   # A thin-walled hollow tube AB of conical shape has constant thickness I and average diameters d A and d B at the ends (see figure). Determine the strain energy U oT the tube when it is subjected to pure torsion by torques T, Determine the angle of twist of the tube. Note: Use the approximate formula / ird^tlA for a thin circular ring; see Case 22 of Appendix E. ### Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347 ### Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347
Chapter 3, Problem 3.9.10P
Textbook Problem
3 views

## A thin-walled hollow tube AB of conical shape has constant thickness I and average diameters dAand dBat the ends (see figure). Determine the strain energy U oT the tube when it is subjected to pure torsion by torques T, Determine the angle of twist of the tube. Note: Use the approximate formula / ird^tlA for a thin circular ring; see Case 22 of Appendix E. (a)

To determine

The strain energy of the tube.

### Explanation of Solution

Write the expression for the variable diameter of the cone.

dx=dA+(dBdAL)x

Here, the length of the tube is L , diameter of the tube at A is dA , and the diameter of the tube at B is dB .

Write the expression for the polar moment of inertia for hollow conical tube.

Ipx=πt4dx3 ....... (I)

Here, thickness of the tube is t .

Substitute dA+(dBdAL)x for dx in Equation (I).

Ipx=πt4[dA+( d B d AL)x]3

Write the expression for the amount of strain energy stored in the hollow conical tube.

U=0LT2dx2GIpx....... (II)

Here, modulus of rigidity is G .

Substitute πt4[dA+( d B d AL)x]3 for Ipx in Equation (II)

(b)

To determine

The angle of twist of the tube.

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find more solutions based on key concepts
Briefly describe an alloy.

Precision Machining Technology (MindTap Course List)

For Problems 16.29 through 16.32, show the dimensions of the object on its orthographic views. 16.32 All dimens...

Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)

Determine the couple-vector that is equivalent to the two couples shown.

International Edition---engineering Mechanics: Statics, 4th Edition

What is risk management, and why is it important? Provide an example.

Systems Analysis and Design (Shelly Cashman Series) (MindTap Course List)

Social Media Companies have created policies that employees must follow when participating in social media ando...

Enhanced Discovering Computers 2017 (Shelly Cashman Series) (MindTap Course List)

If your motherboard supports ECC DDR3 memory, can you substitute non-ECC DDR3 memory?

A+ Guide to Hardware (Standalone Book) (MindTap Course List)

What is the range of addresses that might be assigned by APIPA?

Network+ Guide to Networks (MindTap Course List) 