What is the Resonance Frequency of the Golden Gate Bridge?

[botsgotme]

I would assume that the bridge does have a “natural frequency”-at which it would vibrate. Has it ever been observed? and, could the bridge fail due to undamped oscillation?

[Stranger_On_A_Train]

From Tom Irvine’s Vibrationdata.com website (an excellent resource for all things pertaining to shock and vibration): Golden Gate Bridge Natural Frequencies.

Note that the CalTrans standards require suspension bridges to resist an earthquake equivalent static force (actually acceleration) of 2.0 g. We typically design critical material handling structures to survive an equivalent static acceleration of only 1.5 g, so that is very conservative. Of course the bridge could fail due to a high enough seismic load, but at that point a good portion of the Bay Area may be liquifying and basically sliding into the bay.

Stranger

[dtilque]

But what about the possiblility of wind causing the vibration? It’s not unknown for it to happen

[Enter_the_Flagon]

@dtilque

But what about the possiblility of wind causing the vibration? It’s not unknown for it to happen

From the article (granted, it was quite a ways down) :

According to the two engineers, the failure of the bridge was related to a wind-driven amplification of the torsional oscillation that, unlike a resonance, increases monotonically with increasing wind speed. The fluid dynamics behind that amplification is complicated, but one key element, as described by physicists Daniel Green and William Unruh, is the creation of large-scale vortices above and below the roadway, or deck, of the bridge. Nowadays, bridges are constructed to be rigid and to have mechanisms that damp oscillations. Sometimes they include a slot in the middle of the deck to alleviate pressure differences above and below the road."-The Tacoma Narrows Bridge collapse[15]

[Stranger_On_A_Train]

If you notice, the Tacoma Narrows bridge has a very thin deck. This allowed the flutter (cross-wind) motion of the bridge to couple to a particular speed of the wind that caused it to enter a limit cycle and exceed the structural capability. If you look at a picture of the Golden Gate Bridge or another long suspension bridge, you’ll see a truss structure underneath that stiffens the deck torsionally, which (among other features) prevents it from going into an uncontrolled flutter at any credible wind speed.

By the way, in the days before sophisticated finite element analysis and fluid/structural interaction, although the initial design was done by using rules of thumb and semi-empirical calculations (elastic structural analysis with empirical fudge factors), the design was verified by building a subscale model scaled using non-dimensional analysis and testing it in a wind tunnel. This art for building subscale models, once a common practice in structural engineering, has almost disappeared, which is unfortunate because while monkeying with FEA models can be a lot of fun and allows you to easily run parametric studies, it doesn’t provide the kind of intuition that building physical models does, nor does it give you insight into the limitations of your representation of connections and non-linear behavior which may not be represented in finite element models. I once had a twenty minute argument with an analyst that his model was giving a non-physical result which was settled by building a model out of drinking straws and masking tape showing that the structure wouldn’t respond the way shown on his screen. (It turned out that he had applied constraints with the wrong degrees of freedom because of a mismatch in formatting between the code he was familiar with and the one he was using.)

Stranger

[LSLGuy]

You *must *be smarter than your tools.

Doesn’t matter if it’s a teenager trying to operate a cash register or a structural analyst with a FEA tool.

If your tool is smarter than you are, GIGO is a statistical certainty.