Three-dimensional analysis of asymmetric shear wall structures with connecting and stiffening beams J. Wdowicki ⇑ , E. Wdowicka Institute of Structural Engineering, Poznan University of Technology, Piotrowo 5, 60-965 Poznan, Poland article info Article history: Received 15 September 2011 Revised 5 March 2012 Accepted 26 April 2012 Available online 6 June 2012 Keywords: Shear wall structures Three-dimensional models Asymmetric structures Stiffening beams Continuous connection method Thin-walled beams Vlasov’s theory Tall buildings abstract The paper presents the static analysis of non-planar asymmetric shear wall structures with connecting and stiffening beams. The stiff beams incorporated at the various levels of coupled shear walls improve the stiffness of the structural system of tall buildings. The analysis is based on a variant of the continuous connection method for three-dimensional shear wall structures having stepwise changes in cross-section. In the continuous approach the connecting beams are replaced by equivalent continuous connections. The shear walls are considered as thin-walled beams of open section. The differential equation systems for shear wall structure segments of the constant cross-section are uncoupled by orthogonal eigenvec- tors. The results obtained by the presented method have been compared with those obtained experimen- tally and analytically, given in literature, and a good match has been observed. The proposed method is efficient and can be very useful, particularly, at the preliminary design stage. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction In the design of tall buildings it is essential that the structure is sufficiently stiff to resist the horizontal loads caused by wind and seismic motion. The shear wall structures have been recognized as one of the most efficient structural systems for such a purpose. The methods, which are available for the analysis of shear wall buildings, can be broadly categorized into the following main groups: discrete methods, including a finite element method and a frame analogy method, and continuous methods [1]. The finite element method is the most powerful and versatile method of the analysis of complex structures but nevertheless, there is a scope for the development of other techniques that may have the advantage of greater efficiency for specific forms of structural sys- tems, such as tall structures containing coupled shear walls and cores. Some difficulties concerning a great number of unknowns and ill conditioning of a problem for slender structures, which appear in a discrete model, may be avoided in a simple way using the continuous model. In the continuous approach, the discrete set of horizontal connecting beams is substituted by continuous con- nection. The continuous connection method (CCM) is regarded as the simplest and most efficient method for the design analysis of coupled shear walls. In practice, however, the depth of connecting beams is limited and coupling effect provided by the lintel beams on structural walls may not be sufficient. Therefore, it is sometimes necessary to insert the stiff connecting beams somewhere along the height of the walls. A suitable position for the stiffening beams can be conveniently found at the top of building or at intermediate levels reserved for building services or safety purposes [2]. The stiffened planar coupled shear walls have been analysed in many papers [3–10]. Coull and Low [11] presented the analysis of non-planar coupled shear walls with additional stiff connecting beam at roof level, based on Vlasov’s theory of thin-walled beams and continu- ous medium technique. Emsen et al. [12] studied non-planar cou- pled shear walls with one band of connecting beams and with any number of stiffening beams. The aim of this paper is to present the three-dimensional anal- ysis of shear wall structures with any number of connecting and stiffening beams, using the variant of the continuous connection method (CCM) for structures of variable cross-section [13]. 2. Analysis Equation formulations for a three-dimensional continuous model of the shear wall structure with the constant cross-section have been given, among others, in [14–18]. 0141-0296/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.engstruct.2012.04.038 ⇑ Corresponding author. Tel.: +48 61 6652457; fax: +48 61 6652059. E-mail addresses: jacek.wdowicki@put.poznan.pl (J. Wdowicki), elzbieta.wdowicka@ put.poznan.pl (E. Wdowicka). Engineering Structures 42 (2012) 362–370 Contents lists available at SciVerse ScienceDirect Engineering Structures journal homepage: www.elsevier.com/locate/engstruct