Richard Clark wrote:
On Wed, 18 Mar 2009 11:11:42 -0700, Jim Lux
wrote:

I guess that is the thing they forgot to calculate, or didn't know
how, on the infamous Takoma Narrows Bridge in Washington State which
collapsed when cross winds cause wild vibrations.

That was an unexpected coupling between the force from the wind and
torsional vibration of the roadbed. As the roadbed tilted, it "caught"
more of the wind and had more force applied, moving it further. The
torsional resonance was such that it oscillated with ever greater
amplitude (not much different than a flag flapping, or a blade of grass
in the wind.. not quite like a wind instrument reed, though)

In fact, it was exactly like a reed. The Tacoma Narrows Bridge
exhibited the highest roadbed length to roadbed width ratio of the
designs of that era, and this was a contributing factor.

Reeds don't oscillate torsionally (at least not as the dominant mode)
They're more of a fixed/free beam that oscillates in longitudinal bending.



The bridge was an
architectural feat, with a very delicate looking thin roadbed and much
longer than most other bridges (3rd longest when it was built, some 1500
feet longer than the Golden Gate, for instance).

You can't be third in the list to the GGB and longer both unless you
are speaking of the insignificance of approaches.

The GGB is shorter than the TNB. It was third on the list on July 1,
1940 according to Wa DoT. (Verrazano narrows was built in 1964) George
Washington was built in 31 and was 3500 ft, and was longest until 37,
when GGB was built in 37.

TNB was 5939 ft long (per Washington state DOT). GGB is 4200 ft
(wikipedia gives 5000 ft for the length of the TNB)

T

Moisseiff was also the weak link for both the Narrows bridge and the
GGB closure due to high winds in 1950. He underestimated the dynamic
wind load. Ellis was the inventor of the math, but not a chief
project engineer. In the field of bridge engineering, and especially
for the GGB, there were a lot of Prima Donnas - Strauss the first of
firsts. Moisseiff, by some accounts, appears to have been used as a
resource rather than a principle engineer in the Narrows bridge
construction. The bridge owners conspired to a lot of monkey shines
in cost-cutting choices which turned out to be fatal. They eliminated
the cross bracing from the bridge towers, above and below the roadbed;
and they dispensed with the roadbed stiffening truss.

Moisseiff, along with GGB designers Ammann and Cone, was appointed to
the review board to study why the bridge failed - that was doomed to
failure, too, by the bridge owners (who had their own insurance
problems because they declined to find an outside insurer and decided
to carry the risk themselves). The story of the back room feuding and
remarkable Reaganomic theories are case lessons in planned disaster.

Interesting.