A beam carrying a uniform load is simply supported with the supports set back a distance a

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A beam carrying a uniform load is simply supported with the supports set back a distance a from the ends as shown in the figure. The bending moment at x can be found from summing moments to zero at section x:
ΣM = M + ½ w(a + x)2 €“ ½ wlx = 0
Or
M = w/2 [lx €“ (a + x)2]
Where w is the loading intensity in lbf/in. The designer wishes to minimize the necessary weight of the supporting beam by choosing a setback resulting in the smallest possible maximum bending stress.
(a) If the beam is configured with a = 2.25 in, l = 10 in, and w = 100 lbf/in, find the magnitude of the severest bending moment in the beam.

A beam carrying a uniform load is simply supported with

(b) Since the configuration in part (a) is not optimal, find the optimal setback a that will result in the lightest-weightbeam.

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Shigleys Mechanical Engineering Design

ISBN: 978-1121345317

9th edition

Authors: Richard G. Budynas, J. Keith Nisbett

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