Floor vibrations

Floor vibrations are a common issue in steel-beam floors, however, how much vibration is it “normal”? and more important if an engineer must take action to correct a vibrations problem what can be done. Typically, building users feel uncomfortable with floor vibrations, especially on office and housing buildings. Here are presented some recommendations for correcting floor vibrations in accordance with the literature and previous experiences. 

The AISC Design Guides 11, establishes the guidelines for the design of floor complying with floor vibration limits for comfort. In which it is included the following chart for determining the recommended limits for floor vibrations. It can be noticed that the lowest limit accelerations are for frequencies between 4Hz and 8Hz, and out of this range the allowed accelerations are larger, as much as five times. 

The recommended limit floor accelerations are established for various floors uses, for example for hosing / offices the maximum acceleration would be 0.5% for a frequency between 4Hz and 8Hz. Where the acceleration is measured on percentage of the gravity acceleration (9.81m/s2), and the frequency is how many cycles of vibration does the floor on one second, and the period of vibration (T) is the time that takes the floor to make one complete cycle of vibration, down-up-down, so that the relation between frequency and period is f=1/T.

For a better understanding, a person walks with a frequency between 1.6Hz and 2.2Hz, jogs or run between 2Hz and 4Hz, dances between 1.5 and 2.5Hz, due aerobics between 2 and 2.75Hz, jumps between 1.5 and 2.8Hz, jumps at concerts or sporting events between 1.5 and 3Hz. And as a basics of dynamics it is important to remind that when the system frequency is the same of close to the excitation frequency the effects tends to increase due to the resonance. Therefore, the recommendation for a better comfort would be to design floor systems with frequencies above 8Hz.

From the structural design it relatively simple maintain the vibrations within the recommended range, however it is common that building users comply about floor vibrations on office and housing buildings, in this cases it is necessary to carry out an assessment of the floor vibrations, and there are two ways to do so, complimentary each other: 1) measuring the dynamic properties of the floor, and 2) carrying out an structural analysis.

If it is found that the vibrations are out of the recommended range, the dynamic properties of the floor shall be modified to reduce the floor vibrations, by means of modifying either acceleration or frequency. To do this it is important to keep in mind how these properties are related to the physical properties and characteristics, where the frequency is related to the mass (m) and stiffness(k):

Donde g es la gravedad y D es la deformación de la viga, y para una viga simplemente apoyada se define como:

 And the acceleration (a) is related to the applied force (Po), mass / weight (W) and the fundamental frequency of the beams (fn);  is the damping. The force cannot be modified since it is on the external excitations, therefore the only variables that can be modified are the mass and the frequency.

Therefore, increasing the mass (weight) will shift the floor vibrations to the left in the chart, and increasing the stiffness will shift the floor vibrations to right of the chart (which is preferable). Since increasing the mass reduces the frequency and acceleration, and increasing the stiffness increases the frequency and reduces the accelerations. The increase in mass can be achieved in different ways, for instance pouring an over slab, although it might affect gravity resistance of the structure. Increasing the stiffness, it is typically a simpler and most effective solution and can be achieved by adding bracing to be beams, adding more beams, increasing the inertia of the existing beams, etc. More sophisticated methods for cases where might be critical the vibrations control, such as, laboratories, surgical rooms, etc. the usage of floor dampers to modify the dynamics properties can be an excellent option.

Recently, we analyze a case of a floor in a school building where the floor is typically used for events, such graduations, congresses, etc. and we measured the dynamic properties and the acceleration overpass the maximum recommended, and the frequency was about 6Hz. Besides increase the mass was not an option, we decided to increase the stiffness. The floor is formed by castellated beams 12m in length  with non-composite prefabricated slabs, and the optimal solution was to add lateral bracing to the beams increasing the overall floor stiffness, since the beams were working independently.  For the analysis we use the design guide equations as well as numerical modeling. As a result, the frequency increased, and the acceleration reduced by 38%.

Floor modeling

Vertical frequency

Dynamic response at the beam center