On Ice Shelf Cracking

Tension Cracks in the Brunt Ice Shelf

Yesterday the BBC news website published images showing a large section of the Brunt ice shelf in Antartica, which has separated from the main body of ice and formed a large iceberg. The associated article notes the giant berg to be 1,290 square km on plan. 

The reasons the ice berg formed are no doubt complex, however that isn’t what caught my eye. The thing that interested me can be seen in the close up images. Again, according to the article, the crack that has formed in the ice is approximately 2 km wide, which is a vast dimension relative to the scale of cracks that are normally considered.....at least in the sort of work I am accustomed to.

The reason this interested me was because, despite the macro scale of cracking on display, it has the appearance of something that is familiar to me at a much smaller scale.

 It follows that my explanation of the BBC’s photos is based on extrapolation from small to big. I don’t really know anything about ice shelves or icebergs so admittedly it’s going to be a bit of speculation on my part; though I hope not too much of a stretch.

The defining characteristics of the crack are; clean edges edges; and what seems like debris in the gap. Almost all of the debris is on the left side of the crack and has accumulated adjacent to the iceberg rather than the shelf. To me that is interesting. 

Clean edges, or more importantly the absence of tearing, indicates that the crack is a tension crack i.e. the iceberg has pulled directly away from the ice shelf and has not slid past it.

If there has been a clean break the question arises as to why there is debris within the crack and why it is clustered on one side. I think the most important clue is to be found in the profile of the debris’ edge. It matches the profile of the ice shelf much closer than the profile of the iceberg. This indicates that the debris must have been in contact with the ice shelf.

From this we can deduce that the original crack must be old and that it must have been dormant for a reasonable period of time. We can also deduce that it must have remobilised more recently. The inferred mechanism would be as follows:

At some point in the past a crack opened in the ice shelf. The images do not convey why, but for some reason the crack stopped becoming larger and was for a time stable. This would have allowed new snow to fall within the crack and over time to pack down and form new layers of ice. The crack was starting to fill. 

For some reason, again the images do not convey why, the crack remobilised and the iceberg started to drift further away from the ice shelf. The forces carrying the berg also carried the debris moving it further away from the shelf. I suppose I shouldn’t really call it debris, as that would imply that it fell from the sides of the ice pack, whereas I think it was new snowfall. If it had fallen from the edge I don’t think the crack edges would be as clean as they are.

I like this explanation, because I think it fits the visual evidence in the photo, however it also suggests that the same principles apply at a human scale as they appear to at a continental scale.

For example, old and dormant cracks in a wall can often be identified by evidence of dust and debris accumulating in the gap. If the debris has become dislodged it could indicate that the crack has started to remobilise. Similarly, cracks with clean edges will generally indicate the presence of tension. This in turn indicates movement perpendicular to the direction of the crack. Together these observations can often be used to infer the underlying cause.

In the case of the Brent ice shelf we can infer that the berg has moved perpendicular to the crack, perhaps due to ocean currents at the water’s edge, or perhaps under the influence of gravity if the underlying shore slopes toward the sea. I don’t know the reason, as it is not evident from the images.

Nevertheless, the visual appearance of the crack in the ice shelf does imply the remobilisation, for some reason, of an older crack that was stable for a period of time. Something has changed.

Or, since I don’t know anything about ice shelves or icebergs, perhaps none of my conjectures are true. I shall allow the reader to decide.

On Lock-down Tyres

Why my car tyres are flat?

I left the house this morning and found that my car tyres had gone soft and one was completely flat. This was a rather curious state of affairs, because I had not driven anywhere to acquire a puncture, due to the covid-19 lockdown. I live in a quiet village and have good neighbours with whom I am friendly; so it seemed unlikely that anyone would have tampered with them. Nevertheless, I did inspect the tyres to make sure that there had been no foul play. There was no visible damage to the tyres and layers of grime on the valve cap indicated that it had not been loosened recently.

I like a mystery and this got me to start thinking about whether there was an engineering reason why my car tyres had become soft. The first potential culprit was the weather. The differing seasons bring with them settled and unsettled weather, which is of course linked to air pressure. It would be rational for the internal pressure in the tyres to be affected by changes in external air pressure. While this may have been a factor it did not seem to be a good explanation, because though the weather has been inclement recently it has not been unremarkable. Scotland regularly experiences inclement weather, often far worse than it is now. This begged the question that if weather was responsible for my tyres’ loss of pressure why had it not happened before?

The only thing that was really different to normal was that the car had not been used, as there was nowhere to go during lock-down. Cars normally deteriorate due to wear and tear; inactivity would therefore seem like and odd, and somewhat ironic, causation. That got me to thinking about what the mechanism for such an outcome could be. I soon found myself reverting to type thinking about materials and load paths.

The weight of my car is split between four wheels, but not evenly. With an empty boot [trunk for American readers] the car engine is responsible for there being more load on the front axle than the rear. This was consistent with the front tyres being flatter than those at the rear, so perhaps I was on to something.

Weight is transferred from the rotor to the wheel hub by four bolts and then from the hub to the tyre by air pressure. When I was growing up tyres had a pressurised inner tube, but today there would seem to be reliance on the joint between the hub and tyre being sealed tight by pressure.

The hub must be exerting a downward force onto the pressurised air at the base of the tyre, which is resisted by an equal and opposite upward reaction from my driveway via the tyre. The air inside the tyre does not like being squeezed and will try to escape out of the way causing the sides and top of the tyre to experience an outward thrust that would cause it to be stretched. Thus, the bottom of the tyre would be experiencing compression while the top and sides experience tension. 

With inactivity seemingly the critical factor I concluded that my tyres did not like this state of affairs for an extended period. I reasoned that this might be because they are intended to be spinning, such that each part of their circumference takes its turn at bearing compressive and tensile load.

Conversely if my car remained stationary then the load experienced would become quasi-permanent rather than temporal. This opened up several possibilities. Perhaps constant tension resulted in the structure of the rubber becoming elongated in such a way that it was more permeable to air, or perhaps constant compression made the rubber at the base less flexible and therefore more permeable. 

Alternatively, perhaps the seal between the tyre wall and the hub starts to slip with the constant application of load. It would seem reasonable to postulate that such an effect would become more pronounced as pressure is lost from the tyre, because the seal is reliant on their being a positive pressure.

I am not sure if any of these potential explanations are correct or if they all play a role, however irrespective of this I shall in future be making sure that my car wheels turn regularly; even during covid lock-down. 

I shall view my theory as proven if my tyre problem does not return....we shall see.

On Pentre Ifan

Some observations about Dolmen

This evening I watched a documentary presented by Alice Roberts. I don’t think I have watched a programme presented by Dr Roberts that hasn’t been interesting, and this one was no different, except that the most interesting thing wasn’t strictly the topic. The documentary was about the bluestones of stonehenge, but it strayed ever so slightly to Pentre Ifan in Wales were I was introduced to Dolmens. These are Neolithic structures, which predate Stonehenge. There are lots of them around the world and some are thought to be around 7,000 years old. The Dolmen at Pentre Ifan is a spectacular example, whose massive capstone appears to float above the tips of three standing stones. I expect that’s why I noticed it and why Alice Roberts chose that example.

 

Archaeologists believe that Dolmens were ancestral tombs, because scattered human remains are often found between the standing stones. Some also believe that they were originally buried beneath a mound of earth or smaller stones.

Interesting as these conjectures are I can’t get past the graceful form of the structure. I suspect that archaeologists, for the most part, take for granted that the monument stands, while going to great lengths to try and understand how it got there and how it was built. I think I understand why this is, but there is a certain irony that for such an old object so much more effort is expended on the temporal than the permanent [1].

To me the fact that Pentre Ifan is standing at all is more interesting and is the subject of this post. Maybe on another occasion I’ll fall in to line with everyone else and have a go at speculating how such structures are built, but not today.

I should of course pause to note that I have never seen a Dolmen in person, nor do I really know anything about them, other than tonight’s brief introduction. I am keen to remedy that and will aim to visit some examples when the covid-19 lock-down has ended, however that isn’t going to stop me from donning my engineering hat and doing some speculation of my own. I shall be doing so based on a few images I have pulled off the internet; what could possibly go wrong?

I am going to start with the assumption that the stones are igneous rocks, because they have that appearance and because there are outcrops in the the relevant part of Wales. This ought to make the rock relatively strong; though like any rock it will be brittle and weak in tension.

There is evidence of horizontal fractures in the capping stone and equivalent vertical features in the standing stones. Structurally this is not a terribly efficient arrangement. A stronger arrangement would be to align planes of weakness in the standing stones horizontally so that they are squashed together. For the capping stone it would have been better to align them vertically so as to avoid separation due to shear flow generated by bending forces.

I suspect that this was not done, because creating the great slabs of stone required cleaving them from the parent rock by exploiting the noted weaknesses. Without them stone-age workmen would have had difficulty creating such slabs with primitive tools.

The next thing I notice is that the capping stone appears to be fatter at one end than the other and that the soffit appears to have been cleaved as it progresses towards the thin end. I suspect that it was not originally so.

The fat end is supported by two standing stones, while the thin end is carried by one. In the short axis the fat end of the capping stone can bridge laterally between two close supports. It can possibly do this in direct shear and without inducing bending.

Conversely, in the longitudinal direction the capping stone must span almost 5 meters between the single and double support. This almost certainly results in it experiencing bending. As has been seen in prior posts bending causes the top surface of a beam to experience compression and the soffit to experience tension. 

In order for this to happen a beam will also experience a laminar shear flow in the horizontal direction. This can be understood by imagining a beam divided into horizontal slices. For tension to be experienced on the soffit while compression is experienced on top it is necessary for the imaginary slices to slip past each other.

The consequence of these actions appears to be evident in the structure. Since stone does not deal well with tension it is inevitable that small cracks must have developed in the soffit. There would also have been lateral movement along the rock’s natural horizontal weaknesses. It is conceivable that together these effects led to the soffit spalling, however it is more likely that they were abetted by other effects too.

 

Rainwater will have soaked through the top surface of the slab and migrated under gravity to the soffit. While moisture would evaporate quickly from the top the soffit would remain in the shade helping to keep the stone damp and wet. Persistent dampness will have weakened the rock structure and freeze thaw action would have exploited the many small cracks and natural weaknesses. Eventually the fractured rock would spall until it arrived at a horizontal plane of weakness whereupon the process would start again.

Perhaps another aggravating factor would be expansion and contraction due to the cycle of heating and cooling. Since only the top surface is exposed to the sun there is likely to be a thermal gradient in the capping stone as it warms. During the day the top of the stone would expand relative to the soffit and thereby start to close some of the soffit cracks. Conversely, during the night it would start to contract and thereby re-open the soffit cracks. Thus, by repetition the soffit would slowly be fatigued and further cracks induced.

When considering thermal effects it is worth noting that having only three small points of contact between the capping and standing stones is probably beneficial, because the soffit is free to articulate. More severe cracking would be much more likely if the top surface were free to expand and contract while the soffit was held in place by more restrictive contact. 

It would therefore seem that there is a good explanation as to why the capping stone is fatter at one end than the other, and all else being equal, by what mechanism it will eventually fail.

The standing stones appear to carry the capping stone effortlessly. The fact that they do so with such small points of contact would suggest the compressive strength of the stone must be relatively high. That said, it is assumed that the contact surfaces could not have been prepared to a modern standard and therefore the distribution of load will not be entirely even. This will have allowed load concentrations to be formed which may over time pry and fracture the rock locally.

This is important because compression in the standing stones will cause lateral bursting forces to develop due to passion’s ratio [this is another concept we have seen before]. Within the body of the stone compressive stress is generally low and therefore the bursting forces have little effect, however where load is concentrated stresses are higher. If such stresses coincide with a vertical plane of weakness it could encourage the bursting forces to form a split in the rock. As with the capping stones this could be exacerbated, either by moisture penetration, or by bending induced by one side of the rock being warmed faster than the other. There does seem to be some evidence of such processes at work on the surface of the standing stones.

Another facet of the pictured Dolmen is how it maintains lateral stability. It is self evident that there is no rotational resistance at the junctions between the capping stone and its supports, therefore we must conclude that the standing stones must cantilever from ground level. Since the capping stone bears heavily upon them there will be sufficient friction generated to share lateral load between the standing stones according to their stiffness.

Lateral loads would come from the wind and to a lesser extent thermal effects. There also appears to be a slight incline to the capping stone, which would imply there is a resultant lateral load, due to the stone’s self-weight, to be resisted.

Something else that is structurally relevant, though I am unsure whether it was intended, is the orientation of the standing stones. The two stones at one end are orientated perpendicular to the single stone at the other. Strength being proportional to the cube of depth this arrangement presents the full depth of at least one stone in each orthogonal direction, thus maximising cantilever action in both.

It is also interesting that the end supported by two stones is aligned with the noted incline to the caping stone, thus maximising resistance to the permanent lateral load. The possibility that this was intended is intriguing.

A different explanation would be that since one end of the structure has two supports, and the other just one, there could have been differential settlement. Assuming this were the case the narrow supports would again have been beneficial, because they would have allowed the capping stone to rotate and find a new point of equilibrium. Alternatively, more substantial supports would have likely led to fracture. I have no idea what the bearing strata beneath the standing stones is like, but in the absence of further evidence the mechanism for differential settlement seems plausible.

Of course it is also possible that the fractured soffit could have contributed to creating the observed incline too.

While the depth of embedment of the standing stones is not clear from viewing the surface it seems reasonable to assume that it must be substantial to ensure there is sufficient passive resistance to prevent overturning or sliding of the stones. In a uniform soil it would also be reasonable to assume that bearing pressure would increase with depth.

On paper it is perhaps possible that the stones could be mounted near the ground surface with stability being maintained by their shear size and mass. In the real world this does not seem plausible as the surface of the ground is prone to become waterlogged, there is also the possibility of frost action. Either of these effects could be sufficient to topple the stones.

Two further practical matters exist. Firstly, a shallow footing would be vulnerable to digging near the base when bones were to be buried. 

Secondly, and perhaps more importantly, the processes of standing large stones on end without a crane, or other modern equipment, would seem to make it necessary to tip them into a hole. If said hole were then packed tight with backfill it would lock the stones in place allowing them to behave as cantilevers.

Here I run the risk of getting into the question of how the stones were erected and I said I wasn’t going to do that. I best stop here.

[1] I base this thought on working with a few archaeologists and the number of documentaries there are about erecting Stonehenge, rather than any proper search of the archaeological literature.

On Frocks and Bias

Or why fashionable dresses cling

I like watching movies, but I don’t much care for the process of promoting them or the somewhat cringeworthy awards season that culminates with the Oscars. Writing this in that season, albeit you will be reading this later in the year, I set myself the challenge of finding something Oscars related that involves structural engineering. I assumed that it would likely involve something to do with the staging or set, but eventually I decided to go in a different direction.

Just how do they make those frocks seen on the red carpet hug the body so tightly?

It may not be immediately obvious what figure hugging dresses, of the type worn to award ceremonies, have to do with structures, so your going to need to bear with me. I hope I am not biting off more than I can chew, because I am no fashionista and I don’t know anything about clothes. As always I shall be relying on engineering principles.....

It seems to me that there has never been a time when the human body has not been viewed as art and its form put on display. In this sense not much has changed between the marble sculptures of antiquity to modern day frocks.

That said, one thing that does seem to have changed is that extensive rigging no longer seems necessary to create a tight fit. I suspect that corsets are not terribly comfortable and therefore I expect most ladies welcome their demise.

To understand why we need to understand cloth and how it behaves. We also need to revisit phenomena we have met in a prior post; namely Young’s modulus and Poisson’s ratio. When a material stretches it narrows and when it is squashed it bulges. The amount of narrowing and bulging is directly related to the stiffness of the material; the stiffer the material the less there is. This is why we rarely notice the effect in steel or concrete. Stiffness is the ratio of stress to strain and is known as Young’s modulus, while the ratio of axial stretching or squashing to lateral narrowing or bulging is known as Poisson’s ratio.

Cloth is unlike steel, because its stiffness varies in different orientations. This is due to the way in which it is made. There are two sets of fibres, which are arranged in perpendicular directions. The warp threads are aligned vertically and the weft are weaved above and below. If the cloth is pulled in the direction of the warp there is little stretch in the direction of the tensile force. Similarly the weft threads prevent narrowing in the perpendicular direction. Alternatively, pull in the direction of the weft and again there is little movement in either direction. For this reason cloth is quite stiff in tension, except that is, if it is stretched at 45 degrees to the warp and weft. In this orientation there is considerable stretching and narrowing. Thus, at 45 degrees cloth has a low Young’s Modulus and a high Poisson’s ratio.

A useful analogy would be to compare the stiffness of a structural grid formed of perpendicular members with a lattice formed of diagonal members. Due to rotation at the joints the lattice is poor in tension, but good in shear, while the perpendicular grid is good in tension, but poor in shear.

Now supposing a dressmaker were to arrange and cut the cloth for a dress such that the warp and weft were aligned at 45 degrees to the vertical. I gather this is known as a bias cut. In such circumstances the self weight of the dress would place the cloth in tension, which would cause stretching in the vertical axis and a corresponding contraction in the perpendicular direction. 

Self-evidently the noted contraction would cause the dress to hug more tightly around its wearer. 

I am quite sure that dress makers must have lots of crafty tricks to enhance this effect. Perhaps they use thicker material, folds or stitching to increase the weight of the dress in certain locations or perhaps they vary the composition of the cloth by using threads of different stiffness or looser weave.

I have no idea if these are actual things or not, but they do seem to be reasonable suppositions based on the need to minimise Young’s modulus and maximise Poisson’s ratio. 

I don’t suppose dressmakers communicate in terms of Young’s modulus & Poisson’s ratio, but to make their dresses work as they do I suspect they do have a rather good empirical understanding of cloth. 

All this means that while I have little time for red carpets and awards ceremonies I can at least admire the skill of the dressmaker and their intimate knowledge of fabric. Whether they know it or not the figure hugging designs that have replaced laces and corsets rely on sound engineering principals.

On Ductility

The benefit of elastoplastic materials

One of the most useful structural properties a material can have is ductility. In order to understand why this is so it is first necessary to explain some related concepts. We will start with stress and strain.

Stress is a measure of load intensity; more precisely it is the ratio of force divided by area. This concept can be visualised by considering how it is that someone can lie down on a bed of nails without being harmed, yet if the same person were to tread on a single nail it would pierce their foot. The reason a bed of nails causes no harm is because the person’s weight is spread over the cumulative area of many nails whereas a single nail concentrates a person’s weight over a very small area i.e. the bed of nails applies low stress, while the single nail applies high stress.

When a structural member is exposed to stress it will change in length. If the stress is tensile it will become longer and if it is compressive the reverse is true. If the material is uniform then the elongation or shortening is spread evenly along the length of the member. For example, a member that is half as long will change in length by half as much. The ratio of elongation or shortening per unit length is defined as strain.

Stress and strain are of course related; higher stress will cause higher strain. A useful way of expressing this relationship is to plot a stress-strain graph. The convention is to measure stress on the vertical axis and strain on the horizontal axis.

If a material is ductile, like steel, the relation of stress to strain will be directly proportional resulting in a straight line on our graph [1]. The inclination of the straight line is know as the elastic modulus, for reasons we will see shortly.

There will, however, come a point where strain will increase more quickly than stress and the graph is no longer a straight line. The proportional limit of the material has thus been breached. Soon after this point the graph will become horizontal, which means that strain will increase without a corresponding increase in stress. This threshold is known as the yield stress.

Beyond yield the internal structure of the material will begin to change at an atomic level. This process is known as strain hardening and it results in additional strength, and therefore higher stress, in return for further strains.

Eventually the stress-strain curve will again flatten leading to increased strains, but this time with decreasing stress. The point where this occurs is know as the ultimate stress.

Increased strain accompanied by decreasing stress is a rather curious effect. Why would increasing strain result from a reduced stress? There is of course a rational answer to this question. 

When any material is stretched there is a corresponding narrowing to facilitate the stretch. Generally this is too small to notice, however beyond the point at which the stress-strain curve flattens the effect becomes more pronounced and ‘necking’ occurs.

If we were to calculate true stress, based on a necked [reduced] cross-section, rather than continuing with a nominal stress, based on the original cross-section, then the stress-strain plot would in fact continue to grow. After a period of necking fracture will eventually occur.

Returning to the beginning of our stress-strain plot we can modify our approach. This time instead of continually increasing the stress applied to our test member we can load it to a known stress and then unload it again. We can then increase the stress to a slightly higher value and then unload again. This sequence of loading and unloading may be repeated.

When we do this we find that as long as we remain below the proportional limit the unloaded member will fully recover its original shape and will follow the straight line portion of the stress-strain graph. Beyond the proportional limit a full recovery will not be made; there will be some residual strain left behind.

When the member fully recovers its shape it is said to be elastic. The point at which it loses its elasticity is known as the elastic limit. Beyond the elastic limit materials are considered to be plastic. For many materials, like steel. The proportional limit, yield stress and elastic limit are relatively closer together and are in practise treated as if they were the same. For some materials, such as rubber, the elastic limit lies well beyond the proportional limit.

When large permanent strains start to occur within the plastic zone the term plastic flow is adopted. 

There are several reasons why ductility, incorporating both elastic and plastic behaviour, is important. We shall discuss one of them below and save another for the next post.

Supposing we wished to design a series of floor beams for a new building. The owners would not be terribly happy if they were to permanently deform and sag while the building was in use. For this reason we would want them to remain within the elastic range. We would therefore perform our design based on limiting stresses in the beams to the yield stress of the material.

This would satisfy the requirements for every day use of the building, however supposing an unforeseen or extreme event occurred, which caused the floor to become overloaded. In such circumstances you would not wish the floor beams to fail suddenly and without warning, for this would inevitably lead to a loss of life. 

Self-evidently it would be preferable for there to be a visible warning that something was wrong so that the occupants could vacate the floor safely and remedial action could be taken. This opportunity is provided by plastic behaviour in the floor beams. Although permanent deformation will occur within the plastic range the floor will at least remain stable and safe.

It is fairly obvious how this principle will work if the floor beams are made of steel, but perhaps less so for concrete. After all concrete is not a ductile material. It is weak in tension and fails explosively in compression.

The first problem is solved by casting steel reinforcement into the concrete in zones where the concrete is in tension. The reinforcing bars, rather than the concrete, resist the applied tensile stresses.

The addition of steel reinforcing bars also provides the means to deal with concrete’s lack of ductility. The reinforcement is deliberately designed to have a smaller capacity in tension than the concrete has in compression. This way as the reinforced concrete bends the reinforcing bars in the tension zones will reach their elastic limit before the concrete reaches its brittle limit in the compression zones. This principle is known as under-reinforcement and it is key to all reinforced concrete design. 

Thus reinforced concrete becomes a ductile material.

[1] In this example we are of course assuming the application of tensile stress

On Spider Webs

The influence of structural form.

The last time I tackled a topic from the animal kingdom I looked at Stegosaurus, which is a rather large animal, so on this occasion I have decided to look at something much smaller. As before I still know nothing about animals and have no expertise whatsoever in the fields of biology, zoology and so forth. I shall be looking at the topic from the perspective of a structural engineer and will likely be making all sorts of terminological and other obvious errors. 

My prepared defence against basic dinosaur errors was based around stegosaurus being extinct and therefore nobody really knowing for sure. This time around I don’t have that luxury. Instead I shall base my rebuttals on that most modern phenomena of ‘getting my message out there’. In this mode of thinking errors are acceptable so long as the direction of travel is correct and ones motivation is honourable. 

Now that my new excuse has been set out, lets jump right in.

There is a cliche about spider silk being stronger than steel, which is obligatory to every discussion of Spider’s webs. I thought that I would get it out of the way early. It is perhaps less well known that spider silk is a non-linear material who’s stiffness varies depending on the applied load; it has both a slack and a stiff phase. This unusual property helps webs absorb impact from captured prey.

Although interesting the properties of spider silk are not actually the topic of this post. I shall be taking them as a given. Rather, I would like to take a brief look at the influence of structural form on spider’s webs.

In the hypothetical scenario of Sir Attenborurgh stumbling across this post and deciding to read it he would no doubt want to point out that there are many species of spider and consequently there are many kinds of web to contend with. For simplicity I shall be sticking with the common variety that most people, including me, are familiar with.

It seems to me that webs consist of several different types of member, which exist within a distinct structural hierarchy. In the first instance there are a series of threads which anchor the web to its surroundings, we shall call these the moorings.

The moorings are connected to the corners of an outer primary frame, which encloses the web. At each corner a secondary frame joins both sides of the outer frame together, but without touching the corner.

A series of radial threads extends from the centre of the web onto the primary and secondary frames. Together these members give the web its overall shape.

A spiral thread winds from the centre of the web towards the outer frames. Unlike those discussed thus far the spiral thread is made of a sticky silk, which is thinner than the other members, and is intended to catch the spider’s prey.

Before we consider how this rather spindly arrangement of threads manages to resist the impact of spider prey, and the force of strong winds, it is worth explaining a key structural principle.

The theory of elasticity dictates that when a load has several different load paths to choose from it will always prefer the one which has the greatest stiffness. In simple terms load is distributed between members according to their stiffness with the stiffest parts attracting the most load.

The importance of this principle may be illustrated by considering what would happen if spider’s designed their webs a little differently. Let us suppose that the hypothetical Institution of Web Safety, were to decree that secondary framing was no longer permitted and therefore radial threads must connect directly to the outer primary framing on all sides. Connecting directly to the primary frame, sounds like a simplification of the structural load-path. That must be good, right?

A further implication of the IWS’s directive would be manifest at the corners of the frame; the radials would now be connected directly to the moorings. Again, that must be a worthwhile safety improvement, because load is directed straight to the point of support.

We can test our theory by imagining a hypothetical fly careering into the web. We want the web to absorb the impact without breaking; that would be bad for the spider’s prospect of lunch.

This means that we want the web to spread the impact force across as many structural members as possible. The more members mobilised to resist the applied load the smaller the load each will carry.

Immediately after the fly strikes the sticky spiral the web’s load-path swings into action. The spiral is connected to lots of radials and begins to share its load. But now something has gone wrong, the load has reached a radial which is connected directly to the moorings. Being connected to the point of support this radial is much stiffer than adjacent radials, which are attached to the outer frame, which has started to flex. Load is immediately attracted out of the radials connected to the outer frame in favour of the stiffer pathway. Soon the radial connected to the mooring is carrying nearly all of the load and is stressed to breaking. Our spider’s lunch is about to escape.

Surprised by the evidence of systemic failure in radial web members the IWS takes the decision to withdraw its directive and reinstates secondary framing, which once again must be connected to the outer frame either side of corners.

Soon an unfortunate fly finds itself bumping into a web with newly reinstated secondary framing. Once again the spiral members spring into action and begin to transfer load into the radials, but this time something different happens. Instead of load being directed straight to the moorings it finds itself being directed into the secondary framing which begins to flex before re-directing load back towards the middle of the outer framing and away from the stiff corners.

The outer framing begins to flex and in doing so starts to engage other radials to which it is connected, before long much of the web is flexing and load sharing is being maximised. On this occasion there is going to be no failure. It looks increasingly like the fly is doomed and the spider will be enjoying lunch.

It seems to me that the web’s structural arrangement is designed to avoid stress concentration. This key feature maximises load spread and minimises the stress in individual members. Another consequence of the redistributive process is that the web becomes less vulnerable to local damage; because load can by-pass those areas.

Thus spider webs have a highly efficient structural form optimised for absorbing impact and for ensuring spiders remain well fed.  

On Tensegrity

In the image below the higher of the two cardboard structures appears to be floating above the other without an obvious means of support. It is a clever arrangement, because the eye is tricked into perceiving an illusion. This is probably because we are used to seeing solid structures supported on columns, however in this case it is quite obvious that the three strings, which link the two parts are much too slender to behave that way. 

That said, on closer inspection the structural arrangement is perfectly stable and fully satisfies the laws of equilibrium. While it may be unusual on the eye its load paths are perfectly rational and with a little thought can be readily understood.

The arrangement belongs to a class known as tensegrity structures. Tensegrity being an amalgam of ‘Tensile’ and ‘Integrity’, which was apparently coined by the American architect Buckminster Fuller in the 1960’s. An alternative name ‘floating compression’ structures was coined by the artist Kenneth Snelson, who was a pupil of Fuller, but its usage is less common. This may be because Snelson’s term does not have the aesthetic quality of Fullers. Nevertheless, ‘floating compression’ is a helpful name, because it hints at the underlying illusion.

A tensegrity structure is one where the compression members are arranged so that they do not meet. It is this characteristic which creates the illusion and it requires a careful arrangement of tension members to achieve the effect. The greater the load in the tension members the more stable the structure becomes. In many cases the tension members are actually pre-tensioned to ensure that the structure can retain its form when subjected to external relieving forces, for example the wind.

In the case of the structure shown above perhaps the best way to understand it is to begin with the cantilever arm of the lower structure. A tension hanger suspended from the cantilever carries a second cantilever at the base of the upper structure. At this point the upper structure is unstable it wants to topple to the right by pivoting about the hanger connection.

The tendency to topple is counteracted by two tension members connected from the top of the upper section back to the base of the lower one. Thus equilibrium is preserved.

Perhaps the most famous tensegrity structure is the skylon, which was built in 1951 for the festival of Britain. The base of the cigar shaped column was approximately 15 m above ground level and its tip was almost 90m high.

Some say the skylon mirrored the post war British economy, because it had no obvious means of support[1]. Though this was of course an illusion.... at least in the case of Skylon.

Sadly Sklyon was scrapped in 1952 on the instruction of Winston Churchill, who thought it a symbol of the prior labour government. Not Churchill’s finest moment and a sad end for an inspired structure. 

[1] Not my gag; wish I could remember where I heard it.

On Camping

Some observations about tents

A recent camping trip got me thinking about how tents work; specifically my own. I think it seems obvious to most casual observers that tents are tension structures, but perhaps there is also more to it than that.

I like camping, but I am not obsessive about it. I am therefore not sure if there is a specific name for the type of tent that I own. I shall simply be referring to it as a horseshoe tent, because its cross-section is roughly that shape.

The horseshoe shape is created by an exoskeleton consisting of three arches, two larger ones at the front end and a slightly smaller one at the rear. The smaller one is inclined a little towards the rear of the tent. The rear of the tent is also the location of the sleeping compartment, which is hung between the two arches closest to the back.

The arches themselves are formed of thin plastic tubes, which slot together to form long flexible rods. These are held together by an elastic chord which passes through their center and allows them to be folded away without coming apart. Each rod is inserted into a long pocket stitched to the tent’s waterproof flysheet. Each end of the rod is then inserted over a brass pin attached to the base of the flysheet. Each pin is connected to its neighbour via a nylon strap, which sits beneath the tent’s ground sheet. In the photo below you can see them on the grass before the ground sheet has been laid. 

This is the first structural feature of the tent. The flexible arches have a natural tendency to spring apart, but the tension strap prevents them from doing so. It locks the springiness of the tent rods into place and keeps the rather thin structure rigid.

The next structural feature of the tent is its guylines, which we shall divide into two. The transverse guys i.e. those in the same plane as the arches have only one role, at least so far as I can tell. They anchor the tent to the ground, via the arches, and prevent uplift in stormy weather. I believe this to be the case, because the tent will stand happily without them in calm weather. 

The second set of guylines we shall call longitudinal guys. They are located to the front and rear of the tent. I am sure that they help anchor the tent in stormy weather too, but they also have another, perhaps more important role, as I suspect the transverse guys could do most of the wind resisting work themselves.

It seems to me that the primary role of the longitudinal guys is to stretch out the shape of the tent and to provide it with longitudinal stiffness. The more taught they are made, by adjusting the tensioners, the more rigid the tent becomes. 

It is self evident that to ensure equilibrium i.e. to stop the tent being pulled either forward or back the front and rear guylines must balance each other. What is perhaps less obvious, and is therefore more interesting, is what happens to the tension force after it leaves the guylines. Put another way, what happens between the front and rear guylines to ensure equilibrium. This is what caught my eye and is the underlying reason for this post.

While erecting my tent I had become a little frustrated that the flysheet appeared to be wrinkled and was not sitting flat and smooth as I thought that it should. Then I noticed that the wrinkles had a pattern and that pattern was structurally significant. 

I realised that in any other context an engineer would describe a structure like a tent’s flysheet as a stressed skin. Stressed skin structures resist out of plane loads, for example the wind, by being stretched tight. 

Normally a stressed skin will be fixed along the edges either with a continuous seam or with fixings at close centres. This is because you want the load to be imparted into the thin stressed skin in an even manner. This is not, however, the case with tents.

The tensile loads, which convert the flexible flysheet into a taught stressed skin structure, are imparted at discreet points by the guylines. In the case of my tent via the thin rods that form the horsehoe arches.

The slender rods have little stiffness perpendicular to the arches they form and are of little assistance in distributing the tensile load from the guylines. It is therefore no coincidence that the observed creases extend diagonally from the guyline connections on one arch to the base of the adjacent arch, where it is pegged to the ground.

On closer inspection there is a second set of creases, which start midway between the guyline connection and ground level. This happens to be the point where the rods are connected to the flysheet with plastic clips. 

The question arises, why does the fabric crease and what does it indicate? 

As the flysheet has little thickness it is not good a distributing concentrated load across its own surface. For this reason load applied at discreet points by the guylines causes localised stress in the fabric between points of restraint. Since these parts of the fabric are subject to more stress they stretch more than neighbouring fabric causing the observed creases to appear.

What this phenomena indicates is none-other than the arrangement of internal forces, one might say the load path, in the flysheet. We can visibly see that it has taken up the form of a truss with node points at the parts of the tent that are held stiff. Structures do not often reveal their load path in this way, which makes it all the more interesting.

It is also interesting to note that there are diagonal creases near the top of the tent too. These appear to be the result of the additional section of flysheet that helps ventilates the roof and provides additional stiffness.

One can also detect some creases in a rectangular section of the flysheet at mid height of the first bay. It is difficult to see in the photo, but at this location there is a clear plastic window, covered on the inside by a canvas flap that is used to blank the window for privacy. The clear plastic is a stiffer material than the flysheet around it.

Something else that interested me was why the direction of the creases was in one direction rather than the other. The answer I believe lies in the different geometries, which exist at the front and rear of the tent, and thus vary the angle at which the guylines apply load to the structure. That said, I am also curious to know whether the order in which the guylines were tightened also plays a role. Next time I pitch the tent I shall reverse the sequence and see what happens.

The final observation that ought to be made about my tent, or any tent for that matter concerns the effectiveness of tent pegs. These are short lengths of wire, which are pushed into the ground in order to provide resistance to the the tensile loads in the guylines, including those generated by the full force of the weather. This seems remarkable given their small stature. 

While the angle at which the pegs are pushed into the soil is surely important, friction between the soil and the circumference of the pegs is the primary guard against the pegs being pulled free of the ground. Thus, we can see the ability of friction to resist load is not to be underestimated. It is this same force by which many buildings are supported in soft ground on concrete piles, though in this case the piles are in compression rather than tension like tent pegs.

So it turns out that I needn't have been concerned about the creases in my tent; there doesn’t seem to be anything I could have done about them. This of course wasn’t the main reason I enjoyed my camping trip. Good humour and good company had something to do with that too, however it was quite interesting.