Explanation Given information: The assembly consists of a 6061-T6-aluminum member and a C83400-red-brass member that rest on the rigid plates. The modulus of elasticity of the brass ( E b r ) is 14.6 × 10 3 ksi . The modulus of elasticity of the aluminum ( E a l ) is 10 × 10 3 ksi . The vertical load act on the plate is P . The width of each member ( b ) is 8 in . . The length of each member ( L ) is 30 in . . The thickness of aluminum member ( t a l ) is 6 in . . The thickness of brass member ( t b r ) is 3 in . . Calculation: Show the free-body diagram of the cut part of the assembly as in Figure 1. Refer Figure 1. Here, F b r is force of the brass member and F a l is force of the aluminum member. Calculate the vertical forces by applying the equation of equilibrium: Sum of vertical forces is equal to 0. ∑ F y = 0 F b r + F a l − P = 0 F b r + F a l = P (1) Calculate the moment about point O by applying the equation of equilibrium: Sum of moments about point O is equal to 0. ∑ M O = 0 ( F b r × 7.5 ) + ( F a l × 3 ) − ( P × d ) = 0 7.5 F b r + 3 F a l − P d = 0 7.5 F b r + 3 F a l = P d (2) Calculate the cross-sectional area of the brass member ( A b r ) A b r = b t b r (3) Substitute 8 in . for b and 3 in . for t b r in Equation (3). A b r = 8 × 3 = 24 in . 2 Calculate the cross-sectional area of the aluminum member ( A a l ) A a l = b t a l (4) Substitute 8 in . for b and 6 in . for t a l in Equation (4). A a l = 8 × 6 = 48 in

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ISBN: 9789810694364

Author: Russell C Hibbeler

Publisher: Pearson Education

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Chapter 4.5, Problem 4.67P

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The distance (d) for placing of vertical load on the member.

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Chapter 4.5, Problem 4.66P

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The distance ( d ) for placing of vertical load on the member.

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The distance (d) for placing of vertical load on the member.

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