Length      Safety       Length    Safety     Length    Safety
given in    Weig’t in   given in   Wt. in    given in   Wt. in
Diameters.   Pounds.     Diameters.   Pounds.   Diameters.   Pounds.

6         1000         24         440       42         203
8          960         26         394       44         185
10          910         28         358       46         169
12          860         30         328       48         155
14          810         32         299       50         143
16          760         34         276       52         132
18          710         36         258       54         122
20          660         38         239       56         114
22          570         40         224       58         106
60          99

In tensional strains, the length of the beam does not affect the strength; but in the beams submitted to compression, the length is a most important element, and in the table given above, the safety strains to which beams may be subjected, without crushing or bending, has been given for lengths, varying from 6 to 60 diameters.

PRACTICAL RULES.

=Tensional Strain.=

Let T = whole tensional strain. " S = strength per square inch. " a = sectional area in inches.  Then we have T = Sa.

Now to find the necessary sectional area for resisting any strain, we have the following general formula: 

T
a = —–­
S

[TeX:  $a = \frac{T}{S}$]

or, by substituting the working strengths for the various materials in the formula, we have for wood,

a = T/2000

Wrought Iron, a = T/1500

Cast Iron, a = T/4500

But, in practice, cast iron is seldom used except to resist compression.

=Strains of Compression.= Allowing the same letters to denote the same things as above, we have for

  Wood, a = T/1000

  Wrought Iron, a = T/12000

  Cast Iron, a = T/25000

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 sbd squared
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