## 3 Experimental Results
### Analysis of the Test Results
#### 3.2.7 Vertical Frequency of the Test Slab  
Figure 22 and Table 4 show the change in frequency with time during the test (in Table 4, the temperature used to calculate rate of frequency reduction is the measured value of ST5-1 reinforcement temperature in the slab). The figure shows that throughout the whole test process, the change in the vertical first-order frequency of the two-way slab can also be divided into three stages.  
Figure 21: Corner-time curves of the two slabs.  
Figure 22: Measured change in the first-order vertical frequency and vertical deflection time curve of the two-way slab. (**a**) Slab CS1. (**b**) Slab CS2.  
The initial stage is from the beginning of the test to the 60 th min. In this stage, the bottom of the two-way slab is subject to fire expansion, there is a large temperature gradient in the cross section, and a large number of cracks appear on the slab surface and develop rapidly because the surface is constrained by the clamped end. The vertical deflections in the slab increase rapidly. Damage to the slab leads to a rapid reduction in its stiffness, and the corresponding first-order vertical self-excitation frequency changes significantly. The second stage is from the 60 th min to the 150 th min. In this stage, the vertical deflections increase slowly, and the self-excitation frequency decreases correspondingly. During this period, no new cracks appear on the slab surface, and the existing cracks continue to expand. As the in-plane membrane effect in the central region of the plate changes from compression to tension, the tensile membrane effect develops gradually, the growth rate of the vertical deflections decreases, and the stiffness attenuation rate of the plate decreases significantly compared with the previous stage. The third stage is from the 150 th min to the end of the fire test. In this stage, the vertical deflections increase slowly and linearly, and the vertical frequencies of the slabs decrease slightly, which also reflects the slow attenuation of the stiffness of the slab. Throughout the whole test process, the frequency attenuation of the slab is large, which indicates that the stiffness of the slab experiences great loss under the action of fire.  
Figure 22 shows that the variation in the vertical first-order frequency of the two-way slab is consistent with the variation law of the vertical deflections in the slab, and Figure 23 shows the relationship between change in the frequency and change in the vertical deflection of the two-way slab under fire conditions.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & & \multicolumn{2}{c}{**Fire Time**} & \\ \multirow{2}{*}{**Specimen**} & \multicolumn{2}{c}{**0–60 th min**} & \multicolumn{2}{c}{**60-150 th min**} & \multicolumn{2}{c}{**150 th min to the Fire Test**} \\  & **Frequency** & **Rate of** & **Frequency** & **Rate of** & **Frequency** & **Rate of** \\  & **Reduction** & **Frequency** & **Reduction** & **Frequency** & **Reduction** & **Frequency** \\ \hline \multirow{2}{*}{CS1} & \multirow{2}{*}{9.6\%} & 0.16\%/min, & \multirow{2}{*}{5.3\%} & 0.06\%/min, & \multirow{2}{*}{1.68\%} & 0.06\%/min, \\  & & 0.027\%/\({}^{\circ}\)C & & 0.02\%/\({}^{\circ}\)C & & 0.067\%/\({}^{\circ}\)C \\ \multirow{2}{*}{CS2} & \multirow{2}{*}{9.5\%} & 0.16\%/min, & \multirow{2}{*}{4.3\%} & 0.05\%/min, & \multirow{2}{*}{2.5\%} & 0.04\%/min, \\  & & 0.032\%/\({}^{\circ}\)C & & 0.017\%/\({}^{\circ}\)C & & 0.0005\%/\({}^{\circ}\)C \\ \hline \hline \end{tabular}
\end{table}
Table 4: Vertical first-order frequency variation of two-way slabs during different periods of fire exposure.  
Figure 23: Relationship between the change in the frequency and change in the vertical deflection of the two-way slab under fire exposure. (**a**) Slab CS1. (**b**) Slab CS2.