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Simply supported beam calculator

Reactions, shear, moment, deflection and stress for a uniform load plus a point load, with diagrams.

Inputs

Span and loads
Material and section
Optional: gives the bending stress.
Checks
Applied to reactions, shear, moment and stress. Deflection uses the loads as entered.

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Preliminary results for a linear-elastic, prismatic, simply supported beam with downward loads (Euler-Bernoulli theory, shear deformation ignored). Not a code design check: no lateral-torsional buckling, shear or section-class checks. Verify results and apply the requirements of your design code before relying on them. See the terms of use.
Formulas used

Reactions: RB = (wL²/2 + Pa) / L, RA = wL + P − RB. Moment: M(x) = RAx − wx²/2 − P(x − a)+. Deflection is the sum of the uniform-load curve wx(L³ − 2Lx² + x³)/(24EI) and the point-load curve P·b·x(L² − b² − x²)/(6LEI) for x ≤ a (mirrored for x ≥ a). Units: EI [kN·m²] = E [GPa] × I [cm4] × 0.01. Bending stress = M/Z.

How is it checked?

The calculation code is tested against textbook closed-form results (wL/2, wL²/8, 5wL&sup4;/384EI, PL/4, PL³/48EI, Pab/L), vertical equilibrium, end conditions, mirror symmetry and superposition on hundreds of random cases.

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