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.

As for whether it could have been anticipated? I don't know that
modeling was that advanced back then (1930s).

Charles Ellis (an engineer for the GGB) is the inventor of the math
behind the modern suspension bridge. He developed 33 equations
embracing from 6 to 30 variable to account for shape, structure,
temperature, winds, and stress that were due to both dead and live
loads. The GGB was designed for a wind load of 30 pounds per square
foot at the roadbed and 50 pounds per square foot on the towers. The
thirty pound spec is equivalent to a hurricane, the GGB typically sees
only 10 pounds per square foot for 50MPH winds.

Under the wind load designed to, the towers would bend five inches
(they swayed free, unstressed, 12 feet during construction and an
earthquake).

Basically, Ellis designed the GGB to the sum of all probable stresses,
not their average, not their RMS. The only thing missing was harmonic
amplification. The GGB was closed due to wind in 1950 and later
retrofitted with 5,000 tons of cross bracing (as was the replacement
Narrows bridge).

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 Verezzano span
(designed by GGB engineer Ammann) is only 60 feet longer but carrying
much more weight.

It was much longer and
thinner as compared to other suspension bridges of the time which were
double decked, (SF Oakland Bay Bridge) for instance.. making them
torsionally much stiffer). Interestingly, the designer of Tacoma

More the legacy of (GGB engineer) Russell Cone's assistants.

Narrows (Moisseiff) was also involved in the Golden Gate.

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.

73's
Richard Clark, KB7QHC