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. 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. L/3- L/3 b J2 L/3 Figure 1.2. Shaft with variable cross-section and external torque T.
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. 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. L/3- L/3 b J2 L/3 Figure 1.2. Shaft with variable cross-section and external torque T.
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
Related questions
Question
![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.
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.
L/3-
L/3
b
J2
L/3
Figure 1.2. Shaft with variable cross-section and external torque T.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0b19c45c-45ce-4c27-bac7-d4347db4e836%2F7fc44b9c-d30f-403b-a2cf-e1ab47a2e9a1%2F18abkie_processed.jpeg&w=3840&q=75)
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.
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.
L/3-
L/3
b
J2
L/3
Figure 1.2. Shaft with variable cross-section and external torque T.
AI-Generated Solution
Unlock instant AI solutions
Tap the button
to generate a solution
Recommended textbooks for you
![Elements Of Electromagnetics](https://www.bartleby.com/isbn_cover_images/9780190698614/9780190698614_smallCoverImage.gif)
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
![Mechanics of Materials (10th Edition)](https://www.bartleby.com/isbn_cover_images/9780134319650/9780134319650_smallCoverImage.gif)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
![Thermodynamics: An Engineering Approach](https://www.bartleby.com/isbn_cover_images/9781259822674/9781259822674_smallCoverImage.gif)
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
![Elements Of Electromagnetics](https://www.bartleby.com/isbn_cover_images/9780190698614/9780190698614_smallCoverImage.gif)
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
![Mechanics of Materials (10th Edition)](https://www.bartleby.com/isbn_cover_images/9780134319650/9780134319650_smallCoverImage.gif)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
![Thermodynamics: An Engineering Approach](https://www.bartleby.com/isbn_cover_images/9781259822674/9781259822674_smallCoverImage.gif)
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
![Control Systems Engineering](https://www.bartleby.com/isbn_cover_images/9781118170519/9781118170519_smallCoverImage.gif)
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
![Mechanics of Materials (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781337093347/9781337093347_smallCoverImage.gif)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
![Engineering Mechanics: Statics](https://www.bartleby.com/isbn_cover_images/9781118807330/9781118807330_smallCoverImage.gif)
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY