# Vibration of composite floor structures

In British Standard 6472, ‘Evaluation of human exposure to vibration in buildings (1 Hz to 80 Hz)’, the performance of a floor structure is considered to be satisfactory when the probability of annoyance to users of the floor, or of complaints from then about interference with activities, is low. There can be no simple specification of the dynamic properties that would make a floor structure ‘serviceable’ in this space concerned, and the psychology of its users are all relevant.

An excellent guide to this complex subject is available. It and BS 6472 provided much of the basis for the following introduction to vibration design, which is limited to the situation in the design example a typical floor of an office building, shown if Fig.3.1.

Sources of vibration excitation

Vibration from external sources, such as highway or rail traffic, is rarely severe enough to influence design. If it is, the building should be isolated at foundation level.

Vibration from machinery in the building, such as lifts and traveling cranes, should be isolated at or near its source. In the design of a floor structure, it should be necessary to consider only sources of vibration on or near that floor. Near gymnasia or dance floors, the effects of rhythmic movement of groups of people can be troublesome; but in most buildings only two situations need be considered;

People waling across a floor with a pace frequency between 1.4 Hz and 2.5Hz; and an impulse, such as the effect of the fall of a heavy object.

Typical reactions on floors from people walking have been analysed by Fourier series. The basic fundamental component has an amplitude of about 240N. The second and third harmonics are smaller, but are relevant to design. Fundamental natural frequencies of floor structures (4.2Hz to 7.5 Hz). The number of cycles of this harmonic, as a person walks across the span of a floor, can be sufficient for the amplitude of forced vibration to approach is steady=state value. This situation will be considered in more detail later.

Pedestrian movement causes little vibration of floor structures with f0 exceeding about 7 Hz, but these should be checked for the effect of an impulsive load. The consequences that most influence human reactions are the peak vertical velocity of the floor, which is proportional to the impulse, and the time for the vibration to decay, which increases with reduction in the damping ratio of the floor structure. Design guidance is available for this situation, which is not further discussed here.

**Human reaction to vibration**

Models for human response to continuous vibration are given in BS 6472. For vibration of a floor that supports people who are standing or sitting, rather than lying down, the model consist of a base curve of root-mean-square (r.m.s) acceleration against fundamental natural frequency of the floor, and higher curves of similar shape. These are shown in the double logarithmic plot of Fig.3.26. Each curve represents an approximately uniform level of human response. The base curve denoted by R=1, where R is the response factor, corresponds to a ‘minimal level of adverse comment from occupants’ of sensitive locations such as hospital operating theatres and precision laboratories.

Curves for other values of R are obtained by multiplying the ordinates of the base curve of R. Those for R=4, 8 and 16 are shown. The appropriate value for R for use in design depends on the environment. The British Standard gives:

R=4 for offices

R=8 for workshops

with the comment that use of double those values ‘may result in adverse comment’, which ‘may increase significantly’ if the magnitudes of vibration are quadrupled.

Some relaxation is possible if the vibration is not continuous. Wyatt recommends that a floor subject to a person walking at resonant frequency once a minute could reasonably be permitted a response double the value acceptable for continuous oscillation.