GATE 2018 CE (CE1) – Question 53
The deformable pin-jointed truss has the geometry, loading and member rigidities shown. Given $E=2\times10^{11}$ N/m², A = 10 mm², L = 1 m and P = 1 kN, horizontal displacement at C, to one decimal, is ______ mm.
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Correct answer: 2.60 to 2.80
Explanation
Joint C equilibrium gives diagonal tension $\sqrt2P$ and vertical compression 3P; the bottom chord carries compression P. Bottom shortening moves the left roller right by $PL/(AE)$, while C moves vertically by $-3PL/(AE)$. Diagonal extension gives $(u_C-u_L+v_C)/\sqrt2=PL/(AE)$. Thus $u_C=(4+\sqrt2)PL/(AE)$. Since $PL/(AE)=0.5$ mm, displacement is 2.7 mm rightward.