Influence Line Diagrams MCQ with answer and solution

Concept

For moving concentrated loads on a simply supported beam, the maximum bending moment always occurs under a load.

Formula

M_max at a section = W·a·b/L (load at the section); absolute M_max = WL/4 (single load at mid span)

Step-by-step solution

1. The influence line for bending moment at any section of a simply supported beam is a triangle. 2. Its peak is at the section itself. 3. So the moment at a section is maximum when a load is placed exactly at that section. 4. For a train of loads, the absolute maximum moment also occurs under one of the loads, near mid span. 5. So the maximum bending moment occurs under the load.

Explanation

The ILD for bending moment has its peak at the section. So the maximum moment always comes when a load stands at that point, which means it is under the load. For one single load, this point is the mid span. For a train of loads, it is under one load, close to the centre.

Why the other options are wrong

A: Mid span is correct only for one single load. It is not the general rule. C: Bending moment at the supports of a simply supported beam is always zero. D: The location is not random. It is always under a load.

Shortcut

Moving loads: maximum BM is always under a load. Maximum SF is near the support.

Common mistake

Choosing mid span because it is true for one single point load, while forgetting that the general answer is under the load.