Simple-Span Beam Reactions and Max Moment

Reactions, max shear, and max moment for a simple-span beam under uniform and point loads.

Run the calculator

Example

You enter

Span L (ft) 16
Uniform load w (plf) 200

You get

R left (lb) 1600
Max bending moment 6400 ft-lb

Details, formula, and sources

Left/right reactions, max shear, and max bending moment for a simple-span beam under a uniform load plus an optional point load, by superposition.

UDL: R = wL/2, M = wL^2/8. Point load: R_left = P(L-a)/L, R_right = Pa/L. Combined bending moment M(x) = R_left*x - w*x^2/2 - (x>a ? P*(x-a) : 0), maximized over the span.

Statics / AISC Steel Construction Manual simple-beam diagram formulas (public; also in the AWC/NDS and any statics text), by name.

Public statics; reproduced in any structural text.

Estimate. AHJ and licensed professional govern.

Field names used by the API: span_ft, w_plf, r_left_lb, m_max_ftlb

Support condition simple-span pinned-roller; self-weight not added unless folded into wstatics