(a) Explanation Given information: The inner radius of the split ring is r 1 = 0.8 in . The diameter of the circular cross-section is d = 0.6 in . The forces applied at the centroid of the cross-section, P = Q = 120 lb . Calculation: Show the forces acting on the cross-section of the ring as shown in Figure 1. Refer Figure 1. Calculate the inner radius ( r A ) and outer radius ( r B ) of the split ring as follows: r A = r 1 = 0.8 in . r B = r 1 + d = 0.8 in .+0 .6 in . =1 .4 in . Calculate the mean radius of the split ring using the relation: r ¯ = 1 2 ( r A + r B ) Substitute 0.8 in . for r A and 1.4 in . for r B . r ¯ = 1 2 ( 0.8 + 1.4 ) = 1.1 in . Calculate the radius ( c ) of the cross-section of the split ring as follows: c = d 2 = 0.6 2 = 0.3 in . Calculate the cross-section area of the split ring as follows: A = π c 2 Substitute 0.3 in . for c . A = π ( 0.3 ) 2 = 0.28274 in . 2 Calculate the radius of the neutral surface ( R ) using the relation: R = 1 2 [ r ¯ + r ¯ 2 − c 2 ] Substitute 1.1 in . for r ¯ and 0.3 in . for c . R = 1 2 [ 1.1 + 1.1 2 − 0.3 2 ] = 1 2 [ 1 (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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Chapter 4.10, Problem 175P

(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 174P

Chapter 4.10, Problem 176P

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Find the stress at point A .

Solution Summary: The author shows the forces acting on the cross-section of the ring as shown in Figure 1.