## 3 Proposed Retrofit Strategies
### Retrofit Strategy 2: Addition of Steel Plates with Long-Slotted Holes  
In this retrofitting scheme, a simple beam-to-column connection in the steel gravity frame is enhanced by using a steel plate with two long-slotted holes, which is welded to the column flange and bolted to the beam flange using Grade 8.8 M20 bolts, as shown in Figure 18. The steel plate is 120 mm long, 100 mm wide, and 8 mm thick so that the tensile strength of the plate, bearing strength of the plate at slotted holes, and the shear strength of the bolts are close to each other and the constructional materials can be fully utilized. After loss of the middle column, the bolts can slide through the long slots initially, which is supposed to have minor impact on the collapse resistance of the retrofitted connection. However, as the increase of deformation, the bolts will be in contact with the steel plates eventually and thus additional catenary action can be developed.  
The closeup at the connection regions of the numerical model representing the retrofitted composite frame using retrofit strategy 2 is shown in Figure 19, in which the bolts and steel plates were modeled using solid elements. Three different allowable sliding distances of the bolts through the long slots \(a\) (Figure 18) were considered: 12 mm, 24 mm, and 36 mm, and the corresponding variants of numerical models were termed M0-RS2-a12, M0-RS2-a24, and M0-RS2-a36. The load-displacement curves obtained through static and dynamic pushdown analysis using M0-RS2-X series and M0 are shown in Figure 20a,b, respectively. Clearly, the collapse resistance of the composite frame could be increased substantially after the simple connections were strengthened using retrofit strategy 2 under both static loading conditions and sudden column loss scenarios. When the middle column was pushed down quasi-statically, the static ultimate collapse resistance of the planar gravity frame \(R_{us}\) was increased by 20.7%, 37.5%, and 40.1% after attaching the steel plates with 12 mm, 24 mm, and 36 mm, and the ultimate displacements, \(\Delta_{us}\), of M0-RS2-a12, M0-RS2-a24, and M0-RS2-a36 were 1.05, 1.19, and 1.17 times of that of M0. After the center column was suddenly removed, the dynamic ultimate collapse resistance, \(R_{ud}\), of models M0-RS2-a12, M0-RS2-a24, and M0-RS2-a36 were 31.3%, 45.8%, and 38.9% compared with that of M0, and the peak dynamic displacement under nominal gravity load was around 25% smaller comparing that of M0.  
Figure 18: Retrofit strategy 2 (unit: mm).  
The sources of resistance that contribute to structural robustness, namely catenary action and flexural action, of M0-RS2s were quantitively studied. Generally speaking, the variation laws of catenary action and flexural action of the retrofitted frames with different lengths of long slots pertaining to vertical displacement of the middle column were similar. For example, the development of collapse resistance mechanisms of M0-RS2-a24 and M0 are illustrated in Figure 21. The comparison indicated that retrofit strategy 2 managed to improve the robustness of the gravity frame through the enhancement of the catenary action due to the additional steel plates with long slotted holes without influencing the seismic behavior of the structural system. Since the responses of M0-RS2-a24 and M0-RS2-a36 were quite close, the optimal slotted hole length should range between 24 mm to 36 mm, and 24 mm long slots were used herein.  
Figure 19: Model M0-RS2: connection region.  
Figure 20: Comparison between the unenhanced and enhanced composite frame using retrofit strategy 2.