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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 modulu is constant and equal to G for the entire shaft and that strains are small and linear elastic. L/3 a b 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. J2 L/3- L/3 L/3

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 modulu is constant and equal to G for the entire shaft and that strains are small and linear elastic. L/3 a b 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. J2 L/3- L/3 L/3

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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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 modulu is constant and equal to G for the entire shaft and that strains are small and linear elastic. L/3 a b 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. J2 L/3- L/3 L/3
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 modulu is constant and equal to G for the entire shaft and that strains are small and linear elastic. L/3 a b 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. J2 L/3- L/3 L/3
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