A non-linear response history model for the seismic analysis of high-rise framed buildings

A materially non-linear plane-frame model is presented that is capable of analysing high-rise buildings subjected to earthquake forces. The model represents each storey of the building by an assembly of vertical and horizontal beam elements The model introduces yield hinges with ideal plastic properties in a regular plane frame. The displacements are described by the translation (sway) of each floor and the rotation of all beam–column intersections. The mass is only associated with the translations, and thus the analysis can be carried out as a static condensation of the rotations, combined with integration of the dynamic equations for the translations. The dynamic integration is here carried out by use of the Runge–Kutta scheme. This approach allows a building to be modelled by m( n + 2) degrees of freedom (where m is the number of storeys and n is the number of bays). The rank of the condensed stiffness matrix is only m. Its construction, which requires the inversion of the rotational, rank m( n + 1), stiffness matrix, is required only at time-steps where the pattern of yielding has altered from the previous time-step. This model is particularly attractive for non-linear response history analysis of high-rise buildings as it is efficient, allows each storey to have multiple redundancies, and each connection to be modelled with any suitable moment–rotation relationship. Three verification examples are presented and the results from static push-over analysis are compared with time–history results from the simplified model. The results verify that the model is capable of performing non-linear response history analysis on regular high rise buildings.