Science, Maths & Technology

Tay Bridge Theories: Tom Martin

Updated Wednesday 9th May 2007

Tom Martin believes the Tay Bridge would have fallen, train or no train

Tom Martin gives his opinion on why the Tay Bridge collapsed.

How did you come to investigate the Tay Bridge disaster?

Ian Macleod Copyrighted image Icon Copyright: Used with permission "I can remember, whilst at secondary school, reading a book entitled The High Girders by John Prebble. He made the whole thing very interesting and I wondered if good construction could have saved the bridge. Later on, when I was working as a mathematician at the British Steel Corporation, one of the metallurgists there handed me a copy of the Court of Inquiry Report on the Tay Bridge disaster. He had been interested in the performance of the materials used in the construction of the bridge, especially the cast iron. I read the report a couple of times and wondered if modern analysis techniques could shed new light on the disaster.

Things lay quiet for a couple of years and then I noticed a flyer from Strathclyde University, Glasgow (where I had studied mathematics) advertising an evening class on computer analysis in structural engineering. That caught my eye and I thought that I’d maybe attend. I enrolled on the course, which was run by Professor MacLeod. After the course was finished, I told him I was interested in investigating the Tay Bridge disaster.

After that we both collaborated on the project because he also found it very interesting. It is fourteen years since we started looking at the disaster.

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Theory Summary

We investigated the disaster by utilising modern computer analysis techniques in conjunction with a modern approach to wind loading. The bridge was examined with and without the train on the bridge to see what effect it had on the performance of the pier structure when subject to wind loading. A pier was analysed under various load conditions with a view to proposing a collapse mechanism.

We found that the bridge was simply not strong enough to withstand the wind on that night. The train marginally increases the overturning effect.

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What do you think happened on the night of the disaster?

The collapse scenario given by our model goes along these lines. When the train reached the high girders there was a particularly strong gust of wind. This increased the overturning force enough to cause the base of the windward column to lift, in turn causing the diagonal ties to begin to fail, starting at the second level and developing upwards. This weakens the second level causing the failure of the bolted connections in the column at that level.

Simultaneously, the bracing failure extends upwards. The column support on the leeward side would then become ineffective. That side would start to drop and the whole pier would start to rotate about the second level. As it falls there would be a kickback on the first level causing it to be demolished but retaining most of the first level wreckage on top of the foundation. That would be our collapse scenario.

As all the high girders piers are of the same design only one requires to be considered when analysing the bridge. The presence of the train increases the lateral wind loading and therefore the train makes a difference when it is on the bridge. But, given the wind force (force 10/11 on the Beaufort scale) on that evening, the lateral loading on the other piers could have made them collapse also.

I would put my money that the pier with the train on it was the first one to collapse.

As far as I’m concerned the wind loading is the primary reason for the collapse of the high girders. Once one pier goes it would drag the rest with them. It works like a trigger point.

The low girders that remained standing were much shorter, 145 feet long compared with 245 feet for the high girders. So you’re looking at significantly lower wind loads on them. Also, they weren’t as high, and therefore suffered less overturning effect due to the wind. Computer analysis indicates that these piers were safe for the wind loading that night, which matches up to what actually happened.

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What are the key factors that led you to reach this theory and mechanism of collapse?

The key factor is our ability to model the various scenarios using the three-dimensional elastic frame computer model of the pier. Because you have a mathematical model you have flexibility of examining various loading scenarios.

To build up the model of the pier we used a combination of the engineering drawings and also the Court of Inquiry report and the technical report of Henry Law which gave information such as the weight of the girders. In addition, we used the results of the component testing that was performed for the Inquiry.

These test results were critical for our study as they make such a big difference. For example, the actual bolts that were used for holding down the columns at the base were taken away and tested. We have real figures. I can’t over emphasise what a difference the test results makes to the analysis. It allows one to incorporate the bad construction inherent in the wind bracing members - i.e. they fail at a much lower load than they should have done. So, we really had very good data to build the model - presuppositions were kept to a minimum.

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How does this theory match the actual evidence on the ground?

The pier photographs show uplift on a number of piers, which is of course critical to our theory, which predicted the uplift as the first trigger point. By uplift I mean the windward column lifts two courses of the stone masonry it’s attached to, due to the massive wind loading. And the reason is Sir Thomas Bouch had only anchored the bolts through the two top courses of masonry. He should have anchored into the caissons. A very thin layer of cement was all that held the courses of stone together below the two top courses. You can see a number of piers where this lifting has taken place. The photograph of pier 5 shows clearly the uplift on the west side, for example.

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Does the speed of the wind play a factor in your theory?

The wind speed is the critical factor as it determines the lateral loading on the bridge. The gale, which was blowing along the Tay estuary that night, was at right angles to the bridge, which is the worst scenario. We’ve estimated the wind force at 10 to 11, which was recorded by the local met office, naval officers (stationed on the Tay ) and some local meteorologists.

I don’t think there’s much doubt about the strength of the wind. The main controversy at the time was over the quantification of wind pressure. The science of wind effects on structures was just in its embryonic stage of development then. You need to get from wind velocity to pressure using a drag coefficient, but they had no way of estimating this, especially for reticulated girders used for the Tay Bridge. With modern wind loading codes the drag coefficient is easily calculated, which then allows one to calculate the wind loading on the girders. This is the approach we used for calculating the wind loading on the high girders and the pier structure.

The beauty of a computer model is that you can look at the full range of wind velocities. We studied wind speeds from 44 miles per hour right up to 85 miles per hour.

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Do you have an ethos that guided your investigation?

A good theory is the one that can be tested. The degree to which it can be tested will determine whether it is a weak or strong theory. If you can’t test a theory then it would be classed as non-scientific. The Tay Bridge pier model is a mathematical computer model which allows one to load the structure under different scenarios and simulate what happened that night. The techniques used, by their nature, facilitate a quantitative view of the collapse, which is essential to having the theory accepted by the engineering/scientific community.

Theories, which take a qualitative approach, are by nature more speculative. Tests were done on a limited number of wind bracing members to ascertain their tensile strength. It could be that that some of them on the bridge were weaker than the ones that were tested. Our approach would only work with available tensile test data and not use speculative data.

There could have been other factors involved that we can’t model analytically. But regardless of any factors that may or may not have been involved, based on the force of the wind that evening, the bridge design and the test results for the holding down bolts and wind bracing it was going to collapse. The fundamental cause in our opinion is that the bridge was blown over due to being under designed for the wind loading. Obviously other factors, such as train derailment, could have been involved. However, these factors would act as secondary causes for the collapse.

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How do you rate the quality of the BOT inquiry, both against today’s standards and also those of the 1880s?

I think for its time it was definitely an excellent report. There was a lot of work put in to it. The experts called at the Court of Inquiry were the best in their field and they had testing carried out at Kircaldy’s labs in London.

But having said that, I think that today much more time would be taken over recovering wreckage and subjecting it to more rigorous testing. Instead of testing 14 wind bracing members they’d test a huge amount. They’d go to an awful lot of trouble, and as a consequence I think the report would take much longer to produce.

It was such a big disaster - world famous - that the government got involved and said ‘try and get to the bottom of this’. I think it was a ground-breaking report. However, the court of inquiry report stated that the bridge could have survived if it had been properly constructed. But our modern analysis shows that really it couldn’t have withstood the wind forces experienced on the night of the disaster.

I think there are two dimensions to a disaster. There’s the technical dimension, but underlying this there is the human dimension that is of great importance.

If the building of the Tay Bridge had been better financed, Sir Thomas Bouch may have not compromised the strength and stability of the redesigned piers. Due to the project being behind schedule and over budget, his professional judgement was probably clouded, for example he had intended to use sets of 8 columns instead of 6 for each pier. If one looks at his other bridges it is hard to believe it’s the same man that designed the Tay Bridge. I think the Tay Bridge disaster has a perennial message: professional engineers need to operate at a high level of integrity."

For more details of Tom Martin's theory about the Tay Bridge disaster, visit his website: http://www.taybridgedisaster.co.uk/

The BBC and Open University are not responsible for the content of external websites.

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