The GATE Grind

GATE 2017 CE (CE1) – Question 15

Solid Mechanics · Bending moment and shear force in statically determinate beams · 1 mark · Multiple choice

A simply supported beam carries a uniformly distributed load. Which statement is true?

  1. Maximum or minimum shear force occurs where curvature is zero.
  2. Maximum or minimum bending moment occurs where shear force is zero.
  3. Maximum or minimum bending moment occurs where curvature is zero.
  4. Maximum bending moment and maximum shear force occur at the same section.

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) Maximum or minimum shear force occurs where curvature is zero.; (B) Maximum or minimum bending moment occurs where shear force is zero.

Explanation

Beam equilibrium gives $dM/dx=V$. An interior stationary value of bending moment therefore occurs where shear force $V=0$. For a uniformly loaded simply supported beam, shear vanishes at midspan and the bending moment is maximum there; the largest shear magnitudes occur near the supports. Thus B is the standard interior-extremum answer. For this simply supported beam the end curvature is zero where the shear magnitude is also extreme, supporting A under an endpoint interpretation. The revised official key accepts A OR B.

More Bending moment and shear force in statically determinate beams questions

All Bending moment and shear force in statically determinate beams questions →