Determination of equivalent rigidities of cold-formed steel floor systems for vibration analysis, Part I: Theory

Cold-formed steel (CFS) floor systems have been increasingly used in residential and commercial buildings. The evaluation of vibration performance of these floors is a great challenge to be dealt with in the design stage. One of the reasons is that there is a lack of an applicable procedure to accurately determine the structural properties of the floors for vibration serviceability evaluation. Current design approaches for floor vibration serviceability are based on simplified equivalent models which lack the capability to account for effects of rotationally restrained floor edges and transverse elements. In this study, comprehensive analytical and experimental investigations have been carried out on the elastic rigidities of CFS floors for vibration analysis based on equivalent orthotropic plate model and results are reported in the present paper and its companion paper. In the present paper, the equivalent rigidities were determined by using Rayleigh's method with considerations of the rotational restraints on the joist ends and different transverse elements. Rotational fixity factors were introduced to represent the rotational restraints and restraint coefficients were designated for frequency calculation. A joist contribution factor was defined to suitably consider the stiffness contribution of joists for a vibration mode. Upon validating the proposed flexural rigidities for vibration analysis, a design equation was developed in the companion paper for predicting the fundamental frequency of the floor system for vibration serviceability evaluation. The results obtained from the equation were compared to those of tests. In addition, in the companion paper, rotational fixity factors for different type of CFS framings were discussed for evaluating the fundamental frequency based on the existing experimental data.