# A Simple Estimation Method of Weibull Modulus and Verification with Strength Data
## 5 Discussion
### Industrial Strength Data
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Materials** & **cc/>** & **S** & **CV** & **M\({}_{\text{obs}}\)** & **M\({}_{\text{att}}\)** & N & **Note** & **Ref** \\ \hline CSA G40.20 450W & 450 * & 0.032 & 34.38 & 407 & W shapes & [134] \\ CSA G40.20 450W & 450 * & 0.04 & 27.50 & 10.652 & W shapes & [134] \\ CSA G40.21 300W & 300 * & 0.045 & 24.44 & 973 & Class C/H bars & [134] \\ CSA G40.21 300W & 300 * & 0.062 & 17.74 & 730 & Class C/H bars & [134] \\ CSA G40.21 350W & 350 * & 0.035 & 31.43 & 73 & Class C/H bars & [134] \\ CSA G40.21 350W & 350 * & 0.054 & 20.37 & 188 & Class C/H bars & [134] \\ CSA G40.21 350W & 350 * & 0.056 & 19.64 & 815 & Class C/H bars & [134] \\ CSA G40.21 300W & 300 * & 0.051 & 21.57 & 407 & Class C/H bars & [134] \\ CSA G40.21 300W & 300 * & 0.058 & 18.97 & 374 & Class C/H bars & [134] \\ CSA G40.21 350W & 350 * & 0.049 & 22.45 & 64 & Class C/H bars & [134] \\ CSA G40.21 350W & 350 * & 0.052 & 21.15 & 174 & Class C/H bars & [134] \\ SZ75 steel & 451.00 & 21.7 & 22.86 & 1547 & Reinforcing bars & [135] \\ SS80 850 steel & 695.20 & 42.52 & & 17.98 & 388 & Reinforcing bars & [135] \\ ASTM A615-60 steel & 676.00 & 21.93 & 33.91 & 130 & Reinforcing bars & [136] \\ High C steel wire & 1653 & 19.2 & & 94.7 & 38,470 & Suspension cable & [15] \\ High C steel wire & 1660 & 17.1 & & 97.1 & 45 & Suspension cable & [15] \\  & & & Median m & m range & & \\ Cast iron pipes & & & 9 & 1 to 29 & 512 & Undamaged zone & [137] \\ Cast iron pipes & & & 7 & 1 to 23 & 650 & Light damage & [137] \\ Cast iron pipes & & & 6 & 1 to 23 & 542 & Moderate damage & [137] \\ Cast iron pipes & & & 2 & 1 to 14 & 542 & Heavy damage & [137] \\  & & & Average m & m range & & \\ Graphite & & 9.74 & 6.8 to 13.4 & 2000 & Nuclear grade & [138] \\ \hline \hline \end{tabular}
* Equivalent steel grade;
* Nominal tensile strength for CSA G40 grades. CSA stands for Canadian Standards Association. AB stands for American Bureau of Shipping. Ref. reference number.  
\end{table} 
Table 8: _Cont._Hot-rolled steel [129]  
Evaluating the strength of 703 coils of this high-strength low-alloy (HSLA) steel, S355 MC, the average and S value provided an \(\mathrm{m_{est}}\) of 48.4. See Table 8.  
B. Shipbuilding steels [130]  
The published data of nine groups of shipbuilding steels was tabulated, from which m values were estimated. Steels are types A, B, and C of the American Bureau of Shipping (ABS) and ASTM A7. These grades were superseded by newer grades in the 1960s, but all were weldable low-carbon steels. The \(\mathrm{m_{est}}\) values were from 12 to 48.7. Chinese HSLA steels [131]  
Q235 and Q335 (corresponding to S235 and S355) steels from four steel mills were tested. Data for a total of 20,086 plates was listed, and their \(\mathrm{m_{est}}\) values for six groups each are given in Table 8. The results are tightly distributed between 19-24.6. These steels were made for the penstocks of hydropower stations. The weighted \(\mathrm{m_{est}}\) average was 22.3. Plain carbon and HSLA steels, S235, S355, and S550 [132]  
Standard grade steels had \(\mathrm{m_{est}}\) ranging from 10 to 22. The high S (low \(\mathrm{m_{est}}\)) value for S235 steel was attributed to the mill practice of mixing subgrade steels, but the tests included four different structural shapes, and different processing may also be a factor. In addition, the minimum strength value was 50 MPa below the required strength for equivalent ASTM A283 steel. Hot-rolled steels [133]  
This study provided strength data for various shapes, and those for hot-rolled plates are shown here. Samples counts are large (290 to 4095) and yielded \(\mathrm{m_{est}}\) values of 14 to 27 for five grades of steel. Steel shapes [134]  
This work summarized a collection of Canadian steel data of 34,453 samples. The strength values were mostly collected from mill certificates. For steels of 300, 350, and 450 MPa (nominal) tensile strength, m values were found to range from 18 to 37. The weighted m average was 28.2.