Have you ever wondered why the Eurocodes are so damn annoying to use? I know I have. On my litany of things I hate about the Eurocodes are the way it always feels like you need to get 25 documents together before you can even begin to design anything. Finally, when bored on the train, I decided to see just how valid my complaints were, and how bad the problem is.

Let me present to you an interactive (click on the preview to browse) network graph mapping the references between the Eurocodes:

About the Data

For this map a ‘reference’ is an explicit mention of the code number (e.g. EN 1994-1-2). To avoid picking up the introduction that lists all the Eurocodes, I have excluded any references before the “1 General” header. To make the map clearer I have also ignored general ‘family’ references (e.g. mentions of the EN 1994 suite, rather than a specific part). I have also excluded NA references, etc. as it’s complicated enough without adding the non-EN documents you require.

Believe it or not, I didn’t painstakingly comb through every page of the Eurocodes to collect this data. I made a bot to do it. If you want to know how I made this map, you can check out the source code for the data extractor and plot data file builder here: on my GitHub. Unfortunately this means that the four Eurocodes PDFs with, inexplicably, encoded text have been omitted from this map:

• EN 1995-1-1
• EN 1993-6
• EN 1993-1-10
• EN 1991-1-4

But I never liked them anyway!

So next time you set sail on a voyage through the Eurocodes; don’t forget the map (or set it as your wallpaper!).

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I doubt it’ll come as a surprise to anyone (what with the title of the post an’ all), but I’m a fairly massive Terry Pratchett fan- in fact, for those of you who have been paying attention these last few years, there’s at least three Pratchett quotes littered through Being Brunel. So as the author of the books I have read more times (by a significant factor) than any other, I was sorry to hear that he had passed away last Thursday.

While those of you who are of a more technical persuasion might note that Being Brunel is one of the many sites keeping his name alive in the overhead; I thought a more obvious tribute would be in order. I’ll make the confession now; I had initially aimed to come up with my top ten Pratchett quotes who’s sentiment should be all too familiar to practising engineers- but despite a good few hours of whittling, I’ve only managed to get it down to 21.

Pratchett Quotes for Engineers

Getting an education was a bit like a communicable sexual disease. It made you unsuitable for a lot of jobs and then you had the urge to pass it on. (Hogfather)

Although his body had been around quite a lot, his mind had never gone further than the inside of his own head. (Equal Rites)

“We’ve got a lot of experience of not having any experience” “But the point is… the point is… the point is we’ve not been experienced for a lot longer than you.” (Witches Abroad)

Around the Godde there forms a Shelle of prayers and Ceremonies and Buildings and Priestes and Authority, until at Laste the Godde Dies. Ande this maye notte be noticed. (Small Gods)

His progress through life was hampered by his tremendous sense of his own ignorance, a disability which affects all too few people. (Maskerade)

Anything anyone is still trying to explain to you after two minutes is probably important and anything they give up after a mere minute or so is almost certainly something they shouldn’t have been bothering you with in the first place. (Reaper Man)

Of course, Ankh-Morpork’s citizens had always claimed that the river water was incredibly pure in any case. Any water that had passed through so many kidneys, they reasoned, had to be very pure indeed. (Sourcery)

‘No one knows how to do officering, Fred. That’s why they’re officers. If they’d knew anything, they’d be sergeants.’ (Guards! Guards!)

“As simple as that? You didn’t use magic?” “Only common sense. It’s a lot more reliable in the long run.” (Maskerade)

You had to admire the way perfectly innocent words were mugged, ravished, stripped of all true meaning and decency, and then sent to walk the gutter for Reacher Gilt, although “synergistically” had probably been a whore from the start (Going Postal)

A hint was to Esk what a mosquito bite was to the average rhino because she was already learning that if you ignore the rules people will, half the time, quietly rewrite them so that they don’t apply to you. (Equal Rites)

Demons were like genies or philosophy professors — if you didn’t word things exactly right, they delighted in giving you absolutely accurate and completely misleading answers. (Wyrd Sisters)

It wasn’t that he was unhelpful, but he had the kind of vague, cheerful helpfulness that serious men soon learn to dread. (Mort)

‘The great General Tacticus says that in dangerous times the commander must be like the eagle and see the whole, and yet still be like the hawk and see every detail.’ ‘Yessir,’ said Jackrum, gliding the razor down a cheek. ‘And if he acts like a common tit, sir, he can hang upside down all day and eat fat bacon.’ ‘Er…well said, sergeant.’ (Monstrous Regiment)

Putting up a statue to someone who tried to stop a war is not very, um, statuesque. Of course, if you had butchered five hundred of your own men out of arrogant carelessness, we’d be melting the bronze already. (Jingo)

Every single one of them wanted to be involved in the decision-making process without necessarily going through the intelligence-using process first. (The Last Hero)

Albert grunted. “Do you know what happens to lads who ask too many questions?” Mort thought for a moment. “No,” he said eventually, “what?” There was silence. Then Albert straightened up and said, “Damned if I know. Probably they get answers, and serve ’em right.” (Mort)

You can’t go around building a better world for people. Only people can build a better world for people. Otherwise it’s just a cage. (Witches Abroad)

You did something because it had always been done, and the explanation was “but we’ve always done it this way.” A million dead people can’t have been wrong, can they? (The Fifth Elephant)

Asking someone to repeat a phrase you’d not only heard very clearly but were also exceedingly angry about was around Defcon II in the lexicon of squabble. (Witches Abroad)

One of the universal rules of happiness is: always be wary of any helpful item that weighs less than its operating manual. (Jingo)

If you’ve never picked up a Pratchett book; I’d highly recommend it. It’s all a matter of preference, but I’d say start with a mid-series book (they’re only loosely dependent on each other) like Witches Abroad or Soul Music. They’re all great, but the first ones are in a slightly different style, and the later ones aren’t always as strong…

What can the harvest hope for, if not for the care of the Reaper Man?  (Reaper Man)

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Another year, another artificially inflated car insurance quote, another annoying evening spent searching out a reasonable premium. But this year there was a silver lining to my annual frustration; I discovered a site that essentially reveals just how risky insurers feel the various employments are behind the wheel, which is an answer that begs a question if ever I saw one.

So as a fun exercise I decided to take a look how car insurance brokers rate us civil engineers against our counter parts and colleagues:

Interestingly, we are the lowest insurance risk of almost every other field of engineering (exluding computing); although quantity surveyors win out within construction- getting a premium reduction of 1.5%. To put that into perspective, the lowest premium I could find was for police officers, who enjoy a whopping 7.2% off their car insurance compared to us civil engineers. It also turns out that, while there are many good reasons to become a chartered engineer- cheaper car insurance is not one of them (with no premium reduction for us unchartered civil engineers!).

So next time you car insurance needs renewing- why not consider a stint as a quantity surveyor?

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It’s that most magical time of the year (again), and what better way to celebrate, than a bit of seasonal engineering? Over the last few years I’ve already discussed the miraculous building loading that is Santa Claus and provided you all with an arguably dangerous Christmas Tree modeller; so for 2014 I’ve decided to tackle that fundamental engineering question:

Material Specifications

You might be surprised to learn that there’s a lot of research undertaken into the field of snow construction by various governmental institutions. Alas, this article isn’t going to become a Snowden (pun entirely intended) exposé into a dearth of secret projects to weaponise giant snow people à la Gundam Wing; the mundane truth is: If you want to understand an avalanche, you have to understand snow.

As a material, however, it appears to exist primarily to laugh in the face of structural models. I have now read more than I’ll ever need to know about the engineering properties of snow, and, quite frankly, it makes geotechnical parameters look like works of axiomatic precision. The problem stems from the fact that snow is just loosely packed (starting at around 10-30% the density of water) layers of tiny crystalline ice particles.

This means that it is a highly compressible material (in fact, you can simply crush it until the density approaches 80-90% of water, when it officially becomes ice), that is highly sensitive to temperature (it can melt/disaggregate and re-freeze/bond into new structures through sublimation and sintering) and behaves like everything from a linear-elastic solid to a visco-plastic liquid… To be honest, after losing a few hours of my life to reading about the wonder of snow mechanics; I was yearning for a simple material- like cake!

The thing is, unlike the civil engineering standards of concrete and steel, all these troubles add up to a material where the question isn’t just “will it ever fail?” but “how long do you want it to stand up before it fails; in seconds, preferably…”. If there are any experts in snow engineering who would like to chip in, at this point, that would be perfect- but until then; here are the mechanical properties I’ve deciphered for densely packed snow at sub-zero temperatures that will remain “true” for a given value of time:

• Compressible strength: 3 MPa
• Shear strength: 1 MPa
• Tensile strength: 1 MPa
• Poisson’s ratio: 0.3
• Low creep strength*: 70 kPa
• Density: 7 kN/m³

*The low creep strength is the limiting stress at which the strain rate remains constant; the snow would not start life in a state of failure. It is, however, so low that I doubt we’ll achieve much with it.

The World’s Largest Snowman

The world’s tallest snowman was actually a woman, 32.21m tall, and built by the residents of Bethel, Maine, USA. Right of the bat, however, I’m going to disqualify this entry; somewhat ironically, on the grounds of Architecture.

You see, Bethel (which I assumed they called her) the giant snow woman already encompasses the most efficient engineering form. As I discussed when attempting a similar feat with cake- whenever you’re going for “the world’s tallest”, a pyramid is pretty much the best way to build high for those to whom the words ‘structural efficiency‘ are just a set of random sounds. And although a snow man is hardly anatomically correct, a cone just doesn’t cut it in my book.

We can’t keep building pyramids…

Just for completeness, however: Confined snow under compression tends towards ice. Noting previous research into this topic, the compressive strength of ice is around 8.8MPa. As a rough guide, the loading distribution of a pyramid allows you to build three times higher than the equivalent tower. We can also take an estimate that the snow changes linearly from light and fluffy, to solid ice; essentially making the average density 60% that of water:

As that’s a sizeable fraction of the diameter of the earth, and around about the thickness of the Antarctic ice sheets (so logically, we should be able to go even higher!); I can’t shake the feeling that maybe Maine should have put a bit more effort in…

Failure Mechanisms

A proper snowman is two balls, one a top the other. The bottom ball is required, by Euclid (et al), to be 1.618 times the size of the top; or else our mega-structure will end up offending sensitive eyes. To ensure a good foundation, we’ll allow a zone the same diameter as the head to form a cylindrical pad for the base of the snowman. A similar proportion of bearing area will be provided between the head and the body:

Being Brunel doesn’t make snowmen, but if it did…

At a glance, this gives us two inter-related failure mechanisms (which highlight why the conical-woman is cheating): Either the sides of the body fall off in shear, or it cracks apart as the head pushes through the body and causes it to expand (a rather fatal example for a use of Poisson’s ratio!).

How Big Can You Build A Snowman?

So I’ve waffled on enough; time to take a guess. I mean, er, report my findings after a detailed period of analysis*…

*Ed: It was at this point in the article that I realised I’d picked a stupidly difficult piece of geometry to calculate for! For the sake of simplicity our structure is two spheres in volume; the bearing areas are perfect circular planes and are connected to form an internal core. We’ll negate accessories loading.

Sample shows tensile failure; try again…

The first failure mechanism is caused by the weight of the head cleaving the body in two. As the body ‘squishes’ (technical term) it begins to bulge, and creates tensile forces along the centre of the body ball; exceeding the 70kPa limiting creep stress at 27.5m.

However we’re being a little unfair here, the compressive force decreases the strain rate as our snow packs up to much stronger ice. I’m therefore moved to say that, as long as you think of our snowman as a transient structure, we can use the full elastic tensile limit of 1MPa. From some very rough calculations (lit. unfounded gut-feeling) I’d say it’d last a good few hours in this condition; especially with a bit of maintenance.

Test displays shear failure- try again…

Then comes shear. It’s the sections hanging off the supported bit of our snowman that are causing the shear; so we’ll say that’s everything not within the blunt cone formed between the base and the neck. This means that the weight of the head just transfers in bearing down to the base, but ~60% of the body sphere volume is supported in shear; hanging off the middle. Unexpectedly, we can reach about 130m until the shear passes the limiting creep stress.

No snow men were hurt- except this one…

As the capacity in shear is based on cohesion, it is very sensitive to creep strain- but If you don’t mind the snowman existing for only a couple of seconds, we can push the shear utilisation up to the elastic limit too. So finally, we come to the final failure- compression. Remember I talked about the wonder of snow becoming ice and getting incredibly strong last time? Well, that’s only helpful if you don’t care about the shape (i.e. it becoming a pyramid). So we’re limited to our 3MPa before the snow starts to rupture and crush (n.b. because of the poisons ratio of 0.3, the tensile limit still isn’t exceeded)- which happens at around 320m.

So there you have it, if you want a snowman that’ll last you through the night, stop at 27.5m, if you just want to prove a point- feel free to wind it all the way up to 320m; just don’t come complaining to me when it collapses before you get a photo…

Just for my sadist enjoyment, I’ve decided to attach the spreadsheet containing my workings this year.

Preliminary Snow Man Sizing Spreadsheet

I shall look forward to all the comments pulling apart my methodology, choice of values and formatting choices.

The post Engineering The Tallest Snowman appeared first on Being Brunel.

The ICE has commissioned a music video. And you know what- it’s pretty damn amazing. Honestly; I’m not joking.

I’ve known that a video involving engineers dancing had been in the pipeline for a while, and frankly my natural cynicism grown from too many years in the industry left me fairly nonplussed about the whole affair. Social media is a difficult game to play, and it’s an even harder one when you target is the “yooof of today“.

Today sees the release of the ICE’s Engineering Happiness video, and it’s hard to imagine how they could have done it better. From watching Sir John Armitt bust a move, to a couple of engineers strutting their stuff along a sewage treatment plant; the video is a joy to watch. It doesn’t take itself too seriously, and for that it manages to get the message across that engineering is fun in a way that no amount of project showcasing ever could. More than that, they’ve created something that I’d feel comfortable sharing with my friends inside and outside of the profession alike.

If you haven’t seen it already, you can check the video out here- just don’t forget to share the #engineeringhappiness when you’re done:

So top-hats off to the ICE; it’s an institution that I’m proud to be a member of.

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Thanks to the industry-wide adoption of BIM, acronyms such as IFC (that’s Industry Foundation Classes, for all of you “pen and paper will never die” kids) have entered the common vernacular. As we move towards a future of open collaboration between all parties, it can only be a matter of time before we too will have to express ourselves solely as IFC Schemas to identify commonalities and prevent clash detection.

Acknowledging this future need, I’ve put together this survey to help you determine which IFC best defines you…

If you don’t get the answer you’d always hoped for, feel free to refresh the page and you can keep trying again and again until you get the IFC Schema all the cool kids are using (IfcPropertyResource is tipped to be the ‘must-have’ class this Christmas). Alternatively you can check out the tortured code behind this industry re-defining widget on GitHub.

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This week I learnt that professionals blogging within the construction industry has become enough of a thing for there to be paid courses on the subject. This can only be a good thing. As I am a professional with a relatively successful blog, I thought a post sharing my experience and lessons learned might well be of interest…

Before I begin though- I honestly believe that if more engineers took the time to blog and share what they’re doing with the world, the profession would be much easier to engage with. So if you want to know more, need any help, or just want to promote what you’re doing- feel free to send me an e-mail.

Rule One

If you’re going to start a blog, do it for yourself. I have received the odd compliment or two, enjoyed the thrill of going viral once or twice, and even been interviewed because of it- but blogging takes so much more than it gives; and if you can’t do it because you enjoy it for what it is, then you’ve set yourself up for a fall.

You also need to decide if you’re going to write as yourself, or anonymously. The latter is much harder, and probably only worth it if you’re going to be doing some whistle-blowing. If you’re being yourself- having a look at your employer’s policy; if they don’t have one, or it’s needlessly restrictive, I’d recommend trying to hammer out something before, or soon after, you start. As a side note, Being Brunel isn’t anonymous, I just didn’t want the focus to be about me as a person.

First Steps

Taking the view that you’ve already decided to start blogging, the next step is to decide what to write about. For me, it was clear that the world had enough prominent engineers exchanging rhetoric without me attempting to join in; so I opted to try a more off-beat tact. As a good rule of thumb, I’d say try and write articles that you would actually enjoy reading.

Once you’ve got a vague notion of what you’re going to write, you’ll need a platform. I unequivocally recommend WordPress, which offers simple and free hosting for your blog; making it quick and easy to start writing. At this point you’re going to have to think of a name. Top tips; keep it short and simple, and- if you’re feeling optimistic about the future, have a look on the likes GoDaddy to make sure that no one else owns www.[your-site-name].com already.

The first post is the hardest. Hypocritically, I’d say that you should avoid starting your blogging career with a post about what you’re doing and why you’re doing it. Do keep it short though- you don’t want to burn out too early. I’d also recommend you just get your head down and write it, leave picking themes, changing the layout, writing an ‘about me’ page and all the other superfluous site-setup tasks for now.

Don’t Stop Believing

I might say it jokingly, but I honestly believe the secret to any success I have has come from making a commitment to write a post once every week. The structure is compulsive; making it much harder to abandon or neglect your blog. If you don’t believe me, check online- the world is full of first-post blogs, or those updated in sporadic ‘new year resolution’ fits of activity, only to be abandoned for another two years.

When it comes to knowing what to write, I tend to just jot down ideas for posts, as and when they come, in the back of my diary; remember, not everything you write need be profound or game-changing. I’ve also learnt not to underestimate the amount of time it takes to write a post; when I started I had visions of doing weekly design guides, but I’ve found these are the sort of things that need a few weeks to pull off. Typically I have two posts on the go at any one time; the one for the week, and the ‘big-one‘ for a few weeks time.

Oddly, I’d also say wait until you’ve written about four posts (that’s a month on my schedule) before you start to tell people about the blog. By then you should have hopefully found a rhythm, a bit of a voice, and a vague idea of where you’re going. Now is the time to maybe pretty-up your layout, find a theme, write a heart-felt “about me” page and all that jazz.

Getting Serious

When it comes to making the world aware that you’re now blogging, I found Facebook helpful in my formative months, then LinkedIn (especially if you target groups), followed finally by Twitter- which requires a more significant investment, but is worth it (if only to see what great work other people are doing) when you’re up and going.

After a few months, once you’ve got a feel for it; it might be worth taking your blog a bit more seriously. Consider buying a domain (www.[your-site-name].com), and self-hosting. Migrating from WordPress.com to your own server is easy to do, and gives you the flexibility to use more professional themes and powerful plugins (honestly, I’m not on commission).

Finally, I thought I’d end with a few “tricks of the trade”: Displaying related posts helps people browsing your site to find other articles that might also interest them; the more advance layouts on Being Brunel are done using shortcodes, which are easy enough to write; and Flickr is a wonderful source of free (Creative Commons) images.

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The best thing about being an independent writer is that I can tackle all the hard hitting stories surrounding Civil Engineering as a profession, without fear of repercussion from advertising sponsors. That’s why today I’m delving into this thorny issue, which threatens to strike at the very heart of the industry:

Termites

That’s a tall structure.

If termites had any of the required anatomy, they would laugh with scorn at our pitiful attempts to build tall structures. “Burj what?” they would say, “830m of aerial?!” This is because they quite regularly build termite sky-scrapers, the largest of which scales up to an amazing 2km (human). But that’s not the worst of it, for the majority of these little blighters, the extravagant structures are nothing but glorified ventilation systems to keep the vast civilisation of tunnels air conditioned. Formed of soil, saliva and dung, however, I’m not convinced the construction method will take-off, even with the most dedicated of sustainable developers.

Prairie Dogs

Underground cities.

On the subject of tunnellers; it’s hard not to admire the humble Prairie Dog, which builds an underground town to better defend against the floods, fire, temperatures and predators that strike its natural habitat. When not doing Mexican Waves, they are forever performing maintenance on these underground systems, which include everything from over-flow channels to nurseries. Although typically about 10m long, the largest of these towns was apparently in Texas, covering 65’000 square kilometres and housing over 400 million of the little rodents. That makes it larger both in sprawl and population than anything man-kind has built.

Spiders

Stronger than steel.

Spiders may not be the most popular of creatures, but if you’re looking for the masters of material science and disaster tolerant structures, you needn’t walk much further than your own back garden. Of course, construction is substantially easier if can secrete a substance with the tensile stress of steel, however the most interesting thing about web-silk is the odd stress/strain curve it exhibits. Initially softening and then hardening again when pulled (unlike the elastic/plastic response of most civil engineering materials), this creates a flaw tolerant system where the web always fails exactly at the location of the force. It’s so impressive that MIT are even researching how this can improve the earthquake response of our structures.

Chimpanzees

Nests in the sky.

It seems obvious that our closest animal relations (let’s have none of that creationist stuff here) would engineer their environment. For those who are wondering, Chimpanzees made this list from the vast temporary working platforms (or nests, as they call them) they construct. Depressingly, however, they are the only primates to do so, and even this construction is pretty much it for environmental manipulation. Interestingly, however, work is being down to trace the evolution of tools by our hairy cousins to find out just why we’re the only ones who civil engineer.

Beavers

Dam beavers!

I think we all knew that there would be no way that this list would omit the, frankly adorable, national animal of Canada. Yes, that’s right we’re talking Beavers and their dams. Arguably beavers truly are the civil engineers of the animal kingdom as their works significantly affect the local ecosystem; creating a true built environment where even other animals flourish; in fact, they’ve actually made it onto the crest of the ICE! The effect they have on their surroundings is so pronounced that they are often at odds with us engineers; flooding roads and blocking waterways.

Once again the animals laugh in the face of our technical achievements. The longest beaver dam in the world is visible from space and, at 2790ft, is twice the length of the Hoover dam. Perhaps most fascinating is how similar the construction of a beaver dam is to ours, including spillways, adding curvature to resist high-flows and improvised cofferdams from trees driven into the river bed like piles.

The post Civil Engineering Animals appeared first on Being Brunel.

As a child of an era where PlayStation’s didn’t have numbers after them, my introduction to driving was a fast, furious and blocky affair. To this day I still have fond memories of scaling near-vertical cliffs, bouncing off incredibly rigid trees and glitching my way through the barriers. All of which contributed to a very disappointing learning curve when I finally got behind the wheel.

Out of all my virtual impressions of fatal transportation- racing around a vertical loop remains the most lasting. As and when the time comes that someone stupidly puts me in charge of the world, let me assure you, Civil Engineers will need to be ready to append 360° roller-coaster loop-the-loops to our forever ageing highway infrastructure. Perhaps some of you will scoff at this idea, but we all know that if you’re willing to pay enough someone will build it for you.

The loop-the-loops of my childhood video gaming career were almost always just an extension of the road; which tended to a mean a continuation of the full road depth rising from the ground as a monolithic concrete structure (although in the case of Sonic the Hedgehog it appeared to be a naturally occurring chequered geological formation). In real life, however, my roller coaster experiences have only ever been timber and steel.

Forgetting how it stands up for a moment (I believe this is called architecture), let’s consider the deflected shape of the vertical loop as our bewildered test-granny drives around it. The response is cyclic, and most importantly tensile; the car is doing its best to pull the structure apart. Unfortunately concrete is only really good in compression, which is why everyone’s favourite man-made rock is going to have to sit-out for this one.

As with concrete, doubly so with masonry; despite the superficial similarity to a railway arch the nature of the loading is completely reversed. It also turns out that very few timber loop-the-loop roller-coasters have been built, and even less survive today. By observation (what a great engineering term), our new vertical-loop infrastructure initiative is going to have to be built out of steel.

In the UK the DMRB sets out the basis for highways design in 10 easy steps (and 100 hard ones). A quick browse tells us that the maximum gradient a road should aspire to is 6%; less for busy roads (of which our junctions undoubtedly will be). Playing devils advocate, however, it doesn’t specify an absolute maximum; and thus it is expected that the new loops will get permission with a “departure from standard” for employing vertical gradients between -∞ and +∞.

Annoyingly, however, the DMRB does consider vertical transitions to be essential, and requires them to maintain certain sighting distances and standards of comfort. Arguably the sighting distances are not as bad as all that, as the loop is fully visible from a distance and cars will not be able to halt mid-way through. Similarly typical obstacles such as pedestrians and badgers are unlikely to be found in the blind-spot that the apex will become.

The requirement for comfort comes in at a maximum vertical acceleration of 0.3m/s², and this is a bit of a bugger. Avoiding delving too much into the exciting world of centripetal dynamics, you can say without picking up a pencil that at one point (at least) the vertical acceleration must be 9.81m/s² or else the car will succumb to gravity and fall off, which will arguably be even more uncomfortable.

When approaching this problem I was instinctively concerned with the speed that the car would be doing. A little more though, however, reveals that speed has little to do with this problem; in fact it turns out all we need be is a bit clever about our geometry and we’ll get to prescribe the vertical acceleration at every point. Although allowing for articulated lorries, however, is likely to result in a loop with some significant dimensions! In this case it makes sense to aim for a scenario where the upside-down drivers are subject to the same amount of gravity as upside-up ones.

Throwing some static equilibrium at the problem: people feel like people when they have weight, people have weight when they are subject to gravity, people at the top of the loop are subject to gravity in the wrong direction, they need twice as much gravity to feel like they have weight in the right direction, thus the design force must be twice the weight (not mass) of the traffic. Given the relatively short ‘span’ and the continuous supports this is unlikely to be difficult to design for; although somewhat more ardours than the normal bridge loading!

At a glance I’d say I’m most worried about fatigue- there will be a phenomenal amount of fully reversed cycles on our loop, which is pretty much the absolute worse thing you can do. Providing a steel deck means full penetration welds everywhere. Arguably this will make us very unpopular with the contractors, but it’s unlikely to stand up for any length of time if you do anything else.

Probably the best structural form can be found by looking down (if you’re me, during my commute to work). The humble bicycle wheel is an ideal form; the track will form the rim with spokes running along the central reservation. Spokes are, in this case, essentially tensioned bars; and as the cars attempt to push out the rim, the spokes will hold it all together; resulting in a very stiff structure. In fact, given the concerns surrounding fatigue, it would even be possible to replace the spokes and re-tension the wheel.

Unfortunately, as the cars loop the structure the acceleration will have to come through traction, which will tend to feed the loop through itself. This means that our structure will just happily roll like a hamster wheel; something that might upset the drivers. Extending the bicycle analogy, a break system is likely to be the most effective way of preventing this effect, rather than attempting to hold it steady through the axle (which would involve significant torque). In this case we’ll be talking v-breaks, as a disc approach would spoil the view!

As it turns out, however, a somewhat less permanent version of a highway vertical loop does exist- and thanks to TopGear and Dunlop you can see proof that a car really can loop-the-loop; although I expect that this form is too high in g-force and too low in durability for my 120 year highway designs.

Finally I have to finish off by pointing you in the direction of this guy, who does a much better job than I do at explaining the physics behind the loop.

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What does finding someone who shares your birthday, and a 1:100 storm have in common? They both happen more often than you’d expect. In fact, once there are 23 people in a room, you’ve got as much chance of guessing a coin-toss as finding two people born on the same day. That’s probability for you, about as intuitive as a rock in the face- or something like that.

Having enjoyed my wettest cycle of the year (yes, I know we’re only nine days in); I had good cause to reflect on the irony of having experienced so many “1:100” year storms during my lifetime- while ringing out my socks into the cistern. Perhaps the greatest concern is that the more “1:100” year rains I cycle through, the more likely I am to get equally soaked- confused yet?

The “1 in X” year description of an extreme event is an odd one (know as a Return Period). The cynic in me notes that the phrasing seems designed to dismiss the event as impossible to predict, whilst giving the client the impression that it’ll never happen again. In fact, I sincerely hope that Wikipedia’s article on the subject is accurate when it credits Civil Engineering for the terminology.

In an attempt to demonstrate the wonderful world of Return Periods, I’ve made this little widget. The graph shows the probability of a “1 in X” year event happening over a period of years. By moving the slider you can can change the return period and see how it affects your chances.

Despite everything, however, Return Periods should give hope to all those searching singles; despite there only being a 63% chance that you’ll meet that one “once in a lifetime” person, there’s a 1 in 5 chance that you’ve already met them.

Isn’t probability wonderful.

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