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.

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

On Wed, 18 Mar 2009 17:17:14 -0700, Jim Lux
wrote:
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.

And yet the failure mode I've most seen with them is splitting.
Perhaps this only reveals a limited experience of their failure.

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)

You have inadvertently summed in ordinary approaches. We have freeway
interchanges with more complexity. Bridge span is the significant
indicator of interest. The GGB comes in at 4200 feet suspension span,
yes, the Narrows is much shorter at 2800 suspension span.

If push came to shove about overall length over water, we, here in
Seattle, have vastly larger bridges that float. The I-90 bridge logs
in at 6620 feet, and the 520 bridge pushes that to 7578 feet. Nearby,
we have the Hood Canal bridge that is longer at 7869 feet.

I've been across all five many, many, many times, and I used to live
halfway across the bay on the way to Oakland, by way of the Bay Bridge
in Frisco. The one suspension bridge I refused to drive across is SW
of Colorado Springs, over the Royal Gorge - the highest suspension
bridge (1053 above the river below). Just standing on the approach as
a car goes over gives you the shakes (talk about harmonic coupling).

73's
Richard Clark, KB7QHC

In article , Jim Lux
wrote:

Jon Teske wrote:

If you touch one note above that (B natural on the E string) the
result is a not an octave and a fifth (or high B) above the
fundamental frequency, because lightly stopping the B and causing
it to vibrate on both side of the stop divides the string into thirds.


Jon Teske, W3JT and concert violinist.

And this is why pianos are arranged to strike the string at a point
which suppresses a harmonic which is dissonant. (I think it's the 7th
harmonic which is suppressed)


Hello, and acoustic dissonance is defined by the production of
"unacceptable" beats between the partials (overtones (harmonics)) that
can, but are not generally, exact multiples of the fundamental) generated
by two or more fundamentals. Dissonance can also be defined when two
fundamentals are in close proximity as to produce a kind of "roughness".
Dissonance has no relevance for one fundamental (and its partials). It is
the partials that give a pitch on a particular instrument its quality or
timbre.

There is also a "contextual" dissonance associated with particular
intervals/ chord structures in Western classical music that, due to
accepted practice in a particular era, in many cases bears no relation to
the acoustic dissonance (sounding the chord in isolation (out of
context)). If you want more enlightenment in this area pop on over to
rec.music.theory or rec.music.makers.piano. Sincerely, and 73s from
N4GGO,

John Wood (Code 5550) e-mail:
Naval Research Laboratory
4555 Overlook Avenue, SW
Washington, DC 20375-5337

On Mar 19, 5:44*am, (J. B. Wood) wrote:
In article , Jim Lux

wrote:
Jon Teske wrote:

If you touch one note above that (B natural on the E string) the
result is a not an octave and a fifth (or high B) above the
fundamental frequency, because lightly stopping the B and causing
it to vibrate on both side of the stop divides the string into thirds..

Jon Teske, W3JT *and concert violinist.

And this is why pianos are arranged to strike the string at a point
which suppresses a harmonic which is dissonant. (I think it's the 7th
harmonic which is suppressed)

Hello, and acoustic dissonance is defined by the production of
"unacceptable" beats between the partials (overtones (harmonics)) that
can, but are not generally, exact multiples of the fundamental) generated
by two or more fundamentals. *Dissonance can also be defined when two
fundamentals are in close proximity as to produce a kind of "roughness".
Dissonance has no relevance for one fundamental (and its partials). *It is
the partials that give a pitch on a particular instrument its quality or
timbre.

There is also a "contextual" dissonance associated with particular
intervals/ chord structures in Western classical music that, due to
accepted practice in a particular era, in many cases bears no relation to
the acoustic dissonance (sounding the chord in isolation (out of
context)). *If you want more enlightenment in this area pop on over to
rec.music.theory or rec.music.makers.piano. *Sincerely, and 73s from
N4GGO,

John Wood (Code 5550) * * * *e-mail: * * * * * * * * * *
Naval Research Laboratory
4555 Overlook Avenue, SW
Washington, DC 20375-5337

Hmm, I seem to differ tho I am not a player of violins
With respect to the movement of violin wires and physics
ALL vibrations of a lever or wire is three dimensional unless the ends
are secured encastre where it is damped to a two dimensional swing. An
example is a pendulum where the lever or "bob" is of a short distance
as with a clock where the "hinge" restricts oscillation to two
dimensions. In the case of a pendulum such as seen in certain museums
that are pivoted some 100 feet or more high the oscillations take up a
three dimensional pattern such that it takes many many oscillations
before it can arrive at its starting point. The same analogy can be
applied to a radiator or antenna or any other oscillation as it
follows the same action of a tank circuit which is universal in the
sciences of nature ie the standard model and the conservation of
energy format.