Failure of the Tacoma Narrows Bridge

[Rasine]

i am, thus, attempting to understand the physics of the collapse of the Tacoma Narrows.

can please explain what i have found to be the cause of the final distruction: single-degree-of-freedom torsional flutter?

or if you know anything else about this event, please explain!

 

[Pyrrhus]

If i remember the problem had to do with resonance, You see the winds were making vortices with the same natural frequency of the bridge, thus making the deck of the bridge oscillate with a rather huge amplitude. Another fact is that the wind making the resonance had a speed less than what the bridge was made to handle.

 

[russ_watters]

"torsional flutter" is a way of describing, essentially, aerodynamic resonance. Its the same as when you drop a piece of paper and it flutters back and forth.

In my basic training at the Naval Academy, there was a footbridge with two telephone poles supporting the center span leading to some athletic fields. The resonant frequency was roughly the same as the double-time marching (running) pace. We had been instructed not to march in step across the bridge, but one instructor forgot, marched his squad across, and snapped one of the telephone poles. After that, they replaced the center span with steel, which being much more rigid, has a much higher resonant frequency.

edit: http://www.enm.bris.ac.uk/research/nonlinear/tacoma/tacoma.html is a good site with info, photos, and videos of the Tacoma Narrows bridge failure.

 

[HallsofIvy]

More recent examinations have shown that it is a lot more complicated than simply saying "resonance"! I don't have it with me now but if I remember tomorrow I will post a link to a discussion.

 

[Pyrrhus]

I would like to see those new explanations, Halls. I thought the oscillation due to resonance was more than enough to cause a collapse of the Bridge's deck.

 

[russ_watters]

I'm not certain, but I think the added complexity was due to the aerodynamic forces and the fact that the motion was torsional. The situation I described is more typical of resonance: simple harmonic motion in the axis where the bridge is loaded (vertical), with a driving force that is periodic, but always the same and far too small to cause failure if it were constant.

 

[HallsofIvy]

I don't have web-site references but

Differential Equations by Blanchard, Devaney, and Hall has a long discussion of the Tacoma Narrows bridge and refers to
"Large-amplitude Periodic Oscillations in Suspension Bridges: Some New Connections with Non-linear Analysis" by Lazer and McKenna, SIAM review, vol. 32, no. 4, 1990, pp. 537- 578.

 

[FredGarvin]

Take a look at this thread:

https://www.physicsforums.com/showthread.php?t=62264

 

[Rasine]

thanks to everyone for helping me understand!