## 3 Load-Bearing Analysis of Columns under Impact Load
### Cross-Sectional Bending Moment M  
Five cross-sections are extracted at equal intervals along the height of the column, and the variation curves of the cross-sectional bending moment with the impact time and displacement are analyzed (Figure 15). As shown in Figure 15a, under a horizontal impact, the cross-sectional bending moment oscillated in the range of \(t\) = 0-12 ms at the instant of impact, and the maximum  
Figure 14: \(V\)-\(t\) curve under impact load (influence of velocity). Figure 15: Change in the cross-sectional bending moment during static and impact loading. value of the negative bending moment (\(-9.8\) kN\(\cdot\)m) occurred at the cross-section near the column cap, while the bending moment along the height alternated between the positive and negative directions, which was mainly caused by the inertia effect [23]. At an impact time of 21 ms, the bending moments of the 5 cross-sections almost simultaneously reached the extreme value points (Figure 15a), and the bending moment of the bottom section reached the time when it was closest to the static load bending moment in the entire impact process. In the subsequent process, with a gradual weakening of the external impact and inertia effect, the absolute values of the bending moments of the five cross-sections gradually decreased and began to experience a stable plateau development stage. At this time, the cross-sectional bending moment near the column cap stabilized and fluctuated at a low level (1.5 kN\(\cdot\)m), which was comparable to that under static loading (Figure 15b). Since the bottom position served as the main cross-section of the specimen to bear the bending moment, Figure 15c compares the bottom bending moment vs. the displacement curves under impact and static loads. In general, the bottom bending moments generated by the two load types under the same displacement condition varied in nearly the same manner. After the column had experienced an uncracked concrete stage and entered a concrete cracking stage, the bottom bending moment of the column under impact load gradually developed to its peak (13.99 kN\(\cdot\)m), which was slightly smaller than the peak bending moment under a static load (15.28 kN\(\cdot\)m). To investigate the effect of the impact velocity on the variation in the cross-sectional bending moment, Figure 16a,c shows the time-history curves of the bending moments of the 5 cross-sections of specimens DZ150-4 and DZ150-7, with \(v_{0}\) = 0.4 m/s and \(v_{0}\) = 1.2 m/s, respectively, which are compared with those of specimen DZ150-2 with \(v_{0}\) = 0.8 m/s in Figure 15a. The effect of the increase in velocity on the bending moment response at the instant of impact was mainly reflected in the increase in the positive and negative bending moment values. When \(v_{0}\) was 0.4, 0.8, and 1.2 m/s, the peak negative bending moments were \(-6.99\), \(-9.8\), and \(-12.4\) kN\(\cdot\)m, respectively. In general, although the development of the bending moment at this stage fluctuated, it increased overall. Furthermore, the magnitudes of the bending moments of the five cross-sections under different impact velocities retained the same order, and the bending moments of the two cross-sections at the lower part of the column always maintained a positive direction. In the subsequent impact process, due to the low impact velocity on specimen DZ150-4 (only tensile cracks were observed on the surface of the specimen, and the longitudinal rebars did not yield, thus belonging to damage state I), the cross-sectional bending moment rebounded and decreased after reaching a maximum value of 9.74 kN\(\cdot\)m. For the severely damaged specimen DZ150-7, the bending moment experienced a gradual descending stage.