## 5 Evaluation of Major Design Codes Based on Results of FE Analysis
### Influence of Range of Lateral Bracing Arrangements  
Figure 15 shows the effect of the \(\gamma\)-value on the normalized critical axial force for three types of bridges. It demonstrates that the normalized critical axial force tends to increase with increasing \(\gamma\)-value in the Chinese code and decrease in the Japanese code, respectively. This means that the Chinese and Japanese code overestimates and underestimates the positive effect of \(\gamma\)-value on the critical axial force, respectively. The critical axial force increases with increasing \(\gamma\)-value in the FE analysis results, and the same tendency is obtained by the Chinese code since the value of panel length \(a\) decreases with increasing \(\gamma\)-value. Therefore, the increase in \(\gamma\)-value leads to the increase in the normalized critical axial force in Chinese code. In the Japanese code, there is no parameter relating to the influence of lateral bracing, and thus the critical axial force, according to the Japanese code, is independent of the \(\gamma\)-value. Therefore, a larger \(\gamma\)-value reduces the normalized critical axial force in the Japanese code. Concerning the Eurocode, a tendency for normalized critical axial force to increase with increasing \(\gamma\)-value is observed for a deck-type bridge. In other words, the code overestimates the positive influence of the \(\gamma\)-value in the case of a deck-type bridge. However, this tendency is not the same for through and half-through types. In the Eurocode, the buckling length is determined by the product of \(\beta\)-value and height of the end portals \(h\). A decrease in \(\gamma\)-value results in increased height \(h\), which then leads to a decrease in \(\beta\)-value, as shown in Figure 7. Therefore, the change in critical axial force depends upon the amount of the reduction in \(\beta\)-value and the increment in \(h\)-value with decreasing \(\gamma\)-value. When the \(\gamma\)-value is in the range of 0.23 to 0.55 and 0.73 to 0.86 for a through-type bridge and in the range of 0.23 to 0.41 and 0.73 to 0.86 for a half-through type bridge, the reduction in \(\beta\)-value is larger than the increment in \(h\)-value, so the critical axial force increases with increasing \(\gamma\)-value. Otherwise, the critical axial force decreases with increasing \(\gamma\)-value. When the critical axial force is normalized by FE results,  
Figure 14: Accuracy Evaluation of Multinational Codes on Influence of Rise-to-span Ratio.  
these increasing and decreasing tendencies are slightly reduced since the critical axial force by FE analysis increases with increasing \(\gamma\)-value, especially when the stiffness ratio is small. Therefore, the relationship between normalized critical axial force for through and half-through arch bridges and \(\gamma\)-value is not monotonous. However, for deck-type bridges, \(\beta h\) decreases with increasing \(\gamma\)-value as the reduction in \(\beta\)-value is much larger than the increment in the \(h\)-value, so the critical axial force for deck-type arch bridges increases with escalating \(\gamma\)-value. Further, owing to the relation between critical axial force in FE analysis and the \(\gamma\)-value, the normalized critical axial force for deck-type bridges increases with increasing \(\gamma\)-value in the Eurocode.