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244 STRENGTH OF MATERIALS.
loading and support is as shown in Fig. 22. Where will it
break ? and what is the breaking load ?
FIG. 22.
\
Solution
:
The reaction at y will be }i of the load and the reaction
at x will be ft of the load. The beam will evidently break
either at a, b or n. (Find constant C in Table No. 30 and.
multiply by 0.6, because the beam is round).
Solving for strength at n :
23
X 500 X 0.G
H P =
P =
3
8 X 300 X 8
3X3
P = 213Sy
3 pounds.
Solving for strength at b :
33
X 500 X 0.0
P
5
27 X 300 X I
5X3
P = 4320 pounds.
Solving for strength at a :
23
X 500 X 0.0
P
2
p _ 8 X 300 X 8
5X2
P = 1920 pounds.
Thus, the weakest place in the beam is at a, where it will
break when loaded at b with 1920 pounds. If the load is moved
nearer u, it will at a certain point exert the same breaking stress
on both a and n.
Regular beams of this kind are seldom dealt with, but shafts
or spindles of similar shape and loaded in a similar manner are
frequently used, and their strength and stiffness may be calcu-
lated and their weakest spot ascertained by this way of reason-
ing, which applies as well to hollow as to solid shafts and
spindles made from wrought iron, steel or cast-iron.
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