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GATE 2016 CE (CE2) – Question 43

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

The portal frame shown in the figure is subjected to a uniformly distributed vertical load w (per unit length). The bending moment in the beam at the joint ‘Q’ is

Diagram for GATE 2016 CE (CE2) question 43
  1. Zero
  2. $wL^2/24$ (hogging)
  3. $wL^2/12$ (hogging)
  4. $wL^2/8$ (sagging)

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Show answer and explanation

Correct answer: (A) Zero

Explanation

The roller at S cannot provide horizontal reaction. Horizontal equilibrium therefore also makes the pin’s horizontal reaction at P zero. Each unloaded column consequently has zero shear and zero end moment, since its base moment is zero. Joint equilibrium makes the beam-end moment at Q **zero, A**, despite its rigid connection.