Deflection of Beams MCQ with answer and solution

Concept

Macaulay's method uses singularity (bracket) functions to write one bending moment equation for the whole beam.

Formula

EI d²y/dx² = M(x), with bracket terms <x − a>^n taken as zero when x < a

Step-by-step solution

1. Macaulay's method writes a single bending moment equation for all sections of the beam. 2. It uses special brackets <x − a> that are zero when x < a and equal to (x − a) when x ≥ a. 3. These brackets are called singularity functions. 4. So Macaulay's method is also called the method of singularity functions. 5. Answer is C.

Explanation

In Macaulay's method, one moment equation with bracket terms covers the full beam. These bracket terms are singularity functions. So it is also called the method of singularity functions.

Why the other options are wrong

A: Moment area method uses the area and moment of the M/EI diagram. B: Conjugate beam method uses an imaginary beam loaded with M/EI. D: Mohr's theorems are the basis of the moment area method, not singularity functions.

Shortcut

Singularity function = Macaulay brackets.

Common mistake

Mixing up Mohr's theorems (moment area) with Macaulay's method.