(a) Explanation Show the free-body diagram of the prismatic beam as in Figure 1. Determine the vertical reaction at point B by taking moment at point A . ∑ M A = 0 − ( w × 60 ) × 30 + B y ( 60 ) = 0 B y = 30 w Determine the vertical reaction at point A by resolving the vertical component of forces. ∑ F y = 0 A y − ( w × 60 ) + B y = 0 A y − 60 w + 30 w = 0 A y = 30 w Show the free-body diagram of the section as in Figure 2. Determine the moment at the section by taking moment about the section. ∑ M = 0 M + ( w × x ) × x 2 − 30 w x = 0 M + w x 2 2 − 30 w x = 0 M = 30 w x − w x 2 2 Find the height ( h ) of the tapered beam using the relation. h = a + k x Here, the width of the beam at the ends is a , the height of the beam at mid-point is h , and the length of the beam from left end is x . Substitute 8 in. for h , 4 in. for a , and 30 in. for x . 8 = 4 + k ( 30 ) k = 8 − 4 30 = 2 15 in ./in . Find the section modulus ( S ) of the beam 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 ( a + k x ) for h . S = 1 6 b ( a + k x ) 2 Determine the bending stress ( σ ) in the beam using the relation. σ = M S Substitute ( 30 w x − w x 2 2 ) for M and 1 6 b ( a + k x ) 2 for S . σ = 30 w x − w x 2 2 1 6 b ( a + k x ) 2 = 180 w x − 3 w x 2 b ( a + k x ) 2 Apply the condition d σ d x = 0 to determine the location of the maximum bending stress (b) To determine Find the largest distributed load 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 150P

(a)

To determine

Find the distance of the transverse section at which the maximum normal stress occurs.

(b)

To determine

Find the largest distributed load w.

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Chapter 5.5, Problem 149P

Chapter 5.5, Problem 151P

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Chapter 5 Solutions

Mechanics of Materials, 7th Edition

Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.7 and 5.8 Draw the shear and bending-moment...Ch. 5.1 - 5.7 and 5.8 Draw the shear and bending-moment...Ch. 5.1 - 5.9 and 5.10 Draw the shear and bending-moment...Ch. 5.1 - 5.9 and 5.10 Draw the shear and bending-moment...

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Find the distance of the transverse section at which the maximum normal stress occurs.

Solution Summary: The author shows the free-body diagram of the prismatic beam as in Figure 1. Determine the vertical reaction at point A by resolving vertical component of forces.

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Find the distance of the transverse section at which the maximum normal stress occurs.

Find the largest distributed load w.

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Chapter 5 Solutions