On Breaking Rules

Why codes and standards are not always right

In my page entitled ‘what is structure?’ I began with the following quote attributed to Picasso. 

“Learn the rules like a pro so you can break them like an artist”

I inferred from this that structure does not limit creativity, and went on to argue that structure provides a framework with which to create. From this I deduced that without structure nothing we might seek to create makes sense. In retrospect I realise that I didn’t expand on why engineers, like Picasso, can benefit from breaking the rules that govern structure. I shall try to do that in this post.

This might seem at first to be a tall order, because you might suppose that the rules of engineering are fairly arbitrary and to break them would have unwelcome consequences. To make my case I intend to make a diversion into the subject of racket sports, which I rather enjoy.

After mastering the basic strokes of any racket sport it will soon become clear that there are three possible ways to score points. The first is to hit a shot that your opponent is unable to touch; the clean winner. The second is to hit a shot that stresses their technique and causes them to miss; the forced error. This is normally achieved by making your opponent play his or her shot from an awkward position; perhaps on the run or while stretching. The third way is to hope that your opponent simply makes an unexpected mistake; the unforced error.

While the third case is random, the first two can be induced by clever tactics. Perhaps the simplest, and ultimately most successful, tactic is to maximise the distance your opponent must travel between shots. This will necessitate playing on the run, potentially hitting while stretched and eventually fatigue. 

It follows that if you receive a ball from cross court the rule is to strike back down the line, because your opponent must run the width of the court to play a return shot. Conversely, if you receive a shot from down the line the rule would be to return cross court. Again, your opponent must run the width of the court.

This tactic works really well on a novice player, however it starts to unravel when you find yourself playing another player who knows the same tactical rules that you do. He or she knows that you are going to return cross court from down the line. It follows that as soon as they have hit down the line they will start running to receive your cross court shot. Arriving early on the far side of the court they will quickly turn the tables, by making you run down the other line.

To outmanoeuvre your opponent, and thereby avoid the tables being turned, you must break the rules and hit back down the line from which you received the ball. Your opponent, having set off in the other direction, must turn and run back in the direction from which they came. He or she now finds their technique being stressed again.

Now the rules have changed and you are doing exactly what you learned not to do. This, however, does not negate the rule. If you continue to return in this fashion your opponent will ruthlessly exploit your apparent naivety, as if you did not know the tactical rules to begin with.

The trick is therefore to apply the rules most of the time, but break them just often enough that your opponent cannot take for granted what you will do next and thereby set off early to meet your next shot. 

I accept that this is a rather limited tactical explanation, but it serves as a useful illustration of the cat and mouse game that opposing players must engage in. It also illustrates Picasso’s point that to become an artist you need to know the rules so that you understand how and when to break them.

That is all very well, but how does this principle translate into structural engineering? The structural engineering rule book is provided by the building regulations and by codes of practice. Once a structural arrangement has been selected, a creative process in and of itself, codes and regulations generally provide a fixed methodology for justifying its design, however for several reasons this is not always helpful. You have not mastered structural engineering until you know when and how to depart from their strictures.

In a prior post about pile cap design I demonstrated that a foundation supported by just two piles can be designed in multiple, equally valid, ways. This, however, is not the only reason to think twice about the rule book.

Many current standards have been in use for 20 years or more. It is inconceivable that nothing new has been learned in that time, which could be captured in future standards. It takes time for standards to be revised, however until they are there is no reason why an experienced practitioner cannot take advantage of newer information.

Another reason would be that codes are necessarily general documents intended to cover a broad set of circumstances, however they have evolved to their present form based on what already exists and is common. Consequently, an engineer must know the limits of application for codes of practise and must, when necessary, look to other approaches when something is uncommon.

I think most engineers, though not all, would accept that a design code may not, on some occasions, produce the most efficient design possible, but perhaps fewer would recognise that from time to time codes are habitually applied incorrectly because they are badly written or because they are old and their original meaning has been forgotten. 

Fewer still would recognise that codes can sometimes be plain wrong. While there are some well known examples, identified through catastrophic failure, there are others that are harder to spot, because the circumstances in which they are wrong is rare.

We have learned in this post that a novice tennis player who returns a shot received from down the line back up the same line is not the same as the master who returns up the line to exploit his opponent’s premature movement across the court. 

Similarly, the novice engineer who ignores the requirements of the relevant code or standard through ignorance is not the same as the experienced engineer who sets aside their provisions with good reason.

It is, as Picasso says, necessary to learn the rules so that you can break them.

Postscript

Some may question whether it is legal to ignore codes and standards. It is therefore worth noting what the Building Regulations have to say: 

Approved document A, applicable in England & Wales, says:

‘There is no obligation to adopt any particular solution contained in an approved document if you prefer to meet the relevant requirement some other way’

The technical Handbook, applicable in Scotland, echos similar sentiments when it says:

‘The regulations are mandatory, but……it is quite acceptable to use alternative methods of compliance provided they fully satisfy the regulations’

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 San Petronio

Gravitational equilibrium & the square cube law

‘Gulliver’s Travels’ is a classic of English Literature written by Jonathan Swift in 1726. It is intended to be a satire of human nature and ‘travellers’ tales’. In the book its protagonist visits the fictional countries of Lilliput and Brobdingnag. The citizens of the former are 12 times smaller than Gulliver and in the latter they are 12 times bigger.

Of course every reader of the book knows that Lilliput and Bribdingnag are fictional, but perhaps fewer might realise that they are necessarily fiction in any possible world that follows the same physical laws as our own. The reason for this is described by the square cube law, which was first attributed to Galileo.

According to this law the size of things cannot be indefinitely scaled up, because the physical properties of objects change as they increase in size. Consider a cube with sides one unit long. If we were to double the length of each side then the surface area of each face will increase from 1 to 4 units. The volume of the cube, and by extension the quantity of stuff from which it is made, increases from 1 to 8 units i.e. doubling the linear dimensions causes the surface area to be squared and the volume of stuff to be cubed.

In other words the rate at which the volume and weight of an object increase with size is greater than the rate at which its linear dimensions and surface area increase.

Conversely, the strength of things, normally expressed as a limiting stress, is independent of size [1]. It follows that as things become larger, while retaining their original proportions, they will eventually reach a point where they can no longer support their own weight. This places an upper limit on how big things, including people, can get.

This is a vexing problem for modern day architectural students, who are surprised to learn that the model they have spent hours building does not prove that the structural gymnastics their design requires are viable in the real world.

There is of course an exception to the square cube law, though not a true exception. The square cube law does not cease to work, rather it is not discernible within the normal range of scaling for certain objects.

An example of such an object from the natural world would be a mountain. An equivalent structure form the man-made world would be a pyramid. Both structures come from a class of things that share three key ingredients. Firstly, they are both made of stone, which is a natural material with a very high compressive strength and low tensile strength. Secondly, they are both compression structures that assiduously avoid tension. Thirdly, they are stocky and solid structures. Not solid in the sense that they are strong, though that is indeed true, but solid in the sense that they are not hollow. The implication of being stocky and solid is that they are not prone to buckle, as a slender or thin walled structure is. A second implication of stockiness is a large cross-section, which implies low stress.

These then are the ingredients for subverting Galileo’s square cube law and within the class of things which have these ingredients there is a group of structures that does so with a style and panache that is difficult to surpass. They laugh in the face of the square cube law.

I am of course talking about gothic structures; those great stone cathedrals of the late medieval period with their quadripartite vaults and flying buttresses. I am often asked, mainly by my dad, how it was that medieval masons created such structures in the absence of modern structural theory. The stock answer is that they used rules of thumb, but for me there has to be more to it than that.

How on earth did they manage to design structures, using rules of thumb, that modern analysis shows us to have near perfect proportions. Rules of thumb are intended to apply generally, but must necessarily be derived from the particular. The further a design departs from the particular the less useful a rule of thumb is. 

Gothic structures do have similarities, but there is also great variety in their design, which ought to make rules of thumb less helpful.

Perhaps the answer to this dilemma is to be found in a process of trial and error. While there was undoubtedly a role for trial and error I am not convinced that it played a central role, at least not in the commonly understood sense. I hold this view for several reasons:

Firstly, most cathedrals took hundreds of years to build and though master masons may have worked on several, they would not, in their own lifespan, have time to learn all the necessary forms by trial and error. This brings us back to rules of thumb. Secondly, while there is evidence of design evolution over time there is relatively little evidence of major failures, which is odd given the innovative, and often spectacular, designs adopted. Furthermore, when known failures occurred they were often, though not always, associated with abnormal events like earthquakes or phenomena external to the structure like differential settlement.

We therefore have much evidence of trying daring new things, but scant recorded evidence of failure [2]. This is not entirely a surprise, because cathedrals are expensive and their proprietors were not stupid. Master masons would not have been in charge for long if their structures kept collapsing.

To find a satisfactory explanation I think we need to return to the square cube law. If a structure could be designed to subvert the square cube law then a successful pattern would be successful at any scale. It follows that if you could demonstrate a particular form of structure would stand using a small model made of wood then it would also stand if it was scaled up to full size. 

I do not know whether masons understood that they were subverting the square cube law. I suspect that they didn’t, but I do think that they understood perfectly well the load-paths and principles that were necessary to keep a stone structure in equilibrium. I think they fully understood that tension was the enemy and that gravity must be harnessed to maintain compression in all parts of the structure. 

They were specifically designing structures to achieve gravitational equilibrium and they were doing it by experimentation with scale models. They then used rules of thumb, derived from these models, to scale up their findings to full size structures.

 

Happily for the masons this methodology was just perfect for avoiding the square cube law, whether they knew it or not, and in this way spectacular and innovative designs could be realised without needing to know anything about materials science, stresses or strains.

While this theory involves a heavy dose of speculation it is not without evidential support. For example, we know that Antonio Vicenzo the designer of San Petronio church in Bologna commissioned a model of brick and plaster at circa one eighth scale. It was around 19m long and 6m high. I expect that it was used to convey the design to its proprietors, but I don’t think it is too great a leap to posit that it might also have played a role in the church’s structural design.

[1] I accept that all bets are off at the atomic scale, but we don’t normally consider atomic forces when designing building structures, bridges and the like.

[2] I know that absence of evidence is not evidence of absence, nevertheless evidence is sometimes notable by its absence, particularly when there might be a reasonable expectation to find some.

On Breaking Trains

Or why systems need to be robust

On 22 October 1895 a steam locomotive approached its Paris terminus slightly faster than normal hoping to make up lost time. Except that rather than stopping at Gare Montparnasse, as planned, it crashed through the end of the platform, over the concourse, through the station facade and down onto Place de Renne a full storey below. Apparently, the only casualty was a woman who had the misfortune to be standing in the street and was struck by falling masonry.

 

The question arises, why did the train fail to stop? 

Following the subsequent accident inquiry the hapless locomotive driver is reported to have been fined 50 francs and sentenced to two months in gaol, because he approached the station too fast. One of the guards was fined 25 francs, because he was apparently too pre-occupied with paperwork to apply the hand brake.

One might assume that this was all there was to it, however as it turns out the driver and the guard were not solely responsible. 

It is also believed that the train’s Westinghouse air brakes had rather tragically failed, which seems to me a rather more significant event, but not for the reason that you might think.

Trains were of course a wonderful invention, which had transformed the world by making mass transit possible over long distances. The trouble with steam locomotives, at least in their infancy, was that nobody was quite sure how to stop them.

They travelled faster than anyone had travelled before, but were also big and heavy. The locomotive had a hard enough time stopping itself let alone the passenger cars and goods wagons that followed behind. It was not unusual for the following carriages to catch up with the locomotive when the brakes were applied causing them to collide, first with each other, and then with the back of the locomotive.

In order to make the train stop within a reasonable distance it was realised that brakes had to be added to the carriages too. The obvious difficulty was how to apply the brakes on the locomotive, and all the carriages, at the same time.

Initial solutions were somewhat rudimentary. In the United States a brake man sat on top of the first carriage. When the driver blew the train’s whistle he was responsible for applying the brake on the first carriage. He was then required to run down the roof before leaping onto the next carriage whereupon he applied its brake. This process was repeated until he reached the back of the train. This was, as one could imagine, a rather precarious job and not surprisingly there were many casualties.

The American entrepreneur and engineer George Westinghouse, like everyone else, saw the problem. Unlike everyone else, Westinghouse came up with a solution. He joined the carriages together with airtight hoses and used compressed air to apply the carriage brakes almost simultaneously. The system worked brilliantly, bringing trains to a halt with great effect. For many people the idea of stopping a large heavy object travelling at high speed with nothing more than air had initially seemed a little crazy. When it worked Westinghouse was rightly seen as a genius.

Except that there was a problem that no one at the time had foreseen. If there was a loss of air pressure, due to leak in the system, the breaks wouldn’t work. It is believed that this is exactly what happened at Gare Montparnasse. Understandably, fail safe systems where added to subsequent designs.

Knowing this story I was rather intrigued by the heritage steam train that I happened across while on a recent camping trip in Cumbria. In the images below you can see a red  pipe on the back of the locomotive, which passes between all the carriages and can also be seen at the tail of the last carriage. There is also a small pressure vessel beneath one of the seats in each carriage, but you can’t see that in these pictures.

   

In case you haven’t guessed I rather suspect that what we have here is a rather old fashioned air-break system not unlike those used on early locomotives. I didn’t get chance to investigate further, but I am going to assume its the mark two version.

The next question is what this has to do with a structural engineering blog? The reason I decided to write, other than the fact that I found it interesting, is the principle of robustness. An otherwise brilliant idea, which made a big difference to the safety of trains, was, in its earliest conception, flawed. It wasn’t flawed because it didn’t work. It was flawed because it was vulnerable to miss-use or accidental damage. In short it was not a robust system.

This ought to be a concept familiar to all structural engineers. The archetypal accident, at least in the UK, was the partial collapse of a 22 storey tower block in 1968. The tower stood quite happily until a gas explosion blew out one of its walls, causing the walls and floors above to collapse like a pack of cards. Unfortunately the component parts were not adequately tied together and were therefore unable to bridge over the damaged section of the structure. Four people died and 17 were injured.

The concept of robustness is not necessarily aimed at particular events or circumstances, rather it is intended to provide a degree of resilience against the unforeseen and the unknown. It now seems obvious that structures should not fail the moment the design load case has been exceeded, but it was not always so. 

Of course a supplementary question one might ask is how robust does a structure need to be? How robust is enough? That’s a difficult question to answer, but an ingenuous formulation has been devised, which has come to be known as the principal of ‘disproportionate collapse’. Put simply this means that any damage suffered by a building should not be disproportionate to the event that caused it.

So what is considered proportionate? That’s a rather big question, which perhaps needs its own post at some future point. 

On Carbuncles

Why its worth preserving ugly structures? 

One of the questions I am frequently asked is why buildings and structures that seem to have no aesthetic merit have been Listed for preservation by the conservation authorities. 

I confess that, despite being an enthusiastic exponent of conservation engineering, I too struggle with the requirement to preserve some structures. 

For example, I am quite sure that I share the majority view that brutalist architecture is ugly and the genre has not delivered the utopia that was promised. In saying this I recognise that I am wholly out of step with many, possibly the majority, of architects.

Conversely, I have found that when reading Le Corbusier’s philosophy of brutalist design I am wholly enthused and compelled by his logic. It jars that there is a complete disconnect between the eloquence of his written intent and how it has transferred into the real world. Sadly, it has always been this way with utopian ideas.

So while the public declares that ‘the emperor has no clothes’ the architectural profession continues to be enthralled by Le Corbusier’s philosophy and principles, seemly blind to the simple fact that brutalism has created a legacy of truly miserable buildings that do not work in practise. Lest my architectural friends chide me for suggesting brutalist buildings do not work let me clarify what I mean. 

Whatever their perceived architectural merits, direct experience has taught me that their fabric has not stood the test of time. In many cases the distress and deterioration are intrinsic to their design and detailing. 

Another interesting case would be the preservation of industrial buildings. In this instance I am possibly further away from the majority public opinion, though I don’t think there is an equivalence with brutalist architecture. Redundant industrial architecture generally served a useful purpose in its day and often had a cleverness about its design. For example, the structural efficiency of some cooling towers and gas holders is remarkable.

I would also adopt the view that some industrial design does actually have an aesthetic quality, though perhaps, as an engineer, that is my blind spot. I rather suspect that at some subliminal level understanding why something works converts into an enhanced aesthetic appreciation. 

I suppose if this hunch is true, and I am to apply it consistently, then I fear I must grant my architectural friends some latitude too.

All that being said, while I cannot bring myself to appreciate some Listing decisions, I think that I can shed some light on why the system is so.

The first step is to understand that the point of the Listing system is not to preserve aesthetically beautiful buildings, although many Listed buildings do fulfil that criteria. Nor does it mean that the decision to preserve a particular architect or engineer’s work is because their work is beautiful.

In such cases the important question is why the work of said designer is considered important not whether their work is beautiful. More often than not it is because they changed the way something was done and caused us to think differently about design.

As I have previously noted I can accept that there is an elegance to the writings of Le Corbusier; though I would argue that the theory he expounded has been proven hollow. I would also accept that his designs definitely represent a change in how things were done, though I would argue not necessarily for the better. I imagine that contention will not meet with universal approval and is an argument that is unlikely to be resolved any time soon, but clearly that is not the point.

So what is the point?

In a prior post ‘On Conservation Principles’ I noted that buildings reflect changes in the way we live and work, and also the cultural values that were prevalent at the time. An industrial chimney may be worth preserving, because in its day it was a community’s raison d’etre. The community exists because the factory exists. Preserving the factory preserves evidence of a way of life and a way of working.

This is the point. Some structures are preserved not because of what they look like, but rather because of what they represent. This is the reason I don’t mind working on projects where I don’t necessarily like the aesthetics. I can nevertheless appreciate the history and culture that is involved. If I get really stuck I can still fall back on finding enjoyment in whatever puzzles the project throws up; there are always engineering puzzles to solve[1].

In this sense a nation’s infrastructure and building stock is much like the rest of its history. There are parts to be proud of and there are parts you rather wish hadn’t happened. Unfortunately only the future is still to be written. For better or worse we own our past both good and bad. We should try to understand our Carbuncles**.

[1] that’s not the only reason. I am also not sure that many people would like to live in a world where I got to decide what qualifies as being aesthetic and only what pleased me could be built!

[2] for those too young to remember, in 1984 Prince Charles described a proposed extension to the National Gallery in the following way. “What is proposed seems to me a monstrous carbuncle on the face of a much-loved and elegant friend”. His view got him into bother with Architects at the time, but I just think its a funny phrase.

On Conservation Principles

 

In the past homes were modest, places of work were agricultural and our grandest buildings were temples, cathedrals and palaces. During the industrial age our cathedrals became places of work; great factories and chimneys filled the skyline. Today residential towers exceed in height the tallest spires and chimneys, while in the suburbs two floors are normal. Work is now knowledge based, requiring data centres instead of machine halls and factories, and cathedrals are home to sport.

It follows that, while aesthetic taste changes and is subjective, there is also a class of building that contains in its fabric a record of human activity; our culture and our endeavours. It is self-evident that both types of building should be preserved.

That said, people do not want to live and work in museums and therefore buildings must, as they always have, adapt to change. This requires those of us who work with such buildings to see ourselves as custodians. What we receive from the past we must make fit for the future, so that there remains a living record of that which has passed from memory.

Although we must make every effort to honour evidence of the past and to preserve the character and history of a building, we need not be afraid to repurpose it or to upgrade its fabric and systems.

If we have worked hard to understand what the original designer had in mind, and any subsequent alterations, we will appreciate what is special and individual about a building’s character and personality. What must be preserved and what may be changed. Of course, it is not only important that we preserve the significant parts, how we do it is also important. 

Our starting point should be to do as little ‘as possible, but as much as necessary’. If the structure remains serviceable and observed distress is not progressing ‘do nothing and monitor’ may be the answer.

If intervention is necessary we must remember our role as custodians. Future research may lead to better methods of conservation, therefore what is done today should, where possible, avoid limiting future opportunities. Similarly, some interventions have, by nature, limited life spans, for example, building services. This means that proposed enhancements and repairs ought to be reversible without leaving behind marks.

It is self-evident that materials and methods, which are not compatible with those used originally will be detrimental to a building’s fabric. That said, interventions should have an honesty about their conception. They should be discernible to future engineers and should therefore avoid the temptation to replicate. 

Buildings are not immutable. They were conceived with a purpose, but have been changed by their environment and by their custodians. Conservation means continuing to adapt for the future while sensitively preserving that which is important from the past. This should be done on the tripartite basis of minimal intervention, reversibility and honesty. Projects that follow these principles are normally received favourably by the public and contribute to a better society.

On Hambly's Paradox

Some thoughts about the complexity of design

Hambly’s Paradox is an example which illustrates the difficulty of assessing so called hyperstatic structures i.e. those with redundant members. It was first posited by the eminent structural engineer Edmund Hambly, whose name it bears. 

A milkmaid weighing 600 N sits on a three-legged stool. For what basic force should each leg of the stool be designed?

The answer to the question is of course 200 N. We are, of course, assuming the stool is symmetrical and that the milkmaid is sitting in the centre of the stool.

The milkmaid now sits on a square stool with four legs, one at each corner, and again the stool and the loading are symmetrical. For what basic force should each leg of the stool now be designed?

The obvious answer would be 150 N, however as Hambly points out that would not necessarily be the right answer.

If we assume that the milking stool is stiff and so is the floor on which it sits then inevitably the stool will rock and only three of the legs will be in contact with the floor. Even if raised by only a fraction of a millimetre the load in the fourth leg is unquestionably zero. 

Since, the stool rocks there must be a point where both the fourth leg and the one diagonally opposite are both free of the ground. In such circumstances both legs carry zero load and the remaining two legs must therefore carry 300 N each.

If the stool is instead placed on rough ground the we have no way of knowing which of the legs will or will not be in contact with the ground and therefore every leg must be designed for 300 N.

This is, of course, the paradox. By increasing the number of legs supporting the stool the design load for each has effectively doubled.

The conclusion that we have reached is based on static analysis i.e. our only concern has been to ensure that the stool remains in equilibrium. Such analysis contains a prior assumption the consequences of which have gone unnoticed until now. That is the assumption that we are dealing with rigid bodies. 

This is not how the real world works. All materials deform when subjected to load. The amount of deformation depends on their stiffness. We could consider the stiffness of the milking stool seat and its legs in our assessment, but it is probably sufficient, and somewhat simpler, to consider only the legs.

When the legs are loaded they will shorten a little. The amount they will shorten is proportional to the stiffness of the material they are made of. If the gap between the so called fourth leg and the ground is small it may, as a result of shortening, become in contact with the ground causing the weight of the milkmaid to be redistributed according to the stiffness of each leg. Therefore, depending on the size of the gap the fourth leg may experience a load anywhere between 0 and 300 N.

It follows that thus far geometric imperfections make it almost impossible to predict the actual load in a 4-legged milking stool, even after the elastic properties of each leg has been taken into account.

There is of course one further step we can take, which will restore common sense to milking stool design, but first we must make a further assumption. If we make the milking stool legs relatively stocky then they can reach a state of plasticity [1] without their legs buckling.

In this scenario let us suppose that each leg of the milking stool has been designed to yield at a load P. Let us then suppose that the weight of our milkmaid is 4P. At the outset of our problem the stool is potentially supported on only two legs this means that those two legs are momentarily exposed to a load of 2P each and 4P in total. Each leg shortens elastically until it reaches its yield point whereupon it continues to squash until load is shed into the two adjacent legs. Since the yield point is P load will continue to shed until it is shared equally between all 4 legs. Thus, each leg of the milking stool may be designed for 150 N. 

And just like that our paradox vanishes!

[1] plasticity is a state that exists in a material beyond the point at which it yields. In this state the material will continue to deform without being exposed to any additional load. I may write more about this in another post

[2] My thinking for this post borrows from Jacque Heyman

On Snow & Ice

Engineers are supposed to be numbers people who thrive on logic, objectivity and data. Engineers are not supposed to appreciate subjectivity; and we’re definitely not supposed to like art. At least that’s the theory. The truth is that art isn’t always as subjective as you might think and engineers can and do like art.

Fillippo Brunelleschi is most famous for designing the dome of Florence Cathedral. It is a spectacular structure designed and built using an exceedingly novel method of construction. Both architects and engineers claim Brunelleschi as one of their own, yet his apprenticeship was served in the Arte Delle Seta, where he became a master goldsmith and sculptor. That is how it was in the Renaissance, master builders and designers learned about material and form in the artist’s studio.

One of my favourite modern artists is Andy Goldsworthy. I wouldn’t remotely consider myself an art critic nor would I claim to know what Mr Goldsworthy was thinking when he conceived a particular piece, but I am going to speculate that he has developed a keen sense of material and form through hours of trial and error in the artist’s studio.

I have made this speculation, because he succeeds in combining natural materials with shapes and forms that make complete sense from a structural perspective. He appears to understand exactly what he is doing.

Perhaps my favourite examples of Goldsworthy’s work are those which he creates from snow and ice. I like them for several reasons. The first is because snow and ice illustrate particularly well that material properties can and do vary. For example ice remains solid when cold, but melts when warm.

Just as important, but perhaps more subtle, snow can be squashed and moulded into different shapes while ice is hard and brittle. It would rather fracture than bend.

Both materials have a dislike for tension; though they express their dislike in different ways. Snow will disintegrate and crumble, while ice will crack and fracture. Conversely both snow and ice will quite happily resist compression without difficulty.

It turns out that materials, like people, have temperaments that must be understood to get the most out of them. This Goldsworthy achieves exceedingly well.

If we consider, for example, the ice sculpture shown below. It consists of eight storeys each resembling the columns and entablature of a greek temple or if you prefer the sarsens at stone henge.

 

Just like the designers of those ancient structures, Goldsworthy has realised that tension is the enemy he must subdue. By placing the ice columns close together he prevents the lintels from developing excess tension on their soffits. For a similar reason the columns have been carefully aligned so that load can travel from top to bottom in direct bearing.

Further examples of matching form to material are shown in the sculptures below. One shows an arch constructed from thin wedges of ice and the other from stone and snow. Both resemble the classical form of a traditional masonry arch. 

It is of course well known that arches are compression structures and are therefore inherently suited to materials that dislike tension. With an ample supply of stone, and a primitive form of concrete, it is unsurprising that Roman architecture features arches so prominently.

That said, it is Goldsworthy’s decision to construct his arches in the traditional way using wedges that is interesting, particularly the one made of ice. This choice allows us to get a deeper sense of how arches work.

After finding ourselves unintentionally seated on the ground, everyone has undoubtably discovered that ice is slippery. Knowing this to be true why don’t the pictured ice wedges at the crown of the arch simply slip past each other, under the action of their own self-weight, thus causing the arch to collapse? This is not a trivial question.

In 1695 the Frenchman Philippe de la Hire was the first to compose a theory of masonry arches using mathematics. He began by assuming that the wedge shaped stones (voussoirs) from which arches were formed have infinitely slippery surfaces i.e. the joints between them are frictionless. He then set about tackling the question, how heavy [and by inference how thick] should the voussoirs be to keep an arch stable?

In this most slippery of scenarios it is, by definition, impossible for forces to develop parallel to the joints between voussoirs. The weight of the arch must therefore thrust exactly perpendicular to the joints.

It can be seen from the photos above that the wedges of ice [and thus the joints between them] are vertically aligned at the crown of the arch and therefore at this point the weight of the arch must act horizontally i.e. perpendicular to the joints.

Moving away from the centre of the arch the inclination of the ice becomes steadily flatter. Since, the weight of the arch must still act perpendicular to the joints it is bent around the curve of the arch. 

This is where the problem starts to get interesting. If the arch is built on a flat base, as shown in the image above, La Hire discovered that the weight acting at its base must be infinite or the arch will be unstable, which is obviously wrong.

La Hire rightly concluded that friction must therefore be present between the voussoirs [even if they are made of ice] though it was left for others to account for it in subsequent theories. It is this frictional force that stops the wedges of ice slipping from the arch’s crown.

In some ways it would be satisfactory to end here, but we are not quite ready to finish. There is something else that turns out to be important, which we have not yet discussed. Thus far we have been taking about wedges or voussoirs and the analogy holds reasonably well in the instance of the Goldsworthy’s snow arch.

In the case of his ice arch the analogy is a little imperfect, because the shards of ice are in fact flat and not really wedge shaped al all. We would normally think of a wedge as having a fat and a thin end.

This doesn’t at all undermine what we have said thus far; all of that still holds. What is interesting is that without a fat and thin end the shards of ice are in contact on the inside of the arch, but gaps necessarily open up at the outside edge. The thicker the arch the more pronounced would be the gaps.

The significance of this is the contact area between the shards of ice is only a fraction of their surface areas. Since the ice does not fracture we may infer that the stress in the arch must be quite low and would certainly be in no danger of crushing its component parts. 

This principle was demonstrated in 1846 by Barlow at the Institution of Civil Engineers in London. He built a model arch with six voussoirs using slender prices of wood en lieu of mortar. In progressively withdrew the slips of wood in three locations to show the stability of arch would be maintained.

Taken together the thoughts we have outlined illustrate the key principles of masonry arch design. Namely, friction must be present between the stones; the strength of the stone is of little importance; and finally the stability of an arch relies entirely on its geometry and weight. Since weight is a function of geometry and friction is a function of weight we might just as easily say the stability of an arch is a function of its geometry.

I have no idea whether or not Andy Goldsworthy’s thinking has extended this far, nevertheless the question was worth addressing, because the answer surely enhances our appreciation of his art.

Now I realise in reaching this point that some may be thinking that I have, in discussing geometry and forces, undermined the original premise of this post. You might say that I have turned art into science.

I beg to differ. 

Isn’t the point of modern art it’s subjectivity? Isn’t it supposed to make us think individually about what it represents and then decide how that makes each of us feel? Well, in my subjective view this is what I think it represents. It satisfies my curiosity and that makes me feel happy.