## 4 Axial-Flexural Behavior of Concrete-Encased Steel Columns  
Since axial compression is an uncommon loading scheme in real construction, research on the behavior of the axial-flexural interaction is necessary because the CES bridge piers are typically subjected to a combination of axial force and bending moment. However, there are a few experimental investigations of the eccentric-compressed CES columns. The limited number of experimental investigations reveals the axial-flexural failure mechanism, and Figure 9 illustrates the common failure modes [26]. In other words, tension failure and compression failure are two distinct groups into which axial-flexural failure may fall. Important elements having an impact on the CES column axial behaviors include the concrete strength, the end eccentricity ratio, the slenderness ratio, the structural steel index, and the transverse reinforcement ratio [27].  
Concrete cracking and the occurrence of the longitudinal bars' yield strength at the tension side are characteristics of tension failure, while concrete cover spalling and crushing, rebar buckling, and stirrup opening are features of compression failure. These are followed by the longitudinal rebar yielding at the tension side [29]. While some specimens experience the cover spalling phenomena, it is not as noticeable as it is in specimens that are concentrically compressed. This could be due to the concrete's enhanced deformability under flexural loading and its non-uniform compressive stress distribution [30]. It is possible to approximate the overall deflection along the height as a half sinusoidal wave, and as there is no visible bond slippage between the steel section and the concrete up until failure, the cross-section analysis can assume a flawless bond [31]. It appears that an increase in structural steel strength has minimal effect on the CES strength for columns that have higher relative slenderness ratios due to the flexural buckling failure mode [32].  
Figure 10 presents the axial-flexural behavior of the CES column according to the Architectural Institute of Japan Standard [33].  
Axial force-bending moment (N-M) interaction diagrams are typically utilized to illustrate the axial-flexural capacity of CES columns. These diagrams can be condensed into piece-wise diagrams to make calculations easier. The estimated bending moment capacity is decreased by a reduction coefficient in order to account for the potential non-attainment of the full plastic stress distribution. Figure 11 presents the axial-flexural diagram of a CES column according to [34]. Figure 11a presents the cross-section capacity of CES columns under external forces, through seven interaction diagrams from a 3D surface on the coordinate system. Figure 11b shows cutting of the 3D surface in a longitudinal direction while Figure 11c shows that cutting of the 3D surface in a latitudinal direction results in a bundle of curves [34].  
Figure 9: Failure mode for eccentrically loaded CES column, reprinted with permission from [28], 2021, _Journal of Building Engineering_.  
Another important aspect of the design of the CES columns is the slenderness ration (_L/b_). The Canadian bridge design code CSA-S6 [9] does not include CES section requirements. However, according to the British code BS.5400-5 [35], the slenderness range for columns _L/b_ should be less than or equal to 30 [35].