Does a floor-vibration frequency limit erase the lumber saved by deep, widely spaced joists?

What it found

A first-mode natural-frequency check (f₁ = (π/2L²)√(EIg/w), derived and tested against the static-deflection form) added to the NDS strength and deflection checks of house-spans, for SPF No. 2 floor joists under 10 + 40 psf. The joist alone is modelled, with no subfloor composite action. Any limit up to 10 Hz changes nothing: the longest strength-passing 2x10 at 16 in (15 ft 3 in) already vibrates at 10.1 Hz. At 12 Hz it shortens to 13 ft 11 in, and at 15 Hz the least-lumber joist at a 12 ft span moves from 2x10 at 24 in (0.83 board feet per sq ft) to 2x12 at 24 in (1.00), while at 14 ft the 2x12 at 24 in no longer passes and 2x12 at 16 in (1.50) is needed. The limit in Hz is a policy choice swept here, not a code-book criterion, and the model is conservative by ignoring the subfloor and optimistic by ignoring live-load mass. Stylised.

A figure from its own output

Paper, code and results

• README and method
• Experiments and results
• Code
• Tests

More in Open-source residential construction

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Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.