(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 × 1.2 ) × 0.6 + B y ( 1.2 ) = 0 B y = 0.6 w Determine the vertical reaction at point A by resolving the vertical component of forces. ∑ F y = 0 A y − ( w × 1.2 ) + B y = 0 A y − 1.2 w + 0.6 w = 0 A y = 0.6 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 − 0.6 w x = 0 M + w x 2 2 − 0.6 w x = 0 M = 0.6 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 300 mm for h , 120 mm for a , and 0.6 m for x . 300 = 120 + k ( 0.6 ) k = 300 − 120 0.6 = 300 mm/m 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 ( 0.6 w x − w x 2 2 ) for M and 1 6 b ( a + k x ) 2 for S . σ = 0.6 w x − w x 2 2 1 6 b ( a + k x ) 2 = 3.6 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. d σ d x = d ( 3 (b) To determine Find the maximum normal stress.

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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Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial…

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Chapter 5.5, Problem 149P

(a)

To determine

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

(b)

To determine

Find the maximum normal stress.

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Chapter 5.5, Problem 148P

Chapter 5.5, Problem 150P

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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 maximum normal stress.

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