CalcStack — free, instant, no signup. The interactive calculator loads automatically.
PL/4 and wL²/8 — the two formulas that built the world.
First-pass beam sizing is four classic elastic cases: simply supported or cantilever, point load or uniform. This calculator computes max shear, max bending moment, bending stress from your section modulus, and deflection from E and I — with the deflection ratio checked against common L/240 and L/360 serviceability limits.
Engineering students use it to check homework before submitting; practicing engineers use it to sanity-check software output — if SAP2000 and PL/4 disagree, the model is wrong. DIYers use it before trusting a shelf span or a garage hoist point.
Simply supported with a center point load: M = PL/4. Simply supported with a uniform load: M = wL²/8. Cantilever with end load: M = PL. Cantilever uniform: M = wL²/2. Moment is in lb·ft when P is pounds, w is lb/ft, and L is feet — convert to lb·in before dividing by section modulus for stress.
Common serviceability limits: L/360 for floor beams supporting plaster or brittle finishes, L/240 for roofs, L/180 as an absolute floor. A 10 ft beam at L/360 deflects at most 0.33 inches. Deflection, not strength, governs most floor designs — stiffness (E×I) is usually the binding constraint.
No — use it for feasibility checks, education, and sanity-checking software output. Real design applies code load combinations with safety factors (see the load combination calculator), lateral bracing checks, connection design, and a licensed engineer's stamp. These are elastic formulas for prismatic beams; they do not cover lateral-torsional buckling or shear failure.