From: msb@sq.sq.com (Mark Brader)
Subject: Re: Soldiers breaking step across bridge
Summary: Many details and corrections about various 19th-20th century bridges
Obul: "bridge" is actually the name of a card game
Organization: SoftQuad Inc., Toronto, Canada
Date: Sat, 21 Nov 92 18:02:18 GMT

Rachel Perkins:
} The Tacoma Narrows Bridge did not collapse because of soldiers
} walking across it in lockstep.  It did collapse because the wind
} caused it to vibrate at its resonant frequency. ...

Jay Ashworth:
> Indeed. Jon Bentley, in _More_Programming_Pearls_, (an excellent
> book for other reasons...) mentions that the only suspension bridge
> from that era still standing is the George Washington, in New York.
>   The reason?
> John Roebling, the designer, was an _engineer_. He didn't trust the
> formulas, so he designed the bridge to withstand SIX times the
> predicted wind loading, using the formulas he had to work with...

Jonathan Papai:
] I guess that means that the Roebling bridge between
] Cincinnati and Covington KY doesn't count.  It was built in 1865.
]
] Jon "I thought Roebling designed the Brooklyn Bridge" Papai

Phil Gustafson:
! The Bay and Golden Gate bridges were built at about the same time, and
! seem quite sound.

Russell Nixon:
| I remember hearing some time ago (TM) that the Bronx-Whitestone
| Bridge between the Bronx and Queens in New York City was designed by
| the same person who designed the Tacoma Narrows Bridge (Galloping
| Gertie). The story went that when the TNB failed, a large truss
| beam ... was added to the bridge at the sides of the deck to increase
| its mass and rigidity. ... [Is] the story true or is it another
| sinking library.  Inquiring minds want to know!

Rachel is right -- she refers of course to the *original* bridge at the
Tacoma Narrows, and not the replacement which has stood since 1950.

Jay is right about Bentley's two Programming Pearls books being
excellent, but he is obviously quoting from memory and has got some
things wrong.  The article he's referring to is "The Back of the
Envelope", and it appears not in the second book but the first,
just called _Programming_Pearls_.  You can also find it in the
March 1984 issue of _Communications_of_the_ACM_.  The section that
refers to bridges, incidentally, is actually an extended quotation
from a talk by Vic Vyssotsky.

Vyssotsky begins by talking about the famous Tacoma Narrows Bridge
collapse of 1940, and pointing out that even then, let alone in the
previous century, nobody knew how to model the forces mathematically.
He then asks, "So, why hasn't the Brooklyn Bridge torn itself apart,
like Galloping Gertie?"

Phil is right about the bridges he mentions.  In fact, all 5 of
the 20th century bridges mentioned in the various quoted texts
above were opened within a period of less than 10 years: the
George Washington Bridge in 1931, the (San Francisco) Bay Bridge
in 1936, the Golden Gate Bridge in 1937, the Bronx-Whitestone Bridge
in 1939, and finally, the Tacoma Narrows Bridge in 1940 -- that
one lasted only 4 months.

But Vyssotsky was talking about the *Brooklyn* Bridge, and it was
opened in 1883.  As Jonathan says, John Roebling designed it.
(It isn't mentioned in Bentley's article, but John Roebling died
shortly before construction was to start, and the responsibility for
the job fell on John Bigbootie-- no! I mean, on Washington Roebling.
Perhaps Jay knew this and this is why he thought of "Washington".)

Jay accurately paraphrases Bentley quoting Vyssotsky quoting or
paraphrasing Roebling (it isn't clear which), about the factor of
6 overdesign -- Roebling having made these remarks, incidentally,
when he was alive(!) and therefore before the bridge went up.
Jay misremembers the continuation, though:

| We should design [software] the way John Roebling did [bridges],
| and not the way his contemporaries did -- so far as I know, none
| of the suspension bridges built by Roebling's contemporaries in
| the United States still stands, and a quarter of all the bridges
| of any type built in the U.S. in the 1870s collapsed within ten
| years of construction.

Note, Roebling's *contemporaries*.  As Jonathan says, the Cincinnati-
Covington Bridge of 1866 is still standing -- but *that* one was
another John Roebling job.  Incidentally, both it and the Brooklyn
Bridge were modified -- in 1899 and 1950 respectively -- for greater
strength.

Finally, Russell is right about the Bronx-Whitestone Bridge alterations.
Through the 1930s suspension bridge engineers had been making successive
designs thinner and more flexible, and when the TNB showed that they
had gone too far, other recent constructions were examined and in some
cases modified.  The Golden Gate Bridge also suffered modification,
though in a less obtrusive manner than the Bronx-Whitestone Bridge
where a truss was added on top of each side.  (The BWB also got some
diagonal guy wires, similar to the much more numerous ones that Roebling
put on the Brooklyn Bridge.)

But the part about the same designer is wrong; it was merely a case
of one designer influencing another.  Of the bridges mentioned above,
Othman H. Ammann designed the George Washington, contributed to
Joseph B. Strauss's Golden Gate, and co-designed the Bronx-Whitestone
with Allston Dana; but the Tacoma Narrows Bridge was designed by
Leon Moissieff.  Incidentally, tests were done on a model of the
bridge during construction, specifically to check whether it could be
damaged by harmonic motions.  Unfortunately, Prof. F.B. Farquharson,
who did this, only considered vertical motions and not torsion.
He later produced the well-known film of the collapse -- perhaps he
deliberately omitted torsion so that he could become famous. :-)

My reference for most of this is "The Book of Bridges" by Martin
Hayden (Galahad Books, 1976, ISBN 0-88365-358-3).
-- 
Mark Brader              | "...not one accident in a hundred deserves the name.
SoftQuad Inc., Toronto   |  [This occurrence] was simply the legitimate result
utzoo!sq!msb, msb@sq.com |  of carelessness."           -- Washington Roebling

This article is in the public domain.