Keywords: structure, irregularity, code, earthquakes, dynamic analysis, shear, fundamental modes.

In general, seismic building codes such as the Algerian code (RPA 99) or French (PS92), for instance, recommend direct dynamic analysis as the preferred design method [1,2]. Therefore, these codes do not allow the equivalent static force procedure to be used for the design of structures with vertical irregularities.

The present study evaluates the dynamic behavior of such irregular structures in elevation. It takes into account the variation of the stiffness resulting from the discontinuity of the structure. It investigates the linear seismic behaviour of buildings with one setback in elevation [3,4]. It is based on an adjusted equivalent static procedure that allows the estimation of the seismic lateral load distribution. It focuses on the equivalent lateral force method recommended by the codes, in general, and the RPA 99 code, in particular. The code recommends a specific formula to evaluate the base shear, adequate for the case of regular structures. This formula should be adapted to the case of irregular structures. Based on a pre-established dynamic model, the base shear is investigated and adapted to the case of irregular structures, for which should be taken into consideration the effects of higher modes.

A comparison with the spectral modal analysis results shows that the adjusted static method leads to conservative estimates of storey shears and overturning moments [5,6,7,8]. It is shown that for a certain degree of irregularity, the modal weights of some high modes become more important than the fundamental mode. Then, in spite of the major contribution of the base shear in the second mode, the contribution of the first mode to the displacement and overturning moment remains predominant. Thus, in practice, the first mode should be the only mode to be kept in consideration. Therefore, the resulting seismic loads might then be quite different from those obtained by the equivalent lateral force procedure. In such situations, the corrected equivalent lateral force procedure is adequate to estimate the storey shears and overturning moments. As a consequence of this present study, it is concluded that the spectral modal analysis represents an excellent procedure to evaluate the distribution of seismic loads in irregular structures subjected to strong earthquake motion.

1

RPA 1999 "Règles parasismiques algériennes", Centre National de Recherche Appliquée en Génie Parasismique, Alger, Algeria, 1999.

2

PS 92 "Règles parasismiques françaises", Groupe de coordination des textes techniques, Paris, France, 1992.

3

Wong C.M., Tso W.K., "Seismic loading for buildings with setbacks", Canadian Journal of Civil Engineering, vol. 21, no. 5, 1994, p. 863-871.

4

Humar J.L., Wright E.W., "Earthquake response of steel-framed mulistorey buildings with set-backs", Earthquake Engineering and Structural dynamics, vol. 5, 1977, p.15-39. doi:10.1002/eqe.4290050103

5

Clough R.W., Penzien J., "Dynamics of structures", 2rd Ed. Mc Graw-Hill, Inc., New York, 1993.

6

Tiliouine B., "Dynamique des structures: Aspects vibratoires", G.E.C.O.T.E.C., Alger, 2000.

7

Soize C., "Dynamique des structures, Eléments de base et concepts fondamentaux", Ellipse, Paris, 2001.

8

SEAOC, Seismology Committee, Structural Engineers Association of California, "Recommended lateral force requirements and commentary", 1999 Revision, San Francisco, California, 1999.

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