is affected by the incompressibility
and inextensibility of the material.

The formula for the dimensions of any beam to support a strain
transversely is

4 bd squared
S = ----
l

[TeX: $S = \frac{4 bd^2}{l}$]

S = the ultimate strength in lbs.
b = the breadth in inches.
d = the depth in inches.
l = the length in inches.

=Detrusion.= Detrusion is the crushing against some fixed point, such
as obtains where a brace abuts against a chord, or where a bridge
rests on a bolster; and the shearing of pins, bolts and rivets, also
comes under this head.

=General Abstract.= The resistance to the above mentioned strains
varies as the area of the cross section; so that by doubling the area
we double the strength. Any material will bear a much greater strain
for a short time than for a long one. The working strength of materials,
or the weight which does not injure them enough, to render them unsafe,
is a mooted point, and varies, according to the authority, from 1-3
to 1-10 of the ultimate strength. The ratio of the ultimate strength
to the working strength is called the _factor of safety_.

The following is a table of ultimate and working strengths of
materials, and factors of safety:

Weight Ult. Ult. Working Strengths Factor Safety.
in lbs. Materials. Ext. Comp. Exten. Comp. Tension Comp.

30 Wood. 14,000 7,000 2,000 1,000 7 7
480 Wrou't Iron. 60,000 64,000 15,000 12,000 4 5.33
450 Cast Iron. 18,000 100,000 4,500 25,000 4 4

=Lateral Adhesion.= Lateral adhesion is the resistance offered by the
fibres to sliding past each other in the direction of the grain, as
when a brace is notched into a chord, or tie beam, at its foot, it is
prevented by the lateral adhesion of the fibres from crowding off the
piece, to the depth of the notch, against which it toes. Barlow's
experiments give the lateral adhesion of fir as 600 lbs. per square
inch, and the factor of safety employed varies in practice from 4 to
6, giving a working strength of from 150 to 100 lbs. per square inch.

=TABLE OF COMPRESSIVE RESISTANCE OF TIMBER.=

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