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STRENGTH OF MATERIALS. 259
6*= Deflection in inches.
L = Length of span in feet.
P = Load in pounds.
IV= Weight of beam in pounds.
c = Constant obtained from experiments, or may be ob-
tained from Table No. 31,
For meaning of the other letters, see figure opposite each
formula.
A round beam equal in diameter to the side of a square
beam will deflect 1.698 times as much, and for convenience,
when the deflection of a square or a rectangular beam, whether
solid or hollow, is known, it may be multiplied by 1.7, and the
product is the deflection of a corresponding round, oval, or
elliptical beam of the same material and diameter and laid in
the same relative position and loaded in the same manner as
the calculated beam. It is well to remember that a round or
elliptical beam weighs a little less than a square or rectangular
one, when the sides and diameters are equal, and the deflection
due to its own weight is, therefore, a little less.
TABLE No. 3 1.—Constant c,
Giving deflection in inches per pound of load when a beam one
foot long and one inch square is supported at both ends and
loaded at the center.
Material Constant c. Material. Constant c.
Cast steel,
Wrought iron,
Machinery steel
Cast-iron,
0.0000144*
0.0000156*
0.C000156
0.0000288
Pitch pine,
Spruce,
Pine,
OOO odd000 000
CO
CO
K)
CO
Ol
^
Example.
A beam 6" X 9" of pitch pine, 10 feet long, supported
under both ends, is to be loaded at the center with one-tenth
of its breaking load. Find the load and deflection.
Solution
:
92
X 6 X 4 X 150 291600 __.. ,
2916 pounds.
p 10 X 10
Deflection will be,
103
X 2916 X 0.00024
6- =
93
X 6
100
699.84
4374
= 016 inch.
* The constant 0.0000144 corresponds to a modulus of elasticity of
30,000,000 and the constant 0000156 corresponds to a modulus of elasticity
of 28,000,000 pounds per square inch.
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