GATE 2022 CE (CE1) – Question 51
Consider the linearly elastic plane frame shown in the figure. Members HF, FK and FG are welded together at joint F. Joints K, G and H are fixed supports. A counter-clockwise moment M is applied at joint F. Consider flexural rigidity EI = 105 kN-m2 for each member and neglect axial deformations. If the magnitude (absolute value) of the support moment at H is 10 kN-m, the magnitude (absolute value) of the applied moment M (in kN-m) to maintain static equilibrium is ___________. (round off to the nearest integer)
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Correct answer: 60
Explanation
Neglecting axial deformation fixes joint F against translation, leaving only its rotation θ. All three members have length 5 m and equal EI, so each contributes near-end moment $4EI\theta/5$.
The far-end carry-over moment at H is $2EI\theta/5=10$ kNm, so each near-end moment is 20 kNm. The applied joint moment balances three such contributions: $M=3(20)=\mathbf{60}$ kNm.