Rod elements (1) and (2) shown in Figure 3.2a below are made up of materials having elastic moduli of 2E and E, respectively, and each having a coefficient of thermal expansion of α. Element (1) is hollow, whereas element (2) is solid.
a) For the rods shown in Figure 3.2a, if elements (1) and (2) are given temperature increases of ΔT and 2ΔT, respectively, what is the resulting stress and strain in each element?
b) Suppose now that element (2) is placed concentrically with element (1), with each element connected to ground at end B and joined by a rigid connector at end C, as shown in Figure 3.2b. The rigid connector C enforces the same elongation for the two elements. If again, the rods are given the temperature increases described in a), what is the resulting stress and strain in each element? Assume that there is no heat transfer between the elements at the connector. Compare these answers with that which you found in a) above.
B
c
2d
p
(1)
B
(1)
cross section
L
B
c
d
cross section
(2)
L
cross section
L
Figure 3.2a
Figure 3.2b