# A Simple Estimation Method of Weibull Modulus and Verification with Strength Data
## 4 Material Strength Data
### Historic Wrought Iron and Steel
The first row in Table 2 gives the results of 1810 chain links that were retrieved from the Essex-Merrimack suspension bridge when it was replaced in 1910 [34; 35]. This was built by [PERSON], and was one of the earliest iron suspension bridges in the West. The strength level was high for its age, but the m values were below 10, which was indicative of the brittle state expected of such an old iron. In this case, tests were done on materials after 100 years of continuous use outdoors. The next three rows provide the results of tests conducted at the Franklin Institute in 1837 [35; 36]. Both strength and m values are comparable to the [PERSON] iron. The next eight rows show the test data from [PERSON]'s 1863 book [37]. The selected six groups are given first, grouping the same or related sources of best quality iron, cast steel, and charcoal iron. One group that was noted as \"Govan Ex Best\" produced a high m value of 43, while cast steel had a high strength (580 MPa) and an m value of 17. [PERSON] selected the data of coveted Swedish iron from [PERSON] [35; 37], which gives an m value of 30, justifying its high reputation. The next row, which is noted as charcoal iron, may also be of Swedish origin. The following two rows represents most of [PERSON]'s iron and steel data, totaling 688 tests. These data were tabulated in [38] and were split into two groups by sample diameters. The smaller diameter group had 40 MPa higher strength, but both had low m values of \(\sim\)9, as low-quality iron samples were included. These two datasets represent the general quality level of 1860 iron in the United Kingdom (UK). The next three rows give data from two Indiana bridges (built in 1869 and 1873) [38]. By this time, m values had doubled from the Finley iron, indicating the quality improvement of iron available in the United States (US) Midwest. [PERSON] [39] conducted extensive testing at the US Navy, reporting 846 test results in 1879. For the entire tests, an m value of 26 was comparable to Indiana bridge irons, but the strength was 50 MPa higher. When the data were separated into low-strength and high-strength groups (with overlaps), the m value rose to 42 for the low group, which was comparable to the best data from the 1860 UK, albeit with 30 MPa lower strength. However, a general sampling of US wrought iron still showed the presence of low-quality iron with m values of approximately 10 to 15, as shown by [PERSON] [35; 36]. By the 1880s, steel was widely used, and [PERSON]'s book provided four examples of better materials [40]. These included Bessemer steel, boiler plates, and railroad rail. The last seven rows give the data for patented high strength steel wires, mainly for suspension bridge cables. [PERSON]'s article [41] reported UK test results in the 1880s. The strength reached a level of 1 GPa, but the m value was still 13.7 [15; 44]. At about the same time, wires for the Brooklyn Bridge (finished in 1883) had the strength of 1.1 GPa. Unfortunately, no test data has been located so far. Over the next 20 years, steel technology improved further and provided 1.5-GPa steel wires for the Williamsburg Bridge in New York (finished in 1903). [PERSON] [42] provided 160 test data for the cable wires that were removed during the rehabilitation work in the 1980s, and Weibull analysis was conducted [15; 44], yielding m = 16 with an average tensile strength of 1.5 GPa. The values are remarkable after more than 80 years of use, since these wires did not have galvanizing protection against corrosion. The next four datasets were commented on earlier in the Introduction [23], while the last set was from the Mid-Hudson Bridge [43]. These wires were from suspension bridges after many years of service. As noted before, m values are indicative of the state of corrosion of the suspension cable wires, and are useful in assessing the remaining service life of suspension cables.