Problem 2: A 3/4 inch copper tube (annealed, 30 inches long, 3/4 in ID, 7/8 in OD) is placed in a rigid support and a tensile force is applied until the length has increased by 0.05 in and then released.
a) From Appendix B, the elastic modulus is 17 x 106 psi. The ultimate strength is 32 ksi and the yield strength is 10 ksi. The yield force is
It is true that somewhat more force has to be applied, beyond 1.595 kips, to obtain a permanent set. In fact, the ultimate strength (stress) is 3.2 times larger. As your text points out on page 109, an analysis using the actual stress-strain relationship is beyond the scope of this course. Instead, we use the approximation shown in Figure 2.65. Thus, the maximum force is 1.595 kips.
b) Since the material is elastic up to the yield point, we can use
c) According to the approximation we have decided to use, the force remains constant after reaching the yield point:
d) Note that the material returns along a straight line which is parallel to the original line representing the elastic behavior. Therefore, the permanent set is 0.05 - 0.0176 = 3.24 x 10-2 in.