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GATE 2020 CE (CE1) – Question 51

Solid Mechanics · Simple stress and strain relationships · 2 marks · Numerical answer

A rigid uniform weightless horizontal bar connects three vertical members P, Q and R, each of axial stiffness 10 kN/mm. P and R rest on a rigid horizontal surface; Q initially has a 2 mm bottom gap. Load W moves the bar down 5 mm while it stays horizontal. Find W (kN), nearest integer.

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Correct answer: 129 to 131

Explanation

Each outer member shortens 5 mm and carries $10(5)=50$ kN. The middle member engages after 2 mm and shortens 3 mm, carrying 30 kN. Total load is $50+30+50=\mathbf{130}$ kN.