# Spectrum a spectrum shows the variation of relative

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Spectrum. A spectrum shows the variation of relative amplitude with frequency of the vibration components that contribute to the load or motion. Figure 22 is an example of a frequency spectrum. Acceleration Ratio. The acceleration of a system divid- ed by the acceleration of gravity is referred to as the acceleration ratio. Usually the peak acceleration of the system is used. Floor Panel. A rectangular plan portion of a floor encompassed by the span and an effective width is defined as the floor panel. Bay. A rectangular plan portion of a floor defined by four column locations. Floor Vibration Principles Although human annoyance criteria for vibration have been known for many years, it has only recently become practical to apply such criteria to the design of floor structures. The reason for this is that the problem is complex, the loading complex, and the response complicated - involving a large number of modes of vibration. Experience and research have shown, how- ever, that the problem can be simplified sufficiently to provide practical design criteria. Most floor vibration problems involve repeated forces caused by machinery or by human activities such as dancing, aerobics or walking, although walking is a lit- tle more complicated than the others because the forces change location with each step. In some cases, the applied force is sinusoidal or nearly so. AISC's Steel Design Guide No. 11: Floor Vibrations Due to Human Activities explains in detail the required engineering calculations and assessment techniques. These techniques use acceleration, as a percent of acceleration due to gravity, to measure human percep- tion of floor movement. For example, the tolerance level for quiet environments, residences, offices, churches, etc. is 0.5 percent of gravity (0.005 g ). Figure 21. Typical beam and floor system mode shapes Figure 22. Frequency spectrum
PAGE 23 SYSTEMS Figure 23 shows tolerance levels for a number of situations. Note that the scale is a function of frequency and acceleration. Also, note that the tolerance acceleration level increases as the environment becomes less quiet. For instance, the tolerance level for people participating in aerobics (rhythmic activities) is ten times greater than if they are in a quiet office. To use the scale, the natural floor frequency and the estimated acceleration for an activity must be calculated. The acceleration of a floor system depends on the activity, the natural frequency for the floor, the amount of mass that moves when the floor vibrates, and the damping in the floor. Floor acceleration increases as energy in the activity increases; thus, floor acceleration is greater for aerobics than for walking. Acceleration decreases with increasing weight; the acceleration for a lightweight concrete floor will be greater than that for the same normal weight concrete floor for the same activities. Acceleration decreases with increasing damping.

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