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246 STRENGTH OF MATERIALS.
Solution
:
p _4_C_XJll
/>_ 4X125X6X6X6
8
P = 13,500 pounds.
Note.—C is obtained from Table No. 30, and is multiplied
by 4 because the beam is supported under both ends and loaded
at the center. The beam is square ; therefore the cube of the
thickness is equal to the square of the thickness multiplied by
the width. Consequently, for a square beam (thickness)3 or
(width)3
or square of thickness multiplied by width is the same
thing.
Example 2.
Find the load which will break a spruce beam 8 inches
thick, 4 l
/
2 inches wide, and 8 feet long, supported under both
ends and loaded at the center.
Solution
:
„_ 4CX B X H2
’ ~ L
4X125X4^X8X8
8
P = 18,000 pounds.
Example 3.
Find the load which will break the beam mentioned in
Example 2, if beam is laid flatwise.
4X125X8X4^X4^
b
P = 10,125 pounds.
In the first example the beam is square, 6" X 6" = 36
square inches, and its calculated breaking load is 13,500 pounds.
In the second example the beam is rectangular, 8" X 4*4" =
36 square inches, and laid edgewise its figured breaking load
is 18,000 pounds. In the third example the same beam is laid
flatwise, and its breaking load is only 10,125 pounds. Thus, by
making a beam deep it is possible to secure great strength with
only a small quantity of material, but the limit is soon reached
where it will not be practical to increase the depth at the ex-
pense of the width, because the beam will deflect sidewise and
twist and break if it is not prevented by suitable means. The
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