Alternate representations of dynamic properties and loading

Abstract

This study covers three main topics, which are directly related to dynamic behaviour of structures, namely, representation of mass, damping and loading. These three properties of equation of motion are generally represented by widely accepted approaches. In this thesis, such representations are discussed via comparisons with infrequently used representations and viability of them is investigated. For case study, 50-story core wall structure is chosen. First topic discussed here is mass representation. Indisputably, the most accepted assumption for mass representation is lumped mass approach, which is very practical to construct the matrix or, at least, easy to understand the concept of. Another representation, not common one, consistent mass approach derived by a similar procedure in the method for derivation of stiffness coefficients. Consistent mass matrix has off-diagonal terms as distinct from lumped mass matrix. Since the core wall has a continuous form, it is reasonable to represent its mass distribution with consistent mass approach, which takes into account coupling terms. Effects of consistent mass representation on dynamic response of a 50-storey core-wall tall building are investigated. Second one is damping property which may be evaluated as one of the most controversial aspects of structural dynamics. As it is not possible to derive a damping matrix from the element cross section properties and material properties directly, proportional viscous damping matrix is generally used instead, which is defined in terms of modal damping ratios at certain anchor frequencies. However, viscous damping model has a significant deficiency associated with the energy mechanism. Studies based on experimental data show that dissipated energy per cycle of an oscillating system is essentially independent of the excitation frequency as opposed to dependency inherent in the viscous damping model. Such damping model is called rate-independent or structural damping, which is conveniently modelled in the frequency domain through complex stiffness matrix. One of the aims of this study is to observe the effects of such an alternate damping model on the linear seismic response of a tall building. To this end, a 50-story core-wall tall building system is investigated. Drift and total acceleration response characteristics for a set of earthquake records are obtained from the analyses conducted through Fourier Transform. Last concept, probably the most innovative idea of this study, is related to loading part of equation of motion. It has been long applied that ground accelerations are used directly as force by multiplying floor masses, eventually, relative response quantities are obtained. The underlying idea of this loading concept is based on pseudo-static transmission assumption, which presumes that base displacement, in any time instant, is transmitted throughout building statically and naturally, such movement does not deform the structure. One of the aims of this study is to investigate viability of this concept. The motivation is based on the idea that if the building is tall enough, is it possible to be transmitted of base displacements throughout the building without generating any significant deformation? For this reason, absolute response and relative response quantities of the 50-story core-wall are obtained by using acceleration and displacement loading concepts respectively. Comparative results are given at the end.