The Strangest, Most Spectacular Bridge Collapse (And How We Got It Wrong)

Absolutely nothing to do with sims, aircraft or even games; but I found it an interesting read and thought I’d share:

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Haven’t had time to read the latter 2/3 of the article, but i don’t agree with calling self excitation not a form of resonance. Besides that is just bean counting. In the end, what destroyed the bridge was a resonance catastrophy, period. The forces at work were at no time great enough to destroy the bridge without resonance magnification.

Resonance is some scary stuff. As a pilot…it is the stuff of nightmares. Just glad I’m not a helo pilot…

You should read the last 2/3 of the article, @sobek! It’s a bit soap-boxy, harping on and on about it not being the “resonance” theory, but it is more than semantics. The arguments he lays out and excellent vids demonstrate the point pretty well, if you can read past all the rhetoric!

Although Girdie’s response was oscillatory, not all oscillation is resonance, and, in Girdie’s case, wasn’t due to self-excitation, in the sense of the structure vibration contributing to the increasing amplitude of motion, but rather due to aerodynamic inputs (vortex shedding, in this case) on an elastic body (i.e., aeroelastic flutter). Girdie wasn’t ringing, which is what you’d expect in a resonance catastrophe. She was torn apart by oscillating aerodynamic forces from the vortexes she was creating.

As another example, vortex shedding off of large smokestacks can cause oscillation that destroys the stack - this is the same root cause as the Tacoma Narrows collapse: vortex shedding - but this also isn’t resonance.


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The eddies just transform the steady input into a periodic one. What tore that thing apart was mostly the energy stored in the oscillation. Even though i’m an electrical engineer, i bet you a months salary that the exitation force was at least an order of magnitude too low to destroy that bridge. And regarding the semantics: It would take me 5 minutes to draw you a LC oscillator that can be driven by direct current through a flip flop and a schmitt trigger. Yes the current source is steady, but what takes place in the LC curcuit is resonance and if tuned correctly, will lead to the circuits destruction even though the supply current might be very much below critical levels.

There is no difference between my example and the bridge except the domain (and perhaps the feedback being more complicated). The supposed debunking of resonance is either clickbait or a misunderstanding of the author of self excitation. Resonance is always a component of self excitation.

Edit: Interestingly enough, the author of the mathy example you stated seems to agree with me.

Well, my main take-away from the article was that three people tried to save Tubby the Dog, but he didn’t make it (he was in the car behind this guy). :dog:

[Long read ahead … sorry in advance!]

Hrm, a sparky, eh? Let’s see if I can explain it in electrical terms…

Imagine an LC tank with a 500 µH inductor and 50 µF cap. If I’m doing my math right, the resonant frequency of this circuit component is about 1 KHz.

If I apply a supply voltage to our LC tank, the voltage across the component rises quickly, then descends, then rises, etc., until it finally settles at the supply voltage. The rising and falling oscillates in a sinusoidal pattern that repeats 1,000 times a second (or 1,006.584 for those of you doing math at home). This is the LC tank’s natural frequency. The circuit can be said to resonate at this frequency.

If I pulse the circuit with the right input signal, I can get the peak voltages of this sinusoidal oscillation to be much higher than the input signal. If I do it just right (or wrong?), the peaks of the oscillating voltage will be so high that they’ll arc the inductor, pop the cap, or do some other serious damage. As a sparky, you know it’s very difficult to get that magic smoke back into the component!

This is an example of a “resonant catastrophe” as you mentioned earlier, however, this is not how Girdie died.

Imagine, instead, if we hooked up a complex digital voltage controller to our LC circuit that measured the RMS voltage on the tank and adjusted the input voltage to the tank to achieve some desired mean voltage in a controlled fashion. We could design the controller to meet some specific rise time, settling time, overshoot, etc., with just a little more math.

Imagine now, however, that there’s an error in the controller design. It doesn’t account for transport delay lag in the measurement of the voltage across the tank, which means the controller is always a fraction of second behind the system.

Once the controller gets a desired voltage command, say 10 volts, it increases supply voltage to the LC tank accordingly, but doesn’t actually start reducing the input voltage until too late, meaning the RMS mean voltage of the LC tank has exceeded (overshoots) the desired voltage, to say 12 volts. To compensate, the controller reduces the input voltage but, because of that dratted delay, undershoots the desired voltage on the way down (say 9 volts). Rinse and repeat.

The peaks of the RMS voltage on the LC circuit rise and fall in a sinusoidal fashion, you could call this ringing, but the phenomena driving this oscillation isn’t related to the resonance frequency of the tank circuit. Instead it is the closed-loop system including both the controller and the LC circuit that is creating this oscillation. (To be fair, the characteristics of the LC tank affect this oscillation, but the frequency of this external oscillation may vary quite a bit - a few hertz, a few hundred hertz - but not necessarily be the same frequency as the LC tank resonance frequency.)

Let’s take this to the extreme - if the controller is actually unstable, it will drive that RMS voltage up and down, up and down, with increasing amplitude. Given sufficient input voltage to start with, our unstable controller can even drive the voltage of our LC tank past the limits of the inductor or cap, creating that fatal short or burnout and poof - out goes that magic smoke.

The fact that the runaway voltage is oscillating at some frequency is a critical characteristic of the failure, but this frequency is not the resonance frequency of the LC tank.

Replace “LC tank” with “bridge”, “voltage” with “torisional displacement”, and “controller” with “aeroelastic flutter” and this is pretty much what happened with Girdie. Aeroelastic flutter caused the bridge to oscillate with increasing amplitude until the amplitude got to a failure point on the bridge.

The natural frequency (i.e., resonant frequency) of Girdie was about 1 Hz. The oscillations that tore her apart were measured at about 0.2 Hz. I have no doubt there was a 1 Hz oscillation rippling through Girdie’s structure, but a resonant oscillation of Girdie’s structure was not the cause of failure.

You might call the oscillation frequency in our failed controller system the “resonant frequency” of the closed-loop system, but the distinction between this frequency and the resonant frequency of the LC tank is a big one, and it would be misleading to say the failure of our circuit was “due to resonance”. It was really due to an unstable controller.

Same with Girdie. The failure was the aeroelastic flutter, not the resonant frequency of the bridge structure.

This is why it matters:

If the only lesson people take away from Galloping Girdie is that structural resonance is bad, they will design and build structurally sound structures that can fail in aeroelastic flutter (or hydroelastic flutter and repeat the Tacoma Narrows disaster all over again.

This is probably why the original author got all ranty. Take away the wrong lesson and you’ve learned nothing at all.

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EP, that was quite a long read and a nice thought experiment, however, a few things to consider:

System theory would state that by adding a controller, you have two coupled systems and depending on how they are coupled, you get a different transfer function. There’ll still be a (or several depending on the system) resonance frequency for the whole system.

In the case of the bridge however, you don’t have unlimited “supply voltage”.

Engineers at that time were not idiots and they designed the bridge so it could easily cope with the steady state forces typically encountered during storms. I agree that there is a phenomenon called flutter that is a forced oscillation which may not necessarily occur at a structures eigenfrequency. Looking at the forces at work however, it can not be explained how the forces were enough to fatigue the bridge so quickly without resonance magnification.

It would be interesting to read the scientific papers to see how resonance frequencies were determined. I simply cannot believe that the bridge would oscillate in this way at a frequency differing from a harmonic.

What i believe is that the author of the article mixed the frequencies of the vertical and torsional modes.

Another point that underlines the presence of resonance it that the center part of the bridge oscillates at the second torsional mode. The full centerspan undergoes this coupled movement. This would simply not happen if the bridge was in forced oscillation. The excitation forces were clearly coupled to a natural frequency.

The data is there, the explanations are there, you are more than welcome to look at whichever sets you’d like.

Except that some things don’t compute. :wink:

Another electrical engineer here. I’m inclined to agree with Einstein. And I’m planning on going home and building that tank circuit over the weekend.

Einstein, while you have a very, very good explanation, let me think on trying to come up with a different angle that may help relate it.

It’s not an intuitive conclusion. After reading the first half of that article, I came to the same conclusions as @sobek, and even posted it (thank the Cosmos for the delete button!) before deciding to take a critical look at the problem. I most definitely appreciate and support the skepticism, however - it’s better to defer acceptance of someone else’s conclusion than blindly accept. The best lessons are those self taught, right?

Also, the article comes off as high-and-mighty about slamming the resonant theory, rather than focusing on walking someone through the explanation, so I can’t fault anyone for not taking it at face value. A softer stick would have served better here, IMHO.

I don’t know if it’s necessary to draw out more examples one way or the other - @sobek’s clearly stated his position, I’ve done my best at re-articulating the position given in the paper. At the end of the day, though, the take-away should be that both structural resonance and aeroelastic flutter are important design considerations for structures. If we agree on that, I’m happy.

Now, let’s go flying!

Edit: I should also have added that I’m also fully prepared to accept that the primary cause of the Tacoma Narrows disaster was structural resonance. I’d just need to see the data/math/logic that explains all the observations.

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As i stated earlier it would be really interesting to read the actual scientific papers that the author cobbled together. I haven’t found one though that is in the public domain. Shelling out 30 bucks for a pastime musing is a bit steep. :wink:

At this point my instinct is simply that the author misinterprets the scientific papers about how the excitation process might have worked for attempts to explain the whole phenomenon instead of solely excitation, which from what bits and pieces i saw (of the actual articles) was not the case. I may be wrong, it’s been known to happen.