## 5 The Stress Analysis of the Composite Frame--A Further Numerical Study  
The modeling of the test specimen CF4 was selected as a typical model to study the behavior of the L-shaped composite spatial frames. The horizontal load-versus horizontal displacement curve for a typical sample of a concrete-filled steel tubular frame that was provided by FEA is shown in Figure 10. To investigate the stress state of the frames at different critical locations and under different load \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**CF** & \(P^{0}_{max}\) (**k**N) & \(P^{exp}_{max}\) (**k**N) & \(P^{0}_{max}/P^{exp}_{max}\) & **Standard Deviation** & **Coefficient of Variation** \\ \hline CF1 & 188.7 & 207.5 & 0.909 & & \\ CF2 & 185.8 & 206.1 & 0.902 & & \\ CF3 & 205.4 & 220.7 & 0.931 & 0.014 & 1.5\% \\ CF4 & 200.9 & 216.7 & 0.927 & & \\ \hline \hline \end{tabular} \(P^{0}_{max}\) is the maximum lateral load-carrying capacity of the specimen by FEM \(P^{exp}_{max}\) is the maximum lateral load-carrying capacity of the specimen from experiment.  
\end{table} 
Table 4: Comparison of ultimate values by experiments and finite element model (FEM). Figure 9: Comparison of measured envelops curves and computed monotonic curves. levels, the characteristic points corresponding to the three typical moments are selected in the whole progressive response of the horizontal load-versus horizontal displacement of the frame (see Figure 10). The three characteristic points were taken, as follows: (i) the first point was the yield point of the load-displacement curve of the frame specimen, which means that the composite frame was ending the elastic stage and starts yielding; (ii) the second point was the one corresponding to horizontal peak load \(P_{max}\) (or the position corresponding to \(\Delta_{max}\)) of the frame specimen; and, (iii) the third point was the one where the horizontal load capacity of the frame specimen dropped to 85 percent of the peak amplitude. At this time, the frame almost reached failure limit. The columns and beams in frame structures were bending specimens when constant axial load was applied to columns, and the cyclical load was applied to beam end. Therefore, the stress states are also different at different section positions. Several representative cross-sections of the stress state on the frame column are selected for analysis. The cross-section position number is shown in Figure 11, where sections are taken at the base of the frame column (C11-C14) and the top of the column (C21-C24), respectively. The cross section (B1-B8) was taken at the beam end (plastic hinge) of the frame beam. All sections were taken offset by 100 mm from the edge of the specimen to avoid the influence of the stress concentration at the base of column and the joint. The stress distribution of the core concrete at the bottom and top of both the first-story and second-story columns at different loading levels were shown in Figures 12-15. It could be seen from all figures that there were a tension zone and a compression zone in the cross section. With the horizontal load increasing, the area of the compression zone of the section gradually decreased, shown from (a) to (c) in Figures 12-15. The reason for this phenomenon was that the frame column first subjected the axial load. At the stage, the steel tubular and the concrete were in the state of full section compression. With the increase of the horizontal load, the uniform compression of the entire section was transformed  
Figure 11: Typical section location of CF4. Figure 10: The horizontal load-versus horizontal displacement curve relation of typical L-shaped CFST frames (CF4). into a non-uniform pressure of the core concrete of frame column, and then the tension zone appeared. Corresponding to the different loading levels, the stress of the concrete at the bottom section of the column developed differently.