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Posted by gruhn on June 5, 2008, 1:02 am
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> Eiffel Tower. =A0We found out that Patrick Weidman, a university
The account at physorg.com is woefully inadequate at describing the
problem. It does contain this gem though
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>> Eiffel discovered this form of construction produces no load in
>> the diagonal truss elements commonly used to counteract the
>> bending moment, or torque, of the wind, and hence those truss
>> members could be eliminated,"
Which suggest that it is a lenticular truss.
Which is what Zalewski and Allen suggest in
http://www.amazon.com/Shaping-Structures-Statics-Waclaw-Zalewski/dp/04712899=
65/ref=3Dsr_1_1?ie=3DUTF8&s=3Dbooks&qid=3D1212641275&sr=3D8-1
The physorg article also states that "The tower is composed of four
arched, wrought-iron legs tapering inward to form a single column that
rises to 300 meters, or 986 feet." but kind of skips over the fact
that the arches are not part of the structure. I'd even pick a nit
with them that the legs do not taper. The tower tapers, the legs are,
each (that's the critical bit) of (apparent) constant cross section to
the first deck. Second and this sections do appear to taper the corner
"members".
I think what the "problem" is saying is that the apparent curve of the
tower does not conform to any relatively plain function we can dream
up; but some guy did some numerical analysis and popped out a "single
equation" which is messy but does the job (questions arrise here as to
what he used for data points and what he discarded as not relevant)
but that single equation is in DiffEq land so it has many different
equations as solutions, please find one; so yer man in Colorado said
"dig, he fudged the bottom so we need two equations."
In the end, the article hints at the pointlessness of all this. It
appears that what Eiffel et al really did was draw the tower pretty
and according to lenticular properties and then, using the drawing
solve the tower graphically (see Zalewski and Allen again).
The orignal question "what equation did Eiffel use" seems to just be
wrong and a side effect of number crunching modern engineers. See
http://www.amazon.com/Stress-Analysis-Strapless-Evening-Gown/dp/0138526087/r=
ef=3Dsr_1_1?ie=3DUTF8&s=3Dbooks&qid=3D1212641987&sr=3D1-1
Make it look pretty then let the engineers keep it upright.
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