GATE 2019 CE (CE1) – Question 42
The rigid-jointed frame QRS shown carries P at R. Neglect axial deformation. Both members have length L and stiffness EI. If support S settles by $\Delta=PL^3/(\beta EI)$, its vertical reaction becomes zero when β equals ______.
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Correct answer: (C) 7.5
Explanation
With zero vertical reaction at S, the beam carries all P and the axially inextensible column makes R settle by Δ. Moment balance at R is $-6EI\Delta/L^2+8EI\theta/L=0$, giving $\theta=3\Delta/(4L)$. Beam shear is $$P=\frac{12EI\Delta}{L^3}-\frac{6EI\theta}{L^2}=\frac{7.5EI\Delta}{L^3}.$$ Compare with the given settlement: **β = 7.5, C**.