compatibility conditiontotal strain in steel

Question

Compatibility Condition:

Total strain in steel = Total strain in copper

i.e. 3 × 10^-4 + 1.965 × 10^-5 P_s  = 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        Ps = 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