## 3 Proposed Retrofit Strategies
### Retrofit Strategy 1: Addition of Bolted Seat Angle  
In this retrofit scheme, a simple beam-to-column connection is strengthened by using an L90 seat angle with a length of 150 mm, whose legs are connected to column flange and beam flange using two Grade 8.8 M20 bolts, respectively, as shown in Figure 13. Seat angles with thicknesses of 8 mm, 10 mm, and 12 mm are considered. Figure 12: Collapse resistance of the composite frame. To investigate the effectiveness of retrofit strategy 1 in increasing the collapse resistance of the planar composite frames with simple connections, a series of static and dynamic push-down analysis was conducted using model M0 and M0 -RS1-X, where RS1 denotes the adoption of retrofit strategy 1 and X represents the thickness of the seat angles. For example, M0-RS1-8 represents 8 mm thick seat angles, which are used to strengthen the simple connections. The additional seat angles and bolts, which were used to strengthen the simple connections, were modeled using the same modeling approach with M0. A closeup of the beam-to-column connection region of the model is shown in Figure 14. The static and dynamic responses of M0-RS1-8, M0-RS1-10, M0-RS1-12, and unenhanced model M0 are compared in Figure 15a,b, respectively. Figure 14: Model M0-RS1: connection region. Figure 13: Retrofit strategy 1 (unit: mm). Based on the static push-down analysis results, which are illustrated by Figure 15, the static ultimate collapse resistances (\(R_{us}\)) of M0-RS1-8, M0-RS1-10, and M0-RS1-12 reached 434 kN, 371 kN, and 310 kN, respectively, which were 47.6%, 26.2%, and 5.4% larger compared with that of M0. Additionally, the ultimate failure deformation of the composite frame, \(\Delta_{us}\), which is defined as the vertical displacement of the middle column when fracture occurs to the connections/retrofitted connections, was also increased by 20.8% and 2.3%, respectively, in models M0-RS1-8 and M0-RS1-10. However, compared with the unenhanced composite frame, the ultimate failure deformation of M0-RS1-12 decreased by 10.2%. As the increase of the thickness of the seat angles, the efficiency of retrofit strategy 1 decreased, although differences in responses of M0-RS1-8, M0-RS1-10, and M0-RS1-12 were only observed in the final stages of collapse. This was due to the differences between the failure modes of the additional bolted angle with various thicknesses, as shown in Figure 16. Under large deformation conditions, the seat angles underwent plastic deformation shown in Figure 16 due to the extension of the retrofitted connections to form additional catenary action. When thicker seat angles (10 mm and 12 mm) were used, the bolts connecting the seat angle and column flange were subjected to the combination of excessively large shear force and tensile force, as shown in Figure 16, and eventually, these bolts lost their loading carrying capacities. However, Figure 16 demonstrates that the bolts at the same location were mainly under tension throughout the loading process because the seat angles with smaller thicknesses (8 mm) transferred less amount of shear force to them and thus the seat angles would be torn up before failures of bolts. The additional bolted seat angles with smaller thickness failed in a more ductile manner compared with those with larger thickness and therefore were capable of providing a larger amount of additional catenary action. Under a sudden column loss scenario, similar trends were observed, according to Figure 15. The dynamic ultimate collapse resistance \(R_{ud}\) can be increased by 55.7%, 35.9%, and 22.1% after the simple connections were strengthened by adding seat angles with a thickness of 8 mm, 10 mm, and 12 mm, respectively, and the maximum dynamic vertical displacement of the middle column \(\Delta_{0}\) under nominal gravity loads could be reduced by more than 40%. Figure 15: Comparison between the unenhanced and enhanced composite frame using retrofit strategy 1. The collapse resistance mechanisms of the retrofitted composite frames were analyzed.