Floor Vibration Analysis

Steel beams or joists supporting large open floor areas tend to show motion problems. Impact from human activity, such as walking, jumping, dancing, etc., will excite a floor system in such a way that it vibrates. Vibration caused by human activity is transitory, and as such, is different from vibration caused by rotating machinery or other sources of steady-state vibration. Transient vibrations, in which the occupants are, at the same time, the source and sensor, cannot be isolated and must be controlled by the structure itself.

All floor systems, regardless of the type of construction, are flexible, and as such they respond by vibrating when impacted. The problem arises when the vibration is of an intensity that annoys the occupants. Very few steel joist-concrete slab floor systems exhibit annoying vibrations, except those with wide spans over relatively large areas without partitions. No vibration investigation is required for roofs.

Based on the Lenzen Method, the program checks the adequacy of a steel joist-concrete slab floor system in relation to human perceptibility to vibration, when subjected to an impact from human activity.

Input Data

The input data required by the program consists of slab thickness, concrete strength, unit weight, the unsupported joist span and spacing, and the uniformly distributed design live load. In addition, the percentage of live load acting, and the weight of insulation and flooring are required. Figure to the right shows schematically the required input data.

Example

As an example, consider a 3.5" normal-weight concrete floor slab supported by 20K5 steel joists spaced 3'-0" on centers and 33'-0" long, as shown in the figure to the left.

Check if the transient vibrations are tolerable for human comfort. Design live load is 35 psf. Weight of insulation is 5 psf and live load acting is 10%. f'c=3 ksi.

Output

To specify the joist to be analyzed, choose the Select option from the Design menu or double click the joist designation cell in the template. Once the input data has been completed, the program computes the properties of the composite section and evaluates human perceptibility by relating joist displacement and frequency of vibration.

The figure to the right shows the template related to this program.

By choosing the Graph and View options from the Design menu, the modified Reiher-Meister plot, which relates the frequency of vibration and displacement, is displayed showing the ranges of human perceptibility found experimentally, as well as the location of the point computed in the analysis.

In this example, the vibration is slightly perceptible. Therefore the design is acceptable.