Question

Three pillars, two of aluminium and one of steel support a rigid platform of 250 kN as shown in Fig. If area of each aluminium pillar is 1200 mm² and that of steel pillar is 1000 mm², find the stresses developed in each pillar.

Take E_s = 2 × 10⁵ N/mm² and E_a = 1 × 10⁶ N/mm²

Answer 1

Let force shared by each aluminium pillar be P_a and that shared by steel pillar be P_s .

∴ The forces in vertical direction = 0 → 

P_a + P_s + P_a = 250 

2P_a + P_s = 250 ...(1) 

From compatibility condition, we get

From eqns. (1) and (2), we get 

P_a (2 + 1.111) = 250 

∴ P_a = 80.36 kN 

Hence from eqn. (1), 

P_s = 250 – 2 × 80.36 = 89.28 kN

∴ Stresses developed are