ch01-03 stress & strain & properties
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02 Solutions 46060 5/6/10 1:45 PM Page 14<br />
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*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