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STRENGTH OF MATERIALS. 235
For instance : The beam a in Fig-
ure 5 is four times as strong as the
beam b, if placed on the edge, as shown
in the figure, and loaded on the top ;
but a would be only twice as strong as
b if it was laid on the side and loaded
on top.
U.4in.„
Fig. 5.
1
W
JS1
h-4in. -h
00
|
a b
Formulas and Rules for Calculating Transverse Strength
of Beams.
The fundamental formula for transverse stress in beams is:
Bending Moment = Resisting Moment.
The bending moment for a beam fixed at one end and
loaded at the other (see Fig. 1) is obtained by multiplying the
load by the horizontal distance from the neutral axis to the
point where the load is applied. The distance is taken in
inches and the load in pounds.
The resisting moment is obtained by multiplying the mo-
ment of inertia by the unit stress, tensile or compressive, upon
the fiber most remote from the neutral axis, and dividing the
product by the distance from this fiber to the neutral axis.
The theoretical formula for the transverse strength of a
beam fastened in a horizontal position at one end and loaded at
the extremity of the other end, as shown in Fig. 6, is,
SX /
P =
L X a
When the beam is fastened at one end and loaded evenly
throughout its whole length, as shown in Fig. 7, the formula
will be,
SX I
P = 2 X
LX a
When a beam is placed in a horizontal position and sup-
ported under both ends and loaded in the middle (see Fig. 8)
the formula is,
/ = 4X f
X l
L X a
When a beam is placed in a horizontal position and sup-
ported under both ends and loaded throughout its whole length
(see Fig. 9), the formula will be,
S X I
P=S X
LX a
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