# Seismic Performance Assessments of RC Frame Structures Strengthened by External Precast Wall Panel
## 4 Analytical Approach  
Many researchers [9; 10; 11; 12; 13; 14] have developed nonlinear analysis methods to evaluate the behavior of reinforced concrete walls. In this study, the RC frame structures with non-seismic details were modeled as nonlinear beam-column elements [15; 16; 17; 18], and the modeling of the walls was modified by applying the longitudinal and diagonal line element model (LDLEM) [14; 19]. Figure 11a shows that the LDLEM consists of a beam element with infinite stiffness, and longitudinal and diagonal elements. It is a technique of modeling the longitudinal element to resist flexure, and the diagonal element to resist shear. In LDLEM, the diagonal member simulates the web concrete that resists shear force and is modeled to resist both tension and compression. Previous studies [10; 11; 20] have mainly dealt with barbell-type shear walls or infill wall analysis for seismic strengthening with the use of LDLEM. However, in this case, the two-dimensional elements can be modeled, because the frame and the wall are located on the same plane. For the PC wall proposed in this study, since the precast wall is attached and fixed by anchor bolts on the face the RC frame, it needs to be modeled as a three-dimensional element, unlike in the previous analysis. For this, the precast wall was modeled using LDLEM, and the RC frame was modeled to be in front of the wall as a fiber section. Figure 10: Lateral load-strain relationship of anchor bolts: (**a**) at beam (Specimen FBC) (**b**) at column (Specimen FBC). In general frame structures, bending moment and shear force are generated simultaneously in a beam by seismic loads. However, in the fiber section model, only the behavior of axial force and the bending moment can be defined. In this study, a section aggregator ([PERSON] 2004) [21] was used to reflect the shear behavior in the analysis. The section aggregator analyzes the axial and flexural behaviors with the use of a general fiber section model, as shown in Figure 11b, and reflects the shear force-displacement response defined separately. In this study, the shear behavior of the RC columns was analyzed using a modified compression field theory (MCFT) [22; 23], and the results were then reflected in the fiber section through the section aggregator. The column concrete is modeled by dividing it into the confined concrete inside the lateral reinforcement, and the unconfined concrete outside. For the material model of concrete, [PERSON] (1994)'s  
Figure 11: Analytical modeling approach: (**a**) longitudinal and diagonal line element model (LDLEM) modeling ([PERSON], 2007); (**b**) Section aggregator. model [24] was used; while for the confined concrete, [PERSON] (1988)'s model [25] was used. The reinforcement was modeled using the Giuffre-Menegotto-Pinto model [26]. As described above, for the shear behavior of the column member, the analysis result estimated using MCFT was modeled as the backbone curve of the Pinching 4 model [27] and added to the fiber section analysis model with the use of the section aggregator. With respect to the loading/unloading stiffness and strength degradation characteristics of the Pinching 4 model, the cyclic shear behavior was defined based on the test results of the column, as shown in Figure 12.  
Figure 13 shows the finite element modeling details of Specimens FB, FBC and FPB, respectively. In the Specim FB model presented in Figure 13a, 11 rebar and concrete elements were modeled to match the location of the longitudinal reinforcement placed on the specimen. The inclination angle of the diagonal element, corresponding to the compression strut of the wall, was modeled to 45 degrees to fit the squat wall. In existing shear wall analysis models [10; 11; 20], since the focus has been placed more on the behavior of the wall when modeling barbell-type shear walls or infill walls, the connection between the column and beam was modeled as a pinned connection in the same way as other longitudinal elements.