Compatibility Condition:

Total strain in steel = Total strain in copper

 i.e. 3 × 10^{- 4}  + 1.965 × 10^{- 5} Ps  = 4.5 × 10^{- 4}  + 1.8421 × 10^{- 5} P_c

 Recognising that P_c = - P_s, and dividing both sides by 10^{- 5}, we get

30 + 1.965 P_s = 45 - 1.8421 P_s

or P_s = 45 - 30 /(1.965 + 1.8421)  = 3.94 kN

∴ Stress in steel

= 3.94 × 1000  / (π /4)× 182

= 15.5 N/mm²

∴ Stress in copper = - 3.94 × 1000/ ((π/4) (30² - 18²)) = - 8.71 N/mm²

Note

 Rise in temperature shall cause thermal stresses only if α of tube material is greater than α of bolt material. It α of tube material is smaller; the assembly shall become loose because of rise in temperature, while thermal stresses shall be induced because of fall in temperature.