When to use: Compute support reactions, maximum shear, maximum bending moment, and midspan deflection for a single-span simply supported beam carrying a uniform load w and an optional point load P at distance a. Results check against the L/360 (live load) and L/240 (total load) serviceability limits.
Calculate support reactions, maximum shear, maximum bending moment, and midspan deflection for a simply supported beam carrying a uniform distributed load and an optional point load. Apply static equilibrium principles to instantly verify your structural beam design.
Enter beam span L, uniform load w, point load P at distance a, and section properties E and I. The calculator applies ΣFy = 0 and ΣM = 0 to compute left and right reactions, then evaluates peak shear, maximum moment, and midspan deflection using superposition. Deflection is checked against IBC serviceability limits L/360 (live load) and L/240 (total load).
For uniform load w over span L: R = wL/2, Mmax = wL²/8, δ = 5wL⁴/(384EI). For point load P at distance a from left: R_left = Pb/L, R_right = Pa/L, Mmax = Pab/L, δ = PL³/(48EI) (central). Results are superimposed for combined loading.
Use this tool for preliminary sizing of floor beams, roof rafters, and bridge girders under gravity loads. It assumes a statically determinate, simply supported beam with constant EI. For cantilevers, continuous spans, or indeterminate frames, use the matching specialized calculators.
A reaction force is the force exerted by a support on the beam to maintain static equilibrium. The sum of all reactions must equal the total applied load (ΣFy = 0) and produce zero net moment (ΣM = 0).
L/360 is the IBC serviceability limit for live load deflection, meaning the beam may deflect at most span/360 inches. For a 20 ft span that is 20×12/360 = 0.67 in. The stricter L/240 limit applies to total load deflection.
No — this tool is for simply supported beams only. For a cantilever with a tip load P, the reaction at the fixed support is R = P, the fixed-end moment is M = PL, and tip deflection is δ = PL³/(3EI).
For a simply supported beam with uniform load, maximum moment occurs at midspan. With a point load P at position a, maximum moment occurs at a distance a from the left support (directly under the load). For combined loading evaluate moment at both locations and take the larger value.
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