# Mechanical Properties of ASTM A572 Grades 50 and 60 Steels at High Temperatures
## 3 Results and Discussion
### Proposed Reduction Factors for the Strength and Elastic Modulus
#### 3.2.3 Tensile Strength  
Figure 13 shows the proposed equation for the tensile strength reduction of MS and HSS. The difference in the tensile strength reduction factor was not significant, regardless of the steel grade. As the tensile strength shows the greatest strength in the stress-strain curve, there is no difference depending on the strain level. The tensile strength reduction factor for MS is summarized by Equations (9)-(11), while that for HSS is expressed in Equations (12)-(14). The difference between the reduction factors of MS and HSS is not large, such that it is not necessary to divide them into regression equations. However, if a specific fire design is required above 500 \({}^{\circ}\)C, the equations can be applied separately. * MS (Mild Steel): Tensile Strength Reduction Factor Equation For 25 \({}^{\circ}\)C \(\leq T_{a}\leq\) 300 \({}^{\circ}\)C : \[R_{f,T}=1.\] (9) For 300 \({}^{\circ}\)C \(<T_{a}\leq\) 800 \({}^{\circ}\)C : \[R_{f,T}=-1.9\times 10^{-3}(T_{a})+1.6104.\] (10) For 800 \({}^{\circ}\)C \(<T_{a}\leq\) 1000 \({}^{\circ}\)C : \[R_{f,T}=-3\times 10^{-4}(T_{a})+0.3575\.\] (11)  
Figure 13: Proposed reduction factor for the tensile strength. Figure 14 shows the differences in the yield strength between the tests performed here and other tests from literature surveys (Table 2) at the 0.2% offset strain level. At the 0.2% strain level, the normalized strength factor of MS is lower than that of HSS, which is different from the results of [PERSON] et al. (2013, 2014). The yield strength was compared with the proposed equation, Equations (1)-(6), and standards (EN 1993-1-2 and AISC 2016). The yield strength results of the compared standards and equation at the main temperatures (400, 700 \({}^{\circ}\)C) are summarized in Table 9 from Figure 14. The differences in the reduction factor between MS (Equation (1)) the and standards (EN1993-1-2 and AISC 2016) are all 24% at 400 \({}^{\circ}\)C (Table 9, (a)(1), (b)(1)). Moreover, the HSS ((Equation (4)) and standards (EN1993-1-2 and AISC 2016) are all 7% at 400 \({}^{\circ}\)C (Table 9, (a)(2), (b)(2)). At 700 \({}^{\circ}\)C, the difference in yield strength reduction factor between MS (Equation (2)) and EN1993-1-2 is 3% (Table 9, (d)(1)), and the difference between MS (Equation (2)) and AISC 2016 is 0 (Table 9, (e)(1)). In addition, the difference between HSS (Equation (5)) and EN1993-1-2 is 15% (Table 9, (d)(2)), and the difference between HSS (Equation (5)) and AISC 2016 is 12% (Table 9, (e)(2)). NIST 1907 (2016) was compared with the proposed yield strength equation (Equations (1)-(6)). At 400 \({}^{\circ}\)C, the difference between the yield strength reduction factor of MS (Equation (1)) and NIST was 0% (Table 9, (c)(1)), and the difference between HSS (Equation (4)) and NIST was 16% (Table 9, (c)(2)). At 700 \({}^{\circ}\)C, the difference in the yield strength reduction factor between MS (Equation (1)) and NIST was 5% (Table 9, (f)(1)), and the difference between HSS (Equation (4)) and NIST was 16% (Table 9, (f)(2)). These results mean that HSS (Equations (4)-(6)) is closer to the yield strength reduction factor of Eurocode and AISC than MS (Equations (1)-(3)) at 400 \({}^{\circ}\)C or below. Previously, Eurocode and AISC were known to reflect the yield strength reduction factor of the MS group, but the results were different from the actual data. The regression equation of NIST 1907 (2016) is closer to the yield strength reduction factor of MS (Equations (1)-(3)) than HSS (Equations (4)-(6)) at 400 \({}^{\circ}\)C or below. Because the NIST's regression equation was created based on experimental data from various mild steels, the results were relatively similar to those of the MS (Equations (1)-(3)) equation. Figure 15 shows the regression equation for the proposed elastic modulus reduction factor with a comparison to the literature (Table 2) and code values.