ch01-03 stress & strain & properties
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02 Solutions 46060 5/6/10 1:45 PM Page 5<br />
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2–10. The corners B and D of the square plate are given<br />
the displacements indicated. Determine the shear <strong>strain</strong>s at<br />
A and B.<br />
A<br />
y<br />
16 mm<br />
3 mm<br />
D<br />
B<br />
3 mm 16 mm<br />
x<br />
16 mm<br />
C<br />
16 mm<br />
Applying trigonometry to Fig. a<br />
f = tan - 1 a 13<br />
p rad<br />
b = 39.09° a b = 0.6823 rad<br />
16 180°<br />
a = tan - 1 a 16<br />
p rad<br />
b = 50.91° a b = 0.8885 rad<br />
13 180°<br />
By the definition of shear <strong>strain</strong>,<br />
Ag xy B A = p 2 - 2f = p 2<br />
- 2(0.6823) = 0.206 rad<br />
Ans.<br />
Ag xy B B = p 2 - 2a = p 2<br />
- 2(0.8885) = -0.206 rad<br />
Ans.<br />
5
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