There seems to be real interest in yesterday's post so here comes some more.
A load test was carried out using gritting lorries to apply 518 tonnes to one lane over half the length of the bridge. That's almost exactly 1 tonne per m. That is just a little more than the code required in the 1960s and a half span is the worst possible. The bridge posted these two pictures.
This picture of the load in place was also posted by the Forth Road Bridge (at https://www.forthroadbridge.org/bridge-closure/images/) It's worth watching that, there is a lot to see and pictures accumulating daily.
There is more to see there than was mentioned in the Tweet so I downloaded and drew over the edges to produce this
This isn't absolutely correct, but I think it shows how the main span has gone up at the far end as well as down and how the side spans have been lifted. I think that needs explaining too so here is a sketch.
The grey lines show the original shape and the black the deflected shape. The extra tension in the cable pulls the towers closer together. That lifts the side span and allows the main span to drop. But the load at one side also causes it to sway that way and results in the deflection which is looks like a full parapet height. Since this is a cycle lane, I guess that must be 1.8m.
Most people know me as an arch bridge man but my first love (starting with Clifton) was always the big ones. I worked on Humber for a while and have always maintained the interest. I was wondering what was going on on Forth and guessed it must be a bearing problem from a number of clues (including a friend ordering some of our Moire Tell Tales for urgent application in Edinburgh). Then, as a result of an extended set of links, I got a call from the BBC about talking about this on PM. I was almost immediately stood up in favour of Dave Parker from NCE but my mind was engaged.
So here are my thoughts. First a bit about bearings in general and then some Forth Road Bridge (FRB) specifics.
Civil engineering is mostly about big lumps carrying relatively low stresses. The big lumps (such as bridge decks) are inclined to want to move so they have to be supported in such a way that they can (or designed to cope with the effects of being prevented from moving, but on a big bridge that is impossible). In longer bridges, the big movement is usually expansion and contraction along the length as a result of temperature changes. The range of movement in a straight steel bridge is a little less than 1mm per metre of length over the life. In suspension bridges it might be twice that because of the way the various parts interact.
If we stick with steel bridges, they are typically built to a tolerance of perhaps 3mm locally. Over long lengths 1/500 is typically specified.The fabricators may do better now but that was notoften bettered in the 1960s.
Bearings of the older type with pins and rollers are very fine machines, often built to 0.01mm or better. They depend on good fit and alignment if they are to work well. On Cleddau bridge, when the bearings began to fail,we looked at this alignment issue and found a whole string of issues which I will cover in more detail in the context of FRB. The main point, though, was that the bridge got hot on one side in the morning and the other side in the evening and so bent sideways in a way that was never seriously considered.The movement involved a plan twist of 0.5mm over the 440mm length of the roller. In other words the roller was being scrubbed round instead of simply rolling back and forth.
Anyway, the point here is that the tolerances don't match and trouble ensues.
Now to FRB.
The bridge deck is a steel truss about 7m deep and 25m wide. It is suspended from cables that sag about 75m in the 900m span so around 12:1 span to sag, a very deep structure in a world where beams might get to 30:1.
The truss is supported very frequently from the cable but the end has to be anchored to the tower to allow a smooth transition from the suspended road to the tower. This bearing has to allow expansion and contraction of the better part of a metre whilepreventing up and down movement. It is done by using a long pendulum or drop link, pinned to the tower at the top and to the deck at the bottom.
For symmetry, each side of the truss is supported from 2 links and these can be seen in the photo tweeted by @ForthRoadBridge. The men seen here are standing on the square bottom member of the truss and beside the end vertical. Both sides of the vertical is a drop link. Notice that the link tapers near the bottom.
Before I get to the damage, I want to say a bit more about the bearings and what they have to do.
In plan, the bridge looks very thin. When the wind blows,it moves sideways but the road still has to line up with the gap in the tower. How much does it move sideways? Well, a full carriageway of 7m in the middle. The bearing that prevents this movement at the tower is separate from the drop links and is in the middle of the bottom layer of the truss. The end of the truss rotates about this point, so when the wind blows, one drop link has to swing forward and the other back. Of course the truss wants the pins to rotate with it but the link wants them to stay parallel to the tower and there is one fight.
I have made a very rough sketch of the bottom of the link here.
\In this direction, the pin will tend to bend a little under load but so will the link. It is almost certain, though, that the load will not spread (as the designers hoped) uniformly over the contact area between the pin and the hole in the link.
Now it is time to get to the photo of the damage. It seems to be in the public domain so I have copied it here.
The point where I have marked the crack on my sketch has obviously suffered more stress, and particularly more stress cycling, than anyone expected. This has been going on for 50 years but will have got worse as a result of wear and corrosion.
I suspect that is essentially a fatigue crack. It will have grown from a very small starter, possibly just a minor defect in a weld or even the edge of a perfectly good weld. The crack will have grown very slowly until it reached a critical length and the travelled through the rest at the speed of sound (which is very much faster in steel than in air). The critical length is rather shorter when the steel is cold so the rapid propagation may well have happened in the recent cold snap.
Had the inspectors been looking for a crack they might well have spotted it sooner but there was a firm belief that the stresses were low. Only once the crack had become frighteningly big would it have been visible to an inspector.
So, let's not lambaste today's engineers. They are doing their best with a very difficult situation. For sure, the politicians and the press will have pushed them to keep the bridge open. Remember what Feyman said about the Challenger disaster:
For a successful technology, engineering must take precedence over public relations, for nature cannot be fooled.
These fittings appeared on Twitter this morning from https://twitter.com/CaseyRutland. The left hand one is presumably the bog standard weld and galv. The others, the result of computer optimisation and 3D printing. Pretty spectacular stuff but...
Of course we have no indication of how big this is or what it is for, though I assume those lugs are to take cables with forks or something like that. The fact that they are printed suggests they are relatively small.
So begin with some guesses. This fits as a cap on some form of strut with a ring of ties at odd angles. I guess it must be about 150mm high and the plates about 3mm thick. The printed ones are not, I think, direct replacements but different forms for a similar task. If pressed I would say that No 3 is designed to do a similar job to No 2 with different connections.
There is at least one sense in which the new models are better than the old. They are not hard and angular. One doesn't feel likely to be cut while assembling them. My objections (for I did make objections and was condemned as "old school" as a result) centre on the issue of abrogating the concept of design. Let the computer find the best form.
These forms may be optimised within the constraints imposed by the programmer and the computer operator but where is the designer in this process. Computers are tools and I trust they will always remain so. Actually, they only become tools when equipped with programs and the combination is very powerful. But no fitter would thank you for a spanner with sharp edges. Programs and computers need to be designed to assist not replace the designer.
The form is by no means unconstrained. The computer will have been given a massive array of possible links and allowed to choose which to use and how big to make them. The patch of spiders web at the back of No2 is an indication of that.
Looking for something similarly complex and beautifully designed I had a hunt for the Tobacco dock. It would be interesting to see what the computer made of this.
Of course Rennie started from further back. This branching cast iron support is a more complete thing.
So, where does that get us. 3D printing can release constraints but I suspect that the printed brackets would be many times the cost of the weldment. If there were many of them, the printer could make a pattern from which others could be cast. But what is this filigree going to look like when it has had several coats of paint and begun to accumulate dust and grime? Perhaps that depends where it is going. I have a mental picture of a brand new Leeds station with elegant white trusses dripping with the grease from dozens of dirty diesel locos. Actually, it was beautiful for a few days but quickly showed itself to be not fit for purpose.
My feeling is that the design is incomplete. It needs a bit of human intervention.
I am often exercised by lack of structural stability. Often the problem is retaining walls but occasionally a free standing wall gives trouble. couple of years ago such a wall collapsed in Melbourne killing two people (Google melbourne wall collapse for pictures. It was actually a cavity wall which then had a hoarding attached.)
This afternoon I walked to the station in Exeter to collect some tickets. Climbing back up St Clement's Lane, I looked up to see this:
Oh well, Typepad turns it left but I expect you can see.
Looking down from the top it looks like this:
And a last pic to show the wall construction:
Just a half brick wall with occasional full brick piers. Hardly adequate for a 1.5m wall without the addition of a 1m panel cantilevered off the top.
This note is prompted by an exchange on twitter. 140 chars is definitely not enough.
Roma Agrawal @RomaTheEngineer Amazing that 1800 years after the Romans,we were still building arches in the UK. #engineering #Colosseum #RomaInRoma pic.twitter.com/UZkNwY8Z7l
Griffglen@griffglen Follow @RomaTheEngineer was there a reasonable alternative? what brought about change??
Roma Agrawal@RomaTheEngineer @griffglen @BillHarvey2 I'd say introduction of cheap concrete and steel with building techniques but have copied in the arch expert!
So, here goes.
Putting a load over a gap requires a couple. That is an upward force where the load is and a downward force at the support. Mostly, there are two such couples because the load is shared between two supports. A couple causes rotation unless matched by an equal and opposite couple and that balancing couple usually involves horizontal forces. The further apart the forces can be the smaller they will be. In beams, the two forces are both contained within the beam and so are not very far apart. In arches and cables one force is provided by the earth and the lever can be big. In ancient times there were three ways this could be achieved, but any material with more than a modest tensile strength was essentially organic and therefore likely to rot. Beams could be made from stone but that required high tensile strength and a lot of work to move big stones. Stone arches can be made from small pieces, though the Chinese and Venetians learned that there was real advantage in using bigger pieces over soft ground. From Wikipedia, below.
The bridge is located in Chi'an Village (simplified Chinese: 赤岸镇; traditional Chinese: 赤岸鎮; pinyin: Chì'àn Zhèn), and it's about 100-meter western of the Yazhi Street (雅治街). It goes across the Dragon Creek (traditional Chinese: 龍溪, simplified Chinese: 龙溪, pinyin: Lóng Xī). It is a single span arch bridge. The design is very special: more precisely, its structure feature is girder-arch, and the girders are arranged like ribs. Such design can be found in the famous painting Along the River During the Qingming Festival of Song Dynasty byZhang Zeduan. The bridge was completed in 1213, the sixth year of the Jiading Era (Chinese: 嘉定; pinyin: Jiā Dìng), Southern Song Dynasty. Since then it has never been rebuilt or repaired. Of course, there are secondary costs to building arches, the biggest being the need to put up a temporary bridge to carry the permanent one. If wood is readily available and long life isn’t needed, a wooden arch made from long light pieces, with a woven pattern to produce a measure of bending strength under live load might be the answer. Trajan built such a bridge over the Danube with spans of over 30m and Perronet was still using the same scheme in the 1760s for a temporary support or centre. Even now, essentially all materials with tensile strength are subject to more rapid degradation than those with only compressive strength, but making a bridge last longer than an engineer is relatively easy and building to last “for ever” is no longer regarded as economic. By about 1910, the core of structural engineering teaching had become the study of bending. Arches were still built by rule of thumb, though following Castigliano’s efforts, stress calculations for the indeterminate arch were possible. Unfortunately, they were “known” to produce the wrong “answer” arches cracked when they weren’t supposed to because they were sensitive to abutment movement in a way that simple beams weren’t. It has taken nearly another 100 years for us to become confident in the knowledge that the odd crack doesn’t matter in an arch in the way that it does in a beam. No reinforcement is exposed to corrosion. If the mortar is lime based the arch will flex instead of cracking and the distance between compression and tension will remain as is. Another layer in the problem of analysis is that arch bridges are inherently three dimensional in a way that beam bridges are not. A beam bridge can be assembled from simple 2D elements that are easy to analyse and design. And finally, there is the issue of clearance. These days we don’t want humps in our roads and often it is much easier to get the clearance we need by using a beam. In recent years, many of the problems with building and with analysing arches have been overcome but it will be some time yet before we get back to building them as a common thing.
Once again, the shorthand of twitter leads to anger and misunsderstanding. So lets try a few more words.
What I tried to say was that the march of technology is pretty much inevitable but it behoves teachers to be careful what they chuck out when they embrace it in place of old fashioned techniques. That is not a criticism of students, or of graduates. Indeed, the best students will always pick up the depth of learning needed from somewhere.
The first point I need to make is that I am a Civil/Structural engineer and my views only really fit in that sphere.
In my early years as a student, 1965 since you ask, I spent 2 full afternoons, 2 evenings and much of Sunday each week for the first 13 weeks learning the elements of draughtsmanship and projection. The projection stuff was difficult, many of my colleagues really struggled. I had doe some of the work in school as extra urricular courses. a very few could see instantly what was going on and get straight to the point. In particular we had to learn to project true shapes, angles and lengths from odd views of objects. Time and again since, and certainly with increasing frequency as the years have passed, I have been confronted by details that just don't work because someone thought that a 3view projection told the whole story. The most damaging and obvious case is where a right angle is assumed to be a right angle in a particular view. In face there is only one view in which a right angle appears true.
I am often told that we don't need to teach that suff any more because things can be spun in space in Autocad, but my answer to that is;
Only if they were drawn by someone who understood and only if the user knows they need to do it. It is perfectly easy to draw ipossible things in Autocad and they only eventually show up when some poor joiner/fabricator/steelfixer has to make it work in real space.
If thta necessary skill is removed from the undergraduate course (and in most courses it was at least 20 ears ago) it either needs to be learned somewhere else or we will get unbuildable stuff arriving on site (at best, or collapses through misunderstanding at worst.)
I also mentioned precision, accuracy and surveying. We were browbeaten about this only in surveying, but our only "calculator" worked to 2 or a best 3 significant figures. Computers churn out maybe 15 and users need to understand that is a lie. The most accurate material used in construction is steel. Concrete can be pretty accurate but only if it is done in steel moulds so the stell has to be made first. Steel sections are rolled to a 2% tolerance. That means that for structural engineering work the gravitational constant in SI units is 10 (to the same precision). No matter how good the machine doing the calculation, nothing more than "slide rule accuracy" can ever be achieved in practice.
The real crashes in that scenario stem from serious misunderstandings of accuracy achievable. These days, bridge bearings are most frequently sliding units with plastic layers that can tolerate a certain amount of misalignment. Over recent years I have been working on the bearngs on Cleddau bridge which are rollers machined to about 1 micron but put betwee steel plates that are positioned to +- 3mm. They don't fit. The surrounding steel gets overloaded locally and deforms to improve the fit but it will never be perfect and the rollers will never run true.
More on that story another time. That error was made in 1971, of course, by people who did have training in accuracy and precision.
Some discussion on LinedIn over recent days that ties in closely with something that has been exercising me. In 2007 I became agitated about alterations on Fore Street Exeter, between The Mint and Friernhay Street, neither of which would qualify as streets in normal circumstances.
The alley at the right is The Mint. Freiernhay Street is between the fourth stucco building and the first brick one. As you can see, the third shop is being refitted.
Here is the second building, The Mint Pub.
You might imagine that the pub in the first two buildings has no crosswalls. You might not think that the lack of crosswalls would go beyond the main back wall of the building. But look how far away the TV screen is!
When I saw this, the internal cross walls of the new restaurant were being taken out so only the Victorian shop at the bottom of the group had anything forming a brace. I raised the issue with Building Control but was basically fobbed off and ran out of energy to continue. No doubt, though that the cross walls were gone.
The Bressumer beam is quite substantial and apparently in good condition, but the new support at the right looks sketchy and the wall at the left is clearly inclined somewhat.
I'm pretty sure there is nothing structural behind the posts in the window.
And this makes the slope in the dividing wall clearer.
Here is the right hand end of the beam.
Anyway. Towards the end of march I realised that the victorian shop was being refitted. Another wall was coming out. I chased BC and it has taken over three weeks to get a response. I am assured that is because the person I emailed (named on the web site) had left that week. An email to my MP Ben Bradshaw produced a very rapid response.
The first comment was that the wall that came out was "just a stud partition" and did not require buildings approval because it wasn't strutcural. I beg to differ and will say more on that in another post. In the end, though, the point was that they have to rely on the engineers who submit calculations, they are not engineers themselves.
So, I ask, whose job is it to take care of this sort of thing. "I can only intervene if the building is in imminent danger of collapse."
Imagine what would happen if a Bressumer failed (they are very old) or if a support gave way. The upper floors would arch and there would be nowhere for the thrust to go. Somewhere I had a link to video of one of those going. A search will be mounted. I suspect that even a big car hitting one of those walls would be enough. Not a big risk but....