Frequency estimation of pre-stressed and composite floors
The modern trends towards economy and the use of high strength materials have resulted in long spans and slender floors of low frequencies. These frequencies may be within the range of the first few harmonics of daily life human activities. Though the problem of resonance with walking vibrations, an activity most common on all floors, is unlikely, high amplitude or persistent vibrations due to these low-level excitations may cause alarm to building occupants. There may also be some problems with the most sensitive equipment. These uncomfortable vibrations are a serviceability limit state problem and can only be avoided by ensuring a high floor fundamental natural frequency and damping. There is a need, therefore, for a method to accurately predict the fundamental natural frequency and damping of these floors and to ensure that they are high enough to avoid any resonance or perceptibility problems. Available analytical formulae for the estimation of fundamental natural frequency are not directly applicable to actual floors due to various assumptions. The only method that may be reliably used for static or dynamic analyses is the finite element method because it can conveniently model the three dimensional nature of structures and account for the various boundary conditions and material properties. The research reported in this thesis consists of measuring fundamental natural frequencies and corresponding damping of a range of actual floors. The experimental frequencies have then been compared with those results which are based on the analytical formulae and finite element method. The analytical methods suitable for various categories of floors have been identified. A new linear-elastic single panel or beam finite element model, correlated with the experimental results, has been developed for the accurate estimation of the fundamental natural frequency of these floors. The correct boundary conditions for various categories of floors have been identified. The single-degree-of-freedom (SDOF) formula for the estimation of fundamental natural frequency using static deflections has been modified for the floors tested. This modified SDOF formula can be used for convenient hand calculations by the consultants and designers who want a quick estimation of fundamental natural frequency due to time and cost limitations. The formula may also be used to limit static deflections and, therefore, design loads for any choice of a minimum fundamental natural frequency. Also, new limits on span/depth ratios for flat slabs and span limits for double-T beam floors have been suggested. Similarly, minimum fundamental natural frequencies, damping ratios and maximum static deflections have been suggested for the floors tested. The single panel or beam model may also be used for various parametric studies, both for static and dynamic analyses.