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ch01-03 stress & strain & properties

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02 Solutions 46060 5/6/10 1:45 PM Page 14<br />

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently<br />

exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.<br />

*2–24. A square piece of material is deformed into the<br />

dashed position. Determine the shear <strong>strain</strong> at C. g xy<br />

B<br />

y<br />

15.18 mm<br />

C<br />

15 mm<br />

15.24 mm<br />

A<br />

89.7<br />

15 mm D<br />

15.18 mm<br />

x<br />

(g C ) xy = p 2 - ¢ 89.7°<br />

180° ≤p<br />

= 5.24A10 - 3 B rad<br />

Ans.<br />

•2–25. The guy wire AB of a building frame is originally<br />

unstretched. Due to an earthquake, the two columns of the<br />

frame tilt u = 2°. Determine the approximate normal <strong>strain</strong><br />

in the wire when the frame is in this position. Assume the<br />

columns are rigid and rotate about their lower supports.<br />

B<br />

u 2<br />

u 2<br />

Geometry: The vertical displacement is negligible<br />

x A = (1)¢ 2° ≤p = 0.<strong>03</strong>491 m<br />

180°<br />

x B = (4)¢ 2° ≤p = 0.13963 m<br />

180°<br />

3 m<br />

1 m<br />

4 m<br />

A<br />

x = 4 + x B - x A = 4.10472 m<br />

A¿B¿ =23 2 + 4.10472 2 = 5.08416 m<br />

AB = 23 2 + 4 2 = 5.00 m<br />

Average Normal Strain:<br />

e AB =<br />

A¿B¿ -AB<br />

AB<br />

= 5.08416 - 5<br />

5<br />

= 16.8A10 - 3 B m>m<br />

Ans.<br />

14

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