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

## 01 Solutions 46060

01 Solutions 46060 5/6/10 2:43 PM Page 48 © 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. 1–70. The pedestal supports a load P at its center. If the material has a mass density r, determine the radial dimension r as a function of z so that the average normal stress in the pedestal remains constant. The cross section is circular. P r 1 z r Require: s = P + W 1 A dW dA = P + W 1 = s A = P + W 1 + dW A + dA P dA + W 1 dA = A dW dA = p(r + dr) 2 - pr 2 = 2p r dr (1) dW = pr 2 (rg) dt From Eq. (1) pr 2 (rg) dz = s 2p r dr r rg dz = s 2 dr z r rg dz = 2s L0 L rg z 2s = ln r r 1 ; r = r 1 e ( p 2a )z However, s = P p r 1 2 r 1 dr r r = r 1 e (p r12 rg ) 2P z Ans. 48

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