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27O STRENGTH OF MATERIALS.
Hollow Round Shafts.
In proportion to the amount of material used, around hollow
shaft has more torsional strength than a solid shaft of the same
diameter. This is because the fibers in any shaft exposed to
twisting stress only offer resistance to the load in proportion to
their stretch. Therefore, the fibers near the center are always
in position to offer less resistance than the fibers more remote
from the center.
The formula for torsional strength in round hollow shafts
will be
:
(
D* — d*\
\ D X m J
P — Ultimate breaking load in pounds applied at a leverage
of m feet.
D = Outside diameter of shaft in inches.
d = Inside diameter of shaft in inches.
m = Length of lever in feet.
c = Constant (same as for a solid shaft).
Square Beams Exposed to Torsional Stress.
The theoretical formula for twisting strength (on page 266)
will apply to square as well as round beams. The proportional
strength between a round and a square beam may, therefore, be
compared by using that formula. Let S represent the side of a
square beam and the polar moment of inertia is -} S*.
The distance from the center of the beam to the most
remote fiber in a square beam \s S \f l
/
2 , and, dividing the polar
moment of inertia by this distance, we have,
i ^4
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