From: SFPhysics@aol.com
Date: Fri Feb 16 2001 - 02:27:16 PST
From: SFPhysics@aol.com Message-ID: <8c.27def80.27be5a84@aol.com> Date: Fri, 16 Feb 2001 05:27:16 EST Subject: large structure resonance(s)
> My physics class is studying waves and we just looked at resonance and
> watched the Tacoma Narrows bridge collapse. Students asked how we determine
> the natural frequency of large objects (like bridges and buildings) to make
> sure this doesn't happen again. I don't know the answer. help?
> sally
>>
The real world natural frequency of large objects such as skyscrapers and
bridges is determined via remote sensor accelerometers. Buildings like the
TransAmerica Pyramid and the Golden Gate Bridge have remote accelerometers
attached to various parts of the structure. When wind or an earthquake
"excites" the building the accelerometers can detect the "ringing" (resonant
oscillation) of the structure.
The Golden Gate Bridge was "detuned" by having mass added at various points
so that a standing wave of a particular frequency would affect only a small
portion of the bridge. The Tacoma Narrows Bridge had the resonance extend
the entire length of the span and only had a single traffic deck which could
flex. The Golden Gate Bridge was modified after the Narrows Bridge collapse.
The underside of the deck had stiffeners added to dampen torsion of the
roadbed and energy absorbing struts were incorporated. Then mass additions
broke up the ability of the standing wave to travel across the main cables
because various sections were tuned to different oscillation frequencies.
This is why sitting in your car waiting to pay the toll you can feel your car
move up a down when a large truck goes by but the next large truck may not
give you the same movement. That first truck traveling at just the right
speed may excite the section you are on while a truck of different mass or
one not traveling the same speed may not affect it much. As for the
horizontal motion caused by the wind, the same differentiation of mass
elements under the roadbed keeps the whole bridge from going resonant with
Ĉolian oscillations.
Just envision the classic Physics experiment where different length pendulums
are hung from a common horizontal support. Measured periodic moving of the
support will make only one pendulum swing depending on the period of the
applied motion. If all the pendulums (pendulii?) had the same oscillation
you could get quite a motion going with a small correctly timed force
application. Bridges and buildings now rely on irregular distributions of
mass to *help* keep the whole structure from moving as a unit that would
result in destructive failure. Note also on the Golden Gate the secondary
suspension cable "keepers" (spacers) are located at slightly irregular
intervals to detune them. As current structural engineering progresses more
modifications of the bridge will be done. The new super bridge in Japan has
hydraulically movable weights that can act as active dampeners. What is
earthquake (or wind) safe today will be substandard in the future.
Al Sefl
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