V4.3 — Three-story uniform shear building, modal periods
ExactDescription
The three natural periods of a uniform three-story shear building (lumped floor masses on story stiffnesses) — a discrete, exactly-solvable eigenvalue problem, so no mesh-discretization gap is expected.
Reference
Independent eigenvalue solution of the same tri-diagonal stiffness/mass matrices (closed form for this discrete system); k = 12EI/h³ per story.
Model
Three lumped floor masses stacked vertically and connected by elastic column members, with floor rotation restrained so each story behaves as an ideal shear spring (a classic "shear building" idealization), solved as a Modal load case for its three natural periods.
| Elastic modulus, E | 29,000 ksi |
| Column width, b | 10 in |
| Column depth, d | 10 in |
| Story height, h | 144 in |
| Moment of inertia, I | 833.33 in⁴ |
| Story stiffness, k | 97.12 kip/in |
| Floor mass, m | 1 kip-s²/in |
| Stories | 3 |
Comparison
| Quantity | Reference | vfopro | % diff | Status |
|---|---|---|---|---|
| Mode 1 period (s) | 1.4326 | 1.4326 | +0.00% | Exact |
| Mode 2 period (s) | 0.5113 | 0.5113 | +0.00% | Exact |
| Mode 3 period (s) | 0.3538 | 0.3538 | +0.00% | Exact |
Conclusion
Every reported quantity matched the closed-form value to at least 6 significant figures.
Last updated September 22, 2026 · applies to vfopro 20260922.0.0 or later