## 3 Analysis of the Flexural Performances of CCFSts with Gaps
### Effect of the Angle between Loading Direction and Coronal Gap Axis  
In this section, the effect of the angle between loading direction and coronal gap axis on the flexural capacity of CCFS is investigated, and the height of the coronal-cap gap was fixed as 7.5 mm. The angles between the load direction and coronal gap axis were set to 0\({}^{\circ}\), 45\({}^{\circ}\), 90\({}^{\circ}\), 135\({}^{\circ}\), and 180\({}^{\circ}\), respectively, as illustrated in Figure 6. At the same time, the interface between the core concrete and steel pipe allowed for cohesion and friction. Then, the difference in the flexural capacity of the structures with and without interfacial bonding could be clarified, and the ability of the coupled cohesive-friction cohesive model could be tested. The static displacement load was applied, and the damage fields (SDEGs) of the core concrete are displayed in Figure 7. It should be explained that the SDEG field was chosen because it contains the necessary information on concrete damage. The SDEG field displays the superposition of the tensile damage and compressive damage, and it can comprehensively reflect the complete stiffness degradation distribution inside the structure. The relationship between the SDEG field, tensile damage field, and compressive damage field can be expressed by Equation (22), as follows:  
\[1-SDEG=\left\{ \begin{array}{l}(1-s_{t}DamageT)(1-s_{c}DamageC),\text{Cyclic}\\ (1-DamageT)(1-DamageC),\text{Monotonic}\end{array} \right. \tag{22}\]  
where \(DamageT\) and \(DamageC\) are the damage factors of tension and compression; \(s_{t}\) and \(s_{c}\) are the recovery coefficients of tension and compression, respectively. Monotonic loading was applied in this study. The equivalent plastic strain fields (PEMAGs) of the outer steel tube are displayed in Figure 8.  
As illustrated in Figure 7, in the upper part of the core concrete of the CCFST, the damage shows a continuous status, and a compression failure area formed. However, the lower part of the core concrete shows a strip distribution status. At this area, tensile failure continued to occur. Although the compression failure characteristics under each angle were quite similar, the tensile failure region of 45\({}^{\circ}\) was more concentrated in the middle of the sample. The concentration degree decreased when the angle equaled 90\({}^{\circ}\). The difference was not significant for the other conditions. The equivalent plastic strain field of the outer steel tube reflected the inelastic deformation. It can be seen in Figure 9 that the equivalent  
Figure 6: Changes in the angle between the load direction and coronal gap axis. plastic strains of 0\({}^{\circ}\) and 180\({}^{\circ}\) were much larger than the other angles, and 180\({}^{\circ}\) was the most significant. The equivalent plastic strains were very similar when the angle equaled 45\({}^{\circ}\), 90\({}^{\circ}\), and 135\({}^{\circ}\). The rigid body elements were used as the loading blocks, as shown in Figure 5c. The reference points were coupled to the loading device to control the displacement of the entire loading device and achieve the targeted load. Then, the displacements of the reference points and the reaction forces were extracted. Figure 9 shows the load-displacement curves under various angles. The peak force intuitively reflects the bending bearing capacity of the CCFST. It is clear that the peak forces, ranked from lowest to highest, were 45\({}^{\circ}\), 90\({}^{\circ}\), 135\({}^{\circ}\), 0\({}^{\circ}\), and 180\({}^{\circ}\). Especially, when the angle equaled 0\({}^{\circ}\) and 180\({}^{\circ}\), the peak force was much lower than the other degrees. This phenomenon demonstrates that the flexural capacity of the CCFST will seriously decrease when the gap axis and load direction are parallel. For further comparison, a CCFST model without a mortar interlayer was built, and the contact between the outer steel tube and the core concrete is described by the Coulomb model.