# Piecewise Function Hysteretic Model for Cold-Formed Steel Shear Walls with Reinforced End Studs
## 1 Introduction  
As the main load-bearing components of cold-formed steel (CFS) structures, the definition of a CFS shear wall's hysteretic model is essential for nonlinear dynamic analysis of the structures. At present, full-scale cyclic loading tests are the main way to investigate the shear performance of CFS shear wall, and the definition of the walls' hysteretic characteristics depends largely on test results [1; 2; 3; 4; 5; 6; 7; 8], because those walls have complex configurations and their load-displacement curves exhibit high nonlinearity and pinching together with strength and stiffness deterioration. However, cyclic loading tests fall short with high costs and long experimental periods, amongst other shortcomings; furthermore, the test curves are too complicated to be directly applied in nonlinear analyses of the structures. Therefore, it is necessary to establish a hysteretic model, which can not only be described with simple mathematical expressions, but also reflect the hysteretic characteristics of the wall in order to predict the nonlinear dynamic responses of CFS structures. So far, numerous numerical studies have been conducted on the seismic performance of traditional CFS shear walls with coupled C section end studs [9; 10; 11; 12; 13; 14]. Currently available hysteretic models for the shear behavior of CFS shear wall include Bouc-Wen-Baber-Noori (BWBN) model, evolutionary parameter hysteretic model (EPHM), pivot model, and three-segment nonlinear pinching hysteretic model [5; 6; 7; 8; 9]. The BWBN model was proposed by [PERSON] [15] and [PERSON] [16] based on a single-degree-of-freedom (SDOF) mechanical system of a CFS shear wall; the model can fully reflect the wall's hysteretic characteristics although its mathematical expression which adopts the use of a differential equation cannot obtain an analytical solution, and parameter identification requires a specific algorithm. EPHM, which was proposed by [PERSON] et al. [17] can reveal the effect of loading history on a wall's lateral stiffness although it lacks a good reflection of pinching, also, loading stiffness increases monotonically with the displacement of the wall growing, which differs from reality. [PERSON] et al. [18] and [PERSON] et al. [19] presented the degraded four-line pivot model and three-segment nonlinear pinching hysteretic model, respectively, both of which can describe the hysteretic characteristics of the wall more completely, although their parameter identification processes depend on experimental results. Traditional CFS shear walls with coupled C section end studs are apparently not applicable to mid-rise CFS structures, for both shear strength and fire resistance of the wall cannot satisfy the requirements of mid-rise residential structures [20]. Hence, [PERSON] and [PERSON] [21] proposed a CFS shear wall with continuous concrete-filled rectangular steel tube (CFRST) columns as end studs (see Figure 1), in which double-layer wallboards were arranged on both sides with a staggered configuration in order to enhance the vertical bearing capacity, anti-overturning ability, shear strength, and fire resistance of the wall, thereby allowing it to be applied to mid-rise CFS structures. The subjects of the above hysteretic models focus on the traditional CFS shear walls and are thus confined to low-rise CFS structures, narrowing their applications. Consequently, it is necessary to establish a hysteretic model with a good reflection of hysteretic characteristics of walls according to the configuration of CFS shear walls with reinforced end studs in order to facilitate the nonlinear dynamic analysis of mid-rise CFS structures. A piecewise function hysteretic model of CFS shear walls with reinforced end studs was proposed according to previous experimental hysteretic laws. The very model can fully reflect the relevant hysteretic characteristics (i.e., stiffness deterioration, strength deterioration, and pinching).