Influence Line Diagrams MCQ with answer and solution

Concept

Influence Line Diagram for Bending Moment

Formula

Bending Moment = Load × ILD Ordinate

Step-by-step solution

1. Find the ILD ordinate at mid-span (4 m from left) using similar triangles: Ordinate = 1.5 \* (8 - 4) / 6 = 1.0. 2. Calculate Bending Moment: BM = Load \* ILD Ordinate = 10 kN \* 1.0 = 10 kNm.

Explanation

To find the bending moment at section X-X, multiply the concentrated load by the ordinate of the Influence Line Diagram (ILD) at the point where the load is placed. The total length of the beam is 8 m (2 m left + 6 m right). The mid-span is located at 4 m from the left support. Since the ILD decreases linearly from 1.5 at section X-X (2 m from left) to 0 at the right support (8 m from left), the ILD ordinate at the mid-span (4 m) is calculated using similar triangles as 1.5 × (8 - 4) / 6 = 1.0. Bending Moment = Load × ILD Ordinate = 10 kN × 1.0 = 10 kNm.

Shortcut

For load placed at mid-span (between section and support), the ILD ordinate is half the peak ordinate at the section: BM = Load × (Peak Ordinate / 2) = 10 × (1.5 / 2) = 10 kNm.

Common mistake

Students often incorrectly multiply the load directly by the maximum ILD ordinate at section X-X (1.5) instead of calculating the interpolated ILD ordinate at the load's actual position (mid-span).