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262 STRENGTH OF MATERIALS,
For beams fixed at both ends and loaded at the center,
multiply c by %.
For beams fixed at both ends with the load distributed
evenly throughout their whole length, multiply c by y%.
For beams fixed at one end and loaded at the other, mul-
tiply c by 16.
For beams fixed at one end with load distributed evenly
throughout their whole length, multiply c by 6.
Example.
A square, hollow beam of cast-iron, 8 inches outside and 6
inches inside diameter, and 9-foot span, supported under both
ends, is loaded at the center with 8000 pounds. How much
will it deflect ?
Solution
:
Weight of beam = 9 X 12 X (8
2 — 62
) X 0.26 = 786 pounds.
c _ 93
X (8000 + H X 786) X 0.0000288
84 — 64
y— 729 X 8492 X 0.0000288
4096 — 1296
s _ 178.291
2800
^=0.064 inch.
Example.
How much would this same beam deflect if the load had
been distributed evenly throughout its whole span ?
Solution
:
y _ 98
X 8786 X H X 0.0000288
"
_
84 — 64
y
_ 115.289
2800
.9 = 0.041 inch.
Example.
A round cast-iron beam of 7 inches outside and 5 inches
inside diameter is 4 feet between supports, with a load of 2000
pounds distributed evenly throughout its span. How much will
it deflect, the weight of beam itself not being considered in the
calculation ?
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