For a beam subjected to a uniformly distributed load (UDL) along its entire span, what is the general shape of the bending moment diagram?

Introduction / Context:
Bending moment diagrams (BMD) graphically represent internal bending moments along the length of a beam. Their shape depends on the loading condition. Correctly sketching BMD is a key skill in structural analysis.

Given Data / Assumptions:

• Beam loaded with a uniformly distributed load (UDL).
• Supports are simple (pinned/roller).
• No additional concentrated loads.

Concept / Approach:
The relationship between load (w), shear force (V), and bending moment (M) is:dV/dx = -w, dM/dx = V. For a constant w, V varies linearly and M varies quadratically, hence parabolic.

Step-by-Step Solution:
Start with shear force distribution: linear.Integrate shear force: bending moment curve = parabolic.Maximum moment occurs at mid-span.

Verification / Alternative check:
For span L and UDL intensity w, maximum bending moment at mid-span = wL² / 8, matching the parabolic curve.

Why Other Options Are Wrong:

• Linear: corresponds to point load cases, not UDL.
• Cubical or circular: not relevant to BMD derivations.

Common Pitfalls:

• Confusing shear force shape with bending moment shape.

Final Answer:
parabolic