Vibration in composite floors

To analyse the performance of a floor, first investigate and determine its natural frequency; this can be determined using a 'heel stamp' technique. The natural frequency is sought because energy input at this frequency can cause the magnified 'worst case response' i.e. resonance.

The impulse of a sudden force such as a heel stamp will cause the floor to vibrate to a minute amount at its natural frequency; this can be detected with the use of sensitive monitoring devices known as accelerometers. A magnified response can arise when the 2nd and 3rd harmonics of the walking pace match the floor natural frequency.

The charts below show the responses obtained from a heel stamp test on a typical concrete/steel shuttered floor in a speculative office building in London. In this case, the heel stamp consists of the movement of a person raising his body weight onto toes, then coming down onto heels quickly. In the example given, the body weight of the person undertaking the test was 88kg. The test was repeated 3 times.

Heel stamp acceleration time history for 3 repeated events

The heel stamp excitation procedure can be used to extract the floor's natural frequency and the critical damping percentage. The latter is calculated by taking into consideration 5 cycles from the second peak response. The first impulse arises as the heel engages the floor and is omitted in the peak-to-peak analysis. The floor is then seen to respond in what is termed a damped oscillatory mode and this relates to the lower frequency motion of the floor. After the second peak, progressive damping effects occur and the peaks gradually diminish. (The positions are shown by the twin horizontal lines on the graphs).

Having ascertained the natural frequency of the floor, tests can then be undertaken to determine the response on the basis of one or more persons walking. During walking, a fit and able person will raise their foot by about 50mm before dropping it back down again on the floor. Thus, their mass is lifted and dropped back again at each pace. For every action there is an equal and opposite reaction, and so every time a person's foot touches the ground, the force applied is met by an equal and opposite reaction from the floor. The pace at which the person is walking may be treated as the frequency - each step and the time interval between each step dictating the frequency of the response of the floor. By matching the frequency of the walking steps with that of the floor, it is possible to simulate resonance.

Such an exercise is usually carried out with the aid of a metronome, which emits an audible click at a set frequency, for example 125 paces per minute.

In the above example, the natural frequency of 6.33Hz is in the mid to upper range of floor natural frequencies that are typical of long span floors, so it is not as vulnerable as some long span floors to footfall induced vibration. Floor natural frequency as low as 4Hz is not unknown and floor damping as low as 1.5% has been recorded in some buildings. The floor damping percentage of 3.66% is low, but again not untypical of a steel-framed concrete decked structure. The particular floor was unoccupied; an occupied floor should exhibit a higher level of damping.