## 2 Finite Element Analysis Modeling and Validation  
### Dynamic Ontological Modeling at High Temperatures  
ABAQUS finite element software was used to establish the finite element analysis model of the RPC column and frame structure. The mechanical properties of both concrete materials and steel are affected under fire and blast loading. In this paper, the RPC and steel constitutive models considering high-temperature fire and explosion load are used with reference to previous studies. The RPC high-temperature dynamic compression stress-strain relationship [23] equations are shown in Equations (1)-(10):  
\[\sigma=E_{\mathrm{d}}\varepsilon\bigg{\{}(1-C_{\mathrm{n}})+C_{\mathrm{n}} \exp\left[-\left(\frac{\varepsilon}{F_{0}}\right)^{\mathrm{m}}\right]\bigg{\}} \tag{1}\]  
\[m=\left[-0.56+3V_{\mathrm{f}}+\left(0.35-2V_{\mathrm{f}}\right)\ln\dot{ \varepsilon}\right]\cdot f_{7}(T)+f_{8}(T) \tag{2}\]  
\[F_{0}=\left[0.0062+0.31V_{\mathrm{f}}^{1.7}-0.00167\times(0.1+V_{\mathrm{f}}) \ln\dot{\varepsilon}\right]\cdot f_{9}(T)+f_{10}(T) \tag{3}\]  
\[C_{\mathrm{n}}=\left[0.977-1.4V_{\mathrm{f}}+\left(0.004+0.25V_{\mathrm{f}} \right)\ln\dot{\varepsilon}\right]\cdot f_{11}(T)+f_{12}(T) \tag{4}\]  
\[f_{7}(T)=-0.0188\cdot T+3.26 \tag{5}\]  
\[f_{8}(T)=0.0249\cdot T-1.2336 \tag{6}\]  
\[f_{9}(T)=-0.188\cdot T+12.726 \tag{7}\]  
\[f_{10}(T)=0.00102\cdot T-0.047 \tag{8}\]  
\[f_{11}(T)=0.1011\cdot T-0.658 \tag{9}\]  
\[f_{12}(T)=-0.10107\cdot T+1.5453 \tag{10}\]  
where the formula \(\sigma\) is the stress, in MPa; Ed is the dynamic modulus of elasticity of the concrete, in MPa; m and F\({}_{0}\) are the shape parameter and size parameter, respectively; C\({}_{\mathrm{n}}\) is the introduced dimensionless parameter; V\({}_{\mathrm{f}}\) is the volumetric friction of steel fiber; \(\dot{\varepsilon}\) is the strain rate; \(f_{7}(T)\)-\(f_{12}(T)\) are temperature-dependent parameters; and T is the concrete temperature, in \({}^{\circ}\)C.  
Performing RPC dynamic tensile strength determination tests at high temperatures is difficult, and test data are difficult to obtain; as such, the RPC static tensile stress-strain relationship at high temperatures is used as an alternative [24], with the proposed formula shown in Equation (11):  
\[m=\left[-0.56+3V_{\mathrm{f}}+\left(0.35-2V_{\mathrm{f}}\right)\ln\dot{ \varepsilon}\right]\cdot f_{7}(T)+f_{8}(T) \tag{2}\]0  
where \(f_{\mathrm{t,T}}\) is the tensile strength at temperature T, in MPa; \(f_{\mathrm{t,20}}\) is the tensile strength at room temperature, in MPa; and T is the temperature, in \({}^{\circ}\)C.  
The dynamic ontological relationship at high temperatures for the steels used in this paper is shown in Equation (12). This model combines the advantages of the JC principal model and the Perzyna principal model and is a type of steel principal model that considers the temperature effect and strain rate effect [25]:  
\[m=\left[-0.56+3V_{\mathrm{f}}+\left(0.35-2V_{\mathrm{f}}\right)\ln\dot{ \varepsilon}\right]\cdot f_{7}(T)+f_{8}(T) \tag{2}\]1where \(\sigma_{y}\) represents the yield strength of the material after considering the effect of explosions and fire, \(\sigma_{0}\) is the yield strength of the material; \(\varepsilon\) is the strain; B, n, and K are rulers for the strain hardening influence system; m is the temperature softening coefficient; and the reference strain rate \(\dot{\varepsilon}_{0}\) is taken as 0.0001/s. For the dimensionless temperature \(T^{*}(t)\), the method of determination is shown in Equation (13); the strain rate \(\dot{\varepsilon}(Z)\) under the different proportionality distances is determined by Equation (14); z is the proportionality distance. For the determination method, see Equation (15); in this paper, we determined the proportional distance z selection range to be 0.54 \(\leq\) z \(\leq\) 2.75.