On Fish Bellies

The search for a ‘more rational’ beam

The picture below was taken from a building I conserved and altered. It’s interesting because it’s a rare example of fish-belly beams. They are made of cast-iron and are supported on circular columns, also made of cast iron.

 

Cast Iron columns are common, but fish-belly beams were only manufactured for a short period of time in the nineteenth century. They were simultaneously the culmination of engineering knowledge at the time and a dead end technology that marked the end of an era. There are several reasons why this is the case and I hope to explain some of them in this post.

To understand the paradox it is first necessary to know something about building design and construction materials in the nineteenth century. One of the issues with describing construction history is that it doesn’t always fit into neat periods of time when one technology starts and another ends. In reality developments overlap and there are differences between countries and even within regions of the same country. I don’t really want to devote this post to unpicking historical subtleties so we are going to make some broad generalisations.

For many years traditional buildings had been constructed with load bearing masonry walls and timber floors. This resulted in cellular room layouts with short floor spans that were vulnerable to fire. As industrialisation became more common factories and mills wanted buildings with a more open plan format that were also fire proof.

Engineers responded by replacing the internal walls with columns made of cast iron. Floors were initially still made of timber, but were gradually replaced with ‘jack arches’ made of brick and supported on iron beams. Iron was not fire proof, but it was at least non-combustible and would therefore not contribute to or spread fire.

While these developments were first introduced in mills and factories in the UK they also represent the intellectual origin of high-rise building in the United States. Perhaps that would be a good subject for a later post. 

Today we think of iron and steel, as being strong reliable materials, which are relatively cheap to mass produce, but this was not the case in the nineteenth century. 

Cast iron was strong in compression, however it was much weaker in tension and was also quite brittle. This meant that it was a good material with which to make columns, providing they were loaded concentrically, but beams were more of a challenge. 

When a beam bends it starts to take up a curved profile. The inside surface of the curve, the top of the beam, gets shorter and the outside surface, the bottom of the beam, gets longer. This means that the top of the beam is subject to a compressive force, while the bottom is subject to tension. The tensile and compressive forces are of equal magnitude but act in opposite directions.

Being stronger in compression than tension the governing factor for designing a cast iron beam was therefore its tensile capacity at the bottom of the section. Another important factor was cast iron’s brittle behaviour which meant that an overloaded beam would fracture quickly and without warning. By contrast, modern steel is equally strong in tension and compression and more importantly it is ductile. This means steel beams will deform rather than fracture, thus providing a period of warning to building occupants before failure occurs.

Of course steel was not available when factories and mills were being designed. Wrought iron has similar behavioural properties to steel and was available, but was very expensive and could not be manufactured in large section sizes. That said, while cast iron cost less than wrought iron, it was not exactly cheap either. It follows that finding the most efficient design for cast iron beams was, for a time, the holy grail.

In the 1820’s the person who provided the necessary impetus was William Fairbairn, who owned a large ironworks in Manchester. He enlisted the help of mathematician Eaton Hodgkinson to plan a series of experiments in order to establish a ‘more rational beam’ cross section.

An inverted T beam with a large bottom flange to prevent tensile failure was the first logical step. A smaller top flange was also introduced to prevent compression buckling at the top of the web. Hodgkinson advocated a ratio of 6 to 1. This is counter intuitive to the modern engineer, who is primarily concerned about the top flange of a steel beam buckling. It is however a perfectly sensible approach based on the properties of cast iron.

The next logical step was to consider the distribution of bending force in beams. A bending moment is the product of a force multiplied by the distance to the nearest support. This means that at the supports bending moment is zero rising to a maximum at the centre of the span. If the beam is uniformly loaded then the force in between follows a curved profile.

This meant that if a beam’s flanges were curved on plan, so that they were wider in the middle of the span, they would match the distribution of bending moment along the length of the beam. 

It was also recognised that, while the capacity of a beam is proportional to its width, it is also proportional to the square of its depth. This means that a beam’s depth is actually more significant than its breadth. Matching a beam’s longitudinal profile to the distribution of bending moment would therefore also result in ‘more rational’ cross section. Such beams came to be known as fish-belly beams.

With this a ‘more rational’ beam had truly been realised. It maximised the capacity of a beam while allowing Fairbairn to make them with 20-30 percent less iron. The first building to benefit from the new approach was Orrell’s Mill in 1834. 

Ironically not long after the ‘more rational’ beam had been created it fell out of use. The reason; manufacture of wrought iron and then steel had suddenly become technically and economically viable. This completely changed the parameters of what made a beam economic. Cast-iron, as the name would suggest, is formed by a casting process. A beam can be made to any shape for which a mould can be made. Conversely, wrought iron and steel are rolled into shape from larger billets of metal. Creating a fish-belly profile in wrought iron or steel would therefore require additional fabrication steps. For this reason it was, and remains, more economic to have a mass produced profile that is easy to make than a more efficient profile that is more expensive to make.

And so it was that the rather elegant cast-iron fish-belly beam was redundant almost as soon as it had arrived. It was the nineteenth century equivalent of the Sony mini-disc; a super piece of design that could not compete with the unexpected arrival of MP3 players.

This is of course why it was a joy to discover these rare examples of the fish belly profile and to be given the opportunity to conserve them, although in this case the horizontal profile was uniform.