# Chap5 (1) - M. Vable Mechanics of Materials: Chapter 5...

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M. Vable Mechanics of Materials: Chapter 5 5-1 Printed from: http://www.me.mtu.edu/~mavable/MoM2nd.htm Torsion of Shafts Shafts are structural members with length significantly greater than the largest cross-sectional dimension used in transmitting torque from one plane to another. Learning objectives Understand the theory, its limitations and its applications for design and analysis of Torsion of circular shafts. Develop the discipline to visualize direction of torsional shear stress and the surface on which it acts.

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M. Vable Mechanics of Materials: Chapter 5 5-2 Printed from: http://www.me.mtu.edu/~mavable/MoM2nd.htm C5.1 Three pairs of bars are symmetrically attached to rigid discs at the radii shown. The discs were observed to rotate by angles , , and in the direction of the applied torques T 1 , T 2 , and T 3 respectively. The shear modulus of the bars is 40 ksi and the area of cross-section is 0.04 in 2 . Determine the shear strains in bars AB, CD, and EF. φ 1 1.5 ° = φ 2 3.0 ° = φ 3 2.5 ° =
M. Vable Mechanics of Materials: Chapter 5 5-3 Printed from: http://www.me.mtu.edu/~mavable/MoM2nd.htm Internal Torque 5.1 Equation is independent of material model as it represents static equiv- alency between shear stress and internal torque on a cross-section T ρ V d A ρ τ x θ A d A ==

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M. Vable Mechanics of Materials: Chapter 5 5-4 Printed from: http://www.me.mtu.edu/~mavable/MoM2nd.htm C5.2 A hollow titanium (G Ti = 36 GPa) shaft and a hollow Alumi- num (G Al = 26 GPa) shaft are securely fastened to form a composite shaft as shown in Fig. C5.2. The shear strain γ x θ in polar coordinates at the section is where ρ is in meters and the dimensions of the cross-section are d i = 40 mm, d Al = 80 mm and d Ti = 120 mm. Deter- mine the equivalent internal torque acting at the cross-section. Fig. C5.2 γ x θ 0.05 ρ = d T i A l x θ Titanium Aluminum ρ
M. Vable Mechanics of Materials: Chapter 5 5-5 Printed from: http://www.me.mtu.edu/~mavable/MoM2nd.htm Theory for Circular Shafts Theory Objective (i) to obtain a formula for the relative rotation ( φ 2 - φ 1 ) in terms of the internal torque T .

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## This note was uploaded on 04/20/2010 for the course E M 319 taught by Professor Rodin during the Spring '07 term at University of Texas at Austin.

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Chap5 (1) - M. Vable Mechanics of Materials: Chapter 5...

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