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256 STRENGTH OF MATERIALS.
For beams of symmetrical section it is more convenient to
use the following equally correct but more practical formulas, by
which the deflection is calculated directly from the size of the
beam by simply using a constant obtained by experiment and
reduced by calculation to a unit beam one foot long and one
inch square, thus avoiding both the use of the modulus of elas-
ticity and the moment of inertia.
When beams are supported under both ends and loaded at
the center, and the weight of the beam itself is not considered,
the following formulas may be used for solid rectangular beams
laid in a horizontal position
:
6" = L3
X P X c
3
H* X B
4
. L
L*X B Xc
SX B
3
X P X c
= 4
H* X B X S
P X c
S xH*X B
Z3
X P
B = L* X P X c
P = //S X B X S
SX H* L*Xc
S = Deflection in inches.
//= Thickness of beam in inches.
B — Width of beam in inches.
L = Length of beam in feet.
P = Load in pounds.
c = Constant obtained by experiment, and is the deflec-
tion, in fractions of an inch, which a beam one foot long and
one inch square will have if supported under both ends and
loaded at the center; the average value for this constant is
given in Table No. 31.
For any other mode of loading, see rules and explanations
on page 261.
In previous formulas and rules, the weight of the beam
itself was not considered. The deflection in a beam caused by
its own weight when it is of rectangular shape and uniform
size, and laid in a horizontal position, is obtained by the
formula,
ux yjwx c
H*X B
When both the weight and the load are to be considered,
the deflection in a solid rectangular beam laid in a horizontal
position, supported under both ends and loaded at the center, is
calculated by the formula,
L*(P+y8lV)c
H*X B
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