Inputs
Example data table
| k (N/m) | m (kg) | ζ | F0 (N) | f (Hz) | Participants | Peak accel (%g) | Status |
|---|---|---|---|---|---|---|---|
| 8.0e6 | 1500 | 0.05 | 280 | 2.0 | 1 | ~0.3–0.8 | Often acceptable for offices |
| 5.0e6 | 1200 | 0.03 | 280 | 2.2 | 4 | ~1.0–2.5 | May trigger complaints |
| 1.2e7 | 2000 | 0.08 | 280 | 2.0 | 1 | ~0.1–0.3 | Comfortable in many spaces |
These are illustrative ranges; your project values may differ.
Formula used
The calculator models the floor as a single-degree-of-freedom system with stiffness k, modal mass m, and damping ratio ζ.
- ωn = √(k/m) and fn = ωn / (2π)
- ω = 2π f and r = ω/ωn
- Dynamic magnification factor: DMF = 1 / √((1 − r²)² + (2ζr)²)
- Displacement amplitude: X = (Feff / k) · DMF
- Acceleration amplitude: A = ω² X; sinusoidal RMS is A/√2
Group forcing uses a simplified effective force: Feff = F0 · impact · (1 + sync · (N − 1)).
How to use this calculator
- Pick a unit system and an excitation type, then adjust values.
- Enter effective stiffness and modal mass for the controlling mode.
- Choose a damping ratio reflecting finishes and occupancy.
- Set cadence frequency and force amplitude, or keep the preset.
- For groups, enter participants and a reasonable sync factor.
- Press Calculate to view results above the form.
- Use the CSV or PDF buttons to export the latest report.
For design decisions, validate with detailed models and project criteria.
Technical article
1) Why floor vibration matters
Serviceability vibration can trigger complaints long before strength limits are reached. Occupants often react to acceleration, not deflection, especially for rhythmic activities. For typical occupied spaces, peak acceleration targets are frequently below 1.0%g, and sensitive rooms may require about 0.1%g.
2) The SDOF model behind this tool
The calculator idealizes the controlling mode as a single-degree-of-freedom system. Stiffness k, modal mass m, and damping ratio ζ define the natural frequency fn = (1/2π)√(k/m). Human forcing is represented as harmonic loading at frequency f.
3) Frequency ranges and resonance
Many floor systems show fundamental frequencies roughly in the 4–12 Hz range for common modes, while human pacing is often 1.5–3.5 Hz. Resonance risk increases when the excitation approaches the modal frequency, because the dynamic magnification factor rises rapidly near r = f/fn ≈ 1.
4) Damping values used in practice
Damping is strongly affected by finishes, partitions, and connections. Conceptual studies often begin near ζ = 0.03–0.06 for bare structural floors, and can increase toward 0.08–0.12 with heavier finishes or higher nonstructural participation. Higher damping reduces response around resonance.
5) Load modeling for people and groups
Single-person force amplitude and cadence define the harmonic input. Group activity can raise response when people move in partial synchrony. This tool applies a simple scaling using a synchronization factor from 0 to 1, plus an impact factor to represent more energetic actions or harder contact.
6) Reading displacement and acceleration outputs
Displacement is reported as peak and RMS amplitude, mainly for context. Comfort checks focus on acceleration, reported as both m/s² and percent of gravity. For sinusoidal motion, RMS is peak divided by √2. Use the utilization ratio to see how close you are to the selected limit.
7) Design levers that reduce vibration
Increasing stiffness raises fn and reduces static compliance F/k. Increasing participating mass lowers fn but can reduce acceleration for some forcing cases. Adding damping is often the most direct way to cut resonance peaks. Layout choices can also reduce rhythmic excitation.
8) Using results responsibly
Treat this calculator as a screening tool. Real floors may have multiple modes, spatially varying response, and transient footfall effects. For critical projects, confirm with a modal model, validated damping assumptions, and project-specific vibration criteria for the actual occupancy and equipment.
FAQs
1) What is “modal mass” in this calculator?
Modal mass is the effective mass participating in the controlling vibration mode, not the full building mass. It typically includes tributary slab, beams, partitions, and a portion of live load.
2) Why does response jump near the natural frequency?
Near resonance, dynamic magnification increases because the forcing frequency aligns with the system’s preferred motion. Damping limits the peak, but low damping can still produce large acceleration and noticeable vibration.
3) Should I use peak or RMS acceleration?
Many comfort criteria relate to peak acceleration, while some assessments prefer RMS for steady sinusoidal response. This tool provides both. Match the output to your project guidance and occupancy sensitivity.
4) What damping ratio should I enter?
Start with 0.03–0.06 for preliminary checks. Increase toward 0.08–0.12 if finishes, partitions, and nonstructural elements are expected to contribute. Use measured or referenced values when available.
5) How do groups of people affect vibration?
More participants increase the applied force, and partial synchronization can make the increase stronger. If people move randomly, use a low sync factor. For coordinated activity, increase it cautiously.
6) What does “stiffness k” represent here?
It is the effective stiffness of the floor system for the dominant vibration mode at the point of interest. You can estimate it from structural analysis, testing, or calibrated models of the framing and slab.
7) Can this replace a detailed vibration analysis?
No. It is a fast screening approach for steady harmonic response. Detailed analysis may need multiple modes, spatial response shapes, transient footfall models, and project-specific criteria for equipment and occupants.
Plan floor systems wisely to reduce vibration complaints today.