## 3 Slit Damper Models  
In general, passive energy-dissipating devices have been designed to be incorporated into the bracing system of structural frames. Accordingly, typical steel slit dampers can be installed on the top of chevron-shaped (inverted-V) braces at the concentrically braced frames (CBFs), and attached to the middle of the beam member as shown in Figure 2. The installation of these devices leads to seismic design philosophy based upon increasing ductility and energy dissipation capacity of all types of frame structures. The geometric details for the slit damper (SL) models provided in the reference [21] are illustrated in Figure 3. These slit damper models are manufactured from standard wide flange sections with a number of slits cut from the web, thereby leaving a number of strips between two flanges. The slits are rounded at their ends with the aim of avoiding stress concentration in the reentrant corner. The slit dampers are connected to the main frame member with four bolts, thus removing the possibility of sudden failure due to any imperfections associated with welding.  
Information on the established specimens for the experimental test performed by [PERSON] and [PERSON] [21] is presented in Table 1. The values of variable design parameters illustrated in Figure 3 (_i.e._, _l_o, \(b\), and _t_) are also presented in this table. In this paper, six experimental specimens out of total nine specimens are selected for parametric study. In addition, the 3D FE models used to reproduce the behavior of the slit dampers are calibrated to their experimental test results so as to validate the propriety of the modeling methods. The standard wide flange section with the dimension of 161.8 mm depth by 152.2 mm flange width by 8 mm for web thickness by 11.5 mm for flange thickness was used to construct all slit damper specimens. The standard base material coupons were obtained from the web section. After conducting coupon tests to determine material properties, yield stress, elastic modulus, and hardening ratio were determined to be 316.5 MPa, 206.1 GPa, and 1.5%, respectively. In general, Grade (Gr.) 50 carbon steel includes these material property values. The slit damper specimens labeledfrom SL1 to SL6 in the table can be classified as having _b/l\({}_{o}\)_ ratios ranging from 0.155 to 0.215. The slit dampers with superelastic SMA bending bars are labeled as an additional \"-SMA\" in the last acronym of the model identification (ID), for example, SL1-SMA (see also Table 1).  
These steel slit dampers withstand shear forces (_P_silt) carried from the beam members, and undergo corresponding shear deformations (\(\Delta_{\mathrm{slit}}\)). A part of the web sections can be considered as deep beam sections, which deform due to shearing. Meanwhile, the relatively slender strips behave as a series of partially fixed-end beams with rotational angles (\(\theta\)) at the end supports, and mostly deform in double curvature under bending. Because of rapid section changes at both ends of each strip, plastic hinges attributed to the mechanism of energy dissipation occur under sufficient bending deformation. On the contrary, inflection points characterized by the zero-moment position are generated approximately at the middle of each strip. Including the bending moment diagram drawn along the strip line, the deformation of the slit damper subjected to direct shear force is illustrated in Figure 4. As can be also seen in Figure 3, the bending mechanism of the strip can be determined in accordance with design parameters, such as strip depth (_l\({}_{o}\)_), strip width (_b_), and web thickness (_t_).  
Figure 3: Geometric details for experimental slit damper (SL) models, (**a**): Front View, (**b**): Plan.  
Figure 2: Installation of the slit damper device in the concentrically braced frame.