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GATE 2018 ME (ME2) – Question 43

Mechanics of Materials · Stress, strain and elastic constants · 2 marks · Multiple choice

A bimetallic cylindrical bar of cross-sectional area 1 m² bonds steel (E = 210 GPa) and aluminium (E = 70 GPa) as shown, with both outer ends clamped. Find the interface force P (kN) in the indicated direction to maintain tensile strain $10^{-6}$ in steel and compressive strain of the same magnitude in aluminium.

Diagram for GATE 2018 ME (ME2) question 43
  1. 70
  2. 140
  3. 210
  4. 280

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Show answer and explanation

Correct answer: (D) 280

Explanation

Steel tension is $E_sA\varepsilon=210\times10^9(1)(10^{-6})=210$ kN. Aluminium compression is $70\times10^9(1)(10^{-6})=70$ kN. Both resist the interface’s displacement, so required force is their sum: **280 kN, D**.