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GATE 2021 CE (CE2) – Question 39

Structural Analysis · Statically indeterminate structures: force and displacement methods · 2 marks · Multiple choice

Frame EFG has fixed base E, vertical column EF=2L and horizontal beam FG=L ending in a roller at G. All members have equal EI; FG carries UDL w. Neglect axial deformation. Find vertical reaction at G.

the source diagram and labels are reproduced in the attached image.
  1. 0.375wL
  2. 0.453wL
  3. 0.482wL
  4. 0.500wL

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Correct answer: (C) 0.482wL

Explanation

The column has no applied horizontal resultant, so its top rotational stiffness after allowing sway is EI/(2L). Beam FG, with its far end hinged, has rotational stiffness 3EI/L and fixed-end moment magnitude wL²/8. Joint balance gives rotation wL³/(28EI) and beam end moment −wL²/56. Hence $R_G=wL/2-wL/56=27wL/56=\mathbf{0.48214wL}$, **C**.