(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 top width as zero. The bottom width and top width of the trapezoid cross-section are b 1 = 2.5 in . and b 2 = 0 . 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 2.5 in . for b 1 , 0 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 × ( 2.5 + 0 ) ( 2.5 × 5 − 0 × 2 ) ln 5 2 − 3 × ( 2.5 − 0 ) = 11.25 12.5 ln ( 2.5 ) − 7.5 = 11.25 11.4536 − 7.5 = 11.25 3.953 R = 2.845 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 . 2 Calculate the mean radius ( r ¯ ) of the curved bar using the relation: r ¯ = r 1 + 1 3 h (2) Substitute 2 in (b) To determine Find the stress at point B .

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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Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial …

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Chapter 4.10, Problem 181P

(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 180P

Chapter 4.10, Problem 182P

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Mechanics of Materials, 7th Edition

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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 trapezoid with top width as zero.