## 6 Conclusions  
In this contribution, on the basis of the energy principles and variational principles, by using the displacement superposition method and completely considering the impact of shear lag effect and accordion effect of corrugated steel webs, an analytical method that can determine the natural vibration characteristics of a CBGCSW was developed. The follow conclusions were obtained.  
1. By comparing the natural vibration frequencies calculated by the ANM with those obtained by other methods, the correctness of the ANM and the rationality of the model simplifications were verified. The natural frequencies obtained by ANM agreed well with those measured by experiment. The ANM was more accurate than the elementary beam theory (EBT) in calculating natural frequencies. Compared with the finite element model (FEM), the ANM can illustrate the key factors, such as shear lag effect and accordion effect. The influences of these key factors on the dynamic response can be analyzed more conveniently and rapidly by using the ANM. Hence, the ANM provides a theoretical basis for deriving a practical formula for engineering calculation, and addresses the deficiency of numerical simulation analysis.
2. The shear lag effect on a CBGCSW is under the influence of the order of the natural vibration frequency and span-width ratio. The shear lag effects of six CBGCSW models all increased significantly with the increasing of the mode order. Further, the shear lag effects were significantly larger for the CBGCSWs with smaller span-width ratios. Hence, for practical engineering applications, the shear lag effect on a CBGCSW with a smaller span-width ratio is significant and cannot be neglected.
3. Compared with the natural vibration frequencies of the CBGGSW models, the natural vibration frequencies of the CBGCSW models were significantly lower, which indicates that the impact of the accordion effect is significant. In design and seismic calculations, attention should be paid to this difference between CBGGSWs and CBGCSWs.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Boundary Condition**} & \multirow{2}{*}{**Span–Width Ratio**} & \multicolumn{5}{c}{_gct/\%_} \\ \cline{3-6}  & & **1 st** & **2 nd** & **3 rd** & **4 th** & **5 th** \\ \hline \multirow{3}{*}{Simply supported} & 6.72 & 6.55 & 7.39 & 8.61 & 9.60 & 10.52 \\  & 8.12 & 6.38 & 6.94 & 7.78 & 8.52 & 9.21 \\  & 9.24 & 6.30 & 6.72 & 7.37 & 7.95 & 8.50 \\ \hline \multirow{3}{*}{Fixed-support} & 6.72 & 12.39 & 10.46 & 9.28 & 8.58 & 8.46 \\  & 8.12 & 11.78 & 10.36 & 9.32 & 8.71 & 8.36 \\ \cline{1-1}  & 9.24 & 11.32 & 10.20 & 9.29 & 8.67 & 8.29 \\ \hline \hline \end{tabular}
\end{table}
Table 5: The impact of the accordion effect of the CBGCSW.  
**Author Contributions:** The authors have contributed equally to this work. [PERSON] and [PERSON] conceived and prepared original draft; [PERSON] and [PERSON] contributed analysis tools; [PERSON] and [PERSON] analyzed the data; [PERSON] and [PERSON] reviewed. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the National Natural Science Foundations of China (U1934207 and 51778630), the Experimental Foundations of the New Railway from Chengdu to Lanzhou (CLRQT-2015-010), the Hunan Innovative Provincial Construction Project (2019 RS3009), and the Innovation-driven Plan in Central South University (502501006), the Fundamental Research Funds for the Central Universities of Central South University (2018 szts189).  
**Conflicts of Interest:** The authors declare no conflict of interest.