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GATE 2026 ME – Question 40

Mechanics of Materials · Shear force and bending moment diagrams · 2 marks · Multiple choice

A cantilever beam of length $L$ is subjected to a concentrated load $P$ and a moment $M$ 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)?

A cantilever beam fixed at the left wall. A downward load $P$ acts at the middle, at a distance $L/2$ from the wall. A clockwise moment $M = PL/2$ acts at the free end. Four pairs of SFD and BMD sketches are given as options A to D.
  1. SFD equal to $P$ for the first half and zero for the second half. BMD rises linearly from 0 at the wall to $PL/2$ at mid-span, and stays at $PL/2$ for the second half.
  2. SFD equal to $P$ for the first half and zero for the second half. BMD starts at $PL$ at the wall, falls linearly to $PL/2$ at mid-span, and stays at $PL/2$ for the second half.
  3. SFD equal to $P$ over the whole length. BMD rises linearly from 0 at the wall to $PL/2$ at mid-span, and stays at $PL/2$ for the second half.
  4. SFD equal to $P$ over the whole length. BMD starts at $PL$ at the wall, falls linearly to $PL/2$ at mid-span, and stays at $PL/2$ for the second half.

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Show answer and explanation

Correct answer: (B) SFD equal to $P$ for the first half and zero for the second half. BMD starts at $PL$ at the wall, falls linearly to $PL/2$ at mid-span, and stays at $PL/2$ for the second half.

Explanation

The shear force is $P$ between the wall and the load, and zero beyond the load, because the couple at the end adds no shear. This rules out C and D. The clockwise end moment bends the beam in the same sense as the downward load, so the two moments add. Between the load and the free end the bending moment is constant at $\frac{PL}{2}$. At the wall it is $P \times \frac{L}{2} + \frac{PL}{2} = PL$, and it falls linearly to $\frac{PL}{2}$ at the load. That is diagram B.