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236 STRENGTH OF MATERIALS.
When a beam is laid in a horizontal position, fixed at both
ends and loaded in the middle between fastenings (see Fig. 10),
the formula will be,
P = 8 X ^
L X a
When a beam is laid in a horizontal position, fixed at both
ends and the load evenly distributed over its whole length (see
Fig. 11), the formula will be,
P = 12 X S X l
L X a
P = Breaking load in pounds.
S =. Modulus of rupture, which is 72 times the weight, in
pounds, which will break a beam one inch square and one foot
long when fixed in a horizontal position, as shown in Fig. 6,
and loaded at the extreme end, and which may be taken as
follows :
Cast-iron, 36,000.
Wrought Iron, 50,000.
Spruce and Pine, 9,000.
Pitch Pine, 10,000.
These are the nearest values, in round numbers, of 72 times
the average value of the constant given in Table No. 30.
For the safe load, .S" may be taken as follows :
For timber, 1,000 to 1,200 pounds.
For cast-iron, 3,000 to 5,000 pounds.
For wrought iron, 10,000 to 12,000 pounds.
For steel, 12,000 to 20,000 pounds.
L = Length of beam in inches.
a = The distance in inches from the neutral surface of
the section to the most strained fiber.
/ = Rectangular moment of inertia.
The tables on pages 237 and 238 give the moment of inertia
about the neutral axis X V, and the distance a, for a few of the
most common sections
:
(For explanation of moment of inertia and center of gravity
see page 293).
These formulas have the great advantage of being theoretic-
ally correct for beams of any shape of cross-section, made from
any material, providing the load is within the elastic limit of
the beam, and a correct constant is used for .5* and the correct
value obtained for the moment of inertia.
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