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STRENGTH OF MATERIALS. 255
For beams laid in a horizontal position, fastened at one end
and loaded thoroughout the whole length : (See Fig. 7.)
s= p x £S
8 X E X I
For beams laid in a horizontal position, supported under both
ends and loaded at the center: (See Fig. 8).
s _ P X U
48 X E X I
This formula may be transposed and used to calculate
modulus of elasticity from the results obtained when specimens
are tested for transverse stiffness. Deflection should be care-
fully measured but the specimen must not be bent beyond its
elastic limit ; the modulus of elasticity is calculated by the trans-
posed formula
:
E - P-XV
48 X S X I
For a square specimen I is (side of beam)4
divided by 12.
(See moment of inertia, page 237).
(Also see rule for calculating modulus of elasticity,
page 265).
For beams laid in a horizontal position, supported under both
ends and loaded uniformly throughout their whole length : (See
Fig. 9).
s _ 5 X P X Z3
384X^X7
For beams laid in a horizontal position, fixed at both ends,
and loaded at the center : (See Fig. 10).
6-= P x £S
192XEXI
For beams laid in a horizontal position, fixed at both ends and
loaded uniformly throughout their whole length : (See Fig. 11).
S= P x Z3
384 X E X I
In these formulas the definitions of the letters are
:
S = Deflection in inches.
P = Load in pounds.
L = Length of span in inches.
E = Modulus of elasticity in pounds per square inch.
/— Rectangular moment of inertia. (See pages 237-238).
These formulas are applicable to any shape of section
or material, when the load is within the elastic limit.
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