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This value really varies from 0.75 for rolled I-beam spans to 0.85 for the
longest plate-girder spans.
But in the case of very long spans it is economical to use an alloy when
r r' is equal to or greater than unity. This is because in such spans the
dead load is large in comparison with the live load, even after the latter
has been properly increased for the effect of impact; and because, as before
indicated, the use of the alloy cuts down the weight of metal in the parts
of the structure where it is employed, and thus reduces the total dead load
to be carried by the trusses of the span or spans. The greater the span-length the more marked is the economy of adopting alloy steel.
In Figs. 5a and 5b are given the economic limiting values of r r' for
simple-span and cantilever steam-railway-bridges. The method of using
these diagrams and the formula in Eq. 2 is very simple. It can best be
illustrated by a few examples.
Example No. 1
With standard nickel steel erected at 7¢ per lb. and standard carbon
steel erected at 5 ¢ per lb. will it pay to adopt the alloy for plate-girder
spans? Here we have
r = 7 ÷ 5
r' = 35 ÷ 60
and r r' = 7/5 X 35/60 = 0.82
This is less than the 0.85 given by Eq. 2 for long plate-girder spans,
hence the answer to the question is affirmative.
Example No. 2
Mayarí steel with an elastic limit of 50,000 lbs. per square inch costs
5.5¢ per lb. erected, while carbon steel is worth 4¢. Will it pay to adopt
the alloy for building a double-track span of 275 feet? Here we have
r = 5.5 ÷ 4
r' = 35 ÷ 50
and r r' = 5.5/4 X 35/50 = 0.96
Fig. 5a gives 0.93 as the limit, consequently the use of that alloy under
the market conditions stated would not be economic.
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