An investigation of P-delta effect in conventional seismic design and direct displacement-based design using elasto-plastic SDOF systems

Abstract

The seismic responses of structures are always influenced by P-Δ effects. The significance of this effect may be negligible when the structure responds elastically but is very important when the structure responds into inelastic range. The P-Δ effect usually increases the displacement response of structures. It may even cause dynamic instability when the structure subjected to severe earthquake ground motions. In conventional seismic design codes, the P-Δ effect usually leads to an increase in design base shear. The same approach is used in direct displacement-based design. Various researchers have proposed different relationships for base shear increase which can be used in different seismic design approaches such as force-based design and performance-based design. In this paper, the proposed expressions are reviewed extensively and their adequacy is evaluated by detail. Then two main purposes are pursued: (1) the development of new expressions for strength amplification factor due to P-Δ effect for current force-based design seismic codes; and (2) the modification of equivalent viscous damping or the required additional base shear considering the P-Δ effect in direct displacement-based design procedure. For this purpose, a new algorithm based upon elasto-plastic SDOF system analyses is presented. The algorithm is implemented 102,500 times overall for different periods, ductility levels, stability indices and different earthquake ground motions that each implementation needs a large amount of trial and error process in linear and nonlinear SDOF systems. The results seem to present a good development of the P-Δ effect relations for the seismic design procedures.