For a cantilever beam of length L subjected to a moment M at its free end, the shape of the shear force diagram is:
Try it first: pick an option, then read the explanation.
Correct answer: A. No shear force at any part of the beam
Asked in SSC JE 25/09/2019 (Morning)
Detailed Explanation
The SFD records vertical (transverse) forces. A couple has no resultant force, so it leaves the SFD unchanged — and with no other load, the SFD stays at zero.
Why “No shear force at any part of the beam” Is Correct
There is no shear force at any part of the beam — option (a). The bending moment, by contrast, is constant (M) throughout.
Why the Other Options Are Wrong
- B. Linearly varying with zero at the free end and maximum at the support: A linear SFD needs a UDL.
- C. Parabolic: A parabolic SFD needs a linearly varying load.
- D. Rectangular with a constant value M/L: M/L is the shear for a couple on a simply supported beam, not a cantilever.
Key Point
End couple on a cantilever: SFD = 0, BMD = constant M.
Key Concepts for Students
- Couples affect only the BMD.
- Fixed-end reaction: moment M, vertical force zero.
- dM/dx = V = 0 ⇒ horizontal BMD.
Practice more: this is question 28 in Bending Moment and Shear Force MCQs – Part 2. Try the whole set and check every answer instantly.