As this pamphlet has to do with wooden bridges only, nothing will be
said of the proper relative dimensions of cast-iron columns to sustain
the strains to which they may be subjected, but a table of the
strength of columns will be found further on.
=Transverse Strains.=
Let W = breaking weight in lbs.
" s = constant in table.
" b = breadth in inches.
" d = depth in inches.
" L = length in inches.
Then, for the power of a beam to resist a transverse strain, we shall
have,
4 sbd²
W = ------
L
[TeX: $W = \frac{4 sbd^2}{L}$]
This formula has been derived from experiments made by the most
reliable authorities.
The constant, 1250, adopted for wood in the following formula, is an
average constant, derived from the table, of those woods more commonly
used.
Now to reduce the formula to the most convenient shape for use, we
substitute the value of s, and we have
4 x 1250 bd²
W = ------------,
L
[TeX: $W = \frac{4 \times 1250 bd^2}{L}$]
or
5000 bd²
W = --------.
L
[TeX: $W = \frac{5000 bd^2}{L}$]
But, to reduce the load to the proper working strain, we must divide
this equivalent by 4, the factor of safety, and we shall have
5000 bd²
W = --------.
4L
[TeX: $W = \frac{5000 bd^2}{4 L}$]