## 4 Employment of Proposed Retrofit Strategies to Seismically Designed Steel Frame Structures
### Modeling Approaches and Validation Studies  
A 3-D micro-based finite element model of the prototype building, termed M1 in [PERSON] (2018) and [PERSON] et al. (2018), is used herein. The full 3-D model is shown in Figure 1(a). Compared with the physical-based finite element models, which are mainly composed of solid elements, the modeling approach adopted by M1 is simplified. The model accounts for the composite floor, steel beams and columns, and the two types of connections that are used to join the columns and beams, i.e., moment \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multicolumn{2}{c}{**Retrofitting Scheme 1 (8**} & \multicolumn{2}{c}{**Retrofitting Scheme 2 (24**} \\  & **mm Thick Seat Angles)**} & \multicolumn{2}{c}{**mm Long Slotted Hole)**} \\ \hline \multirow{2}{*}{Static response} & Increase in \(R_{us}\) & 47.6\% & 37.5\% \\  & Increase in \(\Delta_{us}\) & 20.8\% & 18.6\% \\ \multirow{2}{*}{Dynamic response} & Increase in \(R_{ud}\) & 55.7\% & 45.8\% \\  & Decrease in \(\Delta_{0}\) & 42.0\% & 26.6\% \\ \multirow{2}{*}{Additional components} & Seat angle & Plate with long slotted holes \\ \multirow{2}{*}{Additional steel quantity (kg)} & \multirow{2}{*}{13.5 (1.6\% of total weight)} & \multirow{2}{*}{3.4 (0.4\% of total weight)} \\ Attachment of additional components & Bolts & & Welds and bolts \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparisons between retrofit strategy 1 and retrofit strategy 2. Figure 23: Prototype building. connections and fin plate connections. As shown in Figure 24, beams and columns are modeled using fully integrated rectangular shell elements. Shear tab connections are modeled using a single row of shell elements, while the floor slab is modeled using fully integrated four-node, isotropic shell elements connected to the underlying steel beams through rigid links. More details of the model can be found in [PERSON] (2018) and [PERSON] et al. (2018). Simplified models are developed for the planar composite frames represented by Model M0, M0-RS1-8, and M0-RS2-a24 using the modeling approach of M1, as shown in Figure 25. The details of the simplified models for the enhanced connection employing retrofit strategy 1 are presented in Figure 25. The seat angle is modeled using fully integrated rectangular shell elements with a size of approximately 8 mm, and the bolts are modeled using beam elements. The inelastic stress-strain responses of seat angles and bolts are both represented by \(J2\) plasticity models calibrated against experimental data. The bolt holes in the seat angle are physically considered. According to the simulation results of M0-RS1, the failures of the enhanced connections are initiated by the failures of the vertical leg of the seat angle connected to the column flange due to the contact between the bolt head and the seat angle. On the other hand, the shear responses of the bolts also need to be reasonably captured. Therefore, in order to consider these aspects, the bolts' nodes are connected to the nodes of the bolt holes using rigid links. The other end of the bolt element is connected to the beam or column surface because it is reasonable to assume that the bolt is clamped by the flange. In the simplified model representing the simple connection enhanced using retrofit strategy 2, which is presented in Figure 25, the additional steel plate is modeled using shell elements with an opening at the center whose width is equal to the two long slotted holes. The bolts sliding along the long slots are modeled using discrete beam elements, which are only permitted to deform axially within the plane of the additional steel plate. The discrete beam elements are connected to the beam flange using rigid links, and their nodes are connected to the column surface. No resistance is generated initially within the discrete beam elements to model the slide of the bolts along the long slots before they are in contact with the edges of the long slots.