GATE 2019 CE (CE2) – Question 47
The frame shown has an internal hinge G and linear elastic springs at H, with $k_x=k_y=5\times10^5\ \mathrm{kN/m}$ and $k_\theta=3\times10^5\ \mathrm{kN\,m/rad}$. A 30 kN·m moment acts at F. Find rotation of the rotational spring at H (degrees), to three decimal places.
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Correct answer: .005 to .007
Explanation
The roller at E supplies no horizontal reaction. Moment equilibrium of the left subframe gives vertical hinge force $30/3=10$ kN. Across the right 3 m arm this transmits 30 kN·m to the rotational spring. Rotation is $30/(3\times10^5)=0.0001$ rad, or **0.006°** after three-decimal rounding.