## 3 Pushover Analysis  
### Roof Displacement-Base Shear Curve Analysis  
The pushover analysis method evaluates the elasto-plastic seismic performance of a structure through static nonlinear analysis. The most used approach is the capacity spectrum method (CSM), as proposed in FEMA 440. Given the uniform distribution of mass and stiffness along the height of the grain warehouse, an inverted triangular horizontal load pattern was applied in the Y direction. To ensure convergence of the numerical model, horizontal loads were simplified as equivalent point loads. The concentrated load on each floor was calculated using the following expression:  
\[F_{i}=\frac{G_{i}H_{i}}{\sum\limits_{j=1}^{n}G_{j}H_{j}}V_{b} \tag{3}\]  
In the equation, \(F_{i}\) denotes the horizontal point load at floor \(i\); \(G_{i}\) and \(G_{j}\) represent the gravity loads of floors \(i\) and \(j\), respectively; \(H_{i}\) and \(H_{j}\) are the floor heights; \(n\) is the total number of floors; and \(V_{b}\) is the total base shear of the structure. Based on this, the pushover curve was transformed into a spectral acceleration-spectral displacement (\(S_{a}\)-\(S_{d}\)) curve using the modal decomposition response spectrum method. The calculation is as follows:  
\[S_{a}=\frac{V_{b}}{W}g \tag{4}\]  
\[S_{d}=\frac{y_{\text{roof}}}{\Gamma_{\varphi_{\text{root}}}} \tag{5}\]  
\(S_{a}\) is the elastic spectral acceleration, \(S_{d}\) is the elastic spectral displacement, \(W\) is the effective mass of the first mode, \(\varphi_{\text{roof}}\) is the modal amplitude at the roof level, and \(\Gamma\) is the modal participation factor. The seismic demand spectrum was derived from the standard elastic response spectrum. The value of \(S_{a}\) was taken from the design code, while \(S_{d}\) was calculated using the following expression:  
\[S_{d}=\frac{T^{2}}{4\pi^{2}}S_{a} \tag{6}\]  
where \(T\) is the fundamental period of the structure. According to the calculation procedure, the roof displacement-base shear (\(\Delta\)-\(V\)) curves for each case are shown in Figure 10. For clarity and comparison, the \(\Delta\)-\(V\) curves were divided into four performance levels: level A and level B correspond to the first occurrence of plastic hinges at beam ends and column ends, respectively; level C indicates a maximum inter-story drift ratio of 2%; and level D marks the peak base shear. For analysis purposes, the cases were grouped into two sets; the base shear and displacement of the model at different displacement levels are listed in Table 6. \begin{table}
\begin{tabular}{c c c c c} \hline
**No** & **Loading Condition** & **Third Floor** & **Second Floor** & **First Floor** & **Fourth Floor** \\ \hline
1 & FEE & filled & empty & empty & Equipment room \\
2 & FFE & filled & filled & empty & Equipment room \\
3 & FFE & empty & filled & empty & Equipment room \\
4 & EEE & empty & empty & empty & Equipment room \\
5 & FFF & filled & filled & filled & Equipment room \\
6 & EFF & empty & filled & filled & Equipment room \\
7 & EEF & empty & empty & filled & Equipment room \\ \hline \end{tabular} Note: In the table, E denotes empty storage and F denotes filled storage.  
\end{table} 
Table 5: Grain-loading conditions. roof displacements are all below the inter-story drift limits (1/300 and 1/50) specified in the Technical Code for Concrete Filled Steel Tubular Structures (GB50936-2014) [22], confirming that the deformation demands meet code requirements. Compared with FEE, EFE, and FFE conditions, the EEF condition exhibits significantly smaller displacements at all performance levels and is close to EFF and EEE, suggesting that grain loading on the first floor enhances initial stiffness and base shear capacity, effectively limiting seismic displacement. Under rare earthquakes, the FEE condition performs notably worse, with lower base shear and larger displacement, caused by upper mass concentration and insufficient vertical force in the empty bottom story, which accelerates stiffness degradation and leads to early plastic hinge formation.