Explanation Given information: The outer and inner diameter of the pipe is 3 in. and 2.5 in. Calculation: The torsion formula for shear stress in the hollow pipe at point A ( τ A ) is shown below: τ A = T A c J (1) Here, the internal torque at point A is T A , the polar moment of inertia is J , and the outer radius of the segment is c . The polar moment of inertia for a hollow pipe of outer radius r and inner radius r ' is J = π 2 ( r 4 − r ' 4 ) . Outer radius of the hollow shaft is 1.5 in. and the inner radius of the hollow shaft is 1.25 in. The outer radius of the shaft is r . The free body diagram of the pipe to find the internal torque at point A is shown in Figure 1. Use Equilibrium equation to find the internal torque at point A . Sum of moments at x is equal to 0. ∑ M x = 0 T A − 150 ( 2 ) = 0 T A = 300 lb ⋅ ft Substitute r for c and π 2 ( r 4 − r ' 4 ) for J in Equation (1). τ A = T A r π 2 ( r 4 − r ' 4 ) = 2 T A r π ( r 4 − r ' 4 ) Substitute 300 lb ⋅ ft for T A , 1.5 in. for r , and 1.25 in. for r ' . τ A = 2 ( 300 lb ⋅ ft ) ( 1.5 in . ) π ( ( 1.5 in . ) 4 − ( 1.25 in . ) 4 ) = 2 ( 300 lb ⋅ ft ) ( 12 in . 1 ft ) ( 1.5 in . ) π ( ( 1.5 in . ) 4 − ( 1.25 in . ) 4 ) = 1 , 311.57 lb in 2 = 1.31 ksi Therefore, the shear stress developed in the pipe at point A is 1

Statics and Mechanics of Materials (5th Edition)

5th Edition

ISBN: 9780134382869

Author: HIBBELER

Publisher: PEARSON

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Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial…

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Chapter 10.3, Problem 19P

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Find the shear stress in the pipe at point A and B.

Sketch the shear stress on volume elements located at point A and B.

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Chapter 10.3, Problem 18P

Chapter 10.3, Problem 20P

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Statics and Mechanics of Materials (5th Edition)

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Find the shear stress in the pipe at point A and B . Sketch the shear stress on volume elements located at point A and B .

Solution Summary: The free body diagram of the pipe to find the internal torque at point A is shown in Figure 1.

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Find the shear stress in the pipe at point A and B.

Sketch the shear stress on volume elements located at point A and B.

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Chapter 10 Solutions

Find the shear stress in the pipe at point A and B . Sketch the shear stress on volume elements located at point A and B .

Solution Summary: The free body diagram of the pipe to find the internal torque at point A is shown in Figure 1.

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Find the shear stress in the pipe at point A and B. Sketch the shear stress on volume elements located at point A and B.

Want to see the full answer?

Chapter 10 Solutions

Find the shear stress in the pipe at point A and B.

Sketch the shear stress on volume elements located at point A and B.