Explanation Given information: The allowable bending stress is 67 ksi. Calculation: Sketch the state of stress point as shown in Figure 1. Section just to the left of point C is the most critical. both state of stress will yield the same result. Calculate the required diameter using maximum distortion energy. σ a , b = σ 2 ± ( σ 2 ) 2 + τ 2 (1) Here, σ is the stress and τ is the shear stress. Substitute A for σ 2 and B for ( σ 2 ) 2 + τ 2 in Equation (1). σ a = ( A + B ) σ b = ( A − B ) Square on both sides. σ a 2 = ( A + B ) 2 σ b 2 = ( A − B ) σ a σ b = ( A + B ) ( A − B ) σ a 2 − σ a σ b + σ b 2 = A 2 + B 2 + 2 A B − A 2 + B 2 + A 2 + B 2 − 2 A B = A 2 + 3 B 2 = σ 2 4 + 3 ( σ 2 4 + τ 2 ) = σ 2 + 3 τ 2 σ a 2 − σ a σ b + σ b 2 = σ allow 2 (2) Substitute σ 2 + 3 τ 2 for σ a 2 − σ a σ b + σ b 2 in Equation (2). σ 2 + 3 τ 2 = σ allow 2 (3) Find the value of moment of inertia ( I ) as shown below: I = π 4 r 4 (3) Here r is the radius of the shaft. Substitute c for r in Equation (3). I = π 4 c 4 Find the value of moment of inertia ( J ) as shown below: J = π 2 r 4 (4) Here, J is the polar moment of inertia. Substitute c for r in Equation (4). I = π 2 c 4 Express the stress as shown below: σ = M c I (5) Here, M is the moment, c is the centroid of the neutral axis, and I is the moment of inertia. Substitute π 4 c 4 for I in Equation (5)

10th Edition

ISBN: 9780134319650

Author: Russell C. Hibbeler

Publisher: PEARSON

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Design of Shafts and Shaft Components

The shaft is basically defined as the machine element that rotates, is in circular cross-section, it is majorly used to transfer the power from one part of the system to another, or from a power generating machine to a power absorbing machine. The shaft …

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Chapter 11.4, Problem 11.44P

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The required diameter (d) of the shaft.

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Chapter 11.4, Problem 11.43P

Chapter 11.4, Problem 11.45P

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Chapter 11 Solutions

Mechanics of Materials (10th Edition)

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The required diameter ( d ) of the shaft.

Solution Summary: The author calculates the required diameter of the shaft using maximum distortion energy.

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The required diameter (d) of the shaft.

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Chapter 11 Solutions