## 5 Numerical Results
### Reinforced Concrete Column
#### 5.2.2 Analysis of the Load-Carrying Capacity and Displacement  
During the load-carrying capacity and displacement analysis, the results of numerical study for the IB column were compared with the experimental and theoretical results of [PERSON] and [PERSON] [29], and the theoretical results of [PERSON] and [PERSON] [39]. The results for the load-carrying capacity were compared in terms of the cross-section displacement in the mid-span of the column, which can be seen in node 13. Figure 12 shows the results for column IB. The results using the proposed DRM + AL are marked by the solid line. The load-displacement diagram at node 13 using DRM + AL indicates the largest element stiffness among all of the cases that were considered. In this graph, small jumps in the displacements are observed for a load of \(P_{IB}^{\text{DRM+AL}}\,=\,551\,\)kN. This represents the first crack in the tensile concrete  
Figure 12: Numerical results for node 13 of the IB column, compared with experimental and theoretical results from [PERSON] and [PERSON] [29] and [PERSON] and [PERSON] [39]. layer for the middle cross-section of the column. Further developments in the cracking zone of the middle cross-section (and subsequent small jumps in the displacements) were observed at a load of \(P_{IB}^{\mathrm{DRM+AL}}=716.3\,\mathrm{kN}\). The load-carrying capacity, as determined by the numerical method, was \(P_{IB}^{\mathrm{DRM+AL}}=797.1\,\mathrm{kN}\), and the corresponding value for the transverse displacement was \(w_{IA}^{\mathrm{DRM+AL}}=0.71\,\mathrm{cm}\). The softening process in these three cases has similar characteristics. In the experimental analysis, the critical state was indicated at the highest load value of \(P_{IB}^{EXP,LR}=830\,\mathrm{kN}\). The DRM + AL results are the most similar to the experimental results, when compared with other methods. The load-carrying capacity of the column was 4% lower than the experimentally determined load and the displacement corresponding to the load-carrying capacity was 50% lower. The numerically determined load-carrying capacity of the column was 12% higher than the theoretical results of [PERSON] and [PERSON] [39]. The load-carrying capacity from the DRM + AL was 17% larger than [PERSON] and [PERSON]'s results [29], while the displacement was 6% larger. Moreover, the initial stiffens observed in numerical results obtained using DRM + AL differ from the experimental results. This effect is a consequence of the concrete modeling method and it is caused by adopting the idealized properties of structural material, especially the initial deformation modulus. The reduction of displacement values obtained by using DRM + AL is also related to the application of the overcritical damping value in the inelastic effort range of the structure. Figure 13 shows the stress state in subsequent effort steps of the IB column. The load steps are marked by numbers \(\,\)1\(\,\)1\(\,\)-\(\,\)1\(\,\)8\(\,\)\(\,\)\(\,\)\(\,\)and correspond with the load steps indicated in the graph of Figure 12. The first cracks in the tensile concrete layer occur in the cross-sections located near the edges of the column \(\,\)1\(\,\)2\(\,\)\(\,\). Further development of cracks propagates towards the center of the column \(\,\)13-5\(\,\)\(\,\)\(\,\)1. Together with the increase of the load, it is observed that the plasticizing of the more compressed concrete external layer, which develops in an analogous manner to the development of the cracking process, i.e., progresses from the edge's cross-sections towards the mid-span of the column. At the load value \(P_{IB}^{\mathrm{DRM+AL}}=765.8\,\mathrm{kN}\), the process of the concrete softening begins in the cross-sections that are located near the edges. The plasticizing area of the compressed concrete propagates into the internal layers of the cross-section, which is similar to the cracked area \(\,\)1\(\,\)5\(\,\)\(\,\)1.