If a cantilever carries a uniformly varying load (zero at the free end and w per meter at the fixed end) over its entire length, then the shape of a bending moment diagram is a
- ACubic parabolaCorrect
- BQuadratic parabola
- CStraight line
- DTriangle
Solution
Concept
Shape of the BMD for a uniformly varying load
Formula
Load w(x) ∝ x; V ∝ x²; M ∝ x³
Step-by-step solution
1. Load intensity varies linearly with distance from the free end. 2. Shear force varies as x² (parabolic). 3. Bending moment varies as x³ (cubic parabola).
Explanation
The bending moment diagram is one degree higher than the shear force diagram, which is one degree higher than the load diagram. A linear load gives a quadratic SFD and a cubic BMD.
Shortcut
Load: 1st degree → SF: 2nd → BM: 3rd (cubic).
Common mistake
Choosing a quadratic parabola (UDL result).
Correct answer: A) Cubic parabola