To determine The magnitude of the largest elastic load ( P ) that can be applied to the assembly. Explanation Given information: The shank of the steel bolt has a bronze sleeve. The modulus of elasticity of the steel ( E st ) is 200 GPa . The modulus of elasticity of the bronze ( E br ) is 100 GPa . The yield stress of the steel ( σ Y ) st is 640 MPa . The yield stress of the bronze ( σ Y ) br is 520 MPa . The diameter shank of the bolt ( d b ) is 10 mm . The outer diameter of the sleeve ( d s ) is 20 mm . Calculation: Calculate the area of the bolt shank ( A b ) : A b = π 4 d b 2 (1) Substitute 10 mm for d b in Equation (1). A b = π 4 × 10 2 = 25 π mm 2 Calculate the area of the sleeve ( A s ) : A s = π 4 ( d s 2 − d b 2 ) (2) Substitute 20 mm for d s and 10 mm for d b in Equation (2). A s = π 4 × ( 20 2 − 10 2 ) = 75 π mm 2 Show the free-body diagram of the assembly as in Figure 1. Refer Figure 1. Here, P b is force of the bolt shank and P 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 P − P b − P s = 0 P = P b + P s (3) The deformation of the bolt ( Δ b ) is equal to deformation of the sleeve ( Δ s ) . Δ b = Δ s P b L A b E s t = P s L A s E b r P b A b E s t = P s A s E b r (4) Substitute 25 π mm 2 for A b , 75 π mm 2 for A s , 200 GPa for E s t , and 100 GPa for E b r in Equation (4). P b 25 π × ( 200 GPa × 1 kN/mm 1 GPa ) = P s 75 π × ( 200 GPa × 1 kN/mm 1 GPa ) 6

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ISBN: 9789810694364

Author: Russell C Hibbeler

Publisher: Pearson Education

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Chapter 4.9, Problem 4.96P

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The magnitude of the largest elastic load (P) that can be applied to the assembly.

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