This theory, attributed to the late Dr. Peter Lewis, senior lecturer in the Department of Materials Engineering at the Open University, claims that dynamic effects are much more important than had been previously realised (11,12, 21). It is claimed that dynamic effects caused the fatigue failure of the cast iron lugs. The evidence for the dynamic effects is based on the eye witness reports from painters and fitters that the high girders piers oscillated from side to side whenever a train crossed the bridge. On the basis of close inspection of high quality photographs (which show some limited evidence of crack arrest lines) of the failed parts it is claimed that the failure of the cast iron lugs was due to fatigue rather than overstressing. In response to Peter Lewis’s paper (11) and book, further research (15) into the matter was undertaken which showed the evidence for fatigue being the main cause of the collapse is weak.
In a follow up paper (2011) Lewis and Gagg [21] challenge some of the findings of the 2004 paper by Martin & MacLeod. In particular, the following points are raised:
1. “Using modern data can be misleading and should be used very cautiously since modern cast irons have much improved strength when compared with Victorian materials. What data is available in modern textbooks on grey cast iron, suggest that fatigue endurance ratios for thick (>1 in.) grey cast iron samples can fall to as low as 0.34 rather than a value of 0.45 for test specimens cut from 1.2 in. test bars” [21]
2. “Martin and Macleod review some new data of the time to support their claim that the bridge was buffeted by exceptional winds [19]. However, the evidence given to the Inquiry by credible witnesses such as Benjamin Baker and Captain Scott of the training ship Mars moored half-a-mile downriver indicate that the storm that night was not exceptional. Benjamin Baker performed a thorough inspection of the immediate environs of the high girder section and could find no evidence of excessive wind loads. In his testimony, Baker quotes a figure of 15lbf/ft2 (pounds per square foot) for the wind loading”
Point 1:
To address this particular issue I have re-visited wind-induced cumulative fatigue damage analysis of the lugs. From the FE model the natural frequency of the pier was found to be 0.94Hz. This was checked by obtaining the overall stiffness (k=f/x) of the pier and considering the girder weight as a concentrated mass on top of the cantilevering column. The frequency (f =1/2π*sqr(k/m)) obtained was 0.9Hz verifying the dynamic FE analysis.
In an attempt to allow for reduced fatigue life, due to casting defects, conical bolt holes and the consequent stress concentration in the lugs, the fatigue limit has been conservatively taken as 47% [22; page 92 table 24 – grey cast iron with UTS 9 Tons/in2] of the average (40 Tons) of the design strength of the lugs (59 Tons) and the actual average fail load (22.2 Tons; the test result from Court of Inquiry) of the bracing assembly tested (which included the lugs).This gives a wind-induced cumulative fatigue damage of 16%. Reducing the fatigue limit to 33% gives a cumulative fatigue damage of 62%. In addition, the estimated no of non-reversed cycles due to the dynamic action of trains experienced by the bridge in its lifetime would be 370000 which is still low compared with the 1-10 million reverse cycles typically required for fatigue failure with loading near the fatigue limit.
Point 2:
The evidence given for a relatively low strength of the wind by the authors in the paper is weak. Captain Scott on the Mars estimated the wind force to be Beaufort 10/11 with strong gusts every 10 minutes. Perhaps that was not exceptional for him as a deep-sea mariner but it is unusually high and is a wind strength at which structural damage can be expected. But, if particular items were not damaged (windows in signal boxes – Baker, chimneys – lawyers) it does not follow that the wind was not of high strength.
The authors state that the maximum wind pressure was no greater than 15lbsf/ft2 on the night of the disaster (based on Benjamin Baker’s evidence to the Court of Inquiry); this not being sufficient to cause the collapse of the bridge. A wind pressure of 15lbsf/ft2 corresponds to a Beaufort force 8 whereas the estimated Beaufort value was force 10/11. Force 10 (with gust) corresponds to a pressure on the bridge of 65lbsf/ft2. Force 11 (with gust) corresponds to a pressure of 86lbf/ft2 while force 12 (with gust) corresponds to a pressure of 98lbf/ft2 (See tables below).
Tay Bridge disaster 