arches

The Role of Intuition in Engineering, or getting things wrong!

This was prompted by a post on twitter about intuition in arts and science to which a twitter friend, Patrick Sparkes, responded “and engineering”. It made me think about my own work, how I got something wrong and am trying to get it put right.

My involvement with Masonry bridges began with a request to monitor the behaviour of Wade’s bridge in Aberfeldy when it was to be subjected to new heavy loads. Back then in 1981 the bridge was nudging 250 years old. Now that score has reached 286!

Figure 1 That's a piece of new bridge passing over the old Wade bridge in Aberfeldy

The heavy loads were expected to be standard vehicles which were then allowed up to 100 tonnes gross on 5 axles, recently raised from 38 tonnes on 4 axles. I think that the worry was,in a sense, unfounded because agricultural vehicles would certainly haul eg potatoes and grain in full weight wagons. The new load would be Barytes from a mine that was about to be opened. In the even, grain lorries were used to haul it and they were full, taking the gross weight to around 100 tonnes on 5 axles, with a weight balance thrown to the rear of the vehicle, so most likely 3 axles at 25tonnes instead of 8 tonnes.

Anyway, this blog is about engineering bridges and analysis not illegal vehicles.

As we progressed with the monitoring work, it seemed necessary to offer some form of analysis. Then, and now, the standard “analysis” was MEXE. I soon learned that MEXE was not, in any way, an analysis but rather a complex formulation which converted a few basic details about the bridge into a presumed capacity without any real connection with engineering science. The main 18.3m span of the bridge had an expressed ring of 1.5m which is very large the rather smaller side spans had much smaller ”rings”, but the biggest dimension of the stone used was about 600mm. Using a 1.5m ring said the bridge was good for 26 tonne axles but reducing the ring to 600mm was much less encouraging.

I then became aware of Heyman’s work, begun in the 1960s, relating plastic theorems to masonry and offering a calculation scheme that seemed much closer to analysis. He based his work on that of Hooke (the line of thrust, well known in the UK) and De La Hire (check) who had looked at collapse mechanisms. Heyman’s model looked at the minimum arch that would carry a load and looked for 50% spare for security. Like everyone before him looking at bridges, he considered an effective strip to carry the load and adopted that used in MEXE, apparently without question. The spoil fill was treated as dead load only and the structure divided into 12 vertical slices for calculation

My contribution at that stage was to program the system into an HP 41CV pocket computer (to call it a calculator would be an insult. It was about the most powerful portable then available.) The user had to guess the positions where the best thrust would touch the intrados and extrados (henceforth called hinges) so type in say 0, 3, 7, 12 The program calculated moments about each point and worked out the appropriate balancing thrust then computed the offset from the intrados of the thrust at each of 13points with a delay to allow one to rite down the answer. If you were slick, and had graph paper, you could plot the points as they came up. The Hinges would then be moved to the points where the thrust line deviated most from the intrados and the program run again. After typically 3 guesses the result would be consistent with hinges in turn at intrados and extrados of the minimum ring to carry the load.

Then came PCs. A kind HoD allowed me to buy a PC with colour screen and GWBasic and in a 2 week burst I programmed CIRAR which divided the arch into 20 radial segments and applied some modest horizontal pressure from the soil fill. It was still necessary to guess the hinge positions rather than iterating because the calculations took 25 seconds and the user would think the computer had died if you added iterations to that. It did do the plotting though and produced a nice picture on the screen. It was around then I had the idea that we could have a zone of thrust instead of a line. The sort of “one hoss shay” where the arch would be on the point of both crushing and folding.

I showed off the program at a workshop in Edinburgh in 1984 and someone wanted to buy it. Suddenly I was a software vendor. The years went by. The program got refined. Computers got faster. The number of customers grew. People began to ask about viaducts.

And now we get to intuition, which usually needs a trigger. I was doing a lot of travelling then. I remember at the close of a day catching a train from Sheffield to Nottingham and buying a “New Scientist” to pass the time. There was an article that mentioned Occam’s Razor but which, unlike all previous references I had seen, expanded to say it is vain to do with more what can be done with fewer. And I thought… For an arch to get to four hinges it must first go through three. A three hinge arch is calculable. It is the natural stae when the centring is removed. The arch goes into compression and gets shorter and the abutments move apart so we have a shorter arch and a longer span and it must either crack and rotate to fill the gap or flex. Either way, the thrust will go to the extrados near the crown and the intrados near the springing. When a live (concentrated) load is applied the crown hinge will move towards it and at the remote springing the intrados hinge will move up the arch until eventually a fourth hinge forms at the extrados and the arch will fold and collapse.

But the extra load will increase the thrust and cause the piers in a viaduct to move apart slightly compressing the arches each side. In those, the hinges would close and eventually open the other way.

Then I found WHBarlow 1846 in the ICE showing that we cannot know what the thrust really is but we can set limits. And there was the solution to viaducts – we could have whatever thrust we needed from the adjacent span up to the limit where it folded upwards allowing the pier to tip. Too long winded a program, even with the fast computer in 1990, to do the iterative increase bt the picture on screen could respond quickly to manual input and it became a game. Users liked it.

Figure 2 Barlow's model, demonstrated at ICE on 3 Feb 1846 using slips of wood between voussoirs to constrain the position of the thrust.

 

Figure 3 My own model of a single thrust line.

So there we go, intuition, triggered by serendipitous reading.

And then I realised that railway viaducts have solid masonry in the valley and there is more possibility for increasing the thrust (which involves flattening it).

But that was WRONG. Both the original builders and I misunderstood the complexity of the interactions involved.

In 2000, I left the university world and set up as a consultant. I began to see viaducts suffering damage that was obviously caused by load. I couldn’t understand it. But, of course, I already knew that the bridge was more complex than a simple strip and I had begun to realise that the load isn’t (as previously assumed) distributed by the fill into an effective strip but rather the thrust is distributed within the arch from being concentrated under the load to distributed at the abutment or pier. That explains local failures in single spans and some  of the damage in multi spans but not the horizontal cracks appearing in spandrel walls.

I had quite a few pictures of damaged bridges (from earthquakes, bombs and even demolition) where the outer third of each arch remained stuck to the backing after the crown section had fallen but it took far too long to click that this was telling me something important.

Figure 4 London Road viaduct, Brighton, after a bomb took out one pier.

DOH! If the ends of the arch are stuck to the backing, they didn’t drop when the centring was removed and therefore didn’t contribute to the thrust.

And if the thrust is much less than we thought, the capacity for change is also much less. And if you put a load on the end of that solid piece it will rock like a see saw, rotating about a point between the two arches at the top of the solid and above the pier. And the only thing to stop it rocking is its own weight and the stiffness of the spandrel (side) walls.

Figure 5 Section by G W Buck with notes showing how the structure works

The horizontal cracks I was seeing in the walls were at the top of the backing. The walls above were stiff enough and strong enough to work as a beam but the triangle of masonry below was determined to tip and it did. The crack opens and closes on alternate sides of the pier and the arch suffers severe local rotation at the end of the crack. Eventually, bricks fall out. 

And the killer: What produced this sudden damage, was a change of vehicle not a change of load. The two axle 50 tonne bulk hall vehicles were replaced with 4axle bogie vehicles. The spacings changed from 3m, 4m, 3m, 4m, to 1.8m, 3m, 1.8m, 10+m. Suddenly we were putting 100tonnes in a single span and nothing in the span either side. So50 tonnes on the end of a see-saw that might only weigh 200 tonnes to start with. And if two trains passed we got to 100 tonnes on one cantilever.

This is all still intuition. Built from looking at dozens of damaged bridges. But we have measured live load response in a few and it seems to agree with my intuition. Now we need some aggressive testing. Real science where we work out how we might prove the hypothesis is wrong and set about trying. Proving it right is impossible, but engineers work with “right enough for all practical purposes”. What we are using at the moment, my original intuition, has been proved to be not right enough for engineering.

The Role of Intuition in Engineering, or getting things wrong!

This was prompted by a post on twitter about intuition in arts and science to which a twitter friend, Patrick Sparkes, responded “and engineering”. It made me think about my own work, how I got something wrong and am trying to get it put right.

My involvement with Masonry bridges began with a request to monitor the behaviour of Wade’s bridge in Aberfeldy when it was to be subjected to new heavy loads. Back then in 1981 the bridge was nudging 250 years old. Now that score has reached 286!

Figure 1 That's a piece of new bridge passing over the old Wade bridge in Aberfeldy

The heavy loads were expected to be standard vehicles which were then allowed up to 100 tonnes gross on 5 axles, recently raised from 38 tonnes on 4 axles. I think that the worry was,in a sense, unfounded because agricultural vehicles would certainly haul eg potatoes and grain in full weight wagons. The new load would be Barytes from a mine that was about to be opened. In the even, grain lorries were used to haul it and they were full, taking the gross weight to around 100 tonnes on 5 axles, with a weight balance thrown to the rear of the vehicle, so most likely 3 axles at 25tonnes instead of 8 tonnes.

Anyway, this blog is about engineering bridges and analysis not illegal vehicles.

As we progressed with the monitoring work, it seemed necessary to offer some form of analysis. Then, and now, the standard “analysis” was MEXE. I soon learned that MEXE was not, in any way, an analysis but rather a complex formulation which converted a few basic details about the bridge into a presumed capacity without any real connection with engineering science. The main 18.3m span of the bridge had an expressed ring of 1.5m which is very large the rather smaller side spans had much smaller ”rings”, but the biggest dimension of the stone used was about 600mm. Using a 1.5m ring said the bridge was good for 26 tonne axles but reducing the ring to 600mm was much less encouraging.

I then became aware of Heyman’s work, begun in the 1960s, relating plastic theorems to masonry and offering a calculation scheme that seemed much closer to analysis. He based his work on that of Hooke (the line of thrust, well known in the UK) and De La Hire (check) who had looked at collapse mechanisms. Heyman’s model looked at the minimum arch that would carry a load and looked for 50% spare for security. Like everyone before him looking at bridges, he considered an effective strip to carry the load and adopted that used in MEXE, apparently without question. The spoil fill was treated as dead load only and the structure divided into 12 vertical slices for calculation

My contribution at that stage was to program the system into an HP 41CV pocket computer (to call it a calculator would be an insult. It was about the most powerful portable then available.) The user had to guess the positions where the best thrust would touch the intrados and extrados (henceforth called hinges) so type in say 0, 3, 7, 12 The program calculated moments about each point and worked out the appropriate balancing thrust then computed the offset from the intrados of the thrust at each of 13points with a delay to allow one to rite down the answer. If you were slick, and had graph paper, you could plot the points as they came up. The Hinges would then be moved to the points where the thrust line deviated most from the intrados and the program run again. After typically 3 guesses the result would be consistent with hinges in turn at intrados and extrados of the minimum ring to carry the load.

Then came PCs. A kind HoD allowed me to buy a PC with colour screen and GWBasic and in a 2 week burst I programmed CIRAR which divided the arch into 20 radial segments and applied some modest horizontal pressure from the soil fill. It was still necessary to guess the hinge positions rather than iterating because the calculations took 25 seconds and the user would think the computer had died if you added iterations to that. It did do the plotting though and produced a nice picture on the screen. It was around then I had the idea that we could have a zone of thrust instead of a line. The sort of “one hoss shay” where the arch would be on the point of both crushing and folding.

I showed off the program at a workshop in Edinburgh in 1984 and someone wanted to buy it. Suddenly I was a software vendor. The years went by. The program got refined. Computers got faster. The number of customers grew. People began to ask about viaducts.

And now we get to intuition, which usually needs a trigger. I was doing a lot of travelling then. I remember at the close of a day catching a train from Sheffield to Nottingham and buying a “New Scientist” to pass the time. There was an article that mentioned Occam’s Razor but which, unlike all previous references I had seen, expanded to say it is vain to do with more what can be done with fewer. And I thought… For an arch to get to four hinges it must first go through three. A three hinge arch is calculable. It is the natural stae when the centring is removed. The arch goes into compression and gets shorter and the abutments move apart so we have a shorter arch and a longer span and it must either crack and rotate to fill the gap or flex. Either way, the thrust will go to the extrados near the crown and the intrados near the springing. When a live (concentrated) load is applied the crown hinge will move towards it and at the remote springing the intrados hinge will move up the arch until eventually a fourth hinge forms at the extrados and the arch will fold and collapse.

But the extra load will increase the thrust and cause the piers in a viaduct to move apart slightly compressing the arches each side. In those, the hinges would close and eventually open the other way.

Then I found WHBarlow 1846 in the ICE showing that we cannot know what the thrust really is but we can set limits. And there was the solution to viaducts – we could have whatever thrust we needed from the adjacent span up to the limit where it folded upwards allowing the pier to tip. Too long winded a program, even with the fast computer in 1990, to do the iterative increase bt the picture on screen could respond quickly to manual input and it became a game. Users liked it.

Figure 2 Barlow's model, demonstrated at ICE on 3 Feb 1846 using slips of wood between voussoirs to constrain the position of the thrust.

 

Figure 3 My own model of a single thrust line.

So there we go, intuition, triggered by serendipitous reading.

And then I realised that railway viaducts have solid masonry in the valley and there is more possibility for increasing the thrust (which involves flattening it).

But that was WRONG. Both the original builders and I misunderstood the complexity of the interactions involved.

In 2000, I left the university world and set up as a consultant. I began to see viaducts suffering damage that was obviously caused by load. I couldn’t understand it. But, of course, I already knew that the bridge was more complex than a simple strip and I had begun to realise that the load isn’t (as previously assumed) distributed by the fill into an effective strip but rather the thrust is distributed within the arch from being concentrated under the load to distributed at the abutment or pier. That explains local failures in single spans and some  of the damage in multi spans but not the horizontal cracks appearing in spandrel walls.

I had quite a few pictures of damaged bridges (from earthquakes, bombs and even demolition) where the outer third of each arch remained stuck to the backing after the crown section had fallen but it took far too long to click that this was telling me something important.

Figure 4 London Road viaduct, Brighton, after a bomb took out one pier.

DOH! If the ends of the arch are stuck to the backing, they didn’t drop when the centring was removed and therefore didn’t contribute to the thrust.

And if the thrust is much less than we thought, the capacity for change is also much less. And if you put a load on the end of that solid piece it will rock like a see saw, rotating about a point between the two arches at the top of the solid and above the pier. And the only thing to stop it rocking is its own weight and the stiffness of the spandrel (side) walls.

Figure 5 Section by G W Buck with notes showing how the structure works

The horizontal cracks I was seeing in the walls were at the top of the backing. The walls above were stiff enough and strong enough to work as a beam but the triangle of masonry below was determined to tip and it did. The crack opens and closes on alternate sides of the pier and the arch suffers severe local rotation at the end of the crack. Eventually, bricks fall out. 

And the killer: What produced this sudden damage, was a change of vehicle not a change of load. The two axle 50 tonne bulk hall vehicles were replaced with 4axle bogie vehicles. The spacings changed from 3m, 4m, 3m, 4m, to 1.8m, 3m, 1.8m, 10+m. Suddenly we were putting 100tonnes in a single span and nothing in the span either side. So50 tonnes on the end of a see-saw that might only weigh 200 tonnes to start with. And if two trains passed we got to 100 tonnes on one cantilever.

This is all still intuition. Built from looking at dozens of damaged bridges. But we have measured live load response in a few and it seems to agree with my intuition. Now we need some aggressive testing. Real science where we work out how we might prove the hypothesis is wrong and set about trying. Proving it right is impossible, but engineers work with “right enough for all practical purposes”. What we are using at the moment, my original intuition, has been proved to be not right enough for engineering.

Is it a fair test

Exercised this am by the photo below of a test in a first year Civil Engineering lab.

When I did that test in 1965 Prof Evans came down for the first few minutes and pointed out why we used a lever mount setup with two gauges set diametrically opposite. Lets start with that now:

1)Concrete is not a homogeneous material the centre of stiffness will vary through the length and may be offset to one side.

2) There is no chance that the geometric centroid is exactly centred between the plattens and pretty much no chance that the plattens are directly aligned. See also the discussion of bearings in https://www.linkedin.com/pulse/cross-report-781-quality-design-construction-major-bridge-mc-nulty/?published=t

A quick calc says that, if this column is 50x50x200mm and E is 15GPa and the load is eccentric by 0.5mm and the gauge by 70mm the error in strain will be +-20%. Do check my sums please.

A comment in the discussion on twitter was that "in a data rich world, may need to encourage use of #goodenough data" but that begs the question of what is good enough and I would argue that this is very far from good enough.

If students are not taught to consider eccentricity at this stage, then when will they "pick it up". We talk of transferable skills but in engineering almost everything you learn impacts on almost everything you do.

I have seen people who should know better installing very expensive equipment to measure strain on the underside of a brick arch. Strain is nearly always measured as a surrogate for stress (except in this test where the result is used to make that strain to stress calculation). Measuring strain on one face when you KNOW the stiffness varies through thickness and you don't know the thickness anyway and you don't have a clear idea of the basic force involved means it is

NOT A FAIR TEST

It doesn't tell you what you think it does and that is the worst sort of test.

Some years ago I was asked to assist in pricing a monitoring system for a metal (possibly wrought iron, possibly steel, possibly a mixture) bridge. The main structure was a set of arches built up from plates by riveting. Above the arches was a system of trusses distributing load across the width and they were built from angles riveted to gusset plates by one leg. The spec required one strain gauge on any measured member. The load was eccentric so the strut or tie would bend under axial load but the eccentricity was unknown and unknowable. It also probably varied through the length of the member so the gauge might chance to be at a point of maximum or minimum curvature. Because the gauges had to be fitted and cabled over a river by roped access, the cost of installation per gauge would have been several thousand pounds and the results could not tell you anything useful.

The results were later presented at an Institution Meeting as providing good agreement with a computer model. Great. What does that tell you? You might as well just save the money and believe the analysis in the first place. But you had better make damn sure that an error of +- 100% or so wouldn't matter.

That is not least because even if the structure itself were well modelled, the boundary conditions are completely unknown and they typically effect the stresses by +-100% at least. And yes, I do mean that the actual force in a member may have the opposite sign to what you believe.

In many places, the wonderful plastic theorems provide us with a remarkable degree of protection against these errors. However, they only apply if the structure is capable of redistributing stress till it finds a working load path, and it says nothing about stiffness or cracking.

Today's teachers of engineering are between a rock and a hard place. Their employers place a very low value on teaching. A prof who took ten minutes out every Thursday afternoon to introduce a first year lab would soon run out of support.

Many work hard against the odds to deliver great teaching but it is so so easy to forget that lessons not learnt can be much more deadly than those that are misunderstood.

And let's be clear, I don't get everything right by any means. For 30 years engineers have been using my (wrong) idea about how masonry viaducts work. There is a paper in the ICE Bridges journal about that but it is behind a pay wall which is a shameful thing. I need it to be there but am not allowed to distribute copies. Time to discuss how I can make it more public.

 

Stiffness and Force Flow

Two things in quick succession got me going on this. The first was the IStructE structural behaviour example for October. i will come back to that shortly.

The second was this beautiful sketch of the Mathematical Bridge in Cambridge which turned up on Twitter.

 

The sketch above, compared with the pictures below, looks good but actually, it illustrates how finely tuned the geometry is, earning the bridge its name.

If you look carefully at the photo, each radial goes right through three intersections of tangential members. In the sketch, they often don't quite meet.

If we start with the two each side of the centre we can see fairly well how it works. Trace from the first crossing down in each direction and you will find a straight timber running right back to the stone foundation. These straight compression members provide the stuffest path for loads and will carry most of the weight in that part of the bridge.

Move out another step and the longer strut only just reaches the very top of the stone but that's OK because the other leg is shorter and steeper and will carry more of the load.

Move out to the third radial and we find one of the supports is actually horizontal. There is a sort of goal post with inclined sides. The pic below shows the pieces and how they fit together.

When they are assembled there are suddenly a lot more crossings and its easy to see how the goal post is prevented from swaying sideways. Look at the photo above again and you will see that the radials pass outside the tangential timbers shown above. If you look a little more carefully you will see the same on the further frame. In other words, the radials go up both sides of the tangentials. The radials are actually thicker and halved at each intersection. When the two sides come together the tangentials are sandwiched between.

It really is possible to make this all work without bolts. The bottom end of those radials extends below the deck and forms a frame to stop the "arch" from tipping over sideways. The hand rails across the top tie everything together. It's a thing of beauty both to look at and to think about.

And what about the IStructE Journal?

Well, here is the question.

To me, the most important issue here is that compression and tension members are many times stiffer than bending members. There is a sense that this is acknowledged in all fours possible solutions since the big compression is in the verticals and they are shown bending but not getting shorter.

In A and D the horizontal gets shorter. It has no directly applied force. Those two can be dismissed immediately. That leaves B and C and we have to deal with the bending. With load applied to the top beam as shown it will try to sag as at C but the side columns will hold back the end rotation. B is clearly the answer.

The fact that the columns bend in an S is a secondary effect and doesn't provide a distinction between the two closest possibilities.

 

 

Bridges of Exeter

Some time ago I did a tour of Exeter bridges for the Devon Buildings Group. I put together a set of notes which can be downloaded from here if you wish to make the tour yourself.

If you would like it as an ePub so you can read it on your phone then this link is best.

Some notes on bridge engineering were prepared for a meeting in 2008 and can be downloaded as an epub from here.

 

Related articles

Ground floor stability

The Maidenhead Centre

There are a number of drawings from the Brunel era on display in the ICE library just now. David Greenfield raised a question about this on CEHX. The pictures can't be displayed there so here they are.

Looking at the full picture first, the centre is shown in two halves with a break line jst to the left of the mid span. The right hand section is supported on 3 pies such that 5 would be used for the full span. There is a branching tree support from each pile with folding wedges for adjustment and decentring. This section is drawn in beautiful detail and colour washed.

The left hand section is shown plain but also carries dimensions. I think the dimensions are in a different hand so they raise a number of questions, see below. Also, the left had section has 2 piles for support and is set out so that 4 are needed for the full span. ie there would be four trees rather than three and two bits. Also the base of this frame is much higher.

One question, then, is, is this a drawing showing two alternative centres, or were the two frames used side by side so that 9 plies appear to obstruct flow and traffic in the river?

The dimensions are also interesting. I used Excel to convert them to decimals and plot them. At about the quarter point, the resulting line is about 9in below the semi-ellipse that passes through the springings and the crown. So, is the arch not semi-elliptical at all? Did brunel set out a cusp at the crown? The dimension lines have no arrows to indicate where they are measured from and to. It may be that there is say 4in of lagging above this profile. that would mean that Brunel expected a 7in drop at the crown to bring the rise to 24ft (which sounds more reasonable than 24ft3in). That would also imply a slight rise at the quarter point. I haven't checked that out yet, but it seems to hang together.

The list below gives the setting out dimensions and the elliptical equivalents for the half span.

                                                                       

Chainage	Ellipse	Setout
0	0	0
4	8.438643	7.833333
8	11.73998	11
12	14.13681	13.35417
18	16.86026	16.05208
24	18.93015	18.15625
32	21.00112	20.29167
40	22.48035	21.91667
48	23.47996	23.05208
56	24.0598	23.82292
64	24.25	24.25

French coursing in a skew bridge

Old texts on arches differentiate between British and French coursing in skew arches. The British used helical courses where each stone could fit anywhere, or the bricks could go in uncut, but the courses meet the edge at an angle off the right-angle. In the French system, the courses meet the edges at right angles at the expense of some very complex dressing of stone or even brick.

I have read many times about this "French" system, but never seen it. Thanks to an article by Brian George of PHEW in the latest SW newsletter of the ICE, I now find there is such a bridge only a mile from home. Of course I leapt on my bike and went off with my camera.

The photograph shows how complex these bridges are. This one seems to be a three centred arch with a skew of 51deg and spandrels slightly concave in plan and tilted inwards. The dressed stone voussoirs have beds normal to the edge. The brickwork is fiendishly complicated as you can see in this photo.

This might be compared with bridges where the coursing is actually parallel to the abutments. Something that can only really be achieved with good quality stone cut into long voussoirs. I will look out a picture and add it soon.

A Workshop on Arch Bridge Assessment

Assessment of Arch Bridges is most of my life and has been a pivotal issue for over 20 years. I am endlessly challenged by the difficulty of declaring a capacity for a structure where we know so little about the geometry and understand so little about real behaviour. Arch 04 seems a good opportunity to meet with people with similar concerns, and with those who have solved the problems to their own satisfaction. I have promoted a workshop session intended to be largely discussion. The principle topics I would like to see covered are listed below. You may have others. If so, please add them as a comment, or email them to [email protected] if you wish to be less public.

1)      Why assess: Current capacity, Condition, Damage, New loading regimes

In the UK assessment means certifying a capacity. The levels of judgement required are beginning to be reflected in the rate for the job, but I am sure some engineers have sleepless nights. While the loading regime remained largely unchanged, people were comfortable with low grade tools and relatively light inspections, but that doesn't apply any more. On both roads and railways, vehicle loads and particularly frequencies, have risen inexorably and the effect on bridges is beginning to be visible. In earlier times most structural damage was caused by the environment. Now we are not so sure.

2)      What levels of assessment are recognised

Let's begin by suggesting four:

              Empirical models the prime one being MEXE

              Simple models based on Equilibrium in 2 dimensions

              More complex models including material properties

              3D models using FE

My own concern about working down that list is that the input data available becomes progressively less reliable. The element of judgement is then transferred from relatively simple issues like: Can I treat spandrel walls as a secondary load path which provide me with an additional safety (= confidence) factor, to what adjustments do I make to the measured material properties in order to get reasonable answers.

3)      What models are used for analysis at the various levels

There are a number of models in use in the UK and others currently dormant. It is obvious tat there are many more in other countries and more people should know about them. If you have a model you would like to bring to our notice, perhaps a response to this would be a good place.

4)      How do we assess the significance of defects with regard to capacity and serviceability

Most of the analytical models provide very limited ability to deal with deterioration of the structure. For example, it is simple to deal with general loss of mortar from the intrados, but less easy to consider patch lossess, especially if they are very deep. Comments would be welcome.

5)      How do owners prioritise action in assessment, maintenance and repair

Bridge owners in the UK have largely outsourced the assessment process. They still have to steer the work and prioritise it. Are there tools availabel to help?

6)      Assessment of values material properties and their implications.

This is perhaps the most difficult issue. Measuring properties without invsion of the structure is almost impossible. Are the methods used for assessment particularly sensitive to certain parameters? If so how do we progress with methods for obtaining the parameters economically. Failing that, can we really be sure we are making conservative assumptions?

The more comment we can get to te discussion here, the easier it will be to channel efforts when we meet. Please click the button and add your notes.

Sorry it has taken so long to get this up.

Bill

Assessment of arch bridges

Is arch bridge assessment an art or a science? How closely can we predict the limits of servicability? Does the speed or frequency of loads have an effect? How are loads distributed in arches?

I will add some further comment here in the next few days, but this is designed to open a thread of discussion in the lead up to Arch 04, the arch conference in Barcelona on 17th to 19th November.

Damaged arches

Time I was back, and here are some pictures I thought I had lost. They will be the start of a public collection of notes on arch bridge damage.

Let's begin with North Bridge, Doncaster. These photos could not be repeated because the bridge has been reclad since they were taken.

The drop shown here is of long standing and is typical of what happens to bridges on flood plains. the fence posts bolted to the brickwork emphasise the drop in the middle of the first span. Obviously the posts were set out off the brickwork, because the fence has been smoothed through.

The same bridge exhibited this strange condition. It is quite unusual for Staffordshire Blues to deteriorate in this way. the fact that it is very local gives a clue to the fact that a tanker of very nasty chemicals had a crash on the bridge. Note hw the damage is localised. theere is a clear line at the bottom, where the chemical settled on to the backing and came out through the side.

The twisted arch at Randalholme is really very unusual. When it was first described to me I thought it must be a square bridge with walls introduced on the skew later but that doesn't seem tobe the case. can anyone offer a clue as to why it should be built like this?