A cantilever beam of span L carries a clockwise moment M at the free end. The shear force at any point of the beam is:
Try it first: pick an option, then read the explanation.
Correct answer: B. Zero
Asked in SSC JE 11/12/2020 (Evening)
Detailed Explanation
Shear force at a section is the sum of the vertical forces on one side of it. A couple contributes no force, and the fixed end then needs no vertical reaction.
Why “Zero” Is Correct
The shear force is zero everywhere — option (b). (Also, dM/dx = V and the moment is constant, so V must be zero.)
Why the Other Options Are Wrong
- A. M/L²: M/L² has the wrong units for a force.
- C. M/L: M/L appears for a couple on a simply supported beam, not a cantilever.
- D. 2M/L: 2M/L has no basis here.
Key Point
Couple only on a cantilever ⇒ zero shear everywhere.
Key Concepts for Students
- Slope of the BMD = shear; flat BMD ⇒ zero shear.
- The fixed-end reaction is a moment M only.
- A cantilever with an end couple bends into a circular arc.
Practice more: this is question 24 in Bending Moment and Shear Force MCQs – Part 2. Try the whole set and check every answer instantly.