GATE ME 2026 Set 1 — Question 40
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Strength of Materials → Beams & Columns → Shear Force & Bending Moment
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Question
A cantilever beam of length is subjected to a concentrated load at mid-span and an anticlockwise moment at the free end, as shown in the figure below. Neglecting the mass of the beam, which one of the following options is the correct representation of shear force diagram (SFD) and bending moment diagram (BMD)?
Correct answer
(A) [figure]
Solution
Let the fixed end be at and the free end at . Work from the free end so the support reactions are not needed.Shear force. Between the free end and the load () there is no transverse force, so . Between the load and the wall () the shear is . The SFD is a rectangle of height over the left half and zero over the right half, which rules out (C) and (D).Bending moment. For only the end moment acts, so the bending moment is constant with magnitude .For the load adds a moment about the section, being the distance from the section to the load. Because is anticlockwise and the downward load produces the opposite sense, the magnitude isThis is at the wall and at mid-span. So the fixed-end moment is zero (equivalently, ).The BMD therefore rises linearly from at the wall to at mid-span and then stays constant at up to the free end.
- (A) SFD: on the left half, zero on the right; BMD: , then constant. Correct.
- (B) has at the wall, but the wall moment is zero.
- (C) and (D) show shear over the whole length, but the shear is zero beyond the load.
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