Formulas: Mechanical Properties of Structural Steel, Hot-Rolled Reinforcing Steel, and Concrete at Elevated Temperatures

Formula 1

(1) When in the elastic range $[\varepsilon(T)\leq\varepsilon_{p}(T)]$

[\varepsilon(T)\leq\varepsilon_{p}(T)]

F(T)=E(T)\varepsilon(T)

(2) When in the nonlinear range $[\varepsilon_{p}(T)<\varepsilon(T)<\varepsilon_{y}(T)]$

[\varepsilon_{p}(T)<\varepsilon(T)<\varepsilon_{y}(T)]

F(T)=F_{p}(T)-c+\frac{b}{a}\sqrt{a^{2}-[\varepsilon_{y}(T)-\varepsilon(T)]^{2}}

(3) When in the plastic range $[\varepsilon_{y}(T)\leq\varepsilon(T)\leq\varepsilon_{u}(T)]$

[\varepsilon_{y}(T)\leq\varepsilon(T)\leq\varepsilon_{u}(T)]

F(T)=F_{y}(T)

a^{2}\quad=[\varepsilon_{y}(T)-\varepsilon_{p}(T)][\varepsilon_{y}(T)-\varepsilon_{p}(T)+\frac{c}{E(T)}]

b^{2}\quad=E(T)[\varepsilon_{y}(T)-\varepsilon_{p}(T)]c+c^{2}

c\quad=\frac{[F_{y}(T)-F_{p}(T)]^{2}}{E(T)[\varepsilon_{y}(T)-\varepsilon_{p}(T)]-2[F_{y}(T)-F_{p}(T)]}

F_c(T)=f_c^{\prime}(T)\left\{\frac{3\left[\frac{\varepsilon_c(T)}{\varepsilon_{cu}(T)}\right]}{2+\left[\frac{\varepsilon_c(T)}{\varepsilon_{cu}(T)}\right]^3}\right\}