(a) Explanation Given information: The moment ( M ) is 5 kip ⋅ in . . The height ( h ) of the cross-section is 3 in . The inner ( r 1 ) and outer radius ( r 2 ) of the curved bar is 2 in . and 5 in . . Calculation: Consider the cross-section of the bar as trapezoid with bottom width as zero. The bottom width and top width of the trapezoid cross-section are b 1 = 0 in . and b 2 = 2.5 in . Show the formula for the radius ( R ) of the neutral surface for the trapezoidal cross-section as follows: R = 1 2 h 2 ( b 1 + b 2 ) ( b 1 r 2 − b 2 r 1 ) ln r 2 r 1 − h ( b 1 − b 2 ) (1) Substitute 0 for b 1 , 2.5 in . for b 2 , 2 in . for r 1 , 5 in . for r 2 , and 3 in . for h in Equation (1). R = 1 2 × 3 2 × ( 0 + 2.5 ) ( 0 × 5 − 2.5 × 2 ) ln 5 2 − 3 × ( 0 − 2.5 ) = 11.25 − 5 ln ( 2.5 ) + 7.5 = 11.25 − 4.581 + 7.5 = 11.25 2.919 R = 3.85405 in . Calculate the cross-section area ( A ) of the bar as follows: Substitute 2.5 in . for b 1 and 3 in . for h . A = 1 2 b 1 h = 1 2 × 2.5 × 3 = 3.75 in (b) To determine Find the stress at point B .

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ISBN: 9780100257061

Author: BEER

Publisher: YUZU

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Chapter 4.10, Problem 182P

(a)

To determine

Find the stress at point A.

(b)

To determine

Find the stress at point B.

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Chapter 4.10, Problem 181P

Chapter 4.10, Problem 183P

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Find the stress at point A .

Solution Summary: The author calculates the stress at point A, based on the cross-section of the bar as trapezoidal with bottom width as zero.