SHAKEDOWN ANALYSIS OF ELASTIC-PLASTIC TALL BUILDINGS WITH EFFECT OF SHEAR FORCES

In this paper, an effective formulation for shakedown analysis of elastic-plastic tall building is proposed. In this formulation, a numerical solution method is used, suitable for the Finite Element Method analysis of large frames. A single set of external loads is adopted for converting the seismic loading into resultant forces and it is extended to consider arbitrary orientations of the structural members. The theoretical methods of the shakedown analysis are discussed in detail and the formulation has been applied for some types of tall buildings to verify the concept employed and its analytical capabilities. Transient and asymptotic responses can be distinguished for a structure subjected to quasi- static repeated loading cycles above the elastic limit. The former is characterized by the subsequent plastic deformations during the load cycles. The transient phase leads to stress redistribution inside the structure and then the asymptotic cyclic response is achieved with the same time period as the external load. The asymptotic response is independent of the initial boundary conditions and can be both elastic or elastic-plastic depending on the intensity of loading applied to the structure. In the first case, elastic shakedown takes place, i.e. the plastic dissipation is finite and occurs only in the transient phase of deformation. In the second case a steady plastic state is achieved and permanent deformations occur for each subsequent cycle. Two main collapse mechanisms can therefore be manifested: alternating plasticity that leads to a low cyclic fatigue and, incremental collapse resulting in a progressive accumulation of plastic strains leading to some changes of geometry. Both of them significantly affect the structural safety and, therefore, the structure should be designed to work in an extended elastic regime that can be determined using shakedown analysis. Classical shakedown theory is based on the statical and kinematical theorems and currently represent one of the most