## 3 Results and Analysis
### Crowd Load Response Test Results and Analysis  
Table 7 shows the test results where the response was the greatest in each group of tests. Figure 11 shows the acceleration time history curve at the maximal response point of response measurement area 1 under the 1.5 Hz jump condition. Test results showed that, under condition T1 (jumping), the maximal response was 374 mm/s\({}^{2}\); under condition T2 (walking), the maximal response of the test area was 168 mm/s\({}^{2}\); under condition T3 (walking), the maximal response of the testing area was 84.25 mm /s\({}^{2}\); under condition T4 (quickstep), the maximal response of the test area was 279.15 mm/s\({}^{2}\). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Measurement Area** & \multicolumn{3}{c}{**Frequency (Hz)**} \\
**Finite-Element Calculation** & **Measured Value** & **Error** \\ \hline Area 1 & 3.470 & 3.750 & 7.47\% \\ Area 2 & 3.747 & 3.950 & 5.14\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of calculated and measured values of first-order vertical frequency. Figure 10: Radial tilt support around stands at the test site. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{5}{c}{**Mode Order Calculated by Finite Element**} \\ \hline Area 1 (MAC) & & & \\ Measured mode order & 8 & 15 & 20 & 28 \\
1 & 0.0983 & 0.8005 & 0.0063 & 0.0145 \\
2 & 0.0001 & 0.2196 & 0.0084 & 0.0124 \\
3 & 0.0041 & 0.015 & 0.0042 & 0.0311 \\ Area 2 (MAC) & & & & \\ Measured mode order & 8 & 15 & 20 & 28 \\
1 & 0.0436 & 0.2717 & 0.7947 & 0.0231 \\
2 & 0.0004 & 0.0256 & 0.0064 & 0.0222 \\
3 & 0.0324 & 0.001 & 0.0223 & 0.0065 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: MAC of actual measurement and finite-element calculation. The theoretical value was consistent with the actual measured value. The position where the acceleration response is larger in the field test is similar to the maximum response position in the finite element calculation result, and the test value was selected for comparison with the finite-element calculation value of the response (Table 8). Table 8 shows that, except for the T3 working condition, the error between the theoretical and measured values was basically within \(\pm\)15%. The possible reason is that the response value itself under T3 working conditions was relatively small, which led to a large percentage difference due to small changes. Considering the coupling effect of the crowd, the theoretical value of the crowd load response obtained by the finite-element calculation was reduced. The reasons for the impact:  
* auxiliary steel is not horizontal and has an inclination angle (Figure 10);
* bending stiffness has a certain effect on vibration;
* end circumferential wall also affects the vibration response of the structure. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Condition Number**} & \multirow{2}{*}{**Test Group**} & **Peak Value** & **Root Mean** & **Peak Value** & **Root Mean** \\  & & **(m/s\({}^{2}\))** & **Square** & **(m/s\({}^{2}\))** & **Square** \\  & & & **Area 1** & & **Area 2** \\ \hline \multirow{3}{*}{T1} & Group 1 & 0.33400 & 0.06352 & 0.25267 & 0.04582 \\  & Group 2 & 0.37400 & 0.05960 & 0.27900 & 0.06580 \\ \cline{1-1}  & Group 1 & 0.11379 & 0.01550 & 0.16800 & 0.02510 \\ \cline{1-1}  & Group 2 & 0.14000 & 0.02194 & 0.15900 & 0.02695 \\ \cline{1-1}  & Group 1 & 0.08000 & 0.02051 & 0.05133 & 0.01448 \\ \cline{1-1}  & Group 2 & 0.08425 & 0.01813 & 0.04800 & 0.01318 \\ \cline{1-1}  & Group 1 & 0.27915 & 0.03956 & 0.16235 & 0.02357 \\ \cline{1-1}  & Group 2 & 0.22733 & 0.03347 & 0.15112 & 0.02558 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Statistical time-domain results of vertical vibration acceleration. Figure 11: Area 1, maximal response under condition T1. (**a**) Test group 1; (**b**) Test group 2.