GATE 2019 CE (CE1) – Question 49
The shown portal frame has a hinge at P and roller at R. A 50 kN horizontal load acts at R. PQ = 5 m, QR = 10 m and each member has $EI=10^6\ \mathrm{kN\,m^2}$. Find horizontal displacement of R (mm), to one decimal place.
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Correct answer: 24.9 to 25.1
Explanation
Apply a unit horizontal force at R. Its moment rises linearly from zero to 10 along the 10 m column and falls from 10 to zero along the 5 m beam. Virtual work gives $$\delta_R=\frac{50}{10^6}\left(\frac{10^3}{3}+\frac{10^2(5)}3\right)=0.025\ \mathrm m.$$ Thus **25.0 mm**. Both members contribute.