arches

I was just listening to a podcast from January in which there was much discussion of science being only the best explanation we have now. In fact, being a process rather than a pattern of knowledge.

I am an engineer as you see below. I believe that engineering is different from science, but relies upon it. Some people trained as scientists work as engineers and some universities used to teach what they called Engineering Science, though very few do now.

This microcosm of society provides an interesting study in the establishment of fields of "knowledge" that turns out not to be. Engineers often have massive emotional (and economic) commitment to their established knowledge and so resistance to admitting of changed views. I know that the same is true in science but there is a great community of relatively low level engineers who understand that if their "knowledge" proves to be wrong, peoples lives may be at risk.

My particlular interest is in masonry bridges. One might think we understood them thoroughly after all this time but there is one of the differences between engineering and science. Sometimes you cannot know and therefore have to build systems of protection against the lack of knowledge. Sometimes, though, the knowledge becomes deeply ingrained and even written down in codes of practice which are deemed to be correct. If your design can be shown to satisfy the code you cannot be blamed for failure.

But what if the code is wrong?

Through the enlightenment, the division between engineering and science shifted. People made machines and structures before that but they did it based on established practice and sometimes courage then trial and error. Some of the work of Peter Parler, the imperial mason, in Prague shows spectacular invention but it wasn't limited to him by any means.

Robert Hooke and Christopher Wren were polymath scientists. Both practised as architects. Indeed they shared a practice as architects as well as working independently. In their day, architects were structural engineers. As scientists they had to defend their engineering and it took them considerable effort to discover a way to understand arches. In particular t calculate the abutment needed, or buttress if you will, in the new churches they were building.

Around 1900, Castigliano, a railway engineer, invented a whole new "science" of structural behaviour delivering a new analysis of arches. But railway loads were still small compared with the weight of the bridges and in any case bridges aren't just arches.

Things came to something of a head with the introduction of tanks in the first world war. A general couldn't afford to see maybe 5 or 6 tanks get across a bridge and it then fail, leaving his strength isolated and readily destroyed. The RE couldn't help immediately but over maybe 15 years, work was done to turn Castigliano's efforts into something useable in anger.

They recognised that bridges were complex and did some real tests to calibrate things. They found, but didn't recognise, that the behaviour is inescapably three dimensional and proceeded to create a two dimesnionalising model of an effective strip. That effective strip model is demonstrably wrong but how wrong only became obvious when railway axles reached 25 tonnes and damage started to appear where the assessment tool (the code) said it shouldn't.

The trouble is that engineers still cling to the code. One valid comment is that until we have something better we can’t let go of our only support. But something better needs paying for and if money is not made available for that where do we get to?

Bridges are failing. The engineers in the field map the failure onto their codes and treat with established solutions which are unlikely to work in the longer term. Maybe nothing will happen till a bridge actually falls down under a train.

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.