Abstract
In the last decades, the possibility to use the inelastic capacities of structures have driven the seismic design philosophy to conceive structures with ductile elements, able to obtain large deformations without compromising structural safety. In particular, the utilization of high-strength elements combined with the purpose of reducing inertial masses of the construction has highlighted the second-order effect as a result of the “lightweight” structure’s flexibility. Computational aspects of inclusion of the second-order effects in the structural analysis remain an open issue and the most common method in the current design practices uses the stability coefficient θ. The stability coefficient estimates the ratio between the second-order effect and lateral loads’ effects. This coefficient is used then to amplify the lateral loads’ effects in order to consider the second-order effects, within a certain range proposed by codes of practices. In the present paper, we propose a simple approach, as an alternative to the stability coefficient method, in order to take into consideration P-Delta effects for earthquake-resisting ductile frame structures in the design process. The expected plastic deformations, which can be assessed by the behavior factor and the elastic deformations of the structure, are expected to magnify the P-Delta effects compared to those estimated from an elastic approach. The real internal forces are approximated by modifying the stiffness matrix of the structure in such a way as to provide a compatible amplification effect. This concept is herein implemented with a three-step procedure and illustrated with well-documented case studies from the current literature. The obtained results show that the method, although simple, provides a good approximation compared to more refined and computationally expensive methods. The proposed method seems promising for facilitating the design computations and increasing the accuracy of the internal forces considering the second-order effects and the amplification from the inelastic deformations.
Highlights
The primary objective of earthquake engineering is to provide an adequate margin of safety against earthquake loads
Collapse prevention is not a simple goal, which will always demand the acceptance of a small probability of collapse
Analyzing whether it is technically and economically possible to balance the seismic input, the designer may decide to adopt several choices, referring to [5], of which the more frequently embraced is the incrementation of the dissipated hysteretic energy by increasing the structural ductility
Summary
The primary objective of earthquake engineering is to provide an adequate margin of safety against earthquake loads. The linear analyses, adopted in the design process of estimating the internal actions, may count for any nonlinearity by means of two approaches: (i) iterative procedures or (ii) simplified methods. Both are fundamentally based on the structural reanalysis approach [15]. An amplification of the second-order moment, proportional to the evolution of plastic deformations, may be observed for ductile structures during strong earthquakes Such a phenomenon is difficult to be traced during the design process with the stability coefficient only, despite that inelastic deformations can be approximated by amplifying the elastic deformations with the behavior factor q. The approach is adequate for a moment-resisting structural system and could be a relevant instrument for the practitioners involved in the design process
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