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GATE 2020 CE (CE2) – Question 39

Structural Analysis · Deflections of determinate beams, frames and trusses · 2 marks · Multiple choice

Structure RST shown has pin R, roller S and rigid joint S. Members RS and ST have uniform EI. Consider bending only; neglect self-weight and axial stiffening. A horizontal point load P acts at T. Find rotation magnitude at R.

Diagram for GATE 2020 CE (CE2) question 39
  1. $PL^3/(12EI)$
  2. $PL^2/(12EI)$
  3. $PL^2/(6EI)$
  4. $PL/(6EI)$

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Show answer and explanation

Correct answer: (B) $PL^2/(12EI)$

Explanation

The vertical arm applies end couple $M=PL/2$ to span RS. A simply supported beam under an end couple has opposite-end rotation magnitude ML/(6EI). Substitution gives **$PL^2/(12EI)$, B**.