# Incomplete Similarity Error Analysis Method of Steel Frame Structure Based on Correlation
## 3 Results
### Influence of Modular Modulus of Beam-column Components  
The geometric incomplete similarity of members in steel frame has important significance in engineering, for instance, if the plate thickness of the prototype is 15 mm, the similarity ratio is 1:4, on this premise the model of complete similarity should be 3.75 mm. In fact, a plate of this thickness does not exist, so the complete similarity on the premise of 1:4 similarity ratio is impossible. Therefore, it is necessary to investigate the similitude error caused by the geometric incomplete similarity of steel components (beams and columns). This part is based on the common assigning groups in engineering, \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Prototype** & \
\begin{tabular}{c} **Joint Stiffness** \\ **(N-m-rad–1)** \\ \end{tabular} & **Model** &
\begin{tabular}{c} **Joint Stiffness of Completely** \\ **Similar (N-m-rad–1)** \\ \end{tabular} \\ \hline \(\mathrm{J_{S}}\) & \(4\times\mathrm{e}^{7}\) & \(\mathrm{J_{S}}\) & \(6.25\times\mathrm{e}^{5}\) \\ \(\mathrm{J_{W}}\) & \(2.4\times\mathrm{e}^{7}\) & \(\mathrm{J_{W}}\) & \(3.75\times\mathrm{e}^{5}\) \\ \(\mathrm{J_{SC}}\) & \(2\times\mathrm{e}^{8}\) & \(\mathrm{J_{SC}}\) & \(3.125\times\mathrm{e}^{6}\) \\ \(\mathrm{J_{WC}}\) & \(1\times\mathrm{e}^{8}\) & \(\mathrm{J_{WC}}\) & \(1.5625\times\mathrm{e}^{6}\) \\ \hline \hline \end{tabular} Note: \(\mathrm{J_{S}}\): Strong axis; \(\mathrm{J_{W}}\): Weak axis; \(\mathrm{J_{SC}}\): Strong axis of column base; \(\mathrm{J_{WC}}\): Weak axis of column base.  
\end{table} 
Table 4: Joint stiffness of completely similar. Figure 2: Schematic diagram of component and joint grouping. dividing the frame into four groups, which are the edge beams, the middle beams, the edge columns, the middle columns. Global sensitivity is calculated on the basis of the grouping. This paper adopts the method of sensitivity analysis based on the loop nesting of MATLAB (2016, The MathWorks, Inc., Natick, MA, USA) and ANSYS. A model database is established in MATLAB, including model information such as beam height, beam width, plate thickness and joint stiffness, each set of data in MATLAB represents a model in ANSYS. Then the database is introduced into ANSYS to carry out the analysis calculation. After the calculation is completed, the results are returned to MATLAB for statistical analysis and the the resulting cyclic calculation method can realize automated sensitivity analysis, achieving a sensitivity analysis of extremely large amounts of data. A group of 2950 models was calculated; the variation range of all parameters is listed in Table 5.  
The variation ranges of the steel components' height and width should keep consistent for comparison purposes, as should the other parameters (the thickness of flange and web, the joint stiffness). Limiting conditions were added into MATLAB to reject the unqualified component groups, as a result the calculation will accord with engineering practice. Figures 3-14 show the results of sensitivity calculation; every group of components' height and width were shown in the same figure, as did the thickness of flange and web. Figures 3, 5, 7, 9 and 11 show the sensitivity calculation results of height and width. Figures 4, 6, 8, 10 and 12 show the sensitivity calculation results of flange and web's thickness. The results show that keeping the other parameters (force, \(E\), etc.) under the condition of complete similarity, the target variable has a violent change when the side beams' height varies within 50 mm, which indicates the height of side beams have a bigger influence in the situation. When the corner columns' height varies within 100 mm, the target variable is 220-175 mm, when the side columns' height varies within 50 mm, the target variable is 310-180 mm. The middle beams' height and width, the thickness of all the plates, have little influence on the value of the target variable.