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During the last half century several treatises have been written upon
the subject of economy in superstructure design, but unfortunately the
result is simply a waste of good mental energy; for the writers thereof
invariably attack the problem by means of complicated mathematical
investigations, not recognizing the fact that the questions they endeavor to
solve are altogether too intricate to be undertaken by mathematics. The
object of each investigation appears to have been to establish an equation
for the economic depth of truss, or that depth which corresponds to the
minimum amount of metal required for the said truss; and, to start the
investigation, it seems to have been customary to make certain assumptions
which are not even approximately correct. For instance, the principal
assumption of several treatises in French and English is that the sectional
area and the weight of each member of a truss are directly proportional to
its greatest stress; or, in other words, that in proportioning all members of
trusses a constant intensity of working stress is to be used, while in reality
for modern steel bridges the intensities often vary considerably in the same
specifications. Again, no distinction is made between tension and compression members, and no account is taken of the greatly varying amounts
of their percentages of weights of details.
There is, however, one mathematical investigation concerning economic
truss depths which is approximately correct, and which is based on assumptions that are very nearly true; but it holds good only for trusses with parallel chords. It is this:
Let A = weight of the chords,
B = weight of the web,
C = weight of the truss,
and D = depth of the truss.
Then
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