Beam Analysis
Quick and accurate single-beam analysis with shear, moment and deflection diagrams. Direct-stiffness (FEM) Euler-Bernoulli solution for any support layout — simply supported, cantilever, propped, fixed, overhanging or multi-span — under point loads, distributed (trapezoidal) loads and applied moments. Reactions, envelopes and full diagrams, validated against closed-form beam solutions. US units.
Diagrams FEM · Euler-Bernoulli
Reactions ↑ kip
| @ 0.0 ft | 15.0 kip | |
| @ 20.0 ft | 15.0 kip | |
| ΣV equilibrium | 0.000 kip | ≈ 0 |
Envelope max / location
| Vmax | -15.0 kip | @ 20.0 ft |
| Mmax (+) | 75.0 kip·ft | @ 10.0 ft |
| Mmin (−) | 0.0 kip·ft | @ 0.0 ft |
| δmax | 0.621 in | @ 10.0 ft |
Euler-Bernoulli first-order elastic analysis (direct stiffness / FEM) of a single prismatic beam with arbitrary pin/roller/fixed supports, point & distributed (trapezoidal) loads and applied moments — reactions and the shear, moment and deflection diagrams. Sign convention: downward load & deflection positive, sagging moment positive. Shear deformation, axial force, large displacement and dynamic effects are not included. Verify supports and loads independently.