A bimetallic cylindrical bar of cross sectional area 1 m²

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A bimetallic cylindrical bar of cross sectional area 1 m² is made by bonding Steel (Young's modulus = 210 GPa) and Aluminium (Young's modulus = 70 GPa) as shown in the figure. To maintain tensile axial strain of magnitude 10^–6 in steel bar and compressive axial strain of magnitude 10^–6 in Aluminum bar, the magnitude of the required force P(in kN) along the indicated direction is

1. 70
2. 140
3. 210
4. 280

Correct Option: D

Let R_A & R_B be the reation at the supports A & B . For the equilibrium of the bar these reaction must act towards left. so that; R_A + R_B = P
σ_A = ∊Es       σ_B = ∊E_AL
R_A = A∊Es        σR_B = A∊E_AL
R_A = 210KN       R_B = 70 KN
∴ P = R_A +R_B = 70+210uN
P = 280 KN.