Tacoma Bridge Collapse: Physics of Vibration and Sound

[liv]

I changed my mind, I'm not fickle, th stethescope was all i could remember...
Anyway, apparently the tacoma bridge collapse was due to the bridge 'vibrating', and obviously the supports couldn't hold it...

If you know anything about how the sound part of physics fits into this your help would be greatly appreciated...

Thanks

nec hostium timete
nec amicum reusate

 

[Curious3141]

I think you're looking for something on "resonance". Google "resonant frequency" and "natural frequency" and gawk away.

 

[saltydog]

Well, can I mention pushing someone in a swing? If you time it just right, you only have to exert a little bit of extra force on each push to get them moving higher and higher.

 

[FredGarvin]

If you look under the Tacoma Narrows bridge on Google or Yahoo you should find plenty of research material on what is, most likely, the most documented and most debated, bridge collapse in history.

If you can, contact Tom Irvine at VibrationData.com. He has written a paper that discusses the failure. It examines it from a vibration analysis standpoint and discusses the three leading theories. The vibration discussions may be a bit more advanced than you'd like, but it would be a great source.

 

[liv]

Thank you! you've all been heaps of help! )

 

[liv]

i've just found a website whih goes into great detail about the physics behind the TBDisaster. what i don't understand is the winds effect on the bridge...does it mean that any structure can 'resonate' (i'm guessing that means *shake* or move in the frequency 'wave'?) if its hit with the right amount of wind? its quite confusing and i need to understand what I'm talking about...
if you can think of an example that i could try just at home or something, that would be awsome, thanks.

liv

the website address is http://tafkac.org/science/bridge_resonance.html if you want to have a look... )

 

[FredGarvin]

If you read down farther on that page, you will see what is really the heart of what happened. A LOT of people will say that resonance is what has caused the bridge collapse. That is not the case. What is the most plausable is aerodynamic instability. Two analogies that can be drawn are wing flutter on aircraft and transmission line "galloping." If you want to talk about resonance, we can do that as well. But seriously, do not get caught in the common mistake of blaming resonance as the culprit.

What happened, in a nutshell, is that the wind was at 35-42 mph. The bridge's span design (very flexible in torsion and vertical motion) allowed it to start acting somewhat like a wing. The wind caused a deflection until a point was reached where the torsional stiffness of the bridge overcame the pressure build underneath and caused the span to rotate back in the other direction, much like a pendulum. This continued until either the fatigue limit was reached or the material was stressed beyond ultimate stress limits.

A good reference about this is:
K. Billah & R. Scanlan, "Resonanace, Tacoma Narrows Bridge Failure, and Undergraduate Physics Textbooks" Americal Journal of Physics, 1991.

 

[liv]

what do you mean bya "the wind caused a deflection"? and i understand that torsion is "twisting on the long axis" so I'm guessing that the torsional stiffness is when the bridge couldn't twist anymore than it already was...? and (sorry) is pressure build sefl-explanatory? cause I'm not quite sure what that's talking about...

I'm really sorry, I'm only doing yr 12 physics and i can't say I'm top of the class...

From what you told me...this is what i understand...

the wind was blowing at the above speed which caused the bridge to start twisting and turning on its horizontal axis. The bridge's supports couldn't hold the "force" and crumbled...?
Am I close at all? thanks

liv

 

[brewnog]

The key point is that the bridge was vibrating/oscillating. The actual wind speed was well below that which would have caused the bridge to just fall over, the bridge essentially shook itself to death.

Think about what you've learned in Y12 Physics about resonance.

Also, (this isn't entirely right but is fine for Y12 purposes), think about bending a paperclip until it breaks, - bending it once won't cause it to break but if you keep on bending it backwards and forwards, it will eventually crack and break. This is called fatigue. (Well, not quite, but again (and I don't mean to be condescending) it's good enough for Y12.)

 

[FredGarvin]

Think of the the bridge like a wing for a moment. When the wind hits it it starts to lift and twist, putting it in a new position. Now more wind hits hit and it lifts and twists some more. The bridge will keep going like that until the wind isn't strong enough to push it any farther. The bridge will then act like a spring and want to spring back into it's original shape. But when it "snaps" back into it's original shape, it has momentum and goes too far in the other direction (like a pendulum). Once it goes as far as it can in the other direction it would return to it's original position. Once it does that, the whole process starts all over again.

That whole process kept going until the motions fatigued the support stuctures and the bridge collapsed.

Does that make a bit more sense? If you need more clarification, just say the word.

 

[Astronuc]

The wind set up a time varying differential pressure situation - somewhat like periodically tapping a pendulum or swing, or bouncing a ball. Each little push added a little more energy. The problem is similar to that encoutered in vortex shedding.

In the case of the original Tacoma Narrows bridge, the geometry of the bridge was such that there was positive feedback, i.e. the amplitude of oscillation grew, with subsequent cycles. The replacement bridge had much better damping characteristics, both structurally (stiffer deck) and aerodynamically.

 

[brewnog]

Astronuc, the failure WAS due to vortex shedding!

Did I recently hear of a modern bridge which was expected to suffer from exactly the same problem except for the pedestrian handrails breaking up the vortices?

 

[FredGarvin]

Brewnog...I hate to tell you this, but it was NOT vortex shedding. The vortex shedding frequency for that situation was calculated to right at about 1 hz. The torsional mode was estimated by measurements to be 0.2 hz. There are some theories that some flutter vorticies may have contributed to the torsional mode, but there is no real evidence of it.

 

[brewnog]

Brewnog...I hate to tell you this, but it was NOT vortex shedding.

Apologies, I've been misled.

I'll have to discipline my sources! I guess the reason that bridge was used as an example was just because they had a cool video. Are flutter vortices merely a milder form of vortex shedding? And are those spiral things on the top of chimneys a counter-measure of vortex shedding?

 

[FredGarvin]

No problemo. I was a believer of that explanation for quite some time until it was explained to me with numbers.

Flutter vorticies are the typical vorticies seen off of bodies, etc... The big distinguishing factor is their randomness. Karman vorticies are periodic. Karman vorticies are what are what I was referring to in the previous frequency data. The reference I stated above mentions that vortex shedding did play a part, but was not a periodic, Karman vortex.

Here's a pretty good link. There's also a quick blurb on the Narrows bridge and the video.

http://www.galleryoffluidmechanics.com/vortex/karman.htm

 

[liv]

Hey FredGarvin...another one for you...

i asked my teacher, just to verify what you said and he said that it was right (THANKS) but also to look at resonance...you said earlier that it wasn't the cause...but I'm guessing it did have a part to play? wouldyou mind explaining some of it? thanks

liv

______________________
nec hostium timete
nec amicum reusate

 

[liv]

*just out of interest*

one of the other topics you could choose was the zone of silence found in mexico...over a certain area there are no soundwaves at all, no radios, no walkie talkies, nothing to do with sound waves works...don't stress yourselves over it but if you know why or something let us know...thanks x

 

[FredGarvin]

Liv,
I can not say for sure whether or not resonance was a part of the collapse. That is still in debate to this day. However some items can be said about resonance in this case.

If you have an object and strike it and allow it to vibrate, you are essentially exciting it's natural frequencies. These are a set of frequencies that will show up and are a function of the geometry and material the object is made of. There can be quite a few natural frequencies with different wave shapes, or "modes" as they are called.
Eventually the vibrations die out because the object's own mass will dampen the vibrations. To keep the vibrations happening, you have to constantly keep exciting the motions. In the bridge's case, the wind was what was causing the vibrations.

Now, for resonance to happen, there has to be a driving force, i.e. the wind, that is very close to one of the natural frequencies. The wind going through the Tacoma Narrows is extremely turbulent. That means that it's directions and speeds are changing with time. Because the winds were/are so random, it's not possible that resonance could have been induced for a prolonged period of time. What makes the most sense to me is that the bridge experienced very brief moments of resonance, but resonance was not a major driving factor.

To give you a better idea of what resonance is, follow this link and look down towards the bottom of the page. It shows a cantilever beam that is vibrating at it's first 3 bending modes.

http://homepages.strath.ac.uk/~clas16/~fyfe/ansys/dynamic/modal/modal.html

Hope this helps.

 

[liv]

Curious, i know you said resonance and i ended up basing my report on this topic becusae its at we're studying
would you mind if i showed you my report, i'd just like to get your opinion on it...thanks

liv

 

[Curious3141]

Curious, i know you said resonance and i ended up basing my report on this topic becusae its at we're studying
would you mind if i showed you my report, i'd just like to get your opinion on it...thanks

liv

I don't mind, why don't you post it here so that we can all take a look at it and give you our opinions.