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# ch01-03 stress &amp; strain &amp; properties

## 03

03 Solutions 46060 5/7/10 8:45 AM Page 23 © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. *3–32. A shear spring is made by bonding the rubber annulus to a rigid fixed ring and a plug. When an axial load P is placed on the plug, show that the slope at point y in the rubber is dy>dr =-tan g = -tan1P>12phGr22. For small angles we can write dy>dr = -P>12phGr2. Integrate this expression and evaluate the constant of integration using the condition that y = 0 at r = r o . From the result compute the deflection y = d of the plug. r o d P r i r y h y P Shear Stress–Strain Relationship: Applying Hooke’s law with t A = . 2p r h g = t A G = P 2p h G r dy dr P = -tan g = -tan a 2p h G r b (Q.E.D) If g is small, then tan g = g. Therefore, At r = r o , y = 0 Then, y = P 2p h G ln r o r At r = r i , y = d dy dr = - P 2p h G r P dr y = - 2p h G L r y = - 0 = - C = P 2p h G ln r + C P 2p h G ln r o + C P 2p h G ln r o d = P 2p h G ln r o r i Ans. 23

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