Simple-Span Beam Reactions and Max Moment
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.
Formula and source
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.
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