Deflection of Beams MCQ with answer and solution

Concept

Shape of deflection curve under constant moment

Formula

d²y/dx² = M / (EI) = constant

Step-by-step solution

1. From Euler-Bernoulli beam theory, curvature is related to bending moment by d²y/dx² = M / (EI). 2. When bending moment M is constant along the span, the curvature d²y/dx² is a constant C. 3. Integrating once yields slope dy/dx = C·x + C1. 4. Integrating a second time yields deflection y(x) = (C/2)·x² + C1·x + C2, which is the equation of a parabola (quadratic curve). Answer: B

Explanation

In a region where a beam experiences a constant bending moment, the curvature d²y/dx² = M/(EI) is constant. Integrating twice with respect to length yields an equation of degree two, meaning the deflection curve is a quadratic curve (parabolic arc).

Why the other options are wrong

A) A straight line occurs only when bending moment is zero throughout. C) A cubic curve results from linearly varying bending moment (constant shear force). D) The deflection profile is uniquely determined by beam integration.

Shortcut

Constant M -> Linear slope -> Quadratic deflection curve.

Common mistake

Confusing constant curvature with zero curvature, incorrectly expecting a straight line.