## 5 Concrete-Encased Steel Column Behaviors under Cyclic Loads
As stiffness deterioration decreased, the columns with studs shown in Figure 13 demonstrated a greater capacity for deformation and energy dissipation. Many types and strengths of concrete have been used in composite buildings and substantial research in recent years. Concrete with a compressive strength greater than 50 MPa is referred to as high-strength concrete [46]. This type of concrete can be made with premium aggregates and superplasticizers, and its strength can even surpass 100 MPa. The cyclic behavior of CES columns with long webs of cross-shaped steel was more influenced by the concrete strength when the concrete strength rose, increasing the columns' shear capacity and a decrease in their ability to deform [47]. Additionally, as concrete strength  
Figure 13: Cross section of CES column with shear connectors. grew, so did the capacity of long CES columns [39]. The common failure modes of cyclically loaded high-strength CES columns, shear failure, shear-flexural failure, and flexural failure, are shown in Figure 14.  
Based on the lateral displacement capacity of the column and its integration with the curvature distribution, the following equation for the length of the plastic hinge of the CES column is calculated and proposed [26]:  
\[L_{rp}=(0.5d+0.05h)\bigg{\{}(1+0.04t_{ek})\frac{M_{m}}{M_{y0}}-0.25\bigg{\}}+12(D _{r}-12) \tag{16}\]  
In Equation (16), the \(M_{m}\) is the maximal moment, \(M_{y0}\) is the yield moment, \(D_{r}\) is equal to the rebar diameter in mm, and \(t_{ek}\) is the ratio of \(A_{s}/A_{r}\). Here, \(A_{s}\) is defined as the gross area of the steel section, and \(A_{r}\) is the gross area of the longitudinal rebars. Also, \(d\) is considered the effective column depth, and \(h\) is the column length. Figure 15 presents the plastic hinge length along the column height [26]. When assessing seismic performance, the CES column's ductility is an essential metric. As seen in Figure 16, the ductility coefficient is essentially calculated as the ratio of lateral displacement corresponding to ultimate displacement and yield displacement, derived from the specimen's backbone curve. Generally speaking, excellent ductility is considered to be displayed by CES columns with a ductility coeffici  
Figure 14: Typical failure mode of cyclically loaded high-strength CES column, reprinted with permission from [23], 2023, _Journal of Building Engineering_. Figure 15: Plastic hinge length along the column, reprinted with permission from [26], 2010, _Journal of Bridge Engineering_. Given the divergent perspectives, additional experimental research is required to elucidate the impact of steel sections at different load ratios. Effect of Transverse Reinforcement on Behavior of Concrete-Encased Steel ColumnsA large number of research works have been carried out in the past decade on the impact of transversal reinforcement on the behavior of the CES columns. The stirrup effectively confines the core concrete, and the seismic behavior of the CES compression-bending members is directly impacted by the stirrup spacing. It was found that as stirrup spacing increases, bearing capacity and ductility decrease [47]. Additionally, when the stirrup spacing increases from 75 to 100 mm, bearing capacity and ductility are reduced to a higher amount than when the spacing grows from 50 to 75 mm. This indicates that if the stirrup spacing stays below a particular threshold, it does not affect the ductility of CES columns. It suggests that the maximum stirrup spacing interval in the seismic area needs to be restricted. For this reason, the Chinese specification [44] suggests a value of 100 mm as the maximum spacing of stirrups for CES columns [47]. According to the experimental results, the CES column specimens' damage process usually includes the following: the deterioration of the concrete core; local buckling of the H-shaped steel flange; cracking on the buckled steel flange; longitudinal reinforcement bar buckling; and flexural cracks and spalling of the concrete cover at the base of the column.