Question

Three vertical rods carry a tensile load of 80kN. The area of cross-section of each rod is 400mm². Their temperature is raised by 60°C and the load is now so adjusted that they extend equally. Determine the load shared by each rod. The outer two rods are of steel and the middle one is of brass. 

E_S = 2E_B = 200 GPa, α_S = 11 × 10⁻⁶/°C, α_B = 18 × 10⁻⁶/°C.

Answer 1

In this problem, stresses due to temperature change and external load are combined. Due to temperature change or rise in temperature, there will be tensile stress in the steel rod and compressive stress in the brass rod. Due to an external load, the tensile stress in the steel is more than that in the brass, because E_S > E_B. Due to load adjustment, there is an equal deformation in three bars. 

Say total extension in each rod = δ