# Cyclic Tests and Numerical Analyses on Bolt-Connected Precast Reinforced Concrete Deep Beams
## 4 Numerical Study  
### Validation of Finite Element Model  
The numerical study was performed by ANSYS, as presented in Figure 10, and the \"Solid 65\" and \"Pipe20\" elements were selected out to model the mechanical behavior of reinforced concrete. A bilinear model was used for the reinforcements, and the material test results such as the elastic modulus, yield stress and ultimate stress were derived from material test results. The concrete damage plasticity model in ANSYS was used for the concrete material in RDBs, because it considers the nonlinear behavior of concrete after it cracks or crushes. The compressive strength curve was taken from the compressive test results of the concrete, and the tensile cracking strength was estimated as 5.6% of the compressive strength. The 3D 8-node solid element captured the cracking and crippling behavior of the concrete. The same mesh sizes (50 mm) were used to mesh the model. The intersectant nodes in concrete elements and reinforcing bar elements were coupled together at the same positions so that they could cause consistent deformations. The boundary conditions of the bottom and top side of the concrete panel are considered as a fixed connection (at the bottom side, fixed the X, Y, Z, Rot X, Rot Y and Rot Z; at the top side, fixed the Y, Z, Rot X, Rot Y and Rot Z; the X-direction represents the direction that applied lateral loads). The lateral load is assumed as a uniform load to apply to the top side of the concrete panel in the finite element model, and this mechanical assumption was valid by [PERSON] et al. [8].  
Figure 10: Deformation and force diagrams for RDB.  
The limitations of the modeling method are: (1) the effects of bolt connections, including the influence on stress concentration and the weakness on RC walls, are not considered in this model; (2) the bond-slipping deformation between reinforcements and concrete is not considered in the model.  
The comparison between test and FEM results on lateral-loading curves and failure modes are presented in Figures 11 and 12, respectively. There is a relatively close agreement between the test results and FEM results in the elastic and elastic-plastic stage. For the RDB-A, the peak shear force of RDBs during the tests and FEM analysis is 10.35 kN and 12.22 kN, respectively, and it is 39.06 kN and 45.24 kN for RDB-B specimen, respectively. The difference in maximum shear force value between tests and FE models is no more than 18%. Besides, the failure modes of FEM (Figure 12) can predict the position where concrete cracking is in the test specimens at the estimated boundary conditions. Thus, it can be concluded that the numerical method could effectively simulate the nonlinear behavior of the RDBs, especially for the ultimate lateral resistance of RDBs, even though the largest error is about 18%. However, the loading, deformation and degradation changing processes are basically predicted by the numerical method, and it is assumed that the method can be used for the following parametric study to analyze the effects of different parameters on the mechanical performance of RDBs.