Having read John Rapley's biography of Tay Bridge designer Thomas Bouch earlier this year, I picked up Peter Lewis's "Beautiful Railway Bridge of the Silvery Tay" (ISBN 0752431609, Tempus Publishing / The History Press, 2004, 192pp) [amazon.co.uk] with interest.
The author, Dr Peter Lewis, is a senior lecturer in materials engineering at the Open University. He's also the author of a book (and paper [PDF]) on the collapse of Robert Stephenson's Dee Bridge, neither of which I've read. The fall of the Tay Bridge is a case study in the Lewis's OU Forensic Engineering course, and this book-length study gave Lewis the opportunity to explore it in great detail, as well as offering his own theory of why it collapsed.
The book's title is taken from William McGonagall's notorious poem. The poet ended his thoughts on the bridge disaster with the words: "For the stronger we our houses do build / The less chance we have of being killed", which, as a simplistic theory of why the bridge failed, is not far off the mark.
This isn't a book to read to discover much about the bridge's designer Thomas Bouch, or the background to the construction of the Tay Bridge. Rapley's biography already mentioned covers that territory more than adequately, and there are other books on the Tay Bridge collapse such as those by John Thomas and John Prebble (both out-of-print but readily available secondhand), or Andre Gren's "The Bridge Is Down!", although that appears to overlap considerably with Lewis in its reliance on the original eyewitness testimony.
Lewis's book places the focus on the engineering of the bridge, and as is perhaps proper for a forensic study, concentrates on what evidence has survived since the 1879 disaster. This largely consists of statements made by witnesses at the Court of Inquiry which examined the failure, as well as photographs of the bridge debris taken on behalf of the Court (all the photos used in this post are out-of-copyright images taken from Dundee library's website about the disaster).
The Court concluded that the bridge was badly designed, badly built and badly maintained, and all three conclusions are well supported by the evidence. Bouch and his assistants took only limited account of wind loading, with lower wind pressures used than those being applied by contemporary French and American engineers. The factor of safety against failure applied by Bouch was less than many of his peers, something that can only be justified where loads and materials are understood with higher than normal certainty, which was clearly not the case on the Tay Bridge, a lengthy estuarial crossing entering into new engineering territory.
Inadequate ground investigation led to the redesign of the planned masonry piers as trestle piers, with cast iron columns and wrought-iron bracing. A desire not to have to increase the foundation size meant that the inclined support buttresses normally used on trestle piers at the time (by Gustave Eiffel, amongst others) were not adopted.
Bouch's design also relied heavily on the attachment of the bracing to the columns using lugs cast as part of the column itself. These proved difficult to cast, and there was plenty of evidence of them being burned on to the column after casting, as well as of defects being disguised with beaumontage filler. Adding to the problems with the lugs, they were cast with tapered holes, which weren't subsequently drilled square, with the result that stresses were concentrated.
Workers on the bridge noted oscillations as trains passed, although the observations were never properly communicated to the design engineers. The pier bracing ties were tensioned using driven cotters to wedge two sections together, and maintenance work led to these being wedged in the loose rather than taut position, to prevent chattering. The result was that the ties carried less tension as time moved on, severely reducing the piers' ability to withstand wind load.
Lewis puts forward the theory that the bracing lugs failed due to fatigue. This idea relies partly on the reported oscillations, which would tend to produce cyclic stress, and also on close examination of distant photographs showing the fractured lugs. The images reproduced in the book are very difficult to interpret, however.
The fatigue theory is also presented in detail in Lewis and Reynolds' technical paper [PDF].
Some support for the concept of failure caused by dynamic oscillation was offered by Björn Åkesson in "Understanding Bridge Collapses". He noted that the choice of flat bars for the bracing diagonals to the bridge piers meant that they buckled under compression, such that the bars in tension had to carry a greater share of load (up to double). The use of stiffer sections for the bracing would have reduced the tension load on the bracing bars and hence on the lugs.
Åkesson also estimated the natural frequency of a bridge pier as 1 Hz (Martin and MacLeod, whose paper is discussed below, calculated 0.2 Hz, but it's not clear if this allows for the mass of the train). This could have left the piers vulnerable to excitation either by the wind (including vortex shedding effects from a train) or by lateral nosing effects as each axle passed over a vulnerable position (which would be enhanced by reported curvature in the track and in girders damaged during erection but incorporated into the final structure).
The fatigue theory has its critics. In 1995, Tom Martin and Iain MacLeod reviewed the Tay Bridge failure using modern 3d frame analysis software. Their own paper [PDF] explained failure purely in terms of equivalent static loads, and relied on the assumption that there would be small uplift at the column bases, considerably redistributing the forces in the bracing. Where their paper is particularly good is on the issues beyond the strength of the structure, the economic pressures that Bouch was under which may have led him to attempt a more efficient design than was justified by the state of knowledge at the time.
Martin and MacLeod published a further paper [PDF] in 2004, contesting the validity of Lewis's fatigue theory. Some of what they say strikes me as odd: they evaluate fatigue load due to wind, but ignore the possibility of fatigue caused by wobble excited by track defects. I'd think that neither theory is proveable beyond doubt, there can only be different levels of plausibility in the light of the lack of surviving evidence, and the unverifiable assumptions that a computer analysis must rely on.
More information on the competing failure theories can be found on Tom Martin's own website, as well as on an interactive site produced by Peter Lewis where you, too, can attempt to solve the 'mystery' of how the bridge fell.
Overall, I very much enjoyed "Beautiful Railway Bridge of the Silvery Tay". The presentation of the evidence is comprehensive, with many interesting anecdotes recounted by the eyewitnesses. The many different contributing factors to the collapse are generally well-explained and illustrated, although one or two more diagrams would have assisted.
For the modern designer, the question of which cause of failure is correct should be essentially an irrelevance. The statute of limitations has expired and there is no prospect of a victims' law-suit against a long-gone railway company. However, there are clearly many lessons to be learned which remain relevant today.
The somewhat intuitive approach to loads and factors of safety which Bouch could adopt has generally been superseded by the prescriptions of modern design standards. However, there are always matters of engineering judgement remaining, and the need to consider where the uncertainties in designs may lie. If loads today are generally more predictable, I suspect that hidden construction flaws and tolerance incompatibilities remain a potential cause of departure from the results of simplified analysis, ensuring the need to retain robustness beyond that calculated from the standards.
The need for those responsible for maintenance to properly understand how structures were designed to behave is also as important today as it was then. A greater involvement of builders and designers in the long-term maintenance of their creations would often still be of benefit.
The economic desire for ever-lighter structures which clearly drove Bouch is still strong today, and the Tay Bridge disaster emphasises the need for careful consideration of dynamic behaviour when structures are made more slender, and more vulnerable to excitation from unexpected sources.