Explanation Given information: Rotation of the propeller is ω = 15 rad / s . The engine develops the power of 900 kW. Thrust on the shaft is F = 1.23 MN . The outer diameter of the shaft is 250 mm. Calculation: Find the power transmission as shown below. T 0 = P ω Here, P is the power transmission and ω is the rotation. Substitute 900 kW for P and 15 rad / s for ω . T 0 = 900 kW × 10 3 N ⋅ m / s 1 kW 15 rad / s = 60 × 10 3 N ⋅ m Sketch the internal torque and forces for the propeller shaft as shown in Figure 1. Find the section properties as shown below. Find the cross sectional area as shown below. Here, d is the diameter of the shaft. Substitute 250 mm for d . A = π ( 250 mm × 1 m 1 , 000 mm ) 2 4 = 0.04909 m 2 Find the polar moment of inertia as shown below. J = π d 4 32 Substitute 250 mm for d . J = π ( 250 mm × 1 m 1 , 000 mm ) 4 32 = 3.835 × 10 − 4 m 4 Find the normal stress as shown below. σ = N A Here, N is the normal force and A is the cross sectional area. Substitute − 1.23 MN for N and 0.04909 m 2 for A . σ = − 1.23 MN × 10 6 N 1 MN 0.04909 m 2 = − 25.056 × 10 6 N / m 2 Convert the unit from N / m 2 to MPa. σ = − 25.056 × 10 6 N / m 2 × 1 MPa 10 6 N / m 2 = − 25

9th Edition

ISBN: 2810014920922

Author: HIBBELER

Publisher: PEARSON

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Chapter 9, Problem 9.90RP

To determine

The maximum in-plane shear stress at any point located on the surface of the shaft.

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Chapter 9, Problem 9.89RP

Chapter 9, Problem 9.91RP

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Chapter 9 Solutions

MECHANICS OF MATERIALS-TEXT

Ch. 9.3 - In each case, the state of stress x, y, xy...Ch. 9.3 - Given the state of stress shown on the element,...Ch. 9.3 - Determine the normal stress and shear stress...Ch. 9.3 - Determine the equivalent state of stress on an...Ch. 9.3 - Also, find the corresponding orientation of the...Ch. 9.3 - Determine the equivalent state of stress on an...Ch. 9.3 - Determine the maximum principal stress at point B.Ch. 9.3 - Determine the principal stress at point C.Ch. 9.3 - Prove that the sum of the normal stresses x + y =...Ch. 9.3 - 9-2. The state of stress at a point in a member is...

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