Question

Two speel plates are soldered on the two sides of a copper plate. All plates have equal cross–section A each. The coefficient of thermal expansion of copper and steel are α_C and α_S and their Young’s moduli are Y_C and Y_S . The temperature of the plates is raised by t°C and plates retain their shape; the tension in the copper plate is

(1) \(\frac{AY_c+2Y_s}{2Y_cY_s(a_c-a_s)t}\)

(2) \(\frac{2AY_sY_c(a_c-a_s)t}{Y_c+2Y_s}\)

(3) \(\frac{AY_sY_c(a_c-a_s)t}{Y_c+2Y_s}\)

(4) \(\frac{AY_c+2Y_s}{2Y_cY_s(a_c+a_s)t}\)

Answer 1

 (2) \(\frac{2AY_sY_c(a_c-a_s)t}{Y_c+2Y_s}\)

Let F_S be the tension in each of the steel plates and F_C be tension in copper. Then form Fig

F_C = 2F_S .....(1)

Also, 

Thermal expansion in copper + Elastic compression in copper = Thermal expansion in steel + Elastic elogation in steel.

The tension F_C in copper plate is