## Fiber Beam Element Model of A CFST Member with the Strain Rate Effect
### Strain Rate Effect
#### 2.2.1 Strain Rate Effect of Steel
(1) Monotonic loading As shown in Figure 5, loading is assumed to be carried out at a relatively high strain rate \(\dot{\varepsilon}_{\mathrm{H}}\) to point \(A\), where the strain \(\varepsilon_{\mathrm{A}}\) is higher than the elastic ultimate strain \(\varepsilon_{\mathrm{e,S}}\) under the quasi-static strain rate and lower than the elastic ultimate strain \(\varepsilon_{\mathrm{e,H}}\) corresponding to the current strain rate. When the strain rate drops suddenly to \(\dot{\varepsilon}_{\mathrm{M}}\) and loading continues to point \(B\), the strain at this point is \(\varepsilon_{\mathrm{B}}\), which exceeds the elastic strain \(\varepsilon_{\mathrm{e,M}}\) corresponding to \(\dot{\varepsilon}_{\mathrm{M}}\). This is a process in which the elastic deformation at high strain rates is transformed to elastoplastic deformation at low strain rates. After loading continues at a strain rate \(\dot{\varepsilon}_{\mathrm{M}}\) to point \(C\), the following situations may occur: 1 when the strain rate increases to \(\dot{\varepsilon}_{\mathrm{H}}\), the loading first goes elastically along the path from point C to point D. The loading then continues at the strain rate \(\dot{\varepsilon}_{\mathrm{H}}\) along the hardening skeleton curve to failure. 2 When the strain rate decreases to \(\dot{\varepsilon}_{\mathrm{L}}\), considering that stress relaxation may occur during the process from high-speed loading to low-speed loading, in which case the strain remains the same, the stress first decreases from point \(C\) to below \(E\), and loading is carried out at the strain rate \(\dot{\varepsilon}_{\mathrm{L}}\) along the direction from point E to F of the skeleton curve to failure. (2) Cyclic loading  
As shown in Figure 5, loading is assumed to be carried out at a relatively high strain rate \(\dot{\varepsilon}_{H}\) from point O to point A and then at a relatively low strain rate \(\dot{\varepsilon}_{M}\) from point A to point C, after which unloading is performed. At this time, point C is the historical maximum strain point in the tension direction. The steel continues to undergo unloading, reverse reloading, and unloading again to reach point F: 1 When the strain rate increases to \(\dot{\varepsilon}_{H}\), the historical maximum strain point in this direction changes from point C to point C\({}_{1}\). In this case, the stress and strain of C\({}_{1}\) should be redefined according to the strain rate \(\dot{\varepsilon}_{H}\). The reinforcing steel strain is composed of elastic strain and plastic strain. The strain of point C\({}_{1}\) is equal to the sum of the historical maximum plastic strain and the elastic strain, and the stress at point C\({}_{1}\) is the sum of the yield stress at the strain rate \(\dot{\varepsilon}_{H}\). The total stress increment \(\Delta\sigma\) after the hardening branch enters monotonic loading at a quasi-static strain rate \(\dot{\varepsilon}_{S}\). 2 When the strain rate decreases to \(\dot{\varepsilon}_{L}\), the historical maximum strain point changes from point C to point C\({}_{2}\). The method for calculating the stress and strain of point C\({}_{2}\) is the same as that for point C\({}_{1}\). 3 When the strain rate is \(\dot{\varepsilon}_{M}\), the loading path is directly pointed to the maximum historical strain point C of the last cycle.