A relatively simple nonlinear method for the seismic analysis of structures (the N2 method) is presented. It combines the pushover analysis of a multi-degree-of-freedom (MDOF) model with the response spectrum analysis of an equivalent single-degree-of-freedom (SDOF) system. The method is formulated in the acceleration-displacement format, which enables the visual interpretation of the procedure and of the relations between the basic quantities controlling the seismic response. Inelastic spectra, rather than elastic spectra with equivalent damping and period, are applied. This feature represents the major difference with respect to the capacity spectrum method. Moreover, demand quantities can be obtained without iteration. Generally, the results of the N2 method are reasonably accurate, provided that the structure oscillates predominantly in the first mode. Some additional limitations apply. In the paper, the method is described and discussed, and it basic derivations are given. The similarities and differences between the proposed method and the FEMA 273 and ATC 40 nonlinear static analysis procedures are discussed. Application of the method is illustrated by means of an example.

SUMMARYBy means of a graphical procedure, the capacity spectrum method compares the capacity of a structure with the demands of earthquake ground motion on it. In the present version of the method, highly damped elastic spectra have been used to determine seismic demand. A more straightforward approach for the determination of seismic demand is based on the use of the inelastic strength and displacement spectra which can be obtained directly by time-history analyses of inelastic SDOF systems, or indirectly from elastic spectra. The advantages of the two approaches (i.e. the visual representation of the capacity spectrum method and the superior physical basis of inelastic demand spectra) can be combined. In this paper, the idea of using inelastic demand spectra within the capacity spectrum method has been elaborated and is presented in an easy to use format. The approach represents the so-called N2 method formulated in the format of the capacity spectrum method. By reversing the procedure, a direct displacement-based design can be performed. The application of the modi"ed capacity spectrum method is illustrated by means of two examples.

SUMMARYA comprehensive, though relatively simple, non-linear method for the seismic damage analysis of reinforced concrete buildings (the N2 method) has been elaborated. The basic features of the method are: the use of two separate mathematical models, application of the response spectrum approach and of the non-linear static analysis, and the choice of a damage model which includes cumulative damage. The method yields results of reasonable accuracy provided that the structure oscillates predominantly in the first mode. Three variants of a seven-storey building have been used as illustrative examples for the application of the method. Four different types of the analysis, with different degrees of sophistication, have been performed in order to estimate the influence of several assumptions and approximations used in the N2 method.

SUMMARYA procedure for the determination of inelastic design spectra (for strength, displacement, hysteretic and input energy) for systems with a prescribed ductility factor has been developed. All the spectra are consistent (interrelated and based on the same assumptions). This is the first of two companion papers which deals with the 'classical' structural parameters: strength and displacement. The input data are the characteristics of the expected ground motion in terms of a smooth elastic pseudo-acceleration spectrum. Simple, approximate expressions for the strength reduction factor R are proposed. The value of R depends on the natural period of the system, the prescribed ductility factor, the hysteretic behaviour, damping and ground motion. Fairly accurate approximations to the inelastic spectra for strength and displacement can be derived from the elastic spectrum using the proposed values for R.