Simply supported, uniform load
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About this case
How to analyze a simply supported beam with uniform load
This page pre-loads a simply supported beam with a uniform distributed load over the full span. Edit the span, load intensity, or section directly in the calculator. Results update instantly.
Textbook values: reactions R = wL/2, M_max = wL²/8 at midspan, δ_max = 5wL⁴/(384EI) at midspan. Shear diagram is linear from +wL/2 to −wL/2; moment diagram is parabolic.
What to watch for with uniform loads
A partial UDL (not covering the full span) produces different reactions and a piecewise moment diagram with a flatter top. Drag the load ends to model partial coverage — the calculator handles this exactly. For a roof beam, the UDL is typically the tributary area load × spacing; make sure you're not double-counting self-weight (toggle it separately).
Compare with the center point load case: for the same total load (wL = P), the UDL gives half the midspan moment and 5/8 the midspan deflection. A UDL is always less demanding than a center point load for the same total load.
Related calculators
For a beam with both point and distributed loads, use the full simply supported beam calculator. For continuous spans, the two-span continuous case shows how the interior support moment changes the design.