arches

The what and why of arches

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.

Guyue Bridge

 

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).[2][3] 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.[2] 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.[2][3] 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.