This figure featured in the judging of the competing designs for the Clifton Bridge, and refers to the maximum tension in the suspension chains. If you prefer metric units, that is 866 kg per square centimetre – or if you want to be properly modern with SI units, 84.96 megaPascals. (See appendix for conversion).
I have always wondered how this figure was chosen. Was it reasonable? Would we choose this figure nowadays? And why didn’t the judges stick to it?
History
In the original competition for the design of the Clifton Bridge, there were 22 entries featuring a variety of designs, some being more plausible than others, and only some being suspension bridges. The Trustees appointed Thomas Telford to judge them, but he rejected them all and supplied a design of his own, a suspension bridge with very tall piers rising all the way up from the bottom of the gorge. The Trustees initially accepted this design; however it did not find favour with the Bristol public or the investors. Therefore the Trustees invited some of the original competitors to submit further designs for consideration.
In this second round of the competition, there were 14 entries, of which the Trustees selected five (including Telford’s) for serious consideration. All these five were suspension bridges made of iron.
After the short-listing, the Trustees appointed Davies Gilbert (a mathematician rather than an engineer, but also president of the Royal Society) and John Seaward (another mathematician but also an iron manufacturer) to act as judges. This pair decided that the strain within the chains should not exceed 5 ½ tons per square inch. My understanding is that this had not been specified in advance, which would explain why only one entry (Brunel’s) met this criterion.
What is “the tension”?
A rope or chain of uniform thickness suspended between two points falls into a catenary curve. The tension is the force within the chain trying to pull the links apart. This force is maximal at the points of suspension, because it is taking the weight of the whole length of the chain, and is at its minimum in the centre.
If one wishes to make the most efficient use of material, the chain should be made to taper more thinly near the centre so that the force per unit of cross-sectional area is the same along the whole length of the chain. The mathematics of this “catenary of equal strength” was first published in1826 by none other than Davies Gilbert.
It is, of course, difficult in practice to construct such a chain, whose thickness tapers progressively along its length. However, the principle was partially applied at Clifton, because the suspension chains have more bars in each link near the towers (11 alternating with 12) than at the centre (10 or 11).
Tensions of the different entries
The judges carefully considered Telford’s design, but rejected it because of the cost of the massively tall piers. They then calculated the tensions within the chains of the other four entries as follows:-
- Brunel – 4.2 tons/sq in – Judged 2nd
- Rendel – 6.25 tons/sq in – Judged 4th
- Smith & Hawkes – 7.0 tons/sq in – Judged 1st
- Brown – 8.3 tons/sq in – Judged 3rd
The various designers clearly had differing ideas as to what tension was appropriate, and Captain Brown’s is twice that of Brunel’s. But Brown was no slouch – remember that he had built the first vehicular suspension bridge in Britain (the Union Bridge in Berwick-on-Tweed) which is still standing today and carrying vehicles – although admittedly his chains have since been augmented with steel cables.
Did the judges stick to 5 ½ tons?
Despite having set a criterion of 5 ½ tons per square inch, the judges seem to have then ignored it by letting other design features take precedence. Their ranking of the entries bore no relation to the tensions. They chose Smith and Hawkes as the winners, with Brunel second, Brown third and Rendel last.
However, Brunel had a private meeting with Davies Gilbert in which they discussed calculations and certain design details. Brunel was then promoted to first place, but was forced to accept several alterations to his design (in particular shortening the span by building a large protruding abutment on the Leigh Woods side).
Is this figure reasonable?
Because the chains are made of wrought iron, which is no longer used for large structures, it is hard to find a modern criterion. I asked Trish Johnson, and she kindly got information from her consulting engineers, who referred to the “Historic Structural Steelwork Handbook”. This states that in 1879 the recommended value for the average tensile strength of wrought iron was 21 tons/sq in. I have found a paper from 1824 (reference at end) that gives results from varying experiments averaging 29 tons/sq in for the breaking strain.
A design load of 5 ½ tons/sq in would provide a safety factor of about 4, which was a commonly used factor at that time. At that time the use of wrought iron for large structures was at an early stage (large scale production of it had only been developed about 40 years earlier). Furthermore, large suspension bridges were also a new development. Therefore the engineers and judges were dealing with a number of unknowns, and needed to be cautious.
Captain Brown’s design with its tension of 8 tons/sq in would have stood up, but with a much lower safety factor.
How did they choose this figure?
I haven’t seen any account of how the judges chose the figure of 5 ½ tons / sq in. They were probably familiar with the experiments in the 1824 paper. Or maybe they based it on their own experience, or that of their friends. However, I have my own suggestion. Remember that Telford had recently built the much-acclaimed Menai Bridge, and that Davies Gilbert had given Telford considerable mathematical help regarding the design of the chains. When I went to the Menai Bridge visitor centre, I was interested to learn that the tension in the Menai Bridge chains was…..5 ½ tons/sq in! Perhaps DG reckoned that since it had worked at Menai, it would do for Clifton.
And the end result?
When the Clifton bridge was eventually completed, Brunel’s design was modified. The bridge deck was redesigned to be much stronger, and hence heavier, than Brunel had planned. Hawkshaw and Barlow dealt with this by adding a third set of chains, thus increasing the cross-sectional area. The resulting tension was then reckoned to be 4 3/4 tons / sq in. (It may be a little more nowadays due to the later addition of a heavier road surface).
Prior to installation, each chain link was tested to a tension of 10 tons/sq in (as had in fact been recommended by Gilbert and Seaward in their 1831 report). None of the links have failed in the subsequent 156 years – all are original.
And as for the hanging rods
I haven’t found any note about the tension in the hanging rods, so I have made my own estimate. Their diameter is 1 5/8 inches, giving a cross-section of 2.07 sq in. The bridge deck weighs 1,500 tons and there are 162 rods, so each bears a weight of 9.25 tons. Thus the tension is 4.47 tons/sq in – virtually the same as in the suspension chains. Although a number of the hanging rods have failed, this was not due to lack of tensile strength, but due to repeated bending during movement of the bridge. (The articulations that should have compensated for this bending had seized up over the years.)
Article by Jonathan Jewkes
Acknowledgements
I thank the Bridgemaster Trish Johnson, and her structural engineer Samuel Wood of COWI, for their technical advice, and also our archivist Hannah Little for help with some historical details.
Appendix – Conversion to metric units:-
1 imperial ton = 2240 lb = 1016 kg 1 inch = 2.54 cm, so 1 sq in = 6.45 sq cm
So 1 ton per sq in = 1016 / 6.45 = 157.5 kg per sq cm
and 5 ½ tons per sq in = 866 kg per sq cm
Conversion to SI units:-
I kg = 9.81 Newtons. 1 ton = 1,016 kg = 9,966 Newtons 1 sq in = 6.45 sq cm
So 1 ton per sq in = 9988 / 6.45 = 1,544 N per sq cm, or 15,440,000 N per sq metre
1 Newton per sq metre = 1 Pascal
And 5 ½ tons per sq in = 84,968,000 N per sq metre = 84.96 megaPascals
Tensile strength of iron
This lengthy paper from 1824 is entitled “an essay on the strength and stress of timber….”, but the appendix at the end (p 251 onwards) gives experiments on iron, performed in 1814-17.