To determine The torque T applied to the shaft. Explanation Given information: Radius of the elastic core is 0.5 in. Calculation: Sketch the shear strain across the shaft as shown in Figure 1. Find shear stress ( τ 1 ) using Shear stress-strain diagram as shown below: τ 1 γ = 10 × 10 3 0.005 τ 1 = 2 × 10 6 γ (1) Find shear stress ( τ 2 ) using Shear stress-strain diagram as shown below: τ 2 − 10 × 10 3 γ − 0.005 = 15 × 10 3 − 10 × 10 3 0.01 − 0.005 τ 2 − 10 × 10 3 γ − 0.005 = 1 × 10 6 τ 2 − 10 × 10 3 = 1 × 10 6 γ − 5 × 10 3 τ 2 = 1 × 10 6 γ + 5 × 10 3 (2) Find the value of maximum shear strain using the stress-strain diagram: γ max = 0.6 in . 0.5 in . ( 0.005 rad ) = 0.006 rad Relate the shear strain ( γ ) and the radius ( ρ ) function: γ ρ = γ max c γ = γ max c ( ρ ) (3) Substitute 0.6 in. for c and 0.006 rad for γ max in Equation (3). γ = 0.006 rad 0.6 in . ( π ) = 0.01 ρ Substitute 0.01 ρ for γ in Equation (1). τ 1 = 2 × 10 6 ( 0.01 ρ ) = 20 × 10 3 ρ Substitute 0.01 ρ for γ in Equation (1). τ 2 = 1 × 10 6 ( 0.01 ρ ) + 5 × 10 3 = 10 × 10 3 ρ + 5 × 10 3 The expression to find the torque ( T ) in the shaft with radius ( c ) is shown below: T = 2 π ∫ 0 c τ ρ 2 d ρ (4) Rearrange Equation (4) for the shear stress τ 1 and shear stress τ 2

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 5.137P

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The torque T applied to the shaft.

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Chapter 5.10, Problem 5.136P

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