GATE 2017 CE (CE2) – Question 52
For the frame shown, $E=2.5\times10^4$ MPa and $I=8\times10^8$ mm⁴ for all members. The rotation at Q, to one decimal place, is ______ degrees.
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Correct answer: 0.9 to 1.1
Explanation
The overhang transfers net moment $2000(2)-1650(2^2)/2=700$ kN m to Q. With axial deformation neglected, Q has no translation. Each 4 m member ending at a fixed support supplies stiffness $4EI/4$. Since $EI=20000$ kN m², combined stiffness is 40000 kN m/rad. Thus $\theta_Q=700/40000=0.0175$ rad = 1.0° to one decimal.