Explanation Given information: The allowable stress in the bar is σ = 150 MPa . The applied force P = 3 kN . The inner radius of the curved portion of the bar is r 1 = 20 mm . The outer radius of the curved portion of the bar is r 2 = 45 mm . The thickness of the bar is t = 25 mm . The height of the bar is h = 25 mm . Calculation: Sketch the cross section of the bar as shown in Figure 1. Refer to Figure 1. Reduce the internal force transmitted through the section AB to a force couple system at the centroid of section. Calculate the bending moment ( M ) as shown below. M = P ( a + r ¯ ) Here, a is the permissible distance from the line of action of P and r ¯ is the centroid of the bar. Calculate the distance from the center of curvature of the member to the neutral surface ( R ) as shown below. R = h ln r 2 r 1 (1) Calculate the distance from the centroid of the section to the neutral surface ( e ) as shown below. e = r ¯ − R (2) The location of point A is y A = R − r 1 . Calculate the maximum compressive stress at point A ( σ A ) as shown below. σ A = − P A − M y A A e r 1 Substitute P ( a + r ¯ ) for M and R − r 1 for y A . σ A = − P A − P ( a + r ¯ ) ( R − r 1 ) A e r 1 = − P A ( 1 + ( a + r ¯ ) ( R − r 1 ) e r 1 ) = − K P A (3) Hence, the coefficient K = 1 + ( a + r ¯ ) ( R − r 1 ) e r 1 (4) Calculate the distance from the center of curvature of the member to the neutral surface ( R ) as shown below. Substitute 25 mm for h, 20 mm for r 1 , and 45 mm for r 2 in Equation (1)

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ISBN: 8220100257063

Author: BEER

Publisher: YUZU

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Chapter 4, Problem 199RP

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Find the largest permissible distance a from the line of action of the force P.

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Chapter 4, Problem 198RP

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Find the largest permissible distance a from the line of action of the force P .

Solution Summary: The author calculates the largest permissible distance a from the line of action of the force P.

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Find the largest permissible distance a from the line of action of the force P.

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