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STRENGTH OF MATERIALS. 233
TRANSVERSE STRENGTH.
A beam placed in a horizontal position, fastened at one
end and loaded at the other, is exposed to transverse stress,
and will usually bend more or less, as shown (exaggerated) in
Fig. 1, before it will break. The line
F|G -
f *
a b is called the neutral line, and all
,_____^ .,
^ fibres above the neutral line are exposed
"=
:^^5^"llj~ to tensile stress, and all fibers below
~
*"~*^\’x^Nv
are exposed to crushing stress, but the
\*Y neutral fiber is neither stretched nor
y
M^ . compressed. A line drawn in a hori-
/ \ zontal direction, at right angles to, and
^ ^ through the neutral line, is called the
neutral axis with reference to this particular place of the section
of the beam. The neutral axis is considered to pass through
the center of gravity of the section, which, for beams of round,
square or rectangular section, is always in the geometrical cen-
ter. Therefore, all beams of such section will have an equal
amount of material on the upper and under side of the neutral
axis, but it is not always desirable for all materials or for all
kinds of load to have an equal amount of material on both the
side exposed to compression and that exposed to tension. For
instance, cast-iron beams are usually made in T formed sec-
tion and should always be laid so that the largest web is
exposed _
to tensile stress, because cast-iron offers much
more resistance to compression than it does to tension. Cast-
iron beams of such section ought, therefore, to be laid in this
position (T), if fastened at one end and loaded at the other,
but should be laid in this position ( JL ), if they are supported
under both ends and loaded between the supports. If
this is taken into consideration in placing a cast-iron beam, its
ultimate transverse breaking strength is greatly increased, but
under a moderate load the deflection will be practically equal
in either position, because as long as the load is small, well
within the elastic limit, cast-iron will stretch under tensile stress
as much as it will compress under an equal amount of crushing
stress; therefore, the modulus of elasticity for tension and
compression of cast-iron is considered to be equal, but under
increased crushing load the compression becomes less in pro-
portion to the load until the point is reached when the cast-iron
can not compress more, and the casting will break. The
ultimate crushing strength of cast-iron is five to six times as
much as its ultimate tensile strength.
A beam supported under both ends and loaded in the
middle will carry four times as great a load as another beam of
the same size and material fixed at one end and loaded at the
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