Seismic Behaviour and Ductility Evaluation of multi-storey Light timber-frame Buildings by Means of analytical Formulations and numerical Modelling

Abstract

The research activity is focused on the study of both the linear and nonlinear behaviour of light timber-frame shear-walls buildings (called Platform Frame); in the first part the analysis of the linear-elastic behaviour is presented, whereas in the second part the non-linear behaviour is considered. After a short introduction on the state of the art of timber buildings both from the constructive and from the legislative point of view, the linear-elastic behaviour of single timber shear-wall is presented. The analysis of a single timber shear-wall allows to develop an analytical equation and simplified numerical macro-model (called UniTn-Model) which are able to represent the behaviour of a wall both in terms of displacement capacity and, much more important, in terms of stiffness. In fact, the evaluation of the correct walls stiffness constitutes a fundamental step in the seismic analysis of the timber buildings. The later section is based on what stated about the single-wall and it deals firstly with the elastic behaviour of systems composed by single-storey coupled walls and then it analyses systems of multi-storey single-walls. Theses analyses highlighted the influence of the vertical loads on the external force distribution within the shear walls, as well as the changing of the system stiffness caused by the hold-downs state variation. Both these aspects allow to develop some analytical formulations through which the stiffness matrix of full-scale buildings can be determined. Three iterative methods for the application of the Modal Response Spectrum Analysis are also presented; the differences between the methods, from the computational point of view as well as from the analytical one, are emphasized by means of a case study. The second part illustrates the non-linear analysis of a single shear-wall in order to identify the influence of the base components features on the wall ductility, both from the qualitative and the quantitative point of view; the UniTn-Model is hence extended to the non-linear field. It is also determined that the contribution of the nail deformation is not dependent on the nails spacing but it is only dependent on the geometry ratio of the sheathing-panels themselves. This property, analytically determined, is demonstrated on the basis of numerical and experimental analyses, by means of some non-linear F.E.M. analysis and some ad-hoc laboratory tests respectively. In the following section, using what developed for the single shear-wall, the non-linear analysis of single and multi-storey full-scale buildings is performed. The analyses are performed in order to assess the ductility level achievable by the buildings varying the ductility of the base components as well as the failure mechanism. In order to get generalized results and provide reliable values of ductility for the constructive system analysed, a large set of non-linear analysis has been performed through the use of a Matlab code specifically developed. This allowed to determine the ductility level that light timber-frame buildings can reach and to propose a new set of values for the behaviour factor q to be used in the seismic design. In the last section the study of the applicability of the capacity design to the light timber-frame buildings is presented. This study assesses the conditions that make the capacity design physically feasible and economically viable in comparison to the elastic design. The analyses have been conducted by varying both the geometry of the buildings that the seismic force level.