Machinery's Handbook, 31st Edition
RECTANGULAR AND ROUND SOLID BEAMS
269
Table 2b. Round Solid Beams
Stress in Extreme Fibers, f lb/in 2 (N/mm 2 )
Diameter of Beam, d inch (mm)
Beam Length, l inch (mm)
Total Load, W lb (N)
Style of Loading and Support
Beam fixed at one end, loaded at the other
d
1018 3
. l d f W 1018 3 =
. d lW f 1018 3 =
. f lW d 1018 3 =
. W d f
l
=
l
Beam fixed at one end, uniformly loaded
d
5092 3
. l d f W 5092 3 =
. d Wl f 5092 3 =
. f Wl d 5092 3 =
. W d f
l
=
l
Beam supported at both ends, single load in middle
d
2546 3
. l d f W 2546 3 =
. d Wl f 2546 3 =
. f Wl d 2546 3 =
. W d f
l
=
l
Beam supported at both ends, uniformly loaded
d
1273 3
. l d f W 1273 3 =
. d Wl f 1273 3 =
. f Wl d 1273 3 =
. W d f
l
=
l
Beam supported at both ends, single unsymmetrical load
a
c
1018 3
. d l Wac f 1018 3 =
. fl Wac d 1018 3 =
d
. ac d fl
a + c = l
W
=
l
Beam supported at both ends, two symmetrical loads
a a d
l , any length . W d f a 5092 3 =
5092 3
. d Wa f 5092 3 =
. f Wa d 5092 3 =
. a d f
W
=
l
These formulas apply to simple beams resting on supports at the ends.
b
b
W
L
If the formulas are used with metric SI units, W = total load in newtons (N); L = total length between supports in millimeters; E = modulus of elasticity in newtons per millimeter 2 (N/mm 2 ); I = moment of inertia of beam section in mm 4 ; a = fraction of length of beam at each end, that is not loaded = b ÷ L ; and f = deflection in mm. The bending moment M max is in newton-millimeters (N·mm). Note: A load due to the weight of a mass of M kilograms is Mg newtons, where g = approximately 9.81 m/s 2 .
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