The shear force diagram of a cantilever beam carrying a concentrated load at the free end is a/an:
Try it first: pick an option, then read the explanation.
Correct answer: B. rectangle
Asked in SSC JE 2013
Detailed Explanation
Between the free end and the fixed end there is no other load, so the shear force does not change along the beam.
Why “rectangle” Is Correct
The SFD is a rectangle of height W — option (b). The BMD for the same case is a triangle (0 at the free end, Wl at the fixed end).
Why the Other Options Are Wrong
- A. triangle: The triangle is the BMD of this case, or the SFD of a cantilever with UDL.
- C. parabola: A parabolic SFD needs a linearly varying load.
- D. ellipse: SFDs are never elliptical for standard loads.
Key Point
Cantilever + end load: SFD rectangle, BMD triangle.
Key Concepts for Students
- Constant shear means a linear BMD.
- Max moment Wl at the fixed end.
- Adding a UDL makes the SFD a trapezium.
Practice more: this is question 56 in Bending Moment and Shear Force MCQs – Part 4. Try the whole set and check every answer instantly.