Machinery's Handbook, 31st Edition
272
Beams of Uniform Strength Table 3b. Beams of Uniform Strength Throughout Their Length Type of Beam Description Formula a
a c b
Beam supported at both ends. Load concentrated at any point. Depth of beam uniform. Width of beam maximum at point of loading. Outline of beam, two triangles with apexes at points of support.
l
P ac Sbh l 6 2 =
h
P
l
Beam supported at both ends. Load concentrated at any point. Width of beam uniform. Depth of beam maximum at point of loading. Outline of beam is formed by two parabolas with their vertexes at points of support.
b
a
c
P ac Sbh l 6 2 =
b P
Beam supported at both ends. Load concentrated in the middle. Depth of beam uniform. Width of beam maximum at point of loading. Outline of beam, two triangles with apexes at points of support.
b
P l Sbh 3 2 2 =
l
h
P
b
Beam supported at both ends. Load concentrated at center. Width of beam uniform. Depth of beam maximum at point of loading. Outline of beam, two parabolas with vertices at points of support.
P l Sbh 3 2 2 =
l
h P
l b
Beam supported at both ends. Load uniformly distributed. Depth of beam uniform. Width of beam maximum at center. Outline of beam, two parabolas with vertexes at middle of beam.
P l Sbh 3 4 2 =
h Total Load = P
b
Beam supported at both ends. Load uniformly distributed. Width of beam uniform. Depth of beam maximum at center. Outline of beam one-half of an ellipse.
l
P l Sbh 3 4 2 =
h Total Load = P
a For details of English and metric SI units used in the formulas, see footnote on page 271 .
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