Structural Materials: Metallurgy of Bridges

Abstract

This chapter examines metallurgical developments related to bridge construction. Because of availability and cost, iron and steel have played the central role. We examine their roles and applications starting from ancient wrought iron chain bridges; cast iron and steel arch bridges; iron and steel truss bridges, wires, and cables; and finally to spectacular long-span suspension and dazzling cable-stayed bridges.

Appendices

Appendix A: List of Bridges Discussed in This Chapter

Name	Material	Structure	Year built	Location	Country
The Iron Bridge	Cast iron	Arch	1779	Coalbrookdale	UK
Brooklyn Bridge	Steel	Suspension	1883	New York	USA
Akashi Kaikyo Bridge	Steel	Suspension	1998	Hyogo	Japan
Ikitsuki Ohashi Bridge	Steel	Truss	1991	Nagasaki	Japan
New River Gorge Bridge	Steel	Arch	1977	Fayetteville	USA
Golden Gate Bridge	Steel	Suspension	1937	San Francisco	USA
Normandy Bridge	Steel	Cable-stayed	1995	Le Havre	France
Pan Ho Bridge	Iron	Suspension	unknown	Shaanxi	China
Jihong Bridge	Iron	Suspension	1475	Yunnan	China
Shenchuan Iron Bridge	Iron	Suspension	581 or 680	Yunnan	China
Luding Bridge	Iron	Suspension	1706	Sichuan	China
Chung Riwoche Chakzam	Iron	Suspension	Fifteenth century	Tibet	China
Chuka-cha-zum	Iron	Suspension	Fifteenth century	Chuhka	Bhutan
Tachog Lakhang Chakzam	Iron	Suspension	Fifteenth century	Paro	Bhutan
Łażany Bridge	Cast iron	Arch	1796	Łażany	Poland
Mieszczanski Bridge	Cast iron	Arch	1876	Mieszczanski	Poland
Buildwas Bridge	Cast iron	Arch	1796	Buildwas	UK
River Dee Railroad Bridge	Cast iron	Beam	1846	Chester	UK
Tay Bridge	Cast iron	Truss	1879	Dundee	UK
Glorywitz Bridge	Iron	Suspension	1734	Glorywitz	Poland
Winch Bridge	Iron	Suspension	1741	Durham	UK
Jacob’s Creek Bridge	Iron	Suspension	1801	Union Town	USA
Chain Bridge	Iron	Suspension	1801	Georgetown	USA
Dryburgh Abbey Bridge	Iron	Suspension	1817	River Tweed	UK
Union Bridge	Iron	Suspension	1820	River Tweed	UK
Menai Suspension Bridge	Iron	Suspension	1826	Anglesey	UK
Silver Bridge	Steel	Suspension	1928	Pt. Pleasant	USA
Britannia Bridge	Steel	Truss	1850	Anglesey	UK
Royal Albert Bridge	Steel	Truss	1858	Plymouth	UK
Pfaffendorf Bridge	Steel	Truss	1864	Koblenz	Germany
Garabit Viaduct	Steel	Truss	1884	Garabit	France
Ashtabula Railroad Bridge	Steel	Truss	1876	Ashtabula	USA
I-35W Mississippi River Bridge	Steel	Truss arch	1964	Minneapolis	USA
Tacoma Narrows Bridge	Steel	Suspension	1940	Tacoma	USA
Tees Bridge	Iron	Suspension	1749	Durham	UK
Fairmount Hazard-White Bridge	Iron	Suspension	1816	Philadelphia	USA
St. Antoine Bridge	Iron	Suspension	1823	Geneva	Switzerland
Grand Prix Suspendu	Iron	Suspension	1834	Fribourg	Switzerland
Broughton Bridge	Iron	Suspension	1826	Broughton	UK
Brighton Chain Piers	Iron	Suspension	1823	Brighton	UK
Basse-Chaîne Bridge	Iron	Suspension	1832	Angers	France
Fairmount	Iron	Suspension	1842	Philadelphia	USA
Wheeling Bridge	Iron	Suspension	1849	Wheeling	USA
Delaware Bridge	Iron	Suspension	1848	Delaware	USA
Suspension foot bridge	Iron	Suspension	1824	Wissekerke	Belgium
Allegheny Aqueduct	Iron	Suspension	1845	Pittsburgh	USA
Niagara Falls Railroad Bridge	Iron	Suspension	1855	Niagara Falls	USA
Eads Bridge	Steel/iron	Arch	1874	St. Louis	USA
Glasgow Steel Bridge	Steel	Truss	1879	Missouri	USA
Williamsburg Bridge	Steel	Suspension	1903	Williamsburg	USA
Forth Road Bridge	Steel	Suspension	1964	Edinburgh	UK
Forth Rail Bridge	Steel	Truss	1890	Edinburgh	UK
Hell Gate Bridge	Steel	Arch	1919	New York	USA
Sydney Harbour Bridge	Steel	Arch	1932	Sydney	Australia
Bayonne Bridge	Steel	Arch	1931	New York	USA
Hong Kong-Zhuhai-Macau Bridge	Steel	Cable-stayed	2018	Hong Kong	China
San Francisco-Oakland Bay Bridge	Steel	Suspension	1936	San Francisco	USA
Chesapeake Bay Bridge	Steel	Suspension	1952	Maryland	USA
Humber Bridge	Steel	suspension	1981	Kingston	UK

Appendix B: Revisiting Silver Bridge Failure

It has been half a century since the failure of the Silver Bridge, and many publications and discussions have been dedicated to analyzing this incident. The following is an interpretation of the author based on his observations of the body of published research, as opposed to new primary experimental analysis.

The Silver Bridge was built in 1928 at Point Pleasant, West Virginia, across the Ohio River. The bridge was an eyebar-chain suspension bridge with a 214 m span. For each section, two eyebars were used, such that a single joint failure would lead to a bridge collapse. The eyebars were made of a high carbon steel, AISI-1060. The average chemical analysis of the broken eyebar was 0.59% C, 0.66% Mn, 0.145% Si, 0.03% S, and 0.041% P. These were water-quenched from 900 °C and tempered at 650 °C, giving the yield strength of 550 MPa, tensile strength of 830 MPa, elongation of 20%, and reduction in area of 50%. The design stress was 345 MPa. These are within the expected ranges for quenched-and-tempered 1060 steel. In addition, it had the ductile-brittle transition temperature of 104 °C and Charpy V-notch energy of 2.7–5.4 J at −1 °C (temperature at the time of failure). That is, the steel was used in a nominally brittle condition (Anon 1970, 1968b; Bennett 1969; Bennett and Mindlin 1973). However, the final fracture was fully ductile. As noted earlier, low-temperature brittleness of steels was still unknown in 1928, and stress concentration effects (Inglis 1913) were mainly of academic interest. Lichtenstein (1993) reexamined this failure. No change was suggested regarding the earlier conclusions, but he noted that the builder reduced the safety factor to 1.75 and kept the details of heat treatment secret from the outside designer. He also estimated that each of the two eyebars that initiated the failure was under a force of 4.5 MN (83% of the design load).

The Silver Bridge crossed the Ohio River in the east-west direction. The failed eyebar was at the first joint on the west side of the Ohio Tower (west tower), C13. It was the north-side eyebar on the south side chain, designated as #330 (see Fig. 4.20). The initial flat fracture and its direction are marked by a broken line and a small arrow. The National Bureau of Standards (NBS) and Battelle Columbus Lab. investigated the failure. The National Transportation Safety Board (NTSB) concluded that stress-corrosion cracking was responsible for the critical cleavage fracture event from a 3 mm-deep by 4.85 mm-wide crack on eyebar #330. This fracture initiation part is shown in Fig. 4.21a and is from the eyebar head that separated from the shank side and fell into the river. The initiator cracks were on the hole side near the south face, that is, the inner side of C13 joint. This NTSB conclusion fails to explain why the lower side of the eyebar #330 failed in flat mode while the upper part failed in a ductile manner (Bennett and Mindlin 1973). This ductile fracture occurred only after a large plastic deformation occurred in the eyebar head. This is inconsistent with NTSB view of brittle fracture. That is, if a small crack initiated a cleavage fracture of one side of the head, the other side of eyebar #330 should also fail in the same brittle manner. But it appears the material was ductile at the time of fracture, at the ambient temperature of −1 °C. Several more contradictions emerge when one examines NTSB and NBS reports and Bennett and Mindlin article (Anon 1970, 1968b; Bennett 1969; Bennett and Mindlin 1973).

• 1. The initial crack formed a corner clam-shell marking, indicative of fatigue crack initiation (Fig. 4.21a). This was on eyebar #330 and on the inner edge at the hole facing the connection pin of 203 mm diameter. A smaller crack found next to the larger crack, 11 mm total length, also exhibited clam-shell marks. Two arrows point to the center of the two thumbnail cracks. The fracture surface beyond these initiator cracks gave no indication of cleavage cracking and no chevron marks are visible. This crack propagated downward to the outside edge (Fig. 4.20).

• 2. When the flat fracture surface is carefully examined, one observes numerous nearly parallel, locally straight beach marks covering the entire fracture surface, indicative of fatigue. Fatigue striations are expected between these beach marks, but the magnification is inadequate to judge. Since this eyebar was exposed to weather, it is expected that fatigue was assisted by aqueous corrosion. The beach marks are indicated by thin white lines in Fig. 4.21a–c. In cleaned samples (Fig. 4.21a, b), features of the fracture surfaces are reasonably clear. Beach mark spacings were 0.2–0.3 mm at the start, but increased to ~0.8 mm at the mid-section. An overall trend of the beach marks is from the starting cracks at the top left (hole side) to the bottom right (outer edge). The dark band (marked with white arrows shown in Fig. 4.21c) appears to be a group of beach marks near the bottom right. This photograph was taken before cleaning and indications are generally fuzzy. Still, the beach marks can be traced.

• 3. When the broken-off outboard piece is joined to the shank side at the fatigue fracture position using photographic images, the combined image given in Fig. 4.22 represents the deformed eyebar geometry before the separation occurred. At this stage, the size of the hole was found to be enlarged by 28 mm (or 10%). This implies that the hole size was increased while the flat fracture was in progress before the separation occurred. This must have led to the reduction in the stress acting on eyebar #330 from the design value of 345 MPa. Taking the eyebar hole distance of 16.1 m (Bennett and Mindlin 1973), the eyebar strain was reduced by 0.174%, when #330 was elongated by 28 mm. This strain is larger than the applied strain of 0.164% (assuming the design stress of 345 MPa and the Young’s modulus of 210 GPa). A large stress reduction occurred on #330, while loading the parallel eyebar #33 (the south side eyebar) to bear the load beyond its yield load. It was likely that eyebar #330 was deformed gradually as the fatigue crack extended, sharing the load between #33 and #330. Thus, eyebar #33 was also deformed, but data on this regard were absent in the NTSB/NBS reports. The tensile strength of the eyebar steel was 830 MPa (Bennett and Mindlin 1973), so #33 eyebar was able to carry double the design load by itself, though in unbalanced conditions. When the lower side of eyebar #330 severed, the geometry changed into a hook and its load capacity was decreased substantially. Using a mechanics of material formula from Boresi and Sidebottom (1985), the load capacity was calculated as 0.77 MN for the maximum stress reaching the tensile strength of #330 (830 MPa).

Fig. 4.20

Joint C13 of the south cable of the Silver Bridge. Joint C11 on the left (Ohio side) and C15 on the Ohio tower. View from the South to the North. Based on fig. 5b of NTSB Report HAR-71-01. (Anon 1970)

Fig. 4.21

(a) Enlarged fracture initiator cracks. Two arrows point to the center of the two thumb nail cracks. After cleaning. White lines indicate the directions of fatigue beach marks that are visible. (b) The hole-side half of the flat fracture surface of the outside piece. After cleaning. The same orientation as (a) with the two cracks at top left corner. (c) The outside half of the flat fracture surface before cleaning. Two vertical white lines indicate the center position. (Bennett 1969, figs. 5, 6, and 3).

Fig. 4.22

Reconstructed head of eyebar #330. (a) Following fatigue cracking that produced flat fracture of the lower side of this eyebar. The white circle corresponds to the size of the pin, 280 mm in diameter. The white line on the lower side is the joined position of the flat fracture surfaces. The thin white broken curve on the upper side shows the outline of the shank side of the fractured eyebar (Anon 1970)

• 4. When the fractured pieces were matched at the ductile fracture side (Fig. 4.23 from Exhibit 16 (Anon 1968b)), representing the time of final fracture , the hole is enlarged by 35% in the length direction, leaving a 140 mm gap between the flat fracture at the hole side of eyebar #330, as was reported in Anon (1970). The width of the hole at the middle was also enlarged by 26.5%. This hook shape represented the condition before the final ductile fracture, which occurred when the load on eyebar #330 exceeded 0.77 MN. This condition was reached when the loading of eyebar #33 increased by also 0.77 MN (or deformed an additional 3.8 mm). By the time of the eyebar #330 separation, eyebar #33 was loaded higher than this level and the final fracture event was expected immediately.

• 5. Attribution to stress-corrosion cracking due to hydrogen sulfide gas was highly implausible in the wind-swept rural area where the bridge was located. Bennett and Mindlin (1973) immersed fracture test samples to 0.5% H₂S-5% NaCl aqueous solution and found threshold stress-corrosion fracture toughness of 17 MPa√m (or 36 MPa√m for 100+ h). They relied on the H₂S-SCC mechanism to justify their conclusion of brittle fracture of eyebar #330 starting from the small corner crack. If the same 0.5% levels of H₂S gas were present in air, this is two to five times over the lethal levels of H₂S gas, and yet the H₂S concentration is 1000 times less than in the liquid state. No such sources of pollution are known. H₂S is also 20% heavier than air and cannot possibly rise to the C13 joint, which was more than 30 m above the river. Since humans can easily detect 1 ppm level presence of H₂S gas in air, it is unlikely to have high enough levels of H₂S at the eyebar joint while no one noticed what would have been a rotten egg smell around the bridge in non-industrial Eastern Ohio. Ballard and Yakowitz (1970) also found Cl along with S, suggesting another source of S contamination to be from lubricant in the eyebar joint. This presence of Cl is incompatible with the H₂S hypothesis. The H₂S-based mechanism should be discarded.

Fig. 4.23

Photograph of eyebar #330 (Ballard and Yakowitz 1970) with the upper side fractured pieces placed together at the ductile fracture location . The left-side opening represents the deformed shape of eyebar #330 prior to the final fracture

From these observations, a likely fracture scenario is given in the following:

• 6. Fatigue cracks initiated at multiple locations, but two small corner cracks started to propagate, causing a flat fatigue fracture and separating the lower part of the eyebar #330. During the crack propagation and upon fatigue fracture, the hole was enlarged, reducing the applied load.

• 7. Upon the separation of the lower part of #330, the hole enlargement reached 2.8 cm, which was adequate to relieve the load on this eyebar #330, and the parallel eyebar #33 on the south side carried almost the entire load. This was possible as the maximum load (9 MN) of twice the design load was still below the tensile strength, but the deformation imposed on eyebar #33 simultaneously increased the load on eyebar #330 to its reduced capacity of 0.77 MN.

• 8. When eyebar #330 reached its loading capacity, the final ductile fracture of the upper part of eyebar #330 was ensured, followed immediately by the collapse of the bridge.

An alternate fracture mechanism may be considered based on elasticity analysis . At the initiator crack position on eyebar #330, an elastic stress concentration factor was calculated as 3.1 ± 0.4 (Trznadel 1978), which is enough to cause brittle fracture given the crack size and existing load. However, local plastic deformation substantially reduces this stress concentration factor. Applying the Neuber rule (Hertzberg 1996), the maximum stress is found to be less than 570 MPa (3% more than the yield strength) for the applied stress of up to 345 MPa, or the design stress. The calculated maximum stress is 7–8% less than the stress needed to fracture per Bennett and Mindlin (1973), and brittle eyebar fracture cannot be expected. In any event, it is doubtful whether this approach can resolve the issues arising from ductile final fracture and observations of fatigue markings. Bennett and Mindlin (1973) listed corrosion fatigue as a possible mechanism, though they discarded it. If one considers the Silver Bridge location in the Ohio River valley, where acid rain of lower than 4.5 pH had persisted from the 1950s to 2010 (Anon 1978, 2010), corrosion fatigue had to play a significant role in the progressive cracking of the fractured eyebar. Since acid rain continues over wide areas globally, this issue deserves careful consideration. In fact, severe corrosion found on the suspension cables of the Forth Road Bridge in Scotland (Colford 2013) may have also involved acid rain. Incidentally, the pH levels in Scotland were comparable to those of the Ohio River valley (Seinfeld and Pandis 1998).

The above re-examination of the Silver Bridge failure implies that the fail-safe feature was absent in the original design, which used an inadequate safety factor of 1.5. At this level, the working stress was comparable to the fatigue limit and was bound to cause the disaster. Unfortunately, the concept of fatigue crack growth was still not generally understood in 1928, and inspection methods were inadequate in the 1960s. It was also discovered that the post-failure investigation had serious deficiencies. The initial field examination prematurely concluded the flat fracture was due to cleavage. More failure analysis was done, but obvious features in fractography were overlooked as pointed out above. An illogical hydrogen-sulfide hypothesis was introduced and it continues as the prevailing view today. This hypothesis cannot explain the observed cracking as there were no possible industrial or natural sources of hydrogen sulfide gas at high concentrations at the bridge. Although the lack of primary evidence was a serious obstacle, available records led to a more coherent understanding of the sequence of failure events as presented here.

As most bridge maintenance is still primarily reliant on visual inspection, non-destructive evaluation is imperative for executing a systematic approach. Newer methods are starting to be used; for example, the San Francisco-Oakland Bay Bridge, Forth Road Bridge, and Humber Bridge have been continuously monitored using acoustic emission technology (Beabes et al. 2015; Johnson et al. 2012). Acoustic emission and other structural health monitoring methods can be found in recent publications (Kosnik et al. 2011; Ono 2014; Vardanega et al. 2016; Washer 2014; Wevers and Lambrighs 2009).

Appendix C: Weibull Analysis of the Tensile Strength of Williamsburg Bridge Wires

The data set given in Perry (1998) was evaluated for the Weibull shape parameter. Perry provided fracture load values of 160 samples. These values were sorted in increasing order and the number of breaks, B _n, for each increment of 50 lb_f, was determined. Here, n varies from 1 to 50 for the load range of 4800–7200 lb_f. Figure 4.24 shows a point plot of B _n vs. load (in blue), indicating a peak at ~6500 lb_f. By dividing B _n by the total sample number of 160, the probability distribution function (PDF) for wire fracture is obtained. When these are summed, cumulative PDF that varies from 0 to 1 is found, and it is plotted in Fig. 4.24 in red. Note that the distribution is skewed to the lower load unlike the normal (or Gaussian) distribution.

Fig. 4.24

The number of breaks per 50 lb_f load step, B _n (blue points, left scale), and cumulative PDF , F(x) (red points, right scale), against fracture load, x, in lb_f

A Weibull distribution function is defined in terms of cumulative PDF , F(x), as

$$ F(x)=1\hbox{--} \exp\;\left(\hbox{--} {\left(x/{x}_0\right)}^m\right), $$

where m is the shape parameter and x ₀ the scale parameter. In the present case, x is the variable and is taken as the load. It can also be considered as time when one needs to analyze the lifetime of components or structures. This is the simplest distribution and is known as a two-parameter Weibull distribution. By shifting terms and taking the logarithm twice, the above expression can be written as

$$ \ln \left(-\ln \left(1-F(x)\right)\right)=m\;\ln \left(x/{x}_0\right). $$

By plotting the left-hand side against ln(x/x ₀), m can be determined as the slope. The Weibull plot for the Williamsburg wires is shown in Fig. 4.25. Here, x ₀ was taken as the average fracture load of 6170.56 lb_f (or the strength of 1.5 GPa). The point plot was fitted to a linear equation with m = 36.8. That is, these wires have the tensile strength level comparable to some modern wires, but with Stage 4 corrosion per NCHRP-534 (Mayrbaurl and Camo 2004).

Fig. 4.25

Weibull plot of ln(−ln(1 – F)) against ln(x/x ₀). The slope of 36.8 is the shape parameter, m