A higher order continuum model for the dynamic shear behaviour of multi-storey frames

A continuum model is developed to predict the response of multi-storey frames to dynamic excitations. The equations of the proposed theory are derived in a systematic manner using smoothing operations. The order of the theory is kept arbitrary. To appraise the validity of the theory natural frequencies and vibration shapes predicted by discrete and continuum models are compared. This comparison provides valuable information about goodness of the proposed model because natural frequencies and vibration shapes represent spectral structure of the theory. The most crucial finding obtained from the analysis is that, as an implication of the smoothing operations used in the derivation of the theory, one should define an effective height which is equal to the height of the frame plus half of the height of the top storey. The numerical results indicated that the use of effective height in the analysis improves the prediction of the theory considerably. It is found also that the number of modes the continuum model can describe correctly increases with the number of storeys and that the lowest number of storeys for which the theory can be used is three. Further, it is observed that an increase in the order of the theory improves greatly its prediction and that in the presence of non-uniform distributions of frame properties, such as, of mass, stiffness, etc., the theory still remains valid.