## 3 Load-Bearing Analysis of Columns under Impact Load
### Cross-Sectional Shear V  
As shown in Figure 13, five cross-sections are extracted at equal intervals along the height of the column, and the variation curves of the cross-sectional shear with impact time and displacement are analyzed. Figure 12: Comparison of load-displacement curves under impact loads (experimental versus numerical). Figure 13: Change in the cross-sectional shear during static and impact loading. Under impact, at the instant of initial contact between the impactor and the specimen (the impact time \(t\) = 0 to 4.1 ms), due to the influence of the inertial effect [23], the sectional shear force fluctuates violently along the height direction, and a large shear force appears in both the positive and negative directions (Figure 12a), which is due to the inertial force being generated at the moment when the column is impacted. According to the balance of the horizontal force, the impact force can be obtained by adding up the inertial force and the sectional shear force, and the inertia force will change dramatically or even greater than the impact force in the impact process, which will make the sectional shear force fluctuate or even change directions. When \(t\) is 0.82 ms, the cross-sectional shear near the column cap reaches 54.02 kN. With the impact time increasing to 2.4 ms and 4.1 ms, the direction of the cross-sectional shear changes from positive to negative, and the peak absolute value of that is 34.35 kN and 57.4 kN, respectively. Under the same displacement condition, the cross-sectional shear caused by the inertia effect in this stage is far more than that under static load, and the ratio is more than 10 times greater than the shear level of 14.47 kN under the limit state of the static load (Figure 10b). According to the method for calculating the shear strength of the inclined section provided in GB50010-2010 \"Code for Design of Concrete Structures\" [17], the shear capacity of the inclined section of this column specimen is calculated to be 152 kN. In comparison, although the cross-sectional shear of the specimen at the instant of impact was greater than that under a static load, it did not exceed the cross-sectional shear capacity. Therefore, no obvious shear cracks were observed in the upper part of the column after the horizontal impact test. In contrast, for the RC beams with shear-to-span ratios of 6-10 subjected to drop-weight impacts in the literature [24; 25], because the cross-sectional shear at the impact instant exceeded its shear capacity, a shear cone was formed at the mid-span impact point at the instant of initial impact (2 ms), which caused the final shear failure. After the impact time reached 12.3 ms, the shear time-history curves of the five cross-sections coincided, and the variation in the cross-sectional shear along the height of the specimen gradually became consistent (Figure 13a). After the initial impact stage, the specimen entered the stable deformation stage, during which the specimen moved \"together with\" the impactor. As the impact force gradually decreased, the cross-sectional shear decreased significantly. A comparison of Figure 13a,b reveals that at the same displacement level (the displacement atop column \(u_{1}\) ranged from 28 to 35 mm), the cross-sectional shear under impact stabilized at a level of 6.28 kN, while the shear under static load gradually decreased from 9.3 kN to 5.6 kN, which was not a significant difference. In the subsequent process, as the impactor gradually separated from the specimen, the cross-sectional shear slowly decreased to zero and the impact vibration process ended. To investigate the effect of the impact velocity on the variation in cross-sectional shear, Figure 14a,b shows the time-history curves of the shear of the five 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 10a.