# On the Modeling and Analysis of Brittle Failure in Existing R/C Structures Due to Seismic Loads
## 3 Example Application of the Proposed Numerical Simulation Procedures
### Evaluation of the Analyses Results
Peak values, as well as the time instant of their occurrence, are also given in Table 3.  
It is observed that the results of the flexural analysis (Fiber Model), where all the other premature local failure mechanisms were omitted in the model, fail to reproduce the salient characteristics of the response including the intensity of the drift demands by systematically underestimating them. In the s11 case, the analysis results of the fiber model lead to an underestimation of the actual drift demands by 24% in the first and by 69% in the second and third story with regards to the vibration in the \(X\) plan direction. These numbers respectively are 16%, 40%, and 53% in the first, second, and third stories in reference to the vibrations in the \(Y\) plan direction. In the s12 case, the drift demands obtained from analysis of the fiber FE model in the first, second, and third stories were underestimated by 32%, 73%, and 75% in the \(X\) plan direction and by 51%, 63%, and 64% in the \(Y\) plan direction as compared to the drift demands recorded during the testing of the SPEAR building. On the \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Story**} & \multirow{2}{*}{**Column**} & \(M_{\text{u},X}\) & \(\theta_{\mathbf{0.005_{r},\eta,X}}\) & \(M_{\text{a},X}\) & \(\theta_{\mathbf{0.005_{r},\eta,X}}\) & \(M_{\text{lup},X}\) & \(M_{\text{lup},X}\) & \(\theta_{\mathbf{0.005_{r},\eta,X}}\) & \(M_{\text{l},X}\) & \(\theta_{\mathbf{0.005_{r},\eta,X}}\) \\  & & \(M_{\text{u},Y}\) & \(\theta_{\mathbf{0.005_{r},\eta,Y}}\) & \(M_{\text{a},Y}\) & \(\theta_{\mathbf{0.005_{r},\eta,Y}}\) & \(M_{\text{lup},Y}\) & \(\theta_{\mathbf{0.005_{r},\eta,Y}}\) & \(M_{\text{lup},Y}\) & \(M_{\text{l},Y}\) & \(\theta_{\mathbf{0.005_{r},\eta,Y}}\) \\  & & **(kN-m)** & **(rad)** & **(kN-m)** & **(rad)** & **(kN-m)** & **(rad)** & **(kN-m)** & **(rad)** & **(kN-m)** & **(rad)** \\ \hline \multirow{8}{*}{\(1\)} & C1,1 & - & - & - & - & 22.71 & 0.0037 & - & - \\  & & 49.33 & 0.0030 & - & - & 50.64 & 0.0031 & - & - \\  & C2,1 & _?_ & _?_ & _?_ & _?_ & _?_ & _?_ & _?_ & _?_ & _?_ \\  & & 161.01 & 0.0031 & - & - & 141.94 & 0.00027 & 131.98 & 0.0025 \\  & C3,1 & - & - & - & - & 28.25 & 0.0039 & - & - \\  & C4,1 & - & - & - & - & 32.95 & 0.0041 & - & - \\  & C5,1 & - & - & - & - & 46.33 & 0.0043 & - & - \\  & C6,1 & - & - & - & - & 40.99 & 0.0042 & - & - \\  & C7,1 & - & - & - & - & 25.07 & 0.0038 & - & - \\  & C8,1 & - & - & - & - & 35.15 & 0.0041 & - & - \\  & C9,1 & - & - & - & - & 36.47 & 0.0042 & - & - \\ \hline \multirow{8}{*}{\(2\)} & C1,2 & - & - & - & - & 20.29 & 0.0036 & - & - \\  & & 49.94 & 0.0034 & - & - & 43.15 & 0.0029 & - & - \\  & C2,2 & _?_ & _?_ & _?_ & _?_ & _?_ & _?_ & _?_ & _?_ \\  & & 162.98 & 0.0034 & - & - & 119.36 & 0.0025 & 128.15 & 0.0027 \\  & C3,2 & - & - & - & - & 24.31 & 0.0038 & - & - \\  & C4,2 & - & - & - & - & 27.77 & 0.0039 & - & - \\  & C5,2 & - & - & - & - & 39.63 & 0.0042 & - & - \\  & C6,2 & - & - & - & - & 34.60 & 0.0041 & - & - \\  & C7,2 & - & - & - & - & 22.04 & 0.0037 & - & - \\  & C8,2 & - & - & - & - & 29.70 & 0.0040 & - & - \\  & C9,2 & - & - & - & - & 30.47 & 0.0040 & - & - \\ \hline \multirow{8}{*}{\(3\)} & C1,3 & - & - & - & - & 16.75 & 0.0034 & - & - \\  & & 50.32 & 0.0039 & - & - & 33.16 & 0.0025 & - & - \\ \cline{1-1}  & C2,3 & _?_ & _?_ & _?_ & _?_ & _?_ & _?_ & _?_ & _?_ \\ \cline{1-1}  & & 164.20 & 0.0039 & - & - & 89.94 & 0.0021 & 116.04 & 0.0028 \\ \cline{1-1}  & C3,3 & - & - & - & - & 18.78 & 0.0035 & - & - \\ \cline{1-1}  & C4,3 & - & - & - & - & 20.57 & 0.0036 & - & - \\ \cline{1-1}  & C5,3 & - & - & - & - & 29.93 & 0.0040 & - & - \\ \cline{1-1}  & C6,3 & - & - & - & - & 25.39 & 0.0038 & - & - \\ \cline{1-1}  & C7,3 & - & - & - & - & 17.55 & 0.0034 & - & - \\ \cline{1-1}  & C8,3 & - & - & - & - & 22.59 & 0.0037 & - & - \\ \cline{1-1}  & C9,3 & - & - & - & - & 22.36 & 0.0037 & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Moment-Rotation relationships used in the zero-length elements of the SPEAR FE building model.