Explanation Given information: The shaft has a radius of 30 mm. Consideration: The modulus of rigidity for A-36 steel is G = 75 GPa . Express the equation for torsional strain energy as follows: U i = ∑ T 2 L 2 G J = ( ( T A B ) 2 L A B 2 G J ) + ( ( T B C ) 2 L B C 2 G J ) + ( ( T C D ) 2 L C D 2 G J ) (1) Here, T A B is the torsion in the section AB , L A B is length of the member AB , G is torsional rigidity, J is the polar moment of inertia of the shaft, T B C is the torsion in the section BC , L B C is length of the member BC , T C D is the torsion in the section CD , and L C D is length of the member CD . Section AB : Show the free-body diagram of the cross-section AB as in Figure 1. Refer to Figure 1. Moment about x -direction: ∑ M x = 0 T A B = 0 The torsion in the section AB is T A B = 0 . Section BC : Show the free-body diagram of the cross-section BC as in Figure 2. Refer to Figure 2. Moment about x -direction: ∑ M x = 0 T B C − 3 = 0 T B C = 3 kN-m The torsion in the section BC is T B C = 3 kN-m . Section CD : Show the free-body diagram of the cross-section CD as in Figure 3. Refer to Figure 3. Moment about x -direction: ∑ M x = 0 T C D − 3 + 4 = 0 T C D = − 1 kN-m The torsion in the section CD is T C D = 1 kN-m

9th Edition

ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

See similar textbooks

Concept explainers

Strain energy

The term strain indicates the variation in an object's length, area, and volume when the object is subjected to an external force. The external force may be of normal, shear, moment, torque, etc. The strain in an object depends on the types of external f…

Videos

Question

Chapter 14.2, Problem 14.4P

To determine

the torsional strain energy in the A-36 steel shaft.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.2, Problem 14.3P

Chapter 14.2, Problem 14.5P

Students have asked these similar questions

B/40 The body is constructed of a uniform square plate, a uniform straight rod, a uniform quarter‐circular rod, and a particle (negligible dimensions). If each part has the indicated mass, determine the mass moments of inertia of the body about the x‐, y‐, and z‐axes. Answer Given.

(read image) Answer:

(read image) Answer Given

Chapter 14 Solutions

Mechanics of Materials

Ch. 14.2 - A material is subjected to a general state of...Ch. 14.2 - The strain-energy density for plane stress must be...Ch. 14.2 - 14–3. Determine the strain energy in the stepped...Ch. 14.2 - Prob. 14.4P Ch. 14.2 - Using bolts of the same material and...Ch. 14.2 - If P = 60 kN, determine the total strain energy...Ch. 14.2 - Determine the maximum force P and the...Ch. 14.2 - *14–8. Determine the torsional strain energy in...Ch. 14.2 - Determine the torsional strain energy in the A-36...Ch. 14.2 - The shaft assembly is fixed at C. The hollow...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.