ch01-03 stress & strain & properties

03 Solutions 46060 5/7/10 8:45 AM Page 8
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3–11. The stress–strain diagram for a steel alloy having an
original diameter of 0.5 in. and a gauge length of 2 in. is
given in the figure. If the specimen is loaded until it is
stressed to 90 ksi, determine the approximate amount of
elastic recovery and the increase in the gauge length after it
is unloaded.
s (ksi)
105
90
75
60
45
30
15
0 P (in./in.)
0 0.05 0.10 0.15 0.20 0.25 0.30 0.35
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007
From the stress–strain diagram Fig. a, the modulus of elasticity for the steel alloy is
E
1
=
60 ksi - 0
0.002 - 0 ; E = 30.0(103 ) ksi
when the specimen is unloaded, its normal strain recovered along line AB, Fig.a,
which has a gradient of E. Thus
Elastic Recovery = 90
E =
Thus, the permanent set is
90 ksi
30.0(10 3 ) ksi
= 0.003 in>in
Ans.
Then, the increase in gauge length is
P P = 0.05 - 0.003 = 0.047 in>in
¢L =P P L = 0.047(2) = 0.094 in
Ans.
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