Journal of Constructional Steel Research 65 (2009) 542–551 Contents lists available at ScienceDirect Journal of Constructional Steel Research journal homepage: www.elsevier.com/locate/jcsr Natural periods of steel plate shear wall systems Cem Topkaya * , Can Ozan Kurban Department of Civil Engineering, Middle East Technical University, 06531 Ankara, Turkey article info Article history: Received 26 December 2007 Accepted 10 March 2008 Keywords: Steel plate shear wall Natural period Finite element Period elongation Simplified formula abstract In most seismic building codes, the design base acceleration is computed using the natural period of vibration of the structure. Design specifications provide empirical formula to estimate the fundamental natural period of a system. In this study a class of steel plate shear walls, that have uniform properties through their height, was considered. The fundamental natural periods of this class of structures were determined using three dimensional geometrically linear finite element analyses and were compared against the estimates provided by seismic design specifications. Comparisons reveal that estimations using approximate formula can lead to unsatisfactory results. Based on this observation a simple hand method has been developed to predict the fundamental period of a steel plate shear wall. In the development of the hand method the steel plate shear wall has been recognized as a vertical cantilever for which simplified analytical solutions exist. Contributions of shear and bending stiffness of the wall have been explicitly taken into account. Furthermore, this simple method has been extended to dual systems having plate walls and special moment frames in the context of theories on wall-frame structures. Natural period estimations using the method that was developed in this study are compared with the finite element solutions and a good agreement is demonstrated. In addition, the effects of geometrical and material nonlinearities on the fundamental period were explored. The fundamental periods of steel plate walls were investigated at various drift levels. Based on the numerical analysis, elongation of the periods due to buckling and yielding of infill plates were quantified and are presented herein. © 2008 Elsevier Ltd. All rights reserved. 1. Introduction and background Steel plate shear walls (SPSW) can be used in buildings to resist forces produced during an earthquake. In a typical SPSW system steel infill plates that are one story high and one bay wide are connected to stiff horizontal and vertical boundary elements (HBE and VBE). The resulting system is a cantilever which resembles a plate girder. Design philosophies for SPSW systems can be divided into two categories. Earlier designs used thick or stiffened plates to prevent buckling due to shear stresses forming at low load levels. Recent designs employ thinner plates and rely on the post buckling capacity. Experimental and numerical studies [1–16] reported to date revealed that SPSW systems have high stiffness, excellent energy absorption capacity and stable hysteresis characteristics. Most of the seismic building codes [17–19] provide expressions for design base acceleration as a function of the natural period of the structure. Therefore, accurate computation of the fundamental natural period has paramount importance in determining the magnitude of lateral forces in design. For determination of the fundamental period of vibration of the structure, expressions based on methods of structural dynamics * Corresponding author. Tel.: +90 312 210 5462; fax: +90 312 210 7991. E-mail address: ctopkaya@metu.edu.tr (C. Topkaya). (for example Rayleigh’s method or computer based eigenvalue analysis) are permitted by design specifications such as ASCE 7[17], Eurocode 8 [18], and National Building Code of Canada (NBCC) [19]. In addition, design specifications provide empirical formulas to estimate the fundamental period of the structure. Usually, these formulas depend on the type of the structural system, materials used, and the gross dimensions. Traditionally, code period expressions have been derived or validated using measured building periods during earthquakes [20,21]. These expressions are generally adjusted to give lower-bound estimates so that design seismic forces are not underestimated. There are two main uses for these empirical formulas. First, these period formulas are useful in design as the actual structure period is not known before a first trial design is performed. Second, in design codes such as ASCE 7 [17] and NBCC [19], these approximate formulas together with a coefficient are used to provide an upper limit on the fundamental period calculated based on the methods of structural dynamics. In NBCC [19] it is specified that for shear walls the value obtained by such methods not exceed 2.0 times the value determined by empirical expressions. Similarly, in ASCE 7 [17] the basic period can be increased up to 1.4 times for high seismic zones and to 1.7 times for low seismic zones. These restrictions are imposed to safeguard against unreasonable assumptions in the methods of structural dynamics, which may lead to unreasonably long periods and hence unconservative values of base shear. 0143-974X/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jcsr.2008.03.006