In a cantilever beam with a UDL, the shear force varies following the:
Try it first: pick an option, then read the explanation.
Correct answer: A. linear law
Asked in SSC JE 2009
Detailed Explanation
For a cantilever, measure x from the free end: the load beyond the section is w·x.
\[ V_x = wx\ (\text{linear}),\qquad M_x = \frac{wx^2}{2}\ (\text{parabolic}) \]
Why “linear law” Is Correct
The shear force follows a linear law — option (a).
Why the Other Options Are Wrong
- B. parabolic law: The parabolic law applies to the bending moment, not the shear.
- C. both (a) and (b): Shear is linear only.
- D. none of the above: The linear law is correct.
Key Point
UDL: SF linear, BM parabolic.
Key Concepts for Students
- Max shear wl and max moment wl²/2 both occur at the fixed end.
- Triangular load on a cantilever: SF parabolic, BM cubic.
- No load: SF constant, BM linear.
Practice more: this is question 50 in Bending Moment and Shear Force MCQs – Part 4. Try the whole set and check every answer instantly.