   # A simple beam AB of length L is loaded at the left-hand end by a couple of moment M Q (see figure). Determine the angle of rotation 0 , at support A. (Obtain the solution by determining the strain energy of the beam and then using Castigliano's theorem.) ### 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 9, Problem 9.9.1P
Textbook Problem
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## A simple beam AB of length L is loaded at the left-hand end by a couple of moment MQ(see figure).Determine the angle of rotation 0 , at support A. (Obtain the solution by determining the strain energy of the beam and then using Castigliano's theorem.) To determine

The angle of rotation .

### Explanation of Solution

Given information:

Length=LMoment=Mo

Formula used:

Moment=F×D

U=M2dx2EI=Mo22EI0L(1xL)2dx

θA=dUdMo

Calculation:

Let us calculate the reaction at point A;

RA=MoL.......(downward)

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