AN APPROXIMATE METHOD FOR STATIC AND DYNAMIC ANALYSES OF SYMMETRIC WALL-FRAME BUILDINGS KANAT BURAK BOZDOGAN* SUMMARY In this study an approximate method based on the continuum approach and transfer matrix method for static and dynamic analyses of symmetric wall-frame buildings is presented. The whole structure is idealized as a sandwich beam in this method. Initially the differential equation of this equivalent sandwich beam is written; shape functions for each storey can then be obtained by the solution of differential equations. By using boundary conditions and storey transfer matrices obtained from these shape functions, system modes and periods can be calculated. The reliability of the study is shown using several examples. A computer program has been developed in MATLAB and numerical samples have been solved for demonstration of the reliability of this method. The results of the samples show the agreement between the present method and other methods given in the literature. Copyright © 2007 John Wiley & Sons, Ltd.
A number of methods such as ﬁnite element method have been developed for the static and dynamic analysis of wall-frame buildings. While such methods are necessary for ﬁnal design, approximate methods are most helpful at the preliminary design stage. The most widely used approximate calculations are based on the ‘continuum method’. In the literature there are numerous studies concerning the continuum method (Rosman, 1964; Heidebrecht and Stafford Smith, 1973; Basu et al., 1979; Balendra et al., 1984; Stafford Smith and Crowe, 1986; Nollet and Stafford Smith, 1993; Li and Choo, 1996; Toutanji, 1997; Miranda, 1999; Wang et al., 2000; Kuang and Ng, 2000; Zalka, 2001; Hoenderkamp, 2001, 2002; Miranda and Reyes, 2002; Zalka, 2002; Potzta and Kollar, 2003; Reinoso and Miranda, 2005; Miranda and Taghavi, 2005; Taghavi and Miranda, 2005; Boutin et al., 2005; Michel et al., 2006; Georgioussis, 2006; Rafezy et al., 2007). Rosman (1964) proposed a continuum medium method for a pair of high-rise coupled shear walls. Heidebrecht and Stafford Smith (1973) derived the differential equations of a system for buildings with uniform stiffness along the height and obtained closed-form solutions to the lateral deformations, bending moment and shear forces when subjected to a uniform and triangular static lateral load distributions. Basu et al. (1979) designed charts of circular frequencies for coupled shear walls. Li and Choo (1996) proposed a hybrid approach, based on the analysis of equivalent continuous medium and a discrete lumped mass system for free vibration analysis of stiffened pierced walls on ﬂexible foundations. Zalka (2001) derived simpliﬁed expressions for the circular frequency of wall-frame buildings. Tarjan and Kollar (2004) presented a method for approximate earthquake analysis. They derived a
* Correspondence to: Kanat Burak Bozdogan, Civil Engineering Department, Ege University, Bornova, Izmir 35100, Turkey. E-mail: email@example.com
Copyright © 2007 John Wiley & Sons, Ltd.
K. B. BOZDOGAN
simple formula for periods of vibration and internal forces of a building. Reinoso and Miranda (2005) presented a simpliﬁed method to estimate lateral acceleration demands in high-rise buildings subjected to earthquakes. Rafezy et al. (2007) proposed a global analysis approach to the calculation of natural frequencies of asymmetric three-dimensional frame structures. The governing differential equations of substitute systems were formulated using a continuum approach and posed in the form of a simple dynamic member stiffness matrix. In this study, an approximate method based on the continuum system model and transfer matrix approach is suggested for the...