Points of contraflexure for a simply supported beam under UDL A simply supported beam carries a uniformly distributed load over the entire span. How many points of contraflexure (sign change of bending moment within the span) occur?

Introduction / Context:
Points of contraflexure are locations where the bending moment changes sign, i.e., crosses zero within the span. Identifying them is important for reinforcement detailing and structural diagnostics.

Given Data / Assumptions:

• Beam is simply supported.
• Uniformly distributed load (UDL) across the full span.
• No additional couples or varying boundary conditions.

Concept / Approach:
For a simply supported beam under full-span UDL, the bending moment diagram is a single sagging parabola: zero at each support and maximum positive at midspan. There is no internal sign change of bending moment between the supports, therefore no internal point of contraflexure.

Step-by-Step Solution:
Write M(x) for UDL on simply supported beam: M(x) = R_left * x − w * x^2 / 2 (for 0 ≤ x ≤ L).With symmetry, M(0)=0, M(L)=0, and M(x)>0 for 0Hence, there is no x in (0, L) for which M(x)=0 → no contraflexure within the span.

Verification / Alternative check:
Plotting the parabolic bending moment confirms a single positive dome; contraflexure points arise in beams with couples, overhangs, or nonuniform loading, not in this basic case.

Why Other Options Are Wrong:
Options 1, 2, or 3 imply internal zero crossings which do not occur under pure UDL on a simple span.

Common Pitfalls:
Counting the supports as contraflexure points; by convention, points of contraflexure are internal to the span, not at the simple supports where M is trivially zero.

Final Answer:
0