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STRENGTH OF MATERIALS. 247
strongest beam which can be cut from a round log is one hav-
ing the thickness 1% times the width. The stiffest beam cut
from a round log has its thickness 1 T\ times its width. The
best beam for most practical purposes which can be cut from a
round log has its thickness \y
2 times its width; for instance,
4 X 6, or 6 X 9, or 8 X 12, etc. The largest side in a beam
having its thickness \y
2 times its width which can be cut from
a round log is found by multiplying the diameter by 0.832. The
diameter required in a round log to be large enough for such a
beam is found by multiplying the largest side of the beam by
1 .2; for instance, the diameter of a round log to cut 6" X 9" will
be 9" X 1.2 = 10.8 inches, or the diameter of a round log re-
quired to cut 8" X 12" will be 12" X 1.2 = 14.4 inches, etc.
To Calculate the Size of Beam to Carry a Given Load.
Most frequently the load and the length of span are known
and the required size of beam is to be calculated. For a rect-
angular beam there would then be two unknown quantities,
the width and the thickness, but if it is decided to use a beam
having its thickness 1 y
2 times its width, the thickness may be
expressed in terms of the width.
H= Thickness.
B = Width.
H=iy
2 B
Use formula for rectangular beams, page 239, and it will
read,
CX (1%B)*XB
L
This will reduce to,
n _ CX2% X B*
L
This will transpose to,
3
B = ^
P
~
C X 2X
Example.
Find width and thickness of a spruce beam 10 feet long,
when fastened at one end and required to carry, with 8 as factor
of safety, a load of 1800 pounds at the other end, the thickness
to be \y
2 times the width.
When the beam is to carry 1800 pounds, with S as a factor
of safety, its breaking load is 8 X 1800 = 14,400 pounds.
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