Question

In general, a sudden jump in the bending moment diagram is due to the following type of loading condition?

• A. Large point load acting at that point
• B. Concentrated couple acting at that point
• C. Starting point of the UDL
• D. Support reaction at that point

Hint:

Remember the diagram rules: - Point Load $\rightarrow$ Vertical jump in the Shear Force Diagram (SFD). - Concentrated Moment $\rightarrow$ Vertical jump in the Bending Moment Diagram (BMD).

Answer 1

The Correct Option is B

Concept: The relationships between load ($w$), shear force ($V$), and bending moment ($M$) at any cross-section of a beam are governed by the following differential relations: \[ \frac{dV}{dx} = -w \quad \text{and} \quad \frac{dM}{dx} = V \] Integrating these relationships across a localized point reveals how point discontinuities affect the shear force and bending moment diagrams:

• Concentrated Point Load / Support Reaction: Introduces a sudden discontinuity in the shear force equation, resulting in a sharp vertical jump in the Shear Force Diagram (SFD).

• Concentrated Couple / External Moment: Introduces a localized rotational energy concentration at a precise cross-section. Since it acts directly on the rotational equilibrium without altering the transverse shear forces, it creates a sudden vertical jump in the Bending Moment Diagram (BMD).
Thus, a sudden vertical jump in the bending moment diagram signifies the presence of a concentrated external couple at that exact location.