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GATE 2016 CE (CE2) – Question 44

Solid Mechanics · Simple stress and strain relationships · 2 marks · Multiple choice

The hinged structural system shown carries $W=100$ kN. Member properties L,A,E are indicated. Let $L=1$ m, $A=0.05$ m$^2$, and $E=30\times10^6$ N/m$^2$. Which set gives force, stress and change in length of horizontal member QR?

Diagram for GATE 2016 CE (CE2) question 44
  1. Compression 25 kN; stress 250 kN/m²; shortening 0.0118 m
  2. Compression 14.14 kN; stress 141.4 kN/m²; extension 0.0118 m
  3. Compression 100 kN; stress 1000 kN/m²; shortening 0.0417 m
  4. Compression 100 kN; stress 1000 kN/m²; extension 0.0417 m

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Show answer and explanation

Correct answer: (C) Compression 100 kN; stress 1000 kN/m²; shortening 0.0417 m

Explanation

At S, symmetry gives each inclined tension W/sqrt2. At Q or R, horizontal components from the upper and lower inclined members together require QR compression W=100kN. Its area2A=0.10m² gives stress1000kN/m². The official option is **C**, but QR=sqrt2L gives shortening NL/(AE)=100000sqrt2/(0.10·30e6)=0.04714m, not the printed0.0417m.