## 3 Simulating the Behavior of the Concrete-Encased Steel Columns  
For different configurations of the CES columns, the resistance of the confined concrete can be defined accordingly. Moreover, an extensive amount of research has been conducted to gather information regarding past research work on analytical models that consider the effect of confinement and other factors into account in order to simulate the actual mechanism of the CES columns [12]. The CES columns were analyzed using the fiber section model. The section is divided up into \"n\" fibers, which are not necessarily all of identical sizes. The stresses are integrated into the cross-sectional area in order to determine the straining actions, such as moment or  
Figure 3: Typical cross section of CES columns. (**A**) H shape section, (**B**) Combined I shape section, (**C**) I shape section. force. Each steel reinforcing bar, structural steel section, or concrete fiber has a specific set of material properties. Fiber stresses are calculated from them using the \"plane sections remain plane\" theory along with relevant constitutive models. There are several formulas for calculating the strain on the fiber as the loads increase. The section axial strain and curvatures with respect to a fixed reference system were described and they did not have to monitor the evolution of the neutral axis (NA) position [13]. Additionally, the impact of the load on the position of the natural axis (NA) was studied [14]. In order to calculate the stresses of the fibers and modules of elasticity, it should determine a constative model for uniaxial models for steel and concrete including the confinement effect. It was discovered that during an increase in the load, the CES column provided its initial strength against lateral shear. It should be noted that the initial stiffness in the model equations should be considered adequately [15; 16; 17; 18]. The impact of flange shear studs for increasing stiffness and bending strength, the concrete's compressive strength, the mechanism of shear resistance of the CES section, and the necessary confinement level to provide appropriate ductility under seismic loading were all explored [16]. In order to account for the confinement impact on the CES columns made of cross-shaped steel and to predict the analytical axial load-displacement relationships of the columns [19; 20], we adapted [PERSON]'s model. The structural steel segment increases the confining stress in the concrete zone. The confinement regions can be made simpler by transforming the parabolic sections, presented in Figure 4, into rectangular regions [21]. By considering the effect of unstiffened elements of the steel section on the confinement, one-half of the corresponding steel area is taken to calculate the confining stress [22]. As presented in Figure 4, the concrete section in the CES column's cross section is divided into three sections, unconfined concrete (UC), partially confined concrete (PC), and highly confined concrete (HC). The stress-strain curves for the concrete are presented in Figure 5a. The steel section is also divided into three sections, the steel flange and the steel web as presented in Figure 5b, and the longitudinal reinforcement as presented in Figure 5c. Consequently, six distinct uniaxial stress-strain relationships are presented in this section [19]. Due to the steel flanges' bending stiffness, the steel section of the CES column could contribute to the expanded concrete's lateral confining pressure. The Mander model, first introduced for reinforced concrete [16], can be applied to HC in CES columns as long as it is established that the steel section's effective lateral confining pressure exists. Consequently, by closely examining the lateral interaction between the concrete and steel section, a unified stress-strain relation is provided for HC. Based on the Mander model, the stress-strain relationship for PC is established.