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SHAFTING. 361
Formula 1, expressed as a rule, will be
:
Multiply the distance between hangers, measured in feet,
by the transverse load in pounds ; divide this product by 144. and
the cube root of the quotient will be the diameter of the shaft
in inches, calculated with 10 as factor of safety for transverse
strength, but besides strength it is also absolutely necessary to
consider stiffness and allowable deflection.
Shaft not Loaded at the Middle Between the Hangers.
When a shaft is not loaded at the middle of the span, but
somewhere toward one of the hangers, it will carry a heavier
load, with the same degree of safety, than it would if loaded in
the middle, and the ratio is in inverse proportion as the square
of half the distance between hangers to the product of the short
and the long ends of the shaft. For instance, a shaft is six feet
between hangers and loaded at the middle. What would be the
difference in transverse strength if it was loaded two feet from
one hanger and four feet from the other?
3X3 = 9 and 2X4 = 8.
Thus, find the transverse load for a shaft when loaded in
the middle, multiply by 9 and divide by 8, and the quotient is
the load which the same shaft will carry with the same degree
of safety against transverse stress, if loaded two feet from one
end and four feet from the other.
This rule only applies to the transverse strength, and not to
the transverse stiffness of the shaft. For different shapes of
shafts and different modes of loading, see beams, pages 243-244.
When shafts are heavily loaded near one hanger, and the hanger
on the other side of the pulley is further off, most of the load is
thrown on the bearing nearest to the pulley, and this bearing is,
therefore, liable to heat and to cause trouble, even if the shaft
is both stiff and strong enough. ( See reaction on the support
of beams, page 252).
Transverse Deflection in Shafts.
The transverse deflection in a shaft may be calculated by
the formula
:
4 3
^=V £
TC Z
HSB’
s * w c
w— S D± s _ L*W C
S = Deflection in inches.
D = Diameter of shaft in inches.
L = Length of span in feet.
W= Load on middle of shaft in pounds.
C= Constant = 1.7 X constant in Table No. 31, and for
wrought iron or Bessemer steel may be taken as 0.00002652.
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