Design philosophy of DG11 floor vibration
General
The Engineer ensures the safety of building occupants by satisfying all design criteria at the Ultimate Limit State. Similarly, the health of building occupants is partly taken care of when deflection limits at the Serviceability Limit State are satisfied (although this Limit State does have other purposes than simply the health of occupants).
However, for floors that are subject to cyclic or sudden loading, it is the human perception of motion that could cause the performance of a floor to be found unsatisfactory. Such perception is usually related to acceleration levels. In most practical building structures, the reaction of the occupants to floor acceleration varies between irritation and a feeling of insecurity. This is based on the instinctive human perception that motion in a 'solid' building indicates inadequacy or imminent failure.
The working environment also affects the perception of motion. For busy environments, where the occupant is surrounded by the activity that is producing the vibrations, the perception of motion is reduced. In contrast, for quieter environments (such as laboratories and residential dwellings), where the source of vibration is unseen, the perception of motion is significantly heightened.
The design philosophy to ensure that the potential for such human response is minimized, has a number of facets,
- the dynamic excitation causing the vibration i.e. the disturbing force profile, which is force and time dependent. For the sorts of building and occupancy considered here, this is the act of walking.
- the acceptance criteria. This depends upon the type of environment. As discussed above this, in turn, depends upon the involvement of the occupant in the generation of the vibration and also on the nature of the occupancy. The latter is important for laboratories carrying out delicate work, or operating theaters, for example.
- the provided performance. This is the "resonance response function" and is dependent on the system natural frequency and, more importantly, the participating mass. This function is expressed as a ratio of the floor acceleration to the acceleration of gravity.
Dynamic excitation
In a classical spring-mass system that includes a (viscous) damper, when a simple force is applied to the mass to extend (or contract) the spring, the mass moves up and down (oscillates). This movement is significant at first but eventually reduces to zero due to the resistance offered by the damper. In a floor system in a building,
- the mass is the self-weight of the floor and any other loading that is present for the majority of the time that the occupants could be exposed to vibration effects,
- the spring is the stiffness of the floor system, which will have a number of different component beams (joists and girders) and the floor slab,
- the damper is provided by a number of elements that are able to absorb energy from the free vibration of the system. There will be energy absorbed,
- within connections, since they behave 'better' than the ideal that is assumed
- from losses due to the unsymmetrical nature of real buildings e.g. grid layout, and dispersion of loads from furnishings and contents
- from components such as partitions that are out-of-plane of the vibration and interfere with the 'mode'.
The determination of the contribution of each of these components as they affect real floor systems is given in detail in later sections. These describe the 'response' side of the floor system. In order to establish the required performance of the system the 'input' must also be defined i.e. that event, events or continuum that is the 'dynamic excitation'.
In the simple example described at the start of this section the 'input' was simply a force that caused a displacement to the system and was then released. This might be equivalent to a person jumping off a chair onto the floor. However, in the context of the concerns over the vibration of floors, it is not this sort of input that is of interest. The main concern is the excitation of the floor brought about by walking.
Unlike the simple example, walking produces loading that is cyclic. This loading can be idealized into a series of sine curves of load against time. Each curve is an exact multiple of the walking frequency called harmonics. When one of these harmonics of the cyclic loading coincides with the natural frequency of the floor system then resonance is set up. The consequence of resonance that is detected, and may disturb occupants, is the associated peak acceleration. The peak acceleration due to walking is estimated by selecting the lowest harmonic for which the forcing frequency can match a natural frequency of the floor and is dependent upon the applied force (a constant = 0.29kN [65lb] for floors), the mass of the system (the self-weight of the floor plate plus other loading that could be considered as permanent), and the amount of damping in the system (the damping ratio, β).
Hence, the dynamic excitation of a floor is dependent upon the forcing function due to walking and its relationship to the natural frequency of the floor system. It is the level of the peak acceleration that this generates that is particularly important in determining the performance of the floor.
Acceptance criteria for human comfort
The required performance of a floor system is very dependent upon the potential response of humans. Human response is a very complex subject since there is no such thing as a 'standard human'. The perception of vibration will differ from person to person, their body mass varies significantly and the body's reaction will depend upon age, gender etc. The human response has been studied and the acceptance criterion adopted by DG11 was developed using the acceleration limits as recommended by ISO 2631-2, 1989 adjusted for intended occupancy.
The accelerations acceptable for different use of buildings are described using the 'base' limits. Multiplying factors are used to increase the base acceleration limit according to the intended use of the building. The target acceleration ratio of the floor under consideration is given in DG11 guidance as,
- ao/g = 0.5% for offices, residences, churches, schools and quiet areas
- ao/g = 1.5% for shopping malls
You should choose a required acceleration ratio based on both engineering judgement and the advice given in DG11.
A separate acceleration ratio limit for high frequency floors (i.e. those floors with fundamental frequency, fn, in the range 9 < fn <= 15 Hz) also needs to be defined by the Engineer, again based on engineering judgement and with reference to DG11 figure 2-1
Design for walking excitation
The start point is the calculation of the natural frequency of the floor system. The fundamental floor frequency, fn, is evaluated using the Dunkerley relationship for the combined mode.
In accordance with the guidance given at Section 4.1 of DG11, an advisory Warning is displayed when the fundamental frequency of the floor system, fn, is < 3.0 Hz.
Next the 'Equivalent Panel Weight' is required. This is dependent upon the physical size of the floor plate selected and an effective width and/or length.
The calculation requires the 'damping ratio' - this is a user input.
The damping ratio, the effective panel weight, the fundamental frequency of the floor and the constant excitation force are used to calculate the peak acceleration ratio, ap/g.
The design condition is simply,
ap/g ≤ ao/g
For floors with high fundamental frequencies, when the calculated value of fn is in the range 9 Hz < fn ≤ 15 Hz, then an equivalent sinusoidal peak acceleration, aESPA, is checked against the separate acceleration ratio limit for high frequency floors.