Nonlinear Static Analysis Method

Introduction

This chapter allows enlightening the reader, on an elegant method by its graphic power and the speed of diagnosing the existing or newly constructed structure called non-linear static method. By detailing all different steps, which allows the correct accomplishment of this method; and compare these results to those of time history analysis on a real structure example.

Modern seismic design codes allow engineers to use either linear or nonlinear analyses to compute design forces and design displacements. In particular, Eurocode 8 contains four methods of analysis: linear simplified static analysis, linear modal analysis, nonlinear pushover analysis and nonlinear time-history analysis, which can be summarized in the following table. These methods refer to the design and analysis of framed structures, mainly buildings and bridges. The two nonlinear methods require advanced models and advanced nonlinear procedures in order to be fully applicable by design engineers. This chapter gives an overview of the steps followed to implement state-of-the-art nonlinear models in Z_Soil and presents a test-bed application to a reinforced concrete building.

Displacement-based and force-base elements are used in this study. The first is a classical two-node, displacement-based, Euler-Bernoulli frame element. The second is a two-node, force-based, Euler Bernoulli frame element. The main advantage of the second element is that it is “exact” within the relevant frame element theory. This implies that one element per frame member (beam or column) is used in preparing the frame mesh, thus leading to a reduction of the global number of degrees of freedom. The complete theory for the force-based element can be found in (Aydinoglu. 2004).

The nonlinear response of 2D and 3D models of an existing building are presented as a first full-size application. The building is a residential two-storey reinforced concrete building in Bonefro, Italy(Belgasmia 2006), using Z_Soil software(Zimmermann 2006). It is representative of typical residential building construction in Italy in the 1970’s and 1980’s. The design spectrum for the building was obtained from Eurocode 8 (2003) using the local soil properties and the peak ground acceleration given by the new Italian seismic map.

On-Linear Frame Analysis Methods In Eurocode 8

In this section, the nonlinear pushover procedures given by Eurocode 8 are presented. The first procedure is the Nonlinear Pushover Method of Analysis; the second is the Nonlinear Time History Method of Analysis.