| Office (open plan) | 0.005g (0.049 m/s²) | 4-8 Hz | 1.5-3.0% | Open plan, cellular | | Office (quiet) | 0.004g (0.039 m/s²) | 4-8 Hz | 1.5-3.0% | Executive offices | | Residential | 0.005g (0.049 m/s²) | 4-8 Hz | 1.0-2.0% | Apartments, houses | | Shopping | 0.015g (0.147 m/s²) | 4-8 Hz | 2.0-3.0% | Retail, malls | | Gymnasium | 0.03g (0.294 m/s²) | 4-8 Hz | 3.0-4.0% | Sports halls | | Footbridges | 0.007g (0.069 m/s²) | 1.5-3.0 Hz | 0.5-1.0% | Pedestrian bridges |

Natural Frequency of Steel-Concrete Composite Floors

For a simply supported composite floor beam: [ f = \frac{18}{\sqrt{\delta}} ]

Where δ = mid-span deflection (mm) under self-weight + 10% imposed load.

Minimum recommended frequencies:

Floor Natural Frequency Table — Composite Beams

Cellular beams may have lower frequencies by 10-20% due to web openings.

Acceleration Response — Walking Excitation

The peak acceleration due to a single person walking at the critical step frequency:

[ a_{peak} = \frac{F_0 e^{-0.35 f_n}}{\mu \zeta} \times \frac{1}{M} ]

Where:

• F0 = 280 N (walking force harmonic amplitude)
• fn = floor natural frequency (Hz)
• μ = mode shape factor (typically 0.5-0.7 for first mode)
• ζ = damping ratio
• M = modal mass (kg)

Worked Example — Composite Floor Vibration Assessment

Given:

• 406×178 UB 60 composite beam, span 8.0 m, spacing 4.0 m
• 130 mm slab on metal deck (total depth 190 mm)
• Damping: 2.0% (open plan office)
• Permanent load: 4.5 kN/m²

Step 1 — Natural frequency: Icomp (composite section) ≈ 25,000 cm⁴ (approximate composite value) Deflection under self-weight + 10% imposed: w = 4.5 + 0.1 × 3.5 = 4.85 kN/m² Per beam: w = 4.85 × 4.0 = 19.4 kN/m

δ = 5 × 19.4 × 8000⁴ / (384 × 210,000 × 25,000 × 10⁴) = 19.7 mm

f = 18 / √19.7 = 4.06 Hz → Marginal for office (≥ 4.0 Hz)

Step 2 — Acceleration check: Modal mass M ≈ 0.5 × beam self-weight + tributary slab = ~15,000 kg (estimate) Walking force at 4.06 Hz: F = 280 × e^(-0.35 × 4.06) = 280 × 0.246 = 68.9 N

a_peak = 68.9 / (0.5 × 0.02 × 15,000) = 68.9 / 150 = 0.46 m/s² = 0.047g

Step 3 — Compare with criteria: Office limit: 0.005g = 0.049 m/s² a_peak = 0.46 m/s² > 0.049 m/s² → Not satisfactory

Step 4 — Options to improve:

• Increase beam size to 533×210 UB 92: frequency ~5.2 Hz, acceleration reduced by ~35%
• Increase slab depth to 150 mm
• Add intermediate beam to reduce floor panel size
• Increase damping (raised access floor + furniture may add 0.5-1.0% damping)

High-Frequency Floors (f ≥ 8 Hz)

For high-frequency floors (f ≥ 8 Hz), the response is assessed using velocity limits rather than acceleration. The RMS velocity response:

[ v_{RMS} = \frac{0.7 F_0 \times \text{(walking response factor)}}{M \times \omega_n} ]

High-frequency floors are generally not susceptible to walking-induced resonance because the walking step frequency (1.6-2.4 Hz) is well below the fundamental frequency.

SCI P354 Vibration Assessment Procedure

Design Resources

• UK Composite Beam — Composite floor design
• UK Deflection — Serviceability limits
• UK Beam Design — Beam section selection
• UK Steel Beam Sizes — Section properties
• UK Framing Systems — Floor bay layout
• All UK References

Frequently Asked Questions

How is floor vibration assessed in UK steel design?

UK practice follows SCI P354 for floor vibration assessment. Key criteria: natural frequency > 4 Hz for walking, peak acceleration < 0.5% g (0.049 m/s²) for office floors. The assessment procedure calculates: (a) natural frequency from floor stiffness and mass, (b) modal mass of the vibrating panel, (c) damping ratio from floor construction and fit-out, and (d) peak acceleration from walking excitation. SCI P354 provides acceptance criteria for various occupancy types.

What are the SCI P354 acceptability criteria?

SCI P354 defines: low-frequency floors (< 8 Hz) checked against acceleration limits, high-frequency floors (≥ 8 Hz) checked against velocity limits. Office: 0.5% g peak acceleration. Residential: 0.5% g (similar to offices because of lower damping but similar sensitivity). Shopping centres: 1.5% g. Gymnasiums: 3.0% g. Footbridges: 0.7% g. The frequency-weighted RMS acceleration (m/s²) is also checked against the BS 6472 curves for continuous vibration.

What is the relationship between floor frequency and walking excitation?

Walking excitation occurs at step frequencies of 1.6-2.4 Hz (normal walking). The first harmonic of walking (2× step frequency = 3.2-4.8 Hz) is most critical for floor vibration. If the floor's natural frequency is within this range, resonance may occur, amplifying the response. Design aims to either: (a) tune the floor above 4-4.5 Hz to avoid the first harmonic, or (b) tune the floor below 3 Hz (rarely practical) and rely on high damping. For sensitive environments, 6-8 Hz is recommended.

How does damping affect floor vibration response?

Damping in UK composite floors comes from: (a) structural damping (0.5-1.0% of critical for bare steel), (b) concrete slab contribution (0.5-1.5%), (c) finishes and fit-out (0.5-2.0%), (d) partitions and furniture (0.5-2.0%), and (e) occupants (0.5-1.0%). Total damping for an office floor with raised access floor and ceiling: 2.0-3.0% of critical. For residential: 1.0-2.0%. For gyms: 3.0-4.0%. High damping reduces peak acceleration linearly — doubling damping halves the acceleration.

What remedial measures are available for existing floors with vibration issues?

For existing floors with excessive vibration: (a) adding intermediate supports or columns to reduce span (most effective), (b) adding tuned mass dampers (TMDs) near mid-span to absorb vibration energy, (c) increasing mass (adding screed or concrete topping) to reduce acceleration amplitude, (d) adding stiffening beams or strengthening existing beams, (e) changing the floor use to a lower sensitivity class, (f) installing vibration-isolated workstations for sensitive equipment.

Reference only. Verify all values against the current edition of SCI P354 and UK NA to EN 1990. This information does not constitute professional engineering advice.