A cantilever beam of span L carries a clockwise moment M at the free end. The bending moment diagram is:
Try it first: pick an option, then read the explanation.
Correct answer: D. a rectangle with a constant BM = M
Asked in SSC JE 11/12/2020 (Evening)
Detailed Explanation
Whatever section you take, the only action between it and the free end is the couple M, and a couple has the same moment about every point. So the BMD has a constant ordinate.
Why “a rectangle with a constant BM = M” Is Correct
The BMD is a rectangle of constant height M — option (d). M/L has units of force, not moment, so it cannot be a bending moment.
Why the Other Options Are Wrong
- A. a triangle with zero BM at the free end and M/L at the support: A triangular BMD comes from a point load, not a couple; and M/L is a force.
- B. a triangle with zero BM at the support and M at the free end: The moment does not fall to zero at the support — it stays M.
- C. a rectangle with a constant BM = M/L: The shape is right but M/L is not a moment.
Key Point
Cantilever with end couple M: BMD = rectangle of height M; SFD = zero.
Key Concepts for Students
- Check units: a moment divided by a length is a force.
- Point load at free end → triangular BMD; UDL → parabolic BMD.
- This is a case of pure bending.
Practice more: this is question 23 in Bending Moment and Shear Force MCQs – Part 2. Try the whole set and check every answer instantly.