Modal Analysis Calculator
Solves the actual eigenvalue problem for a multi-degree-of-freedom lumped-mass shear building — real periods, real mode shapes, real modal participation factors. The companion, rigorous counterpart to the Building Response Lab's illustrative animation.
Floor mass & stiffness
What's being solved — auto-generated from the sliders, or edit directly in the per-floor table tab.
| Floor | Height (m) | Mass (t) | Storey stiffness (MN/m) |
|---|
Modal properties
Period, frequency, participation factor and effective mass for every computed mode.
| Mode | T (s) | f (Hz) | ω (rad/s) | Participation L | Effective mass (%) | Cumulative (%) |
|---|
Mode shapes
Each mode shown as its own animated sway — real eigenvectors, oscillating at that mode's own natural frequency. Shapes are scaled to a common visual amplitude; only the shape and period are physically meaningful, not the amplitude shown.
Engineering note — Idealised lumped-mass shear-building model (rigid diaphragms, no torsion, no P-Δ or soil-structure interaction). Periods and mode shapes are exact for that idealisation, but the idealisation itself is a simplification. For education only — not for structural design, code compliance, or a substitute for full 3D FE modal analysis.
Not for design or code compliance