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STRENGTH OF MATERIALS. 25
1
Round Wooden Beams.
A round beam has 0-589 times the strength of a square
beam of same length and material, when the diameter is equal
to the side of the square beam. The area of a square beam
compared to the area of the round beam is as 0.7854 to 1 ; there-
fore it might seem as if that also should be the proportion be-
tween their strength, which is the case for tensile, crush-
ing and shearing strength, but not for transverse strength
or for deflection, because the material is not applied to such
advantage in the round beam as it is in the square one. AH
preceding formulas for transverse strength of square beams may
also be used for round beams if only constant C is multiplied
by 0.589, or, say, 0.6.
Thus, the formula for a round beam fastened at one end
and loaded at the other will be :
0.6 C X Z>3
P = ^
Note.—In a round beam, of course, it will be Ds
instead of
Jf2 B for a rectangular one.
Example.
Find the load in pounds which will break a spruce beam 12
feet long and 6 inches in diameter when supported under both
ends and loaded at the center. (Find constant C in Table No. 30.)
Solution
:
4 X 0.6 C X D*
P — L
„ 4 X 0.6 X 125 X 6 X 6 X 6
P = 12
P = 5400 pounds.
To Calculate the Size of Round Beams to Carry a Given
Load When Span is Known.
Where the load and span are known, the diameter of the
beam is calculated, when fastened at one end and loaded at the
other, by the formula :
D = ^
PXLX factor of safety
0.6 C
Rule.
Multiply together the load in pounds, factor of safety and
length of span in feet, divide this product by six-tenths of the
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