Beam Calculator
Reactions, shear force, bending moment and deflection for simply supported, cantilever and fixed-fixed beams under point loads, UDLs, trapezoidal loads and applied moments.
Applied factors (1.35G + 1.50(Q/W/S)) — G: 1.35, Q: 1.50, W: 1.50, S: 1.50.
Reactions and internal forces follow classical elastic (Euler–Bernoulli) beam theory. Simply supported and cantilever cases use direct statics; fixed-fixed uses fixed-end-moment superposition; propped cantilever uses the force method (compatibility at the prop). Deflections assume constant EI. The EC/ACI togglesets units and BMD sign convention, and determines which load-combination and section-stress rules Auto EC/Auto ACI and the Stress Check use — it does not itself perform a member design check against either code.Auto ECgenerates EN 1990 §6.4.3.2/§6.5.3 combinations (leading action + ψ0-reduced accompanying actions) from whichever load types (G/Q/W/S) are present;Auto ACIgenerates the ACI 318-19 §5.3.1 / ASCE 7-22 §2.3.1 basic LRFD set.
Sign convention: sagging (positive) moment is plotted below the axis — Eurocode convention, matching the deflected shape below.
This is the deflection under the ULS-factored combination above — it is nota serviceability check. Compare the Serviceability (SLS) Deflection panel below against any L/δ limit (e.g. L/250, L/360).
EN 1990 §6.5.3 service combinations, using unfactored/psi-reduced characteristic loads — never ULS factors.
| x (m) | V (kN) | M (kN·m) | δ (mm) |
|---|---|---|---|
| 0.00V_max · M_min | 55.50 | 0.00 | 0.00 |
| 1.50 | 35.25 | 68.06 | 15.26 |
| 3.00M_max · δ_max | -15.00 | 105.75 | 21.70 |
| 4.50 | -35.25 | 68.06 | 15.26 |
| 6.00V_min | -55.50 | 0.00 | 0.00 |
Highlighted rows mark the governing extremes: Vmax/Vmin, Mmax/Mmin and δmax.