# Macro-Modelling Approach for the In-Plane Cyclic Response of Cold-Formed Steel Partition Walls
## 1 Introduction  
It has been demonstrated during past earthquakes that non-structural elements could be vulnerable to a relatively low intensity ground shaking which induces negligible structural damage [1; 2; 3]. Reports on the investigation of earthquake-induced-loss, therefore, show that economic loss due to non-structural elements exceeds that due to structural members [4]. The loss of non-structural elements largely results from moderate or extensive damages to the cold-formed steel (CFS) partition walls that are potentially required to be repaired or completely replaced after an earthquake. A CFS partition wall usually consists of tracks, studs, gypsum boards, their joints and connections between tracks and structural members. Mitigation of seismic damage to CFS partition walls is recognized as an important approach to reduce potential economic burdens for a building. This implies that the seismic performance of CFS partition walls needs to be rigorously identified, and then evaluated through reliable analytical prediction of their cyclic response behavior. Various research on the analytical modelling of CFS walls has been carried out [5; 6; 7]. Previous studies focused on the analytical modelling of structural shear walls consisting of CFS members. There is, however, limited research on modeling capturing the structural behavior of CFS partition walls used for a nonstructural component [8; 9]. Of the limited number of available analytical models for CFS partition walls, [PERSON] [10] and [PERSON] and [PERSON] [11], respectively, proposed micro finite element modelling or lumped modelling approaches. Based on the experimental results identifying the cyclic response of individual partition walls [12; 13], [PERSON] and [PERSON] [14], [PERSON] et al. [15], and [PERSON] and [PERSON] [16] suggested analytical modellings which can define the hysteresis ofCFS partition walls using several deterministic parameters such as the initial stiffness, yield strength, post-yielding stiffness ratio, etc. These models also utilize coefficients for calibrating a peak-oriented hysteretic model to reflect their possible variations. Although the global cyclic behavior of a CFS partition wall represented by a single lumped element can be easily captured, it is hard to estimate its local behavior and damage mechanism. [PERSON] et al. [17] suggested a more detailed analytical modelling, called a phenomenological model. This model was constructed using nonlinear and/or linear multi-spring elements which can represent the main components of CFS partition walls and their connections. Such a modeling approach has been considered a powerful one in terms of simulating the global nonlinear force-displacement relations of a CFS partition wall and its local damage sequence under seismic attack. Applications of the detailed model are questionable because of the time-consuming computations in time-history dynamic analyses and numerical complexities. Similar to the models with a single lumped element, deterministic parameters are still needed to construct the hysteresis rules that should be determined by component-level experimental results of components and connections of a CFS partition wall. The previously developed macro-models for CFS partition walls should be improved to overcome the disadvantages mentioned above. In order to address this, a more effective analytical modelling approach needs to be developed to easily construct and simulate the monotonic and cyclic responses of CFS partition walls. This study aims to propose a macro-analytical model for capturing in-plane responses of CFS partition walls which can be constructed with a simple modelling procedure and less computational effort. Furthermore, the model captures the component damage states of a CFS partition wall under imposed excitation. This paper first describes damage states of typical CFS partition walls.