# A Simple Estimation Method of Weibull Modulus and Verification with Strength Data
## 4 Material Strength Data
### Historic Wrought Iron and Steel
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Historical Iron/Steel** & **\textless{}0\textgreater{}** & **S** & **\textless{}0\textgreater{}/SD** & **m\textgreater{}obs** & **m\textless{}net** & **N** & **m\textgreater{}obs/m\textless{}** & **Note** & **D/V** & **Ref** \\ \hline Finley 1810 & 338.0 & 40.54 & 8.34 & 8.08 & 9.17 & 26 & 0.881 & & Wrought iron & D & [34] \\ Franklin Inst 1837 & 369.9 & 31.66 & 11.68 & 10.16 & 12.85 & 11 & 0.791 & & Wrought iron & D & [35] \\ Franklin Inst 1837 & 358.7 & 40.86 & 8.78 & 8.85 & 9.66 & 11 & 0.916 & & Wrought iron & D & [35] \\ Franklin Inst 1837 & 354.9 & 40.89 & 8.68 & 8.92 & 9.55 & 36 & 0.934 & & Wrought iron & D & [36] \\ Kirkaddy Book 1862 & 425.6 & 20.21 & 21.06 & 25.3 & 23.16 & 32 & 1.092 & Yorkshire from three works & D & [37] \\ Kirkaddy Book 1862 & 377.6 & 27.14 & 13.19 & 15.2 & 15.30 & 24 & 0.993 & Consett Best long & D & [37] \\ Kirkaddy Book 1862 & 582.4 & 39.06 & 14.91 & 17.39 & 16.40 & 12 & 1.060 & Naylor cast steel & D & [37] \\ Kirkaddy Book 1862 & 401.0 & 12.17 & 32.95 & 43.07 & 36.24 & 16 & 1.188 & Govern Ex B best & D & [37] \\ Kirkaddy Book 1862 & 362.5 & 11.52 & 31.47 & 29.99 & 34.61 & 17 & 0.866 & 1860 Swedish iron & D & [35] \\ Kirkaddy Book 1862 & 406.1 & 17.29 & 23.49 & 28.6 & 25.84 & 16 & 1.107 & Bradley charcoal iron & D & [37] \\ Kirkaddy Book 1862 & 382.4 & 48.76 & 7.84 & 7.69 & 8.63 & 325 & 0.892 & Thick bar \(>0.7^{o}\) & D & [37] \\ Kirkaddy Book 1862 & 339.7 & 40.28 & 8.43 & 9.65 & 9.28 & 363 & 1.040 & Thin bar \(<0.7^{o}\) & D & [37] \\ Indiana bridges & 329.3 & 18.14 & 18.15 & 21 & 19.97 & 19 & 1.052 & Bridge eyed 1869 & D & [38] \\ Indiana bridges & 322.9 & 17.04 & 18.95 & 19.8 & 20.84 & 16 & 0.950 & Bridge red 1873 & D & [38] \\ Indiana bridges & 326.4 & 15.71 & 20.78 & 22.6 & 22.85 & 14 & 0.989 & Low values cut off & D & [38] \\ Beardslee (US Navy) 1879 & 371.1 & 18.59 & 19.96 & 26.15 & 21.96 & 846 & 1.191 & 1879 whole data & D & [39] \\ Beardslee (US Navy) 1879 & 362.1 & 9.99 & 36.25 & 42.39 & 39.87 & 580 & 1.063 & High values cut off & D & [39] \\ Beardslee (US Navy) 1879 & 391.7 & 14.57 & 26.88 & 29.2 & 29.57 & 456 & 0.988 & Low values cut off & D & [39] \\ Beardslee (US Navy) 1879 & 390.8 & 20.36 & 19.20 & 19.44 & 21.12 & 69 & 0.921 & Small diameter & D & [39] \\ Late 150 sourses & 339.0 & 37.01 & 9.16 & 9.99 & 10.08 & 16 & 0.991 & Wrought iron & D & [36] \\ Holley 1877 & 314.9 & 23.03 & 13.67 & 15.83 & 15.04 & 8 & 1.052 & Wrought iron & D & [35] \\ Unwin 1910 & 473.5 & 11.23 & 42.16 & 44.5 & 46.38 & 14 & 0.959 & Besserstet 1880s & D & [40] \\ Unwin 1910 & 332.7 & 22.70 & 14.66 & 15.2 & 16.12 & 21 & 0.943 & Boiler plate, 1880s & D & [40] \\ Unwin 1910 & 345.8 & 9.71 & 35.61 & 39.2 & 39.17 & 17 & 1.001 & Boiler plate, 1880s & D & [40] \\ Unwin 1910 & 500.7 & 39.40 & 13.98 & 12.2 & 15.37 & 12 & 0.794 & Steel Rtail, 1880s & D & [40] \\ Percy 1886 & 1092.0 & 87.8 & 12.44 & 13.7 & 13.68 & 35 & 1.001 & 1886 patented wire & D & [41] \\ Williamsburg Br 1903 & 1499.0 & 113 & 13.27 & 16 & 14.59 & 160 & 1.096 & 1903 cable wire & D & [42] \\
534 report Br wires & 1649.0 & 29.7 & 55.52 & 70.6 & 61.07 & 20 & 1.156 & Stage 1,2 corrosion & V & [23] \\
534 report Br wires & 1628.0 & 39.3 & 41.42 & 52.4 & 45.57 & 15 & 1.150 & Stage 3 corrosion & V & [23] \\
534 report Br wires & 1595.0 & 60 & 26.58 & 33.4 & 29.24 & 15 & 1.142 & Stage 4 corrosion & V & [23] \\
534 report Br wires & 1383.0 & 181.5 & 7.62 & 9.1 & 8.38 & 15 & 1.086 & Stage 4 with cracks & V & [23] \\ Mid-Hudson Br & 1609.1 & 51.66 & 31.15 & 32.07 & 34.26 & NA & 0.936 & Stage 2,3 corrosion & V & [43] \\ \hline \hline \end{tabular} D/V stands for data type of D = digitized and V = Values from the literature. Ref = reference number. Br = bridge. <0\textgreater{} = average strength. S = standard deviation. <-0\textgreater{}/\textless{}; mobs = observed Weibull modulus value. Most = estimated m value from Equation (14). N = sample counts.  
\end{table} 
Table 2: Listing of data for wrought iron and steel of the 19 th century to the early 20 th century.