A simply supported beam carries a distributed load of zero intensity over one support, increasing linearly to w over the other support. The shape of the BMD is:
Try it first: pick an option, then read the explanation.
Correct answer: C. cubic parabola
Asked in SSC JE 2013
Detailed Explanation
Load of degree 1 (linear) ⇒ shear of degree 2 ⇒ moment of degree 3.
\[ M_x = \frac{wl}{6}x - \frac{wx^3}{6l} \]
The highest power of x is 3, so the BMD is a third-degree (cubic) curve.
Why “cubic parabola” Is Correct
The BMD is a cubic parabola — option (c). Its peak, wl²/(9√3), lies at l/√3 from the zero-load support.
Why the Other Options Are Wrong
- A. linear: A linear BMD occurs only on unloaded segments.
- B. parabolic: A (quadratic) parabola comes from a UDL.
- D. zero: The beam is loaded, so the BM is not zero.
Key Point
Triangular load ⇒ SFD quadratic, BMD cubic.
Key Concepts for Students
- Each integration raises the degree by one.
- The SFD here is a second-degree curve.
- Max BM at x = l/√3 from the zero end.
Practice more: this is question 54 in Bending Moment and Shear Force MCQs – Part 4. Try the whole set and check every answer instantly.