# Seismic Performance of Reinforced Concrete Short Columns Subjected to Freeze-Thaw Cycles
## 3 Test Results and Analysis
### Shear Deformation  
In general, the lateral deformation of the tested columns is comprised of three components, i.e., flexure, longitudinal bar slip, and shear deformation. In this experiment, the development of inclined cracks was altered with increasing FTCs, and accordingly, the shear response was focused and its contributions to the total deformation were analyzed. It is assumed that the shear deformation is mainly concentrated at the plastic hinge region as shown in Figure 11. According to the data from the instruments attached to the tested columns, the shear distortion \(\gamma\) at the plastic region is estimated by the following equation:  
\[\gamma=\Delta_{sh}/l=\frac{1}{2}\Bigg{[}\sqrt{\left(d+\xi_{1}\right)^{2}-l^{2 }}-\sqrt{\left(d+\xi_{2}\right)^{2}-l^{2}}\Bigg{]} \tag{3}\]  
where, \(\Delta_{\text{sh}}\) is the shear displacement at the plastic region; \(\xi_{1}\) and \(\xi_{2}\) are the displacements measured from the diagonal LVDTs, as shown in Figure 5, respectively. Therefore, force-shear deformation responses at the plastic region were obtained and are presented in Figure 12. We note that the recording of shear displacements of specimens ZD-0 and ZD-1 terminated at the first cycle of 1.8% drift because of non-negligible measurement errors happened at the final stage.  
Figure 10: Theoretical strength of specimens under different numbers of FTCs.  
It appears that the shear displacement history of specimen ZD-1 is close to that of specimen ZD-0 but different from specimen ZD-2. For the case of specimen ZD-2, a considerable increase of shear deformation in the post-peak portion was seen, particularly in the negative directions. This unevenly increased in two directions owing to the uneven widening of major inclined cracks in the two loading directions, which was also observed from the picture of failure patterns (see Figure 6). However, this asymmetry appears more gradually in column ZD-0 and ZD-1.  
The contribution of the shear component to the total lateral displacement of all specimens was calculated at the critical levels including cracking, yielding, peak, and ultimate point, as illustrated in Figure 13. The results indicate that for all the tested columns, the shear contributions were relatively small in the elastic range, whereas this quantity increased significantly at the ultimate point, i.e., where the drift of shear strength degradation began to drop rapidly. The average growth rate was 2.3 times from the cracking to the ultimate state. Secondly, for columns with freeze-thaw damage (ZD-1 and ZD-2), the shear deformation always tended to occupy a larger proportion than that of the control column (ZD-0) at the listed critical points. Typically, for the most damaged specimen ZD-2, approximately 24% of the total deformation was due to shear at the defined ultimate displacement, while this quantity was only 17% for the undamaged specimen ZD-0. The interpretations for the large shear displacement of ZD-2 are summarized as follows: The tensile strength of concrete would also be reduced by the action of FTC as the compressive strength and even severely as quantified in several studies [10; 34]. This reduction would cause the increase in length and width of the incline cracks during the cyclic tests, and decreasing in numbers, as shown in Figure 7. Therefore, the shear displacement appears to be larger.  
Figure 11: Calculation diagram of shear displacement.  
Figure 12: Measured lateral load versus shear distortion.