###### Abstract
According to the composition rule, the stress-strain relationship of the SFCB can be appropriately simulated as the linear superposition of steel reinforcement and FRP. The schematic stress-strain relationship of this composite bar can be seen in Figure 1.  
Suppose that the outside fiber has fine interface bonding and harmonious deformation with the inner steel bar in the process of loading, that is, they have the same strain in one section. The stress-strain relationship of a SFCB under uniaxial tensile loading can be accurately simulated by the composite superposition principle [14] using Equation (1). \[\sigma_{\text{sf}}=\left\{ \begin{array}{cc}\left(E_{\text{s}}A_{\text{s}}+E _{\text{f}}A_{\text{f}}\epsilon_{\text{sf}}\right)/A&0\leq\varepsilon_{\text {sf}}<\varepsilon_{\text{sf}}\\ \left(f_{\text{y}}A_{\text{s}}+E_{\text{f}}A_{\text{f}}\epsilon_{\text{sf}} \right)/A&\varepsilon_{\text{sf}}\leq\varepsilon_{\text{sf}}<\varepsilon_{ \text{sf}}\\ \sigma_{\text{s}}A_{\text{s}}/A&\varepsilon_{\text{sf}}\geq\varepsilon_{\text {sf}}\end{array} \right. \tag{1}\]  
where, \(\sigma_{\text{sf}}\) and \(\varepsilon_{\text{sf}}\) are tensile stress and strain of composite bar, respectively; \(E_{\text{f}}\) and \(A_{\text{f}}\) are elastic modulus and cross-sectional area of the composite bar's outer FRP, respectively; and \(A\) is the total cross-sectional area of the composite bar. The stress-strain relation of compression is described as Equation (2). \[\sigma^{\prime}{}_{\text{sf}}=\left\{ \begin{array}{cc}E_{\text{s}}A_{\text{ s}}\cdot\varepsilon^{\prime}{}_{\text{sf}}/A&0\leq\varepsilon^{\prime}{}_{\text{sf}} <\varepsilon^{\prime}{}_{\text{sf}}\\ f^{\prime}{}_{\text{y}}A_{\text{s}}/A&\varepsilon^{\prime}{}_{\text{sf}}\geq \varepsilon^{\prime}{}_{\text{sf}}\end{array} \right. \tag{2}\]  
where, \(\sigma^{\prime}{}_{\text{sf}}\) and \(\varepsilon^{\prime}{}_{\text{sf}}\) are compressive stress and strain of composite bar, while\(f^{\prime}{}_{\text{y}}\) and \(E^{\prime}{}_{\text{s}}\) are compressive yield stress and elastic modulus of inner steel bar. By comparing test curves of SFCB specimens and conventional steel bar specimens, it was found that the residual deformation of SFCB was less than that of a conventional steel bar when unloading  
Figure 1: Stress-strain relation of steel and fiber reinforced polymer (FRP) superposition. from peak strain after yielding. Further, the stress-strain relationship of SFCB under a cyclic tensile load is provided through monotonic tensile and reciprocating tensile tests according to composition rule, providing the inner steel bar has same deformation with the composite bar. Previous studies have indicated that compared with conventional steel bar, steel-fiber composite bar has good anti-corrosion performance and designable post-yield stiffness. When the conventional RC member encounters seismic excitation, it is difficult to achieve stable post-yield stiffness due to the large plastic deformation of the steel bar. For the purpose of achieving the seismic fortification goals of \"reparable after a medium earthquake\" and \"collapse after a major earthquake\", SFCB is considered to be the ideal replacement for steel bar in concrete members for structural design and application. Up to now, many experimental studies have been conducted on the mechanical performance of the SFCB [15] and concrete members reinforced with SFCB, including simply supported beams [16], columns [17], column-beam connections [18], and the bonding behavior of SFCB with concrete by pull-out performance [19]. To date, the material has been investigated primarily through experiments, while few effective numerical simulations have been conducted to study the seismic behaviors of the frame beam members [20]. It is essential to explore a simulation framework due to the limited number of experiments. RC frame beams are an important supporting member of frame structure. They also play a crucial role in resisting horizontal seismic action.