Floor Vibrations 861 General Discussion

Building floors are subjected to a variety of vibrational loads that come from building occupancy. Although almost all loads except dead loads are nonstatic, internal sources of vibration that might be a cause of concern in an office or a residential building are the oscillating machinery, passage of vehicles, and various types of impact loads such as those caused by dancing, athletic activities, and even pedestrian traffic. The trend in the design of floor framing systems of high rises is for long spans using structural systems of minimum weight. To this end, high-strength steel with lightweight concrete topping is routinely employed. With the use of lightweight concrete, most building codes allow for a reduction in the thickness of slab required for fire rating. This results in a further reduction in the mass and stiffness of the structural system, thereby increasing the period of the structure, which at times may approach the period of the source causing the vibration. Resonance may occur, causing large forces and amplitudes of vibration.

The performance of floor systems can be greatly improved by adding nonstructural elements such as partitions and ceilings, which contribute greatly to the damping of vibrations. Nonstructural elements may also add to mass and stiffness to produce the desired degree of solidity. Although the essential requirement in establishing the adequacy of a floor system is its strength, large deflections and strongly perceptible vibrations can be objectionable for several reasons: 1) Excessive deflections and vibrations may give the user the negative impression that the building is not solid. In retail areas, for example, the china may rattle every time someone goes by, or mirrors in dressing rooms of clothing stores may shake, giving the customer the somewhat nebulous but real feeling that the structure is not solid. In extreme cases, vibration may cause damage to the structure as a result of loosening of connections, brittle fracture of welds, etc. It is therefore important that the structure be able to absorb impact forces and vibrations but not respond with humanly perceptible shaking or bouncing. Monolithic concrete buildings are more solid in this respect as compared to light-framed buildings with steel or precast concrete; 2) Excessive deflection may result in curvature or misalignments perceptible to the eye; 3) Large deflections may result in fracture of more recently installed architectural elements such as plaster or masonry; and 4) Large deflections may result in the transfer of load to nonstructural elements such as curtain wall frames.

It is difficult to establish general criteria related to perception of vibrations. Feeling of bounciness varies from person to person, and what is objectionable to some may be barely noticeable to others. Among the criteria employed in the design of floor systems are limitations on the span-to-depth ratio and flexibility, which normally lead to deeper sections than would be required from strength considerations alone. It is somewhat dubious that these limitations assure occupants' comfort.

Recognizing that there is no single scale by which the limit of tolerable deflection can be defined, the AISC specification does not specify any limit on the span-to-depth ratios for floor framing members. However, as a guide, the commentary on the specification recommends that the depth of fully stressed beams and girders in floors should not be less than (Fy/800) times the span. If beams of lesser depth are used, it is recommended that the allowable bending stresses be decreased in the same ratio as the depth. Where human comfort is the criterion for limiting motion, the commentary recommends that the depth of steel beams supporting large open floor areas free of partitions and other sources of damping should not be less than one-twentieth of the span, to minimize perception of transient vibration due to pedestrian traffic.

Thus there is no clear-cut requirement on the flexibility to limit the perception of vibration by occupants. Flexibility limits are given, however, from other considerations such as fracture of architectural elements like plaster ceilings. The rule-of-thumb limitations are 1/150 to 1/180 of the span for visibly perceptible curvature and 1/240 to 1/360 of the span for curvature likely to result in fracture of applied ceiling finishes.

In the design of floor systems, fatigue damage due to transient vibrations is not a consideration because it is tacitly assumed that the number of cycles to which the floor system is subjected is well within the fatigue limitations. However, damage due to fatigue can be a cause of concern in floors subjected to aerobic exercise activities.

Human response is directly related to the characteristics of the vertical motion of the floor system. Users perceive floor vibrations more strongly when standing or sitting on the floor than when walking across it. Human response to vibration seems to be a factor for consideration in design only when a significant proportion of the users will be standing, walking slowly, or seated.

Most of the experiments done on human response to vibrations are related to the physical safety and performance abilities of physically conditioned young subjects in a vibrating environment such as the research supported by NASA and various defense agencies. Very little information is available on the comfort of humans subjected to unexpected vibrations during the course of their normal duties such as slowly walking across a floor or sitting at a desk. Comfort is a subjective human response and defies scientific quantification. Different people report the same vibrations to be perceptible, unpleasant, or even intolerable. A measure for human response to steady sinusoidal vibration (taken from Ref. 60) is shown in Fig. 8.33a. Although there is no simple physical characteristic of vibration that completely defines the human response, there is enough evidence to suggest that acceleration associated in the frequency range of 1 to 10 Hz is

Figure 8.33a. Response to sustained harmonic vibration.

the preferable criterion. This is the range for normally encountered natural frequencies of floor beams. Investigations have shown that human susceptibility to building floor vibrations is influenced by the rate at which the vibrations decay; people tend to be less sensitive to vibrations that decay rapidly. In fact, experiments have shown that people do not react to vibrations that persist for fewer than five cycles.

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