Beam Calculator

By statics — both a simply supported beam and a cantilever are statically determinate, so reactions come directly from ΣF = 0 and ΣM = 0, with no assumptions needed about the beam's stiffness. Shear and bending moment are then exact closed-form sums of every load's effect (this is not an approximation).

From the standard Euler-Bernoulli relationship — curvature equals bending moment divided by EI — integrated twice numerically over a fine mesh, with the beam's known boundary conditions (zero deflection at both supports for a simply supported beam; zero deflection and zero slope at the fixed end of a cantilever). Checked against four textbook closed-form results (simply supported and cantilever, point load and full UDL), it matches to within about 0.001%.

Positive bending moment follows the standard sagging convention — the beam curves like a smile, with tension on the underside. Deflection is shown downward-positive (bigger number = the beam has sagged more), which is the more intuitive reading for checking against a serviceability limit.

Common serviceability deflection guides: span/360 is often used as a limit under live/imposed load to avoid cracking brittle finishes (plaster, tiles) or doors and windows binding; span/250 is a looser total-load limit for general appearance and function. They are rules of thumb, not a substitute for a full design check against your governing code.

No. This gives you the analysis — reactions, internal forces and deflection for a given span and loading — which is the starting point for design, not the end of it. Section adequacy (bending, shear, deflection capacity) still needs checking against your material's design code (e.g. BS 8110 / Eurocode 2 for concrete, BS 5950 / EC3 for steel).