To determine The average normal stress developed in the bolt shank and sleeve ( σ b and σ s ) . Explanation Given information: Initially the A-36 bolt shank fits snugly against the rigid caps E and F on the 6061-T6 aluminum sleeve. The modulus of elasticity of the steel ( E st ) is 200 × 10 3 N/mm 2 . The modulus of elasticity of the aluminum ( E al ) is 68.9 × 10 3 N/mm 2 . The diameter of the bolt shank ( d b ) is 60 mm . The outer diameter of the sleeve ( D s ) is 250 mm . The thickness of the sleeve ( t ) is 15 mm . The length of the bolt shank ( L b ) is 500 mm . The length of the sleeve ( L s ) is 450 mm . Calculation: Show the free-body diagram of the cut part of the assembly as in Figure 1. Refer Figure 1. Here, F b is force of the bolt shank and F s is force of the sleeve. Calculate the vertical forces by applying the equation of equilibrium: Sum of vertical forces is equal to 0. ∑ F y = 0 F s − F b = 0 (1) When the nut is tightened 3 4 of a turn, the unconstrained bolt will be shortened by deformation due to bolt shank ( δ b ) . Therefore, δ b = 3 4 × 1 = 0.75 mm Calculate the area of the bolt shank ( A b ) : A b = π 4 d b 2 (2) Substitute 60 mm for d b in Equation (2). A b = π 4 × 60 2 = 2827.43 mm 2 Calculate the inner diameter area of the sleeve ( d s ) : d s = D s − 2 t (3) Substitute 250 mm for D s and 15 mm for t in Equation (3). d s = 250 − ( 2 × 15 ) = 220 mm Calculate the area of the sleeve ( A s ) : A s = π 4 ( D s 2 − d s 2 ) (4) Substitute 250 mm for D s and 220 mm for d s in Equation (4). A s = π 4 × ( 250 2 − 220 2 ) = 11074.11 mm 2 Show the initial and final position of the assembly as in Figure 2. Refer Figure 2. Here, δ b is deformation due to bolt shank, δ F b is deformation due to F b , and δ F s is deformation due to F s . Calculate the forces of the bolt shank and sleeve ( F b and F s ) using the deformation: δ b − δ F b = δ F b δ b − F b L b A b E st = F s L s A s E al (5) Substitute 0.75 mm for δ b , 500 mm for L b , 450 mm for L s , 2827

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ISBN: 9789810694364

Author: Russell C Hibbeler

Publisher: Pearson Education

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Chapter 4.5, Problem 4.65P

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The average normal stress developed in the bolt shank and sleeve (σb and σs) .

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Chapter 4.5, Problem 4.64P

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