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(a) If the shaft is subjected to an external torque T at point b, find the angle of twist of point b with respect to point a. (b) If the shaft is subjected to an external torque T at point a, as shown in Figure 1.2, find the angle of twist of point a with respect to point b.

(a) If the shaft is subjected to an external torque T at point b, find the angle of twist of point b with respect to point a. (b) If the shaft is subjected to an external torque T at point a, as shown in Figure 1.2, find the angle of twist of point a with respect to point b.

International Edition---engineering Mechanics: Statics, 4th Edition
International Edition---engineering Mechanics: Statics, 4th Edition
4th Edition
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:Andrew Pytel And Jaan Kiusalaas
Chapter9: Moments And Products Of Inertia Of Areas
Section: Chapter Questions
Problem 9.74P
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A long circular shaft of length L with variable cross-section is fixed onto rigid walls as shown in Figure 1.1. The polar moment of inertia of the L/3-long segment (J₁) with a larger cross section is three times larger than that of a 2L/3-long segment (J2) on the right. Assume the shear modulus is constant and equal to G for the entire shaft and that strains are small and linear elastic. a b L/3 L/3 L/3 Figure 1.1. Shaft with variable cross-section and external torque T. (a) If the shaft is subjected to an external torque T at point b, find the angle of twist of point b with respect to point a. (b) If the shaft is subjected to an external torque T at point a, as shown in Figure 1.2, find the angle of twist of point a with respect to point b. T J₂ b L/3 L/3 L/3 Figure 1.2. Shaft with variable cross-section and external torque T.
Transcribed Image Text:A long circular shaft of length L with variable cross-section is fixed onto rigid walls as shown in Figure 1.1. The polar moment of inertia of the L/3-long segment (J₁) with a larger cross section is three times larger than that of a 2L/3-long segment (J2) on the right. Assume the shear modulus is constant and equal to G for the entire shaft and that strains are small and linear elastic. a b L/3 L/3 L/3 Figure 1.1. Shaft with variable cross-section and external torque T. (a) If the shaft is subjected to an external torque T at point b, find the angle of twist of point b with respect to point a. (b) If the shaft is subjected to an external torque T at point a, as shown in Figure 1.2, find the angle of twist of point a with respect to point b. T J₂ b L/3 L/3 L/3 Figure 1.2. Shaft with variable cross-section and external torque T.
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