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GATE 2023 CE (CE1) – Question 49

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

Consider the beam shown in the figure (not to scale), on a hinge support at end A and a roller support at end B. The beam has a constant flexural rigidity, and is subjected to the external moments of magnitude $M$ at one-third spans, as shown in the figure. Which of the following statements is/are TRUE?

a simply supported beam AB of three equal spans $L$. Two moments of magnitude $M$ act at the two one-third points, one anticlockwise on the left and one clockwise on the right (opposite senses, forming a pair that cancels).
  1. Support reactions are zero
  2. Shear force is zero everywhere
  3. Bending moment is zero everywhere
  4. Deflection is zero everywhere

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Show answer and explanation

Correct answer: (A) Support reactions are zero; (B) Shear force is zero everywhere

Explanation

The two moments are equal and opposite, so they give no resultant force and no net moment. Equilibrium then needs no support reactions (A), and the shear force is zero everywhere (B). The bending moment is zero in the outer thirds and equal to $M$ in the middle third, so it is not zero everywhere (C false), and the beam bends in the middle part, so the deflection is not zero (D false).