Uniformly distributed load (UDL) as an equivalent point load\n\nA uniformly distributed load along a span is often replaced by a single equivalent point load at its centroid. This equivalence is valid for reactions and overall moments, but is it valid “for all sorts of calculations”? Choose the correct statement.

Introduction / Context:
Replacing a uniformly distributed load (UDL) by a single resultant at its centroid simplifies equilibrium calculations. However, engineers must know when this replacement preserves internal effects such as shear and bending moment distributions and deflections.

Given Data / Assumptions:

• UDL of intensity w applied over a beam span.
• Equivalent resultant W placed at the centroid of the load length.
• Linear elastic beam theory.

Concept / Approach:
The single resultant is strictly equivalent to the distributed load for global statics: total force and resultant moment about any point are the same. But internal distributions (shear and bending moment at intermediate sections) and deflections depend on the load’s spread, not just its resultant.

Step-by-Step Solution:
Reactions: Same for UDL and its resultant since ΣF and ΣM are preserved.Shear diagram: For UDL, shear varies linearly; for a point load, it jumps at the load location—these are not identical.Moment diagram: For UDL, moment is parabolic; for a point load, it is piecewise linear—again not identical.Deflection: Slope/deflection shapes differ; superposition requires the true load distribution.

Verification / Alternative check:
Compute M(x) for a midspan UDL versus an equivalent point load; internal M(x) curves are different even though support reactions match, confirming that equivalence is not universal.

Why Other Options Are Wrong:
“Correct” claims universal validity, which is false. The other restricted statements are unjustified; the limitation is on internal distributions, not on support type or determinacy alone.

Common Pitfalls:
Using the resultant load to build shear/moment diagrams or deflection curves; forgetting that distributed loading shapes the internal response.

Final Answer:
Incorrect