# Definition of Static Nonlinear Procedure and Flexibility-Based Model with Application on 2D Model for an Existing Structure and Comparing Results with Time History Analysis

Mourad Belgasmia (Setif 1 University, Algeria)
DOI: 10.4018/978-1-5225-0588-4.ch003

## Abstract

This chapter presents in one hand the definition of the pushover procedure based on Eurocode 8, and displacement based and force base elements which will be used in this study, and the application of the pushover procedure based to Eurocode 8 to nonlinear framed structure model and comparison with time history analysis. As test-bed application, we consider a two-story reinforced concrete building in Bonefro, Italy. It is representative of typical residential building construction in Italy in the 1970's and 1980's. The aim of this chapter is to compare 2D model for both modal and uniform load distributions with time history analysis. In another hand an Application to two-story RC Frame using force base elements without soil and with taking into account soil in order to have an idea of the soil modelisation effect with the structure in the results
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## Nonlinear Static Pushover Analysis According To Eurocode 8

The nonlinear pushover analysis consists of applying monotonically increasing constant shape lateral load distributions to the structure under consideration. The structure model can be either 2D or 3D. In particular, EC8 states that for buildings with plan regularity, 2D analysis of single plane frames can be performed, while for buildings with plan irregularity a complete 3D model is necessary. Given that the nonlinear methods are particularly interesting for existing buildings, which are rarely regular, a 3D model is required in most cases.

The nonlinear pushover procedure in EC8 follows the N2 method developed by Fajfar (1999, 2002). The N2 method was developed using a shear building model, i.e. a frame model with floors rigid in their planes. Furthermore, vertical displacement is typically neglected in the method and only the two horizontal ground motion components, x and y, are considered. Extension to the general case of a fully deformable frame is straightforward.

The N2 method consists of applying two load distributions to the frame:

• 1.

A “modal” (or “triangular”) pattern, that is a load shape proportional to the mass matrix multiplied by the first elastic mode shape, ;

• 2.

A “uniform” pattern, that is a mass proportional load shape, .

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