Shear Force and Bending Moment MCQ with answer and solution

Concept

A point load on a cantilever gives a linear BM. An upward load reverses the usual hogging moment into a sagging moment.

Formula

M_x = P × x (x measured from free end)

Step-by-step solution

1. Take a section at distance x from the free end. 2. BM = P × x. This varies linearly with x: zero at the free end and P×L at the support. 3. A downward load on a cantilever gives hogging (tension at top). 4. Here the load acts upward (against gravity), so the beam bends concave upward and the moment is sagging (tension at bottom). 5. So the BM is linear and sagging.

Explanation

A point load gives a BM that increases linearly from the free end to the fixed end. Because the load acts upward, the beam bends like a smile, so the moment is sagging.

Why the other options are wrong

A: hogging is for a downward load. C and D: a parabolic BM comes from a uniformly distributed load, not a point load.

Shortcut

Point load means linear BM, UDL means parabolic BM. Reverse the load direction and you reverse the sign of the BM.

Common mistake

Writing hogging out of habit, without noticing that the load acts against gravity.