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266 STRENGTH OF MATERIALS.
Allowable Deflection.
The greatest amount of deflection which may be allowed in
different kinds of construction can only be determined by prac-
tical experience and good judgment of the designer. As a rule,
in iron work the deflection is seldom allowed to exceed j-^Vo °f the
span, which is equal to T^, or 0.008 inch per foot of span. Line
shaftings are sometimes allowed to deflect t1
l¥ of the distance
between hangers which is equal to 0.01 inch per foot of span,
but head shafts carrying large pulleys are generally not allowed
to deflect more than 0.005 per foot of span.
In woodwork, considerable more deflection is allowed than
in iron structures. Beams in houses are frequently allowed to
deflect -^0, or even t|q of the span; this is equal to 0.024 to
0.025 inch*, per foot of span. Woodwork to which machinery is
to be fastened must never be allowed to deflect so much. Such
woodwork must always be so stiff that it supports the machinery,
and not vice versaj for instance, in beams or posts by which
hangers and shafting are supported, it is not all-sufficient that
they are strong enough, but they must also always be stiff enough.
In factories it is very important that floor beams as well
as beams supporting heavy shafting have sufficient stiff-
ness as well as strength. Floors in factories are frequently
loaded up to 300 pounds per square foot of surface. For floors
in public buildings, which are never loaded with more than the
weight of the people who can get room, the load will hardly ex-
ceed 150 pounds per square foot of surface. Floors in tene-
ment houses are seldom loaded more than 60 pounds per square
foot.
Slate roofs weigh about 8.5 pounds per square foot of
surface. Snow may be reckoned, when newly fallen, to weigh
5 to 15 pounds per cubic foot, and when saturated with water
it may weigh 40 to 50 pounds per cubic foot. Usual practice is
to allow 15 to 20 pounds per square foot for snow and wind on
roofs.
TORSIONAL STRENGTH.
The fundamental formula for torsional strength is,
Pm= S —
a
Pm = Twisting moment, and is the product of the length
of the arm, m, in inches and the force, P, in pounds.
.5* = Constant computed from experiments, and is some-
times called the modulus of torsion; its value usually agrees
closely to the ultimate shearing strength per square inch of the
material.
J == Polar moment of inertia (see page 297).
a = The distance in inches from the axis about which the
twisting occurs to the most remote part of the cross section.
* 0.025 is one-fortieth inch per foot of span,
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