The bending moment M is constant over a length l of a beam. The shear force over this length is:
Try it first: pick an option, then read the explanation.
Asked in SSC JE 2008
Detailed Explanation
Shear force is the rate of change of bending moment along the beam: V = dM/dx. Disputed key: the book gives (a) M/l, but that would apply only if the moment changed by M over the length l.
\[ V = \frac{dM}{dx} = \frac{d(\text{constant})}{dx} = 0 \]
Why “none of the above” Is Correct
A constant bending moment means zero slope of the BMD, so the shear force is zero — a state of pure bending, as in the middle third of a beam under two equal symmetric loads. None of the options M/l, M/2l or M/4l is zero, so the correct choice is (d) none of the above.
Why the Other Options Are Wrong
- A. M/l: M/l is the shear only if M changes by M over the length l (linear BMD) — the book's key, but not what the question states.
- B. M/2l: M/2l has no basis.
- C. M/4l: M/4l has no basis.
Key Point
dM/dx = V: constant M ⇒ zero shear (pure bending).
Key Concepts for Students
- Pure bending zone: constant M, V = 0.
- Linear BMD ⇒ constant shear equal to its slope.
- Book key (a) is flagged as disputed on this page.
Practice more: this is question 66 in Bending and Shear Stress MCQs – Part 5. Try the whole set and check every answer instantly.