Floor Vibration

Floor Vibration (also known as footfall vibrations) can pose a significant nuisance to building occupants, particularly in office buildings. Building tenant's and developers expect the building to meet certain serviceability standards, especially for high-end newly built developments. When issues crop up, it could be a cause for complaints or claims against the architect or design consultant.

Let's first explore the main cause of floor vibrations.

Floor Vibration

In general, footfall vibration varies from 1.8 to 2.5 Hz. This range represents actions from a slow stroll to a very brisk walk. When these frequencies match the vertical frequencies of the floor structure, there may be dynamic excitation.

These frequencies will also have an impact at the second harmonic (2 x frequency). For example, a brisk walk with a 2.5 Hz frequency will have large input energy at 2.5 Hz and a second large peak at 5.0 Hz. Therefore many codes recommend to keep the floor framing frequencies above 5.0 Hz.

What is the Floor Framing Frequency?

From general structural dynamics, the frequency of a structure is related to it's stiffness and mass, and shown in the equation below.

We can observe that frequency is proportional to stiffness, and inversely proportional to the mass. If the floor beams are too shallow, or too long, then they will have a low stiffness, and therefore a low frequency. Furthermore, the heavier a floor is, the lower it's fundamental frequency will be.

By the way, we can calculate the floor frequency by using a structural analysis model and running a modal analysis. Another popular method is to use the analytical procedures set out in AISC DG11.

Estimating Floor Framing Stiffness

In the interest of doing a quick check, one can use the following equation to quickly determine the fundamental frequency of a floor framing system:

Where δ is the largest floor deflection in mm. Normally this is calculated using zero live load or at the very least, a considerably reduced live load (to reflect service conditions).

As an example, if the largest deflection is 18 mm, then the fundamental frequency will be approximately 18/√18 = 4.03 Hz. If we want to keep the floor frequency above 5.0 Hz, we have to generally keep the deflection below about 12 mm.

Detailed Analysis

Even though controlling the frequency is important, a better indication of floor vibration issues can be provided by estimating the floor accelerations. The acceleration estimates account for the floor frequency as well as the floor mass, and damping. 

If you have the time-history wave forms representing the various walking motions, you can run a time-history analysis and input the motions at the point of largest deflection. With the results, run a Fourier transform and check the 1/3 octave band of the results. Then compare to given criteria.

※ What are the Criteria for Floor Vibrations? Summarised in 1-Minute

※ How to Mitigate Floor Vibrations? Summarised in 1-Minute

Other Considerations

A few different considerations have to be taken when doing a detailed floor vibration analysis:

1. Secondary Beam End Conditions
2. Single person or multiple people
3. Damping Ratio