To determine The torque T applied to the shaft. Explanation Given information: The maximum shear strain is 0.01 rad. Calculation: Sketch the shear stress-strain diagram as shown in Figure 1. Refer to Figure 1. The value of maximum shear strain ( γ max ) occurs at the radius ( c ) of the shaft with the value of 0.01 rad. Sketch the shear strain across the shaft as shown in Figure 2. Relate the shear strain ( γ ) and the radius ( ρ ) function: γ ρ = γ max c γ = γ max c ( ρ ) (1) Substitute 0.5 in. for ρ , 0.75 in. for c , and 0.01 rad for γ max in Equation (1). γ = 0.01 rad 0.75 in . ( 0.5 in . ) = 0.006667 rad Find shear stress using Figure 1 as shown below: τ − 10 0.006667 − 0.005 = 15 − 10 0.01 − 0.005 τ − 10 0.001667 = 5 0.005 τ = 11.667 ksi Sketch the shear stress distribution across the shaft as shown in Figure 3. The expression for shear stress in terms of ρ using Figure 1 is shown below: τ − 11.667 ρ − 0.5 = 15 − 11.667 0.75 − 0.50 τ − 11.667 ρ − 0.5 = 3.333 0.25 τ − 11.667 = 13.332 ρ − 6.666 τ = 13.332 ρ + 5.001 The expression to find the torque ( T ) in the shaft with inner radius ( c i ) and outer radius ( c 0 ) is shown below: T = 2 π ∫ c i c 0 τ ρ 2 d ρ (2) Substitute 13

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 5.10, Problem 5.136P

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The torque T applied to the shaft.

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Chapter 5.10, Problem 5.135P

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