Explanation Given information: The force F = 12 lb The angle of the bend shaft is 90 ° . Calculation: Show the free body diagram of bent shaft as shown in Figure 1. N x is normal force in x direction and M x is moment in x direction. Refer to Figure 1: Determine the internal loadings as follows: Refer Figure 1: Apply equilibrium conditions the force in y direction. ∑ F y = 0 N y − 12 = 0 N y = 12 lb Take moment about x axis. ∑ M x = 0 M x − 12 ( 3 ) = 0 M x = 36 lb ⋅ in Take moment about z axis. ∑ M z = 0 M z − 12 ( 8 ) = 0 M z = 96 lb ⋅ in Calculate the moment of inertia ( I ) of the bend shaft as follows: I = 1 4 π r 4 (1) Here, r is the radius of the bent shaft. Substitute 0.625 in. for r in Equation (1). I = 1 4 π ( 0.625 ) 4 = 0.1198 in 4 Calculate the Area ( A ) of the bend shaft as follows: A = π r 2 (2) Substitute 0.625 in. for r in Equation (2). A = π ( 0.625 ) 2 = 1.2272 in 4 Calculate the normal stress ( σ D ) at point D along y axis as follows: ( σ D ) y = N y A − M x z I (5) Here M x moment about x direction, N y is normal force in y direction, I is the moment of inertia, A is the area of the cross section, and z is the distance. Substitute 12 lb for N y , 0.1198 in 4 for I , 1.2272 in 4 for A , 36 lb ⋅ in for M x and 0.625 in. fir z in Equation (5). ( σ D ) y = 12 1.2272 − 36 ( 0.625 ) 0.1198 = 9

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ISBN: 9789810694364

Author: Russell C Hibbeler

Publisher: Pearson Education

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Chapter 8.2, Problem 8.48P

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The stress components (σD) at point D of bent shaft.

The stress components (σE) at point E of bent shaft.

The shear stress (τD) at point D of bent shaft.

The shear stress (τE) at point E of bent shaft.

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Chapter 8.2, Problem 8.47P

Chapter 8.2, Problem 8.49P

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The stress components ( σ D ) at point D of bent shaft. The stress components ( σ E ) at point E of bent shaft. The shear stress ( τ D ) at point D of bent shaft. The shear stress ( τ E ) at point E of bent shaft.

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The stress components (σD) at point D of bent shaft. The stress components (σE) at point E of bent shaft. The shear stress (τD) at point D of bent shaft. The shear stress (τE) at point E of bent shaft.

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Chapter 8 Solutions

The stress components (σD) at point D of bent shaft.

The stress components (σE) at point E of bent shaft.

The shear stress (τD) at point D of bent shaft.

The shear stress (τE) at point E of bent shaft.