Floor Vibration — AISC Design Guide 11 Walking Excitation Check

Floor vibration is a serviceability problem, not a strength problem. A floor can pass every strength and deflection check but still be unacceptable to occupants if it bounces perceptibly when someone walks across it. Steel-framed composite floors are particularly susceptible because they combine light weight with long spans, producing low natural frequencies that coincide with the frequency range of human walking (1.6–2.2 Hz for normal pace). AISC Design Guide 11, 2nd Edition provides the standard assessment method for walking-induced vibration.

The DG11 criterion

The fundamental check compares the peak acceleration from walking excitation to a tolerance limit:

ap/g = P0 × exp(-0.35 × fn) / (beta × W) ≤ ao/g

Where:

• ap/g = peak acceleration as a fraction of gravity
• P0 = constant force representing a walking person = 65 lb (0.29 kN)
• fn = fundamental natural frequency of the floor bay (Hz)
• beta = damping ratio (fraction of critical damping)
• W = effective weight of the floor panel participating in vibration (lb)
• ao/g = acceleration tolerance limit

Acceleration tolerance limits

For offices, the floor passes if ap/g ≤ 0.005 (0.5% of gravity). This is extremely stringent — the human body is remarkably sensitive to vertical acceleration at frequencies between 4 and 8 Hz.

Damping ratio values

Most office designs use beta = 0.025 (ceiling + ductwork, but open-plan with few partitions).

Calculating natural frequency (fn)

The natural frequency depends on the combined stiffness and mass of the beam-girder system. For a simply supported composite beam:

fn = 0.18 × sqrt(g / delta_j)    where delta_j is the midspan deflection under sustained load (inches)

The sustained load includes the slab self-weight, superimposed dead load, and 10–25% of the design live load (representing the "normally present" furniture and occupants — not the full code live load).

For a two-way system (beams supported on girders), the combined frequency is:

fn = 0.18 × sqrt(g / (delta_j + delta_g))

Where delta_j = beam midspan deflection and delta_g = girder midspan deflection (both under sustained loads). The girder deflection should be calculated at the beam connection point.

Worked example — office floor vibration check

Given: W16x26 composite beams at 10 ft o.c., span 35 ft. W24x55 composite girder, span 30 ft. 3" deck + 3.25" LW concrete (unit weight = 110 pcf). SDL = 15 psf, partition load = 10 psf. Office occupancy.

Step 1 — Beam frequency: Sustained load on beam: slab = 42 psf × 10 ft = 420 plf. SDL = 15 × 10 = 150 plf. Partitions = 10 × 10 = 100 plf. Beam = 26 plf. Total w = 696 plf = 0.058 kli. I_composite = 935 in4 (from composite section properties with full Itr). delta_j = 5 × w × L4 / (384 × E × I) = 5 × 0.058 × (420)4 / (384 × 29000 × 935) = 0.87 in. fn,beam = 0.18 × sqrt(386/0.87) = 3.79 Hz.

Step 2 — Girder frequency: Girder carries beam reactions at third points. Equivalent uniform load for two-point loading pattern. I_girder,composite = 3200 in4. Girder deflection delta_g = 0.35 in (calculated from beam reactions). fn,girder = 0.18 × sqrt(386/0.35) = 5.98 Hz.

Step 3 — Combined frequency: fn = 0.18 × sqrt(386 / (0.87 + 0.35)) = 0.18 × sqrt(316) = 3.20 Hz.

Step 4 — Effective weight: W_beam = wj × Bj × Lj, where Bj = beam panel width (affected by beam spacing and span). Per DG11 Section 4.1, Bj = Cj × (Ds/Dj)^0.25 × Lj, where Ds = slab stiffness, Dj = beam transformed stiffness per unit width. Typical W ≈ 90,000 lb for this bay.

Step 5 — Peak acceleration: beta = 0.025 (office, ceiling, no full-height partitions). ap/g = 65 × exp(-0.35 × 3.20) / (0.025 × 90000) = 65 × 0.326 / 2250 = 0.0094 = 0.94% g > 0.5% g limit — FAILS.

Resolution: Increase beam size to W18x35 (higher stiffness → higher fn → lower ap/g) or add girder stiffness. This is a classic case where vibration, not strength or deflection, controls the beam size.

Code comparison

AISC Design Guide 11 (USA): The primary reference for US practice. Uses the resonance acceleration method with P0 = 65 lb. Covers walking, rhythmic activity, and sensitive equipment. Does not have the force of a code requirement but is universally adopted by specification.

SCI P354 (UK/Europe): Uses a response factor approach based on BS 6472 and EN 1990 Annex A1.4.4. The walking force model is more detailed (Fourier series with harmonic components). The acceptance criterion is expressed as a response factor R (multiplier of the base perception threshold), typically R ≤ 8 for offices. SCI P354 generally produces more conservative results than DG11 for long-span floors.

AS 3600-2018 / CCAA T53 (Australia): No standalone vibration design guide equivalent to DG11. Australian practice typically references DG11 directly or uses the Concrete Centre guide (CCIP-016) for composite floors. AS 3600 Section 2.3.4 requires consideration of vibration for prestressed floors but provides no specific method for steel composite floors.

Common mistakes engineers make

1. Using full design live load to calculate fn. The natural frequency should be calculated using the mass actually present on the floor during normal use — typically 10–25% of the code live load (11 psf for a 50 psf office). Using the full 50 psf live load artificially increases the mass, lowers fn, and produces an unconservative result (lower fn means higher ap/g from the exponential).

2. Checking only the beam and ignoring the girder flexibility. The combined system frequency is always lower than the individual beam or girder frequency. A beam with fn = 7 Hz on a flexible girder with fn = 5 Hz gives a combined fn of approximately 4.1 Hz — potentially below the acceptable range.

3. Assuming that a stiffer floor is always better. Increasing stiffness raises fn, which reduces the walking excitation (due to the exponential decay). However, increasing stiffness also reduces deflection delta_j, which reduces the effective weight W. If W drops proportionally, the net effect on ap/g can be neutral. Both frequency and mass must be evaluated together.

4. Ignoring adjacent bays. DG11 calculates an effective panel width that can extend beyond the bay directly being loaded. If adjacent bays have different stiffness or mass (e.g., a stairwell opening, a setback, or a change in beam size), the effective weight calculation must account for the actual boundary conditions.

Run this calculation

• Beam Calculator
• Section Properties Database

Related references

• How to Verify Calculations
• composite beam design
• beam deflection limits reference
• structural beam formulas reference
• steel beam capacity calculator
• Castellated Beam
• Floor Systems

Disclaimer

This page is for educational and reference use only. It does not constitute professional engineering advice. All design values must be verified against the applicable standard and project specification before use. The site operator disclaims liability for any loss arising from the use of this information.