# Macro-Modelling Approach for the In-Plane Cyclic Response of Cold-Formed Steel Partition Walls
## 5 Conclusions  
In order to address disadvantages of previously developed macro-models for in-plane deformational CFS partition walls and improve them, this paper proposes an analytical model which can be constructed with a simple modelling procedure capable of tracing the behaviors of GBs, studs and screw connections, and less computational effort with no numerical instability. From the global in-plane response of a CFS partition wall exposed to earthquakes, the important behavior of each component is identified. Structural properties of screw connection are determined considering two different phases: (1) before and (2) after the contact between a GB and RC slab occurs. The dominant contact phenomenon is utilized to decide structural properties of gypsum boards since friction forces in the interface between their corner and the web of tracks are the only contribution to the global in-plane response of a CFS partition wall. The cyclic response of CFS studs is governed by torsional buckling in the direction of its weak axis. The buckling behavior is used for determining the structural properties of studs. Based on the structural properties of screw connections, GBs, and studs, a procedure in a flow-chart format is suggested to determine the lateral force-displacement relation of a CFS partition wall. The flow chart consists of several sub-routines related to the structural behavior of all components in the partition wall: screw connections, GBs, and CFS studs. The analysis model constructed with discretized lumped springs of influential sub-components is developed for this study. Three spring assemblies are introduced to represent the hysteresis of the sub-components including studs, screw connections, and GBs. The spring assemblies for studs and  
Figure 18: Damage-to-drift ratio relation of the reference specimens (from [PERSON] et al. [34], [PERSON] et al. [35]. GBs are constructed with a primary spring and a gap element while that for screw connection is made of only a primary spring element. The suggested analytical model of CFS partition walls is verified with the results obtained from tests of two full scale specimens. The comparison between the analytical and experimental force-displacement curves shows that the analytical model captures the overall strength and stiffness degradation and pinching behavior well. In addition, the estimated damage states in the analytical model are compared with the experimental observations. The initial stiffness reduction and damage propagation of the screw connections and their pullout and pull-though resulting in strength degradation are well predicted by the analytical model. The occurrences of damage, such as crushing or breaking of GBs and buckling of studs, can be properly captured in the proposed model. The out-of-plane behavior of CFS partition walls might induce detrimental effects on their in-plane behaviors as applied lateral displacements being increased when severe damage to the tracks such as failure of PAFs occurs. Their out-of-plane behavior is mainly governed by the plastic response of the flanges of tracks, which is easily modeled. However, their in-plane behavior is more complicated and is, in turn, difficult analytically model. Therefore, this study focuses on the in-plane behavior of CFS partition walls and develops a macro-modelling approach to capture them only. Nonetheless, bounding effects between out-of-plane and in-plane CFS partition walls are still considered. To address this, further investigating their interaction between out-of-plane and in-plane behaviors of CFS partition walls with additional experimental programs is required and the suggested analytical model could be adjusted by reflecting experimental results. Original draft manuscript, D.-H.S. ; supervision and review writing, H.-J.K. All authors have read and agreed to the published version of the manuscript.