# The Mechanical Properties of Reinforced Concrete Columns with Longitudinal Pre-Embedded Holes
## 4 Ductility  
The ductility coefficient of the reinforced concrete column is an important index for measuring the plastic deformation capacity. It reflects the member's ability to undergo deformation without sudden failure after reaching its ultimate bearing capacity. The ductility coefficient is usually expressed by the displacement ductility coefficient, which is the ratio of the displacement of the column at the time of failure to the yield displacement. The calculation formula is shown in Equation (6), and the displacement ductility coefficient of each specimen column is shown in Table 5.  
\[\mu_{\Delta}=\frac{\Delta_{u}}{\Delta_{y}} \tag{6}\]  
where \(\Delta_{u}\)--the displacement of the member when it reaches the ultimate bearing capacity; \(\Delta_{y}\)--the displacement of a member at yield strength.  
Figure 20: Impact of slenderness ratio on load–displacement curve of columns with longitudinal pre-embedded holes.  
As can be seen from Figure 21, the ductility coefficient of the specimen gradually decreases with the increase in the diameter of the opening hole. Compared with the solid column, the ductility coefficient of the longitudinally pre-embedded hole reinforced concrete column decreases by 3.2-3.6%, but the decrease is small and within the allowable range of the project. The higher the concrete strength of the specimen, the more the ductility of the specimen decreases in significance. According to Figure 18, as the strength of the concrete increases, the decreasing section of the load-displacement curve becomes steeper, which indicates that the ductility is lower. This is mainly because as the strength of the concrete increases, the ultimate compressive strain of the concrete decreases, and the brittleness of the material increases, which limits the overall deformation ability of the column, resulting in a ductility decline of the specimen. With the increase in the stirrup ratio of the specimen, the ductility coefficient of the specimen also increases, mainly because the stirrup can effectively limit the transverse expansion of the concrete, delay the crushing and crack expansion of the concrete, improve the ultimate compressive strain of the concrete, and effectively improve the stress distribution in the area of the embedded hole, reduce the stress concentration around the hole, and delay the development of cracks. However, when the slenderness ratio of the column increases, the ductility coefficient of the specimen shows a downward trend, which is mainly because the increase in the slenderness ratio reduces the stability of the column and leaves it more prone to instability failure, thus weakening the overall deformation ability. In addition, the second-order effect of the column will be increased, further accelerating the stiffness degradation and failure of the specimen column, resulting in the decline of the ductility of the column.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Specimen Number** & \(\Delta_{y}\)**/mm** & \(\Delta_{u}\)**/mm** & \(\mu_{\Delta}\) \\ \hline Z0 & 2.07 & 9.72 & 4.70 \\ Z50-1 & 2.07 & 9.42 & 4.55 \\ Z50-2 & 1.84 & 10.31 & 5.60 \\ Z50-3 & 2.38 & 9.00 & 3.78 \\ Z50-4 & 2.39 & 8.87 & 3.71 \\ Z50-5 & 2.70 & 9.02 & 3.34 \\ Z50-6 & 2.11 & 9.72 & 4.61 \\ Z50-7 & 1.51 & 7.96 & 5.27 \\ Z50-8 & 2.50 & 11.28 & 4.51 \\ Z50-9 & 3.01 & 13.41 & 4.46 \\ Z50-10 & 2.68 & 9.00 & 3.36 \\ Z75-1 & 2.08 & 9.46 & 4.55 \\ Z75-2 & 2.19 & 10.39 & 4.74 \\ Z75-3 & 2.38 & 9.74 & 4.09 \\ Z75-4 & 2.42 & 8.88 & 3.67 \\ Z75-5 & 2.73 & 8.24 & 3.02 \\ Z75-6 & 2.12 & 9.77 & 4.61 \\ Z75-7 & 9.35 & 9.87 & 1.06 \\ Z90-1 & 2.15 & 9.73 & 4.53 \\ Z90-2 & 2.08 & 10.31 & 4.96 \\ Z90-3 & 2.10 & 9.15 & 4.36 \\ Z90-4 & 2.40 & 8.59 & 3.58 \\ Z90-5 & 2.66 & 7.90 & 2.97 \\ Z90-6 & 2.12 & 9.79 & 4.62 \\ Z90-7 & 2.34 & 9.45 & 4.04 \\ \hline \end{tabular}
\end{table}
Table 5: Displacement ductility coefficient of each specimen column.