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2 60 STRENGTH OF MATERIALS.
Therefore, if this beam had been curved 0.10 inch upward,
by increasing its thickness on the upper side, it would have been
straight after the load was applied.*
In this example the weight of the beam itself is not
considered either in figuring the strength or the deflection,
because the beam is comparatively short in proportion to its
width and thickness. The weight of the beam itself will only
be about 200 pounds, and this will be of no account in propor-
tion to the load that the beam will carry, with 10 as a factor of
safety. The weight of the beam will increase its deflection oniy
0.006 inch. In such a beam the danger is probably greater from
crushing of the ends at the supports, if it has not enough bear-
ing surface. In long beams the weight of the beam must not
be neglected, either in calculating safe load or in calculating
deflection.
Example 2.
A round bar of wrought iron is 5 feet long and 3 inches in
diameter, and loaded at the center with 800 pounds. How much
will it deflect? A round bar of iron 3 inches in diameter and
5 feet long weighs 119 pounds. (See table of weights of iron,
page 143.)
Solution
:
_ 53
X (800 + ’
/s X 11 9) X 1.7 X 0.0000156
^S - ""3""*
S = 0.0359 inch.
Thus, such a shaft loaded with 800 pounds will deflect rffj
of an inch in the length of 5 feet, or 60 inches. If the deflec-
tion must not exceed t^q of the span (see page 266), then the
greatest allowable deflection for this span would be 0.04 inch,
and the calculated deflection is within this limit.
Note.—y-Vo °f the span is equal to a deflection of 0.008
inch per foot of length.
Example 3.
A shaft of machinery steel, 11 inches in diameter and 6 feet
between bearings, carries in the center a 12-ton fly wheel. How
much deflection will the weight of the fly wheel cause ?
Note.—Such shafts are usually considered as a beam sup-
ported under both ends. (See formula for deflection in solid
round beams, page 258.)
Solution:
12 tons = 24.000 pounds. (Weight of shaft is not taken
into consideration.)
* This is a thing frequently done in practice.
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