If a cantilever beam of length L is subjected to a couple M₀ at its free end, then:
Try it first: pick an option, then read the explanation.
Correct answer: C. the beam has a constant bending moment (M₀) throughout
Asked in SSC JE 16/11/2022
Detailed Explanation
Cut the cantilever at any section and look at the part towards the free end. The only action on it is the couple M₀. A couple has the same moment about every point, so the bending moment does not depend on where the section is.
For any section at distance x from the free end: \( M_x = M_0 \) (independent of x), \( V_x = 0 \).
Why “the beam has a constant bending moment (M₀) throughout” Is Correct
The BMD is a rectangle: a constant bending moment M₀ throughout — option (c). The beam is in pure bending and bends into a circular arc.
Why the Other Options Are Wrong
- A. the BMD is a straight line increasing linearly from the free end: A linear BMD needs a transverse force; a couple gives none.
- B. the BMD is a straight line increasing linearly from the fixed end: Same reason — there is no shear, so the BMD has zero slope.
- D. the BMD cannot be predicted from the given data: It can be predicted exactly: M₀ everywhere.
Key Point
End couple on a cantilever ⇒ pure bending: M = M₀ constant, V = 0.
Key Concepts for Students
- dM/dx = V; with V = 0 the BMD is horizontal.
- Pure bending bends a beam into a circular arc (radius R = EI/M).
- The fixed end resists with a moment equal and opposite to M₀.
Practice more: this is question 17 in Bending Moment and Shear Force MCQs – Part 2. Try the whole set and check every answer instantly.