Tacoma-Narrows Bridge

The collapse of the Tacoma-Narrows Bridge is certainly one of the most spectacular and, compared to the possibilities available at the time, one of the best documented disasters in engineering history. Even today, almost eight decades after the collapse of the bridge, the breathtaking pictures are still used very often. Although the physical phenomena that led to the collapse have been known and explained for many decades, the Tacoma-Narrows-Bridge persists as an example of a resonance catastrophe. This is wrong, at least as far as the final reason for the collapse is concerned. There are two reasons for this, a technical one and a human one, but more about this later. Furthermore, the question arises whether a comparable event could also happen today.

Briefly to the background. At the time of its planning and construction, in the years 38-40 of the last century, the Tacoma-Narrows-Bridge had the third longest span of all suspension bridges worldwide. At the same time, however, it was by far the slimmest bridge construction. Just four months after the opening ceremony, the bridge collapsed. What were the reasons for this?

Why wasn't it a resonance disaster?

According to the definition, two conditions must be fulfilled for a resonance catastrophe to occur. On the one hand, the oscillating system must be excited by a periodic force close to its natural frequencies and, on the other hand, the energy absorbed by the excitation must be greater than the energy that is withdrawn from the system by damping. If both are met, this leads to a continuous increase in amplitude until the system finally collapses.

At the Tacoma-Narrows bridge, only the first of the two conditions was met. Even at low wind speeds across the roadway, the pressure conditions between the top and bottom of the roadway and the periodic vortex separation of the Kármán vortex street could cause the bridge to oscillate transverse to the longitudinal axis of the bridge, but the upward and downward movement of the roadway also changed the flow conditions. On the one hand it influenced the vortex formation itself, on the other hand it caused a vertical flow resistance against the movement direction. The resulting forces thus worked against the initial excitation. The vibrating system has thus stabilized itself.

Vortex strength with transverse flow and an angle of inclination of 0°
(red=left-handed; blue=right-handed)

Pressure conditions with transverse flow and an angle of inclination of 0°
(red= positive pressure; blue= negative pressure)

The general tendency of the bridge to oscillate led to the nickname "galloping gertie" among the population, whose movement was actually triggered by a harmonic excitation near the natural bending frequency. But for the reasons mentioned, this did not change into an uncontrolled pattern. At the wind speed of 42mph (18.8m/s) on the day of the accident, the frequency of natural vortex detachment was already significantly higher than the natural frequency of the bridge. A periodic excitation force and thus the basis for a resonance catastrophe can therefore be ruled out.

What caused the collapse instead?

The circumstances were much more complex. Instead of an external force, whose magnitude was only dependent on time, causing the bridge to vibrate in torsion, an aerodynamically induced self-excitation occurred. At first, the flow caused a deflection of the road surface, which also changed the flow angle and thus the entire flow profile. In the neutral zero position, angle of inclination 0°, there was a more negative pressure on average over time on the upper side of the road than on the bottom side, the conditions were reversed when the road was deflected counterclockwise.

Vortex strength with transverse flow and an angle of inclination of +5°
(red=left-handed; blue=right-handed)

Pressure conditions with transverse flow and an angle of inclination of +5°
(red= positive pressure; blue= negative pressure)

In this case, there was a negative pressure on the bottom of the road, which was significantly stronger than on the top. The greater the inclination of the road, the greater this effect became. The same applies to the flow resistance. This also increased with increasing oscillation amplitude of the bridge. The resulting force from drag and lift acting on the bridge showed in the direction of the flow and downwards.

When swinging back, the picture was very similar. The greater the angle of inclination of the roadway in a clockwise direction, the greater the drag and the lift forces. The resulting effect in this case was in the direction of the flow and upwards.

Vortex strength with transverse flow and an angle of inclination of -5°
(red=left-handed; blue=right-handed)

Pressure conditions with transverse flow and an angle of inclination of -5°
(red= positive pressure; blue= negative pressure)

Only a decreasing wind force could have prevented the catastrophe at this time. Since this did not happen, what had to happen inevitably happened. The crash into the depths of the Tacoma-Narrows Bridge roadway begins at 11:02 a.m. on 7 November 1940 and ends a few minutes later with the last parts of the bridge coming loose.

What does this mean for the simulation?

The two previously discussed causes of vibration excitation are simulated using two completely different simulation methods. In the first case, the excitation by the vortex separation resulting from the Kármánschen vortex road, it would be possible to describe the task with a frequency response analysis. This is relatively simple. However, since frequency response analysis is only used to search for possible resonance cases, the same would happen as 80 years ago, when only static load cases were considered. Because the method would be the wrong one, the real danger would not be recognized correctly! Only the "galloping gertie" would be coming to the light. For this reason, changes might be made that would perhaps also prevent the real cause of the disaster, unconsciously so to speak. But that would be nothing more than pure fortune!

In the second case, the numerical effort is significantly greater. The problem would have to be treated in a coupled, transient fluid-structure simulation for a complete description. Practically with the bridge length of 1.5km this is not a practicable way. The model size and the numerical effort would be much too great. That is why a different approach is needed.

You are interested in how we solved the task?
We'll be happy to tell you. Please feel free to contact us!

Regardless of the numerical challenges for this particular case, experts are needed to correctly assess the technical situation from the very beginning and to select the appropriate methods. There must also be time to get to the root of the problem. Especially when the borders of the known are left behind! In this case this was the extreme slenderness of the bridge.

Disasters are more than simple physics!

As I mentioned at the beginning, the technical aspects of this disaster have been investigated in more than detail. Much more thorough and in-depth than we have done here. But why was the Tacoma-Narrows Bridge built so slim? Why have they been constructed so filigree? Here, too, we cannot question from a distance as thoroughly as the others may have already done. But we can ask a few fundamental questions. Was it the urge for a new superlative, the desire to prove it to oneself and others? Were there economic considerations, i.e. the fight for the contract on price? Or was it simply the deadline pressure that did not give the responsible persons the time to test the construction beyond the applicable standards? Would it not have been necessary to do just that, since the construction workers had already observed the first signs of the bridge's tendency to vibrate before its completion and reported them to those responsible?

In our opinion, the real reason for the catastrophe lies in some mixture of these or other similar questions, let's call them "human factors". While technical knowledge has led to new and better standards and design guidelines, in other words, we have learned from our mistakes, the "human factors" are still present today. Man has not changed in his nature, not even the external circumstances. As a result, a comparable disastrous event can happen again at any time. It does not have to be a bridge that collapses, but some "simple" component. One that nobody sees, but you and your company will have a lot of trouble and costs if things go wrong.

In order for this not to be the case, the right conclusions must be drawn from what has happened. In addition to the general conditions and the "human" factors, the concept and planning phase in particular plays a key role. In order to minimize errors and reduce costs, it is necessary to proceed particularly thoroughly in these project phases. Here lies (almost) the whole responsibility. From our point of view, a very important aspect here is the early involvement of the simulation experts in the development process.

It is better for everyone involved to understand in advance what could happen,
than to find out in retrospect what had happened!