by the wind and led to the start of the negative damping which caused the bridge to fail.