Design of a simply supported R.C.C. beam subjected to uniformly distributed load (U.D.L.) — the governing bending moment location for flexural design is at:

Introduction / Context:
In beam design, correctly identifying the critical bending moment location is the first step. For a simply supported beam under a uniformly distributed load (U.D.L.), the maximum positive bending moment occurs at midspan, which then governs the main flexural reinforcement design for sagging moments.

Given Data / Assumptions:

• Support condition: simply supported (no end fixity).
• Loading: uniformly distributed load across the span.
• Objective: find the section where bending moment is maximum.

Concept / Approach:

For a simply supported beam with U.D.L., the shear force diagram is linear and the bending moment diagram is parabolic with its peak at the center. The maximum sagging moment value is wL^2/8 at midspan (where w is load per unit length and L the span). Therefore, the design for main tension reinforcement is typically controlled by the midspan section.

Step-by-Step Solution:

Verification / Alternative check (if short method exists):

Draw the bending moment diagram: a concave-down parabola peaking at midspan. This visual confirmation matches the analytic result.

Why Other Options Are Wrong:

Supports (A) carry zero bending moment for a pin support in the ideal model; “every section” (C) is not meaningful; quarter-span (D) is not where maximum occurs; near free edges (E) is irrelevant to simply supported beams.

Common Pitfalls (misconceptions, mistakes):

Confusing shear maxima near supports with moment maxima; forgetting that fixed or continuous beams shift critical sections toward supports for hogging moments.

Final Answer:

mid span