An Approximate Method for Static and Dynamic Analyses of Symmetric Wall-Frame Buildings
THE STRUCTURAL DESIGN OF TALL AND SPECIAL BUILDINGS Struct. Design Tall Spec. Build. 18, 279–290 (2009) Published online 25 September 2007 in Wiley Interscience (www.interscience.wiley.com). DOI: 10.1002/tal.409
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.
1.
INTRODUCTION
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;
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.
1.
INTRODUCTION
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;
References: Balendra T, Swaddiwudhipong S, Quek ST, Lee LS. 1984. Free vibration of asymmetric shear wall-frame buildings. Earthquake Engineering and Structural Dynamics 12: 629–650. Basu A, Nagpal AK, Bajaj RS, Guliani A. 1979. Dynamic characteristics of coupled shear walls. Journal of the Structural Division, ASCE 105: 1637–1651. Boutin C, Hans S, Ibraim E, Roussillon P. 2005. In situ experiments and seismic analysis of existing buildings. Part II: Seismic integrity threshold. Earthquake Engineering and Structural Dynamics 34: 1531– 1546. Geourgoussis KG. 2006. A simple model for assessing and modal response quantities in symmetrical buildings. Structural Design of Tall and Special Buildings 15: 139–151. Heidebrecht AC, Stafford Smith B. 1973. Approximate analysis of tall wall-frame structures. Journal of the Structural Division, ASCE 99(2): 199–221. Hoenderkamp JCD. 2001. Elastic analysis of asymmetric tall building structures. Structural Design of Tall Buildings 10: 245–261. Hoenderkamp JCD. 2002. A simplified analysis of high-rise structures with cores. Structural Design of Tall Buildings 11: 93–107. Kuang JS, Ng SC. 2000. Coupled lateral-torsion vibration of asymmetric shear wall structures. Thin Walled Structures 38(2): 93–104. Li GQ, Choo BS. 1996. A continuous–discrete approach to the free vibration analysis of stiffened pierced walls on flexible foundations. International Journal of Solids and Structures 33(2): 249–263. MATLAB V7·1. 2004. Users manual. Mathworks: Natick, MA. Michel C, Hans S, Gueguen P, Boutin C. 2006. In situ experiment and modelling of RC structure using ambient vibration and Timoshenko beam. In First European Conference on Earthquake Engineering and Seismology, Geneva, Switzerland, 3–8 September. Miranda E. 1999. Approximate lateral drift demands in multi-story buildings subjected to earthquakes. Journal of the Structural Division, ASCE 125(4): 417–425. Miranda E, Reyes JC. 2002. Approximate lateral drift demands in multi-story buildings with nonuniform stiffness. Journal of the Structural Division, ASCE 128(7): 840–849. Miranda E, Taghavi S. 2005. Approximate floor acceleration demands in multistorey buildings I: Formulation. Journal of the Structural Division, ASCE 131(2): 203–211. Nollet JM, Stafford Smith B. 1993. Behavior of curtailed wall-frame structures. Journal of the Structural Division, ASCE 119(10): 2835–2853. Potzta G, Kollar LP. 2003. Analysis of building structures by replacement sandwich beams. International Journal of Solids and Structures 40: 535–553. Rafezy B, Zare A, Howson PW. 2007. Coupled lateral-torsional frequencies of asymmetric, three dimensional frame structures. International Journal of Solids and Structures 44: 128–144. Reinoso E, Miranda E. 2005. Estimation of floor acceleration demands in high rise buildings during earthquakes. Structural Design of Tall and Special Buildings 14: 107–130. Rosman R. 1964. Approximate analysis of shear walls subject to lateral loads. Proceedings of the American Concrete Institute 61(6): 717–734. Stafford Smith B, Crowe E. 1986. Estimating periods of vibration of tall buildings. Journal of Structural Engineering, ASCE 112(5): 1005–1019. Swaddiwudhipong S, Lee LS, Zhou Q. 2001. Effect of axial deformation on vibration of tall buildings. Structural Design of Tall Buildings 10: 79–91. Taghavi S, Miranda E. 2005. Approximate floor acceleration demands in multistorey buildings II: Applications. Journal of the Structural Division, ASCE 131(2): 212–220. Tarjan G, Kollar PL. 2004. Approximate analysis of building structures with identical stories subjected to earthquakes. International Journal of Solids and Structures 41(5–6): 1411–1433. Copyright © 2007 John Wiley & Sons, Ltd. Struct. Design Tall Spec. Build. 18, 279–290 (2009) DOI: 10.1002/tal 290 K. B. BOZDOGAN Toutanji H. 1997. The effect of foundation flexibility on the interaction of walls and frames. Engineering Structures 19(12): 1036–1042. Wang Y, Arnaouti C, Guo S. 2000. A simple approximate formulation for the first two frequencies of asymmetric wall-frame multi-storey building structures. Journal of Sound and Vibration 236(1): 141–160. Zalka KA. 2001. A simplified method for calculation of the natural frequencies of wall-frame buildings. Engineering Structures 23: 1544–1555. Zalka K. 2002. Buckling analysis of buildings braced by frameworks, shear walls and cores. Structural Design of Tall Buildings 11: 197–219. Copyright © 2007 John Wiley & Sons, Ltd. Struct. Design Tall Spec. Build. 18, 279–290 (2009) DOI: 10.1002/tal