On Treehouse Masters

The Genius of Pete Nelson   

In recent years one of my favourite TV shows has been ‘Tree House Masters’. Sadly I do not believe further episodes are planned. Every week the show followed the exploits of the Nelson Treehouse Company and its eponymous leader Pete Nelson, as they embarked on another building project.

Perhaps Pete Nelson’s greatest genius is convincing a British engineer to enjoy his rather un-British manner. I can’t help it, I find his boundless energy and enthusiasm completely infectious. That said, the thing that a really like, and the reason Pete gets a post devoted to his work, is that despite describing himself as an architect I think he gets to call himself an honorary engineer. Not only are his designs architecturally elegant and beautiful, but the engineering is too. He clearly has a sound understanding of structural load-paths and he unquestionably understands trees and timber.

I rather suspect that Nelson Treehouse has reached the hallowed status that few designers have whereby people want to buy a treehouse with Nelson’s badge on it. They don’t just want to buy a treehouse, they want a Nelson Treehouse.

On that basis Nelson don’t need an endorsement from a blog that nobody reads so I am going to stick to what I know and that is engineering.

Once a grove of suitable trees has been selected to provide columns for the structure it seems to me that the most important factor in treehouse design, at least from the point of view of an engineer, is dealing with movement. 

Trees sway in the wind and like small children have a habit of setting off in different directions at the same time. If this cannot be accommodated then unwelcome stresses will be locked into the construction causing it to become distressed. This is particularly unwelcome if it damages one or more of the supporting trees.

Trees’ ability to sway is important, nature intends them to behave this way so that they can concentrate on growing tall quickly; there is a race to reach sunlight in the forest canopy. Spending their scarce energy reserves growing impossibly large foundations and a thick heavy trunk is undesirable in the race to the top.

The reason this approach is successful highlights the difference between stability, strength and stiffness. Wind blowing on a tree will exert a lateral force, primarily on the canopy, which is the largest part. This force is transferred via the trunk into the roots, which are spread widely like the foundations of a building.

Wind is of course a dynamic load that gusts and billows rather than a constant static force. This is important. As a strong gust catches the tree its trunk will start to yield by swaying. As the structure moves it is not offering resistance to the applied load. Obviously resistance must be achieved at some point or the tree will simply fall over, however swaying buys the tree time while the wind gust diminishes. In this way the bending stresses experienced by the trunk are somewhat reduced i.e. low stiffness attracts low stresses. Or in other words a flexible tree does not need to be as strong as a stiff one to prevent the trunk from snapping. 

Similarly, a flexible tree exerts a smaller overturning force on the root structure, which means that it takes less effort to remain stable than if the tree were stiff i.e. it is less likely to topple the tree.

Another interesting consideration is that tall thin structures tend to be aero elastic. In simple terms this means that when they move in the wind they generate their own eddies and currents that induce further movement in the structure. A feedback loop is set up, which can make them dynamically unstable.

I have a hunch, and it is only hunch, that evergreen trees, which tend to be the tallest trees, retain their covering to help damp out these effects. I realise that someone is going to point me to some very tall deciduous trees; I expect in a rainforest. I haven’t worked out this theory in full, but in my defence I would point to the use of buttresses in large rainforest trees.

Movement is also inherent to the way in which trees age. As they get older they grow taller and fatter. Fortunately trees increase in height from the top and not from the bottom, otherwise treehouses would gradually become higher and the entrance ladder would need to become longer. The bigger issue by far is growth in the size of a tree’s girth. This is really important because of how trees work.

Crudely speaking all of the action happens in the 20 annular rings located closest to the tree’s bark. These rings contain sap wood and they are responsible for conveying the nutrients required by the tree to live. You could think of them like arteries.

If a structure is connected too tightly around a tree’s trunk it will dig into the sapwood as the tree grows and it will begin to choke the tree. There is something all together unpleasant about this. Since the tree is compelled by nature to grow, a tight structure will condemn it to be slowly strangled by that same growth. As this happens it will ooze sap from its wounds. It follows that a less destructive method of connection must be found. 

Nelson have an array of different hangers and connectors that they use to erect tree houses, but they essentially boil down to two types, which have a common method of attachment. A fixed connector that anchors the treehouse and a sliding connector, which permits a treehouse to take vertical support from a tree while allowing the tree to sway horizontally. For each construction a mixture of fixed and sliding connectors must be arranged such that the treehouse is stable while simultaneously being free to move in each direction.

The steel connector attached to the trees is ingenious. The embedded end is of small diameter and has a thread. It is screwed into the tree. The middle of the connector has a larger diameter and is smooth. It is partially embedded in the tree and forms a bearing surface, which increases as the tree grows and envelopes it. The outer section of the connector is also smooth and provides a seating for supporting beams. As the tree grows in diameter beams can slide along the seating without damaging the tree.

There is obviously more to treehouse design than this, but this is the part that interests me the most.

I would highly recommend checking out the Nelson Treehouse Company website or buying one of Pete Nelson’s books. Not because he needs any publicity from me, but because you might just find yourself inspired by one of his fabulous designs.

On Resistance & Reaction

Surprising qualities of timber in fire

The photograph below is relatively grainy, but is reasonably well known in the field of structural fire engineering. I first came across it at University, however I haven’t been able to determine its original source. I understand that it dates to 1906 and was taken in San Francisco, which could imply that it was linked to the large and devastating earthquake of that year. 

That said, as the sub-title for this post suggests this is not a post about earthquakes. Any relevance to the San Francisco earthquake would be due to the widespread fires that it caused.

That is because the image above pictures a fire damaged roof with steel beams sagging over a supporting timber, which has, by contrast, retained its structural integrity. This is rather interesting, because it defies the common sense view that steel is a superior material to timber in a fire. Self-evidently something else is going on.

For a number of years the timber industry has been promoting timber’s credentials as a green material, however recently I have noticed that it has become rather more active in promoting timber as a good fire resisting material. It has almost become a cliche that timber is better in fire than steel. The photograph above would certainly appear to support this claim. 

I suspect that this new found advocacy for timber’s fire resisting qualities is a response to a number of recent fires; tragically some with significant loss of life.

Yet somehow the facts don’t quite seem to fit do they. Steel buildings don’t burn down and you don’t throw steel onto your campfire to make it burn. It is perhaps a good time to recycle the analogy I deployed in my post titled ‘On Howe Trusses Work’, for this is another case of there being several layers of understanding i.e. a deeper magic.

We should probably start by trying to define what we mean by fire resistance. This is not as easy as you might think. There are normally three attributes that constitute fire resistance. The first is load capacity. This is the ability of a structure to retain its strength and stability in a fire. The second is integrity. This is the ability of a structure to contain a fire and prevent the passage of hot gases through splits, gaps and fissures. The final attribute is insulation. This is the ability of a structure to prevent the transfer of heat from the face of structure exposed to fire to the unexposed face.

The photograph above demonstrates that in respect of load-bearing capacity an adequately sized timber will retain its integrity longer than steel. It is also reasonably clear that timber is a good insulator while steel is a good conductor. Placing your hand on the back of a steel plate placed in front of a fire would hurt more than a sheet of timber, at least to begin with.

Integrity is perhaps harder to judge. Timber will eventually burn through, however steel is more likely to open a gap by distorting. I shall declare this category a draw, as the inference one draws depends largely on the boundaries that are set.

Based on this rather crude assessment we reach the surprising conclusion that timber is indeed more resistant to fire than steel by a score of 2.5 to 0.5. The trouble is that this isn’t the whole story, because ‘fire resistance’ is not the same as ‘reaction to fire’.

Reaction to fire means how easily a material can be ignited and how much it contributes to the growth of a fire. On this measure timber unquestionably fairs worse than steel. Steel is of course classified as a non-combustible material.

It follows that when we talk about fire resistance in engineering we are not actually talking about the common meaning.

Using engineering definitions it may be concluded that during the ignition and growth phase of a fire ‘reaction to fire’ is the more significant material property, however once a fire is fully developed ‘resistance to fire’ becomes more important. Thus, whether steel or timber is considered better depends on timing.

That said, if we must decide then I would choose reaction to fire as more important, because resistance becomes moot if a fire doesn’t start in the first place. That is not to say that resistance isn’t important, because a steel building doesn’t stop someone from leaving a pile of combustible material in the lobby, which could catch fire. 

Another consideration would be the continued existence of historic buildings. It would not be a good idea to simply demolish those which are made of timber, because of the perceived fire risk. We need tools to understand how they will behave when subjected to fire so that mitigation can be established.

There are of course many other examples that could be considered, however these are sufficient to demonstrate that structural fire engineering is a complex business that requires a proper examination of all the relevant factors in a given circumstance.

Incidentally the reason why timber has good resistance to fire is related to its insulating properties. When timber burns it starts to char at a predictable rate. As the charring layer forms it insulates the timber beneath helping to prevent ignition at depth. For this reason steel fixings in timber can be problematic, because they conduct heat into the core of a section.

Since the rate of charring is known an engineer can calculate, for a given duration, a sacrificial thickness of timber that will be charred, while leaving a residual section of timber capable of supporting the required load.

Rates of charring do vary between timber species; the predominant factor being density. Broadly speaking the denser a wood the slower its rate of combustibility and its associated charring rate. 

This knowledge, while sounding modern, is not new. Jarrah, a hardwood [1] was commonly used for railway sleepers in tunnels and on bridges, because of its slow charring response to hot tinders falling from steam engines.

It is worth noting, however, that the relationship between density and fire resistance is not universal. Some woods have chemical contents that make them more likely to burn, however even in such cases density does tend to be the more dominant factor.

[1] it is a common misconception that hardwoods, as the name would suggest, are by definition harder and denser than softwoods. This is a useful general rule, but is not strictly true. Balsa, which is used for model aeroplanes, is a hard wood, while the rather strong pitch pine is a softwood.

 

On Accidental Bridges

The robustness of brick walls

I came across this rather interesting photo, which shows the remains of a partially demolished nineteenth century mill. 

The picture is dominated by a large brick wall, which is suspended above ground level. The original load-path for its support appears to have been an arcade consisting of cast iron columns carried on masonry arches. 

To the left of the image one of the arches has been altered. The profile of its voussoirs has been straightened on one side and the arch infilled with modern brickwork. The infill brickwork is in turn supported on a modern beam and post structure, which is likely formed of hot rolled steelwork.

Below the centre of the wall two of the cast iron columns have been pushed over. The one on the left is clearly visible, while the one on the right is a little harder to pick out. Its head can be detected, because it is still connected to the wrought iron rods that would have been used to resist thrusts at its abutments. To the right of the photo the rods can still be seen linking the remaining iron columns.

It is also evident that the masonry arches which would have been carried by the missing columns have collapsed. It is assumed that rubble, which can be seen at the base of the picture, is what remains of them.

What is of course remarkable is that the brick wall continues to stand. It has found a way of bridging between the steel column on the left and the cast iron column on the right. This is interesting for several reasons.

Since the span is roughly equal to the height of the wall it is reasonable to assume that it has achieved this feat by acting as a deep beam. Were the deep beam made of concrete it would be normal to assess it using a ‘strut and tie’ model. This means imagining a triangular load path in the wall. The two vertices of the triangle form compressive struts, which are sat over the supporting columns, while reinforcement in the base of the wall would complete the triangle by resisting lateral thrusts from the inclined struts. An alternative way of considering this model would be to think of it as a tied arch, as the principle would be similar. Indeed, post failure the residual brickwork appears to have formed a crude arch between the column supports.

In this case there is no concrete and no reinforcement, because the wall is made of brick. Brick is good in compression, which would seem to make either an arch, or compressive struts, a viable load path, however there is no equivalent for the reinforcement, which is required to complete the triangle. 

Brickwork is poor in tension and therefore the base of the wall ought to have failed, however there seems little evidence of distress other than the smaller arches giving way to form a larger, if somewhat makeshift arch.

This means the deep beam must, on this occasion, have a different mechanism for resisting lateral thrust. Two options seem plausible, though one seems more likely than the other. 

It is possible that there are rigid load-resisting structures located just out of picture on either side of the image, however if this were the case then there would be no need for the wrought iron ties, which originally held the column heads together.

It seems more likely that the weight of the brick located above the arch supports is sufficient to divert the arch thrusts back to the vertical i.e. it behaves like heavy bridge abutments. Both headers and stretchers can be seen in the brickwork suggesting that the wall is at least a full brick thick and would therefore be relatively heavy.

Looking carefully at the image there is also evidence of pockets in the brickwork, which would have seated beams in the wall. In fact the remains of an I-shaped steel beam can still be seen embedded on the left hand side. It was presumably easier to cut the beam off at the support than to completely remove it during prior alteration works. This may be relevant because the load carried by the wall must have been reduced. This in turn means the thrust is less.

Since two columns are missing we would ordinarily expect those which remain to take 100% more load. For this reason a reduction in load carried by the wall is of significant benefit to the columns too.

So it would seem that a structure whose intended load-path has been compromised has managed to find an alternative load-path demonstrating rather well that structures will exhaust all possible ways of standing before they collapses.

This does not mean that we would necessarily wish to rely on this load path in the long-term, but nevertheless it is a reminder for engineers that there is more than one way of looking at a problem….in this case an accidental bridge.

 

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.