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264 STRENGTH OF MATERIALS.
Side of the beam — ^
L* P c
A round beam supported under both ends and loaded at the
center may be calculated by the formula
:
Diameter of beam = a/:
Z3
P 1.7 c
S
A rectangular beam supported under both ends and loaded
at the center, and having its depth iy
2 times its width, may be
calculated by the formula :
4
V3
L? P c
——-
—
L = Length of span in feet.
P = Center load in pounds.
S= Given deflection in inches.
c = Constant given in Table No. 31.
Note.—These three formulas are only approximate, as
the weight of the beam itself is not considered ; but if
necessary, after the size of beam is obtained, its weight may
be calculated and five-eighths of it added to the center load,
P\ and using the same formula again, another beam may
be calculated for this new center-load, and this new calculation
will give a beam only a mere trifle too small. Constants in
Table No. 31 are for beams supported under both ends and
loaded at the center. For any other mode of loading or fasten-
ing, constant c must be multiplied according to rules on
page 261.
To Find the Constant for Deflection.
If experiments are made upon rectangular beams, use
formula,
’
S H* B
LHP + n W)
Example.
Calculate the constant c, or deflection in inches per pound
of load, for a beam of 1 foot span and 1 inch square, supported
under both ends and loaded at the center, when experiments are
made upon a pitch pine beam 40 feet long, 12 " by 8", weighing
1200 pounds and deflecting 1% inches for a center-load of 500
pounds.
Solution:
1.5 X 123
X 8
403
X (500 4- H X 1200)
c = 0.000259 inch.
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