Cold-formed steel floor vibration
Walking vibration of a floor of cold-formed C-section joists bearing on walls: the joist panel's natural frequency, its effective weight and the predicted acceleration against the engineer's limit, by AISC Design Guide 11, 2nd Ed. (2016), the method the cold-formed steel industry applies to these floors. Every limit, damping ratio and driving force is an input with the Guide's value prefilled; the Guide gives recommendations, not code limits.
The steel floor vibration type covers beam, joist and girder floors with the girder and combined modes; this type is the joist panel of a cold-formed floor, with a sheathed floor option and the Guide's high-frequency method, which light cold-formed floors often need.
Inputs of the floor vibration #
- Joists: an SSMA designation or custom dimensions, the spacing, the span, the floor width across the joists (Bj is at most two thirds of it), a free edge (Cj = 1.0), and continuity (the effective weight × 1.5 of DG11 4.1.2, your call).
- Floor: concrete on steel deck (depth above the deck, rib height, unit weight, f′c, and whether the slab acts with the joist: DG11 3.2 takes composite action for vibration where the deck is fastened) or sheathing (its stiffness Ds across the joists, your value from the panel's EI and any topping).
- Day-to-day loads (DG11 3.3, not design loads): the deck or slab, the actual superimposed dead load, and the live load (11 psf for paper offices in the Guide; less for residences).
- Criteria: damping ratio β (Table 4-2, cumulative), driving force Po (65 lb), the acceleration limit ao/g (0.5 %g offices and residences), how the limit is taken above 9 Hz, and a minimum frequency (DG11: floors below 3 Hz should be avoided).
Auto-design varies the SSMA joist (lightest first) and the joist spacing, for the least joist steel per square foot. The span, floor, loads, damping and limits are kept.
Checks performed #
| Check | Basis |
|---|---|
| Transformed moment of inertia (1.35 Ec, slab width S up to 0.4 L) | DG11 3.2 |
| Natural frequency fn = 0.18 √(g/Δ) | DG11 Eq. 3-3 |
| Effective width and weight, Bj = Cj (Ds/Dj)^¼ Lj ≤ ⅔ floor width, W = w Bj Lj | DG11 Eqs. 4-2, 4-3 |
| Walking, fn ≤ 9 Hz: ap/g = Po exp(−0.35 fn)/(β W) ≤ ao/g | DG11 Eq. 4-1, Table 4-1 |
| Walking, 9 to 15.4 Hz: equivalent sinusoidal peak acceleration ≤ the limit | DG11 Eqs. 2-10, 2-11, Table 2-2 |
| Above 15.4 Hz | DG11 2.2.2: no criterion (a note) |
| Minimum frequency | DG11 4.1 (your value) |
Limitations #
- Joist panel only: joists on bearing walls or stiff supports. A floor on beams or girders needs the combined mode (the steel floor vibration type).
- Above 9 Hz the limit of DG11 Figure 2-1 is taken as rising in proportion to the frequency above 8 Hz (the ISO baseline shape the figure follows), to confirm against the code text; choose the flat limit to be conservative.
- The text of Eq. 2-10 in the library copy is garbled; it was rebuilt from Eqs. 1-6 and 2-7 to 2-9 as the Guide derives it, which gives its printed constant 154 (to confirm against the code text).
- Rhythmic activity, sensitive equipment, and the joists' strength and deflection are not part of this calculation.
Verification examples #
Verification status: 7 values compared in 2 examples (0 published, 2 hand calculations from the cited equations): 7 within tolerance, 0 recorded deviations. No published example: every value is a hand calculation. That checks the program against this reading of the code, not the reading itself. Code basis: not yet recorded for this module.
No published worked example of a cold-formed joist floor is in the free library (the CFSEI technical note on floor vibration is not on disk). The values are hand calculations of DG11 Eqs. 3-3, 4-1 to 4-3 and 2-10 with the SSMA Guide (2022) section properties.