(a) Explanation Given information: The uniform thickness of the beam is h . The length of the beam is L . The width of the beam is b . The maximum width of the beam is b 0 . Calculation: Consider a section from free end of the beam. Draw the free-body diagram of the section as in Figure 1. Determine the moment at the section by taking moment about the section. ∑ M = 0 − M − w ( L − x ) × ( L − x ) 2 = 0 − M − w ( L − x ) 2 2 = 0 M = − w ( L − x ) 2 2 Determine the section modulus ( S ) of the beam using the relation. S = | M | σ a l l Here, the allowable stress in the beam is σ a l l . Substitute w ( L − x ) 2 2 for | M | . S = w ( L − x ) 2 2 σ a l l = w ( L − x ) 2 2 σ a l l Determine the section modulus ( S ) of the rectangular cross section using the relation. S = 1 6 b h 2 Here, the width of the beam is b and the depth of the beam is h . Substitute w ( L − x ) 2 2 σ a l l for S (b) To determine The maximum allowable value of w .

7th Edition

ISBN: 9780073398235

Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David F. Mazurek

Publisher: McGraw-Hill Education

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Chapter 5.5, Problem 139P

(a)

To determine

Express b in terms of x, L, and b0.

(b)

To determine

The maximum allowable value of w.

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Chapter 5.5, Problem 138P

Chapter 5.5, Problem 140P

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Express b in terms of x , L , and b 0 .

Solution Summary: The author describes the expression for b in terms of x, L, and b_0.