To determine The state of stress ( σ A , σ B ) at point A and B . The shear stress ( τ A , τ B ) at point A and B . Explanation Given information: Calculation : The outer radius of the shaft is 1.5 in . The inner radius of the shaft is 1 in . Calculation: Show the free body diagram upper cut segment as shown in Figure 1. Here, N is the force acting vertical direction and T is the torque moment. Refer Figure 1: The equilibrium force along horizontal direction is equal to zero. ∑ F x = 0 N − 1 , 200 = 0 N = 1 , 200 lb ∑ M x = 0 T − 3 , 000 = 0 T = 3 , 000 lb ⋅ ft Express to find the area ( A ) of the tubular shaft using the relation: A = π ( R 2 − r 2 ) (1) Here, r is the inner radius and R is the outer radius. Substitute 1.5 in. for R and 1 in. for r in Equation (1). A = π ( 1.5 2 − 1 2 ) = 1.25 π in 2 Calculate the polar moment of inertia ( J ) as follows: J = π 2 ( R 4 − r 4 ) (2) Substitute 1.5 in. for R and 1 in. for r in Equation (2). J = π 2 ( 1.5 4 − 1 4 ) = π 2 4.0625 = 2.03125 π in 4 Determine the state of the stress at point A and B as follows: The normal stress contributed by axial stress only. σ A = σ B = N A (3) Here, N is the normal force and A is the area of the shaft. Substitute − 1 , 200 lb for N and 1.25 π in 2 for A in Equation (3). σ A = σ B = − 1 , 200 1.25 π = 306 psi ( Compression ) Thus, the state of stress at point A is B is 306 psi ( C ) _ Shear stress: Shear stress is contributed by torsion shear stress only

9th Edition

ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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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 8.2, Problem 8.35P

To determine

The state of stress (σA,σB) at point A and B.

The shear stress (τA,τB) at point A and B.

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Chapter 8.2, Problem 8.34P

Chapter 8.2, Problem 8.36P

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The state of stress ( σ A , σ B ) at point A and B . The shear stress ( τ A , τ B ) at point A and B .

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The state of stress (σA,σB) at point A and B. The shear stress (τA,τB) at point A and B.

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The state of stress (σA,σB) at point A and B.

The shear stress (τA,τB) at point A and B.