Beams of Uniform Strength Machinery's Handbook, 31st Edition
271
Table 3a. Beams of Uniform Strength Throughout Their Length Type of Beam Description Formula a
d
Load at one end. Width of beam uniform. Depth of beam decreasing towards loaded end. Outline of beam-shape, parabola with vertex at loaded end.
l
2
P l Sbh 6 =
h
P
d
Load at one end. Width of beam uniform. Depth of beam decreasing towards loaded end. Outline of beam, one-half of a parabola with vertex at loaded end. Beam may be reversed so that upper edge is parabolic.
l
2
P l Sbh 6 =
h
P
b
Load at one end. Depth of beam uniform. Width of beam decreasing towards loaded end. Outline of beam triangular, with apex at loaded end.
2
l
P l Sbh 6 =
h
P
b
1 h 2
Beam of approximately uniform strength. Load at one end. Width of beam uniform. Depth of beam decreasing towards loaded end, but not tapering to a sharp point.
l
2
P l Sbh 6 =
h
P
b
Uniformly distributed load. Width of beam uniform. Depth of beam decreasing towards outer end. Outline of beam, right-angle triangle.
l
2
P l Sbh 3 =
h
Total Load = P
b
Uniformly distributed load. Depth of beam uniform. Width of beam gradually decreasing towards outer end. Outline of beam is formed by two parabolas which are tangent to each other at their vertexes at the outer end of the beam.
l
2
P l Sbh 3 =
h Total Load = P
a In the formulas, P = load in pounds; S = safe stress in lb/in 2 ; and a, b, c, h, and l are in inches. If metric SI units are used, P is in newtons (N); S = safe stress in N/mm 2 ; and a, b, c, h, and l are in millimeters.
Copyright 2020, Industrial Press, Inc.
ebooks.industrialpress.com
Made with FlippingBook - Share PDF online