## 3 Load-Bearing Analysis of Columns under Impact Load
### Cross-Sectional Bending Moment M
It is worth noting that Figure 15c also shows that the \(M\)-\(t\) curve of the bottom cross-section has a secondary decrease, which refers to the phenomenon where the \(M\)-\(t\) curve drops from the peak bending moment to a plateau stage with a high bending moment and then drops again to a second plateau stage with a low bending moment. Figure 16b,d compare the changes in the bending moments of the bottom cross-section under static loading and dynamic loading, respectively. For specimen DZ150-4 in damage state I, the change in the bending moment under impact followed the curve under static load and rebounded and decreased before reaching the yield point under static load, indicating that it was still in the elastic stage. For specimen DZ150-2 in damage state II, the peak bending moment only exceeded the yield point, as shown in Figure 15c. Figure 16d shows that during the impact process, the peak bending moment of specimen DZ150-7 in damage state III reached the ultimate bending moment under static loading.Therefore, the bottom bending moment can be employed as an indicator to compare the responses of a structure under impact loads and static loads, respectively, in order to effectively evaluate the damage state of a specimen. In summary, due to the existence of the inertia effect, the cross-sectional bending moment oscillates, the maximum value of the negative bending moment appears at the cross-section near the column cap, and the bending moment along the height alternately changes in the positive and negative directions. For the bottom cross-section subjected to the maximum bending moment, the bottom bending moments generated by the two types of loads under the same displacement condition change almost identically. Effect of Different Combinations of \(m\) and \(v_{0}\) on the Dynamic Response of the Column with the Same \(E_{\mathrm{k}}\)  
In existing studies, \(m\) and \(v_{0}\) as two factors are usually considered separately to investigate their influences on the dynamic response of members. The existence of different combinations of the two factors for the same \(E_{\mathrm{k}}\) increases the difficulty in evaluating the dynamic response of the structure. To date, the influences of different combinations of \(m\) and \(v_{0}\) under the same \(E_{\mathrm{k}}\) on the dynamic response of RC columns has still not been studied. Therefore, this study conducts a parametric analysis under different levels of \(E_{\mathrm{k}}\) which includes multiple combinations of \(m\) and \(v_{0}\). In the analysis, different combinations of \(m\) and \(v_{0}\) at different levels of impact kinetic energy \(E_{\mathrm{k}}\) are applied to analyze the dynamic responses of RC column members under impact using the abovementioned FE model of RC columns and considering the material strain rate effect. The specimens in the literature [16], which had a cross-sectional side length of 150 mm, an axial compression ratio of 0.1, and a reinforcement ratio of 2.7%, were employed as basic calculation models. A total of 4 sets of impact kinetic energy \(E_{\mathrm{k}}\) were designed, where each set of models contained 10 numerical examples with different values of \(m\) (ranging from 0.2 to 40 t) and \(v_{0}\). The models are named in the format of \"DZ150-\(E_{\mathrm{k}}\)-impact mass\", and the specific parameter information is listed in Table 4.  
Figure 16: Variation of the section’s bending moment during static load and different impact velocity. Figure 17a-c summarizes the variation patterns of the impact duration \(t_{\rm d}\), maximum bottom bending moment \(M_{\rm max}\), and maximum displacement \(u_{\rm max}\) with an increase in \(m\) for the same \(E_{\rm k}\). Clearly, \(t_{\rm d}\) increases as \(m\) increases, mainly because the decrease in the impact velocity \(v_{0}\) significantly reduces the deformation rate of the specimen.