Which of the following best describes the behaviour of a simply supported beam under a uniformly distributed load?
- AThe maximum bending moment occurs at the supports
- BThe shear force is zero at midspanCorrect
- CThe deflection is maximum at the quarter points
- DThe bending moment diagram is triangular
Solution
Concept
Simply supported beam under uniformly distributed load
Formula
NONE
Step-by-step solution
1. Simply supported beams under uniformly distributed loading exhibit quadratic bending moment variations. 2. Shear force changes linearly along the span and crosses zero at midspan where bending moment reaches its maximum. Answer: B
Explanation
Under a uniformly distributed load, the shear force diagram for a simply supported beam varies linearly from positive at one support to negative at the other, passing through zero at midspan. Because the derivative of the bending moment is equal to the shear force, the maximum bending moment occurs where shear force is zero. Thus, option B is correct.
Why the other options are wrong
A) Bending moment is zero at simple end supports for a uniformly distributed load. C) Maximum deflection for a symmetric load occurs at the center, not at quarter points.
Shortcut
Under symmetric UDL, shear force crosses zero at midspan, where the bending moment reaches its maximum.
Common mistake
Confusing support locations with midspan behavior and assuming maximum bending moment occurs at the supports (option A).
Correct answer: B) The shear force is zero at midspan