# Analysis of Fire Resistance of Prestressed Concrete T-Beam Based on ABAQUS Numerical Simulation
## 2 Finite Element Model Building and Verification
### Finite Element Model and Simulation
#### 2.1.2 Calculation Model of Fire Resistance Analysis  
For the fire resistance analysis of prestressed concrete T-beams, finite element simulations were carried out using the sequential thermal-force coupling analysis method. On the basis of the completed temperature field model, the static analysis was carried out, and the mesh size was kept consistent with that of the temperature field model for the accuracy of the temperature of the cells in the static analysis model. The mechanical properties of the component materials will deteriorate under the action of high temperatures; domestic and foreign scholars have conducted much experimental research on these materials. The high-temperature mechanical properties of concrete in this paper are shown in Table 3, the high-temperature mechanical properties of steel are shown in Table 4, and the high-temperature mechanical properties of the prestressing bar are shown in Table 5. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Thermal Parameters** & **Formula** & **References** \\ \hline Heat transfer coefficient & \(\lambda_{c}=1.72-1.72\times 10^{-3}T+7.16\times 10^{-7}T^{2}\) & ([PERSON] et al. [13]) \\ Heat capacity & \(C_{\text{C}}=\begin{cases}900&20\ ^{\circ}\text{C}<T\leq 100\ ^{\circ}\text{C}\\ 900+(T-100)&100\ ^{\circ}\text{C}<T\leq 200\ ^{\circ}\text{C}\\ 1000+(T-200)/2&200\ ^{\circ}\text{C}<T\leq 400\ ^{\circ}\text{C}\\ 1100&400\ ^{\circ}\text{C}<T\leq 1200\ ^{\circ}\text{C}\\ \text{Density}&\rho_{c}=2400\ kg/m^{3}\end{cases}\) & (Eurocode2 [14]) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Thermal parameters of concrete at elevated temperature. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Thermal Parameters** & **Formula** & **References** \\ \hline Heat transfer coefficient & \(\lambda_{s}=\begin{cases}54-0.0333T&20\ ^{\circ}\text{C}<T<800\ ^{\circ}\text{C}\\ 27.3&T>800\ ^{\circ}\text{C}\\ \end{cases}\) & (Eurocode3 [15]) \\ Heat capacity & \(C_{s}=473+20.1\times 10^{-2}T+38.1\times 10^{-5}T^{2}\) & ([PERSON] et al. [16]) \\ Density & \(\rho_{s}=7850\ kg/m^{3}\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Thermal parameters of steel at elevated temperature. \begin{table} \begin{tabular}{c c c} \hline \hline
**Mechanical Properties** & **Formula** & **References** \\ \hline Stress–strain principal structure relationship & \(y=\begin{cases}2.2x-1.4x^{2}+0.2x^{3}&x<1\\ 0.8x-1)\text{ }+x&x\geq 1\\ y=\frac{c}{f_{c}(1)}&x=\frac{c}{f_{p}^{2}}\\ \end{cases}\) & ([PERSON] et al. [13]) \\ Tensile–compressive strength & \(\frac{f_{c}(T)}{f_{p}}=\frac{1}{1+18\left(\frac{1}{200}\right)^{1.4}}&20\ ^{\circ}\text{C}\leq T\leq 1000\ ^{\circ}\text{C}\\ \text{Thermal expansion}&\begin{cases}\frac{f_{c}(T)}{f_{p}}=1-0.001T&20\ ^{\circ}\text{C}\leq T\leq 1000\ ^{\circ}\text{C}\\ \end{cases}\) & ([PERSON] et al. [13]) \\ Thermal expansion & \(\alpha_{c}=\frac{28T}{100}\times 10^{-6}\) & ([PERSON] et al. [17]) \\ Elasticity & \(E_{c}(T)=\begin{cases}(1-0.0015T)E_{C}&20\ ^{\circ}\text{C}\leq T\leq 200\ ^{\circ}\text{C}\\ (0.87-8.4\times 10^{-4}T)E_{C}&200\ ^{\circ}\text{C}<T\leq 700\ ^{\circ}\text{C}\\ 0.28E_{C}&T>700\ ^{\circ}\text{C}\\ \end{cases}\) & ([PERSON] et al. [18]) \\ \hline \hline \end{tabular}  Note: “\(\sigma\)” represents the stress of concrete and “\(\epsilon\)” indicates the strain of concrete at high temperature; “\(\epsilon_{p}\)” represents the peak strain of concrete at normal temperature; “\(\epsilon_{p}\)” represents the peak strain of concrete at high temperature; “\(\epsilon_{c}\)(T)” represents the compressive strength of concrete and “\(f_{c}\)(T)” represents the tensile strength of concrete at high temperature; “\(f_{c}\)” represents the compressive strength of concrete and “\(f_{c}\)” represents the tensile strength of concrete at normal temperature; “\(\epsilon_{a}\)” represents the thermal expansion of concrete; “\(E_{c}\)(T)” represents the elasticity of concrete at high temperature; “\(E_{c}\)” represents the elasticity of concrete at normal temperature.