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- เผยแพร่เมื่อ 20 มิ.ย. 2019
- Flying buttresses are a necessary part of medieval cathedrals. We can understand them using basic ideas from statics. They were needed because the builders wanted to have large open spaces inside buildings that are made from stone and stone is only useful in compression. Flying buttresses hold up thin, high walls and allow the interior spaces to be open.
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It's been 12 years since I've been in your class (boy do I feel old), but I'm really glad you make these videos. Feels like I'm back in your classroom again! Thanks!
How nice! Thanks :-)
This is a cool, simple explanation. I googled "How high does a building need to be to require a flying buttress and this video popped up" It doesn't answer the question exactly but the general terms are nice.
Showing the bowing out of the structure just made all the pieces fit together in my head.
Man were our ancestors clever
Thank you for the lesson in flying buttresses. Straightforward and very well presented. Much appreciated.
@4:51 and following: "Historically, they may have collapsed. They didn't have any math. They couldn't describe what they wanted to do mathematically. They had to try things. If you go back in history, it wouldn't surprise me if some of these things collapsed early on."
They _did_ have math (Euclidean geometry, mainly), but not much in the way of computational math other than sums and differences (and most of that done with Roman numerals rather than "ciphers" - Arabic or Indian numerals that we used today; zero notation would have been nonexistent, so no place value notation, as such). However, basic geometry was an empirically sufficient mathematical basis, given the historic record.
Some buildings did indeed collapse "early on" (during construction or shortly after completion). Sometimes, modifications (the late addition of a hubristically large crossing tower, for instance) might cause excessive loading of columns or foundations which were originally built for lesser loads, leading to damage or even collapse. Not a few buildings or parts of buildings collapsed after foundations subsided due to changing water table levels or destabilizing adjacent construction. Moisture ingress, due to poor detailing or inadequate maintenance, and the subsequently ensuing frost heave sometimes split walls apart, leading to local failure. The chaos of the French Revolution probably destroyed as many such structures as any other single cause, and no amount of design or engineering could avert _that_ mode of failure.
The problem of designing large clear spans for construction in stone was approached as a geometry problem, not a strength of materials problem. The compressive strength of stone is rarely less than 10X the nominal loading, even in very highly loaded members, e.g. the crossing columns supporting the aforementioned keeping-up-with-the-Jonses crossing tower (small imperfections of stereotomy or construction may increase the actual loading, locally, above the nominal calculated load). In most parts of large structures, loading is more like 1/20th to 1/50th of the compressive strength of the stone, i.e. the strength of the stone is effectively infinite for any reasonable size of structure (even mud brick or compressed earth block structures can be safely built several stories high).
That being the case, the proper geometry, selected to ensure compression-only loading, was sufficient as a design criterion, and strength of materials considerations could be safely ignored. The proper geometry (and a safe assembly procedure) could be proven out by carefully constructed stereotomically correct scale models. Plans for an existing building (thus known to be stable and safe) could simply be scaled up (down) to make a larger (smaller) version. Acceptable proportions were codified as rules of thumb, easily remembered and reconstructed elsewhere by Euclidean geometry using string, compass and straight edge. Later, hanging catenary scale models were sometimes used (most extravagantly by Gaudi, for Sagrada Familia and Parc Guell), then sketches or photos made of the purely tensile shapes of those models so that the compressive lines of force when inverted could be properly surrounded by structural material (the "middle third" rule was commonly used - i.e. keep the line of thrust within the middle one third of the thickness of the vault). Beginning in the mid-1800s, graphical statics slowly became a more common method of finding the lines of thrust, rather than constructing physical scale models.
Today, there are computer models being developed to help architects and designers to specify compression only structures for various complicated load cases. Philipe Block's "Thrust Network Analysis", developed when he was a PhD student at MIT (he's now at ETH Zurich), brings James Clerk Maxwell's graphical statics from the two dimensional drawing board to three dimensional digital space. One implementation of TNA can be had as a plug-in for Rhino 3D.
For anyone interested in a more academic approach to the topic, Jaques Heyman's translation (with his own commentary added) of Coulomb's "Memoir on Statics" is a good start, or his book "The Stone Skeleton". Santiago Huerta has written many articles analyzing historical structures and medieval building theory in light of modern engineering knowledge, the vast majority of which articles are open access.
All of this is to say that the architects and engineers of the past were pretty clever, and were able to do things that we would be hard pressed to replicate today, even though we may have a better theoretical understanding now of what they did back then, when the only math they had available was constructive geometry. The daring of some of these people was astounding, building structures which could never be approved today, but which have stood for hundreds of years.
I'm a Civil Engineer from Pakistan graduated in 2020. Sir I was lucky to find your channel in 2016 and learned a lot from you during my degree and still learning. Allah bless you
the arch underside of the flying buttress would aid in not tipping the post over by shifting some of the compression inward alongside heavy weight
very well done- thank you for giving context the entire time as well
Loving this, thank you! Very professional and well articulated.
5:55 that's exactly what we've lost as a species, the ability to see the big picture. We've spent so long trying to find the miniscule, the infinite, that we've lost sight of existence itself. That's why things like the pyramids confound us because we could never imagine a project so massive.
Except the pyramids were made for specific individuals in a matter of years or decades, not centuries. And humanity has made many similarly massive and far more complex structures, like dams and bridges spanning tens of kilometres, or tunnels under mountains. No one person conceived and built these things; they were group efforts to serve society for the next 100 years, or more.
Sacred geometry.
True. Probably built over places of significance to channel energy or something
I really enjoyed the video!
Thanks :-)
Yes, Professor, I agree that "statics is the most useful class ever" (right after typing class in high school); but, 34 years after teaching Statics (as a graduate assistant), I still look at almost everything as a statics problem! (I guess if all you have is a hammer, everything looks like a nail, eh?) Love your videos.
Thanks very much. Statics was the class that made me feel like I was on the way to becoming an engineer. As I think about it, that was 37 years ago. Yikes.
This video was great. I went by a gothic cathedral (decorative gothic style) on my way home so I wanted to learn about it's design.
I'm glad the video helped :-)
They had no technology? They had no math? You've got to be kidding me. You're describing the cutting-edge technology and math of the time!
Thank you, Sir.
Very inspiring video.
Thanks, I hope these videos are helpful to you :-)
Those are not posts outside the structure. Those are called external pier buttresses. What you define as "flying buttresses" are not exactly drawn. Your drawing conflates the curves of the lower interior side aisle bays that are under the side roof with the flying buttresses. Flying buttresses, to be exact, are composed of a vertical external buttress pier (this can extend outwards or be detached from the lower wall) and an upper arch that spans the top of the external buttress pier and points of outward stress between windows in the upper clerestory. The flying buttresses are placed at equal distances along the length of the structure. Internally, the spacing of flying buttresses correspond to the elongation of compound piers upwards into the clerestory zone. *But* flying arches are not buttressed by other flying arches on the lower half of the structure (the arches never hit the ground) in a continuous line....vertical buttress piers (your posts) do repeat, but not as a bracing element of one another...instead down the length of the structure equidistantly. In later Gothic structures, the upper arches that fly can be divided into two smaller arches with a pinnacle between them, but still on one vertical buttress pier that runs straight from the highest point to the ground. So, I'd say medieval masons did have a great deal of technological and mathematical knowledge.
I’m going to have to crack open a cold one and do some architectural research guided by your detailed post. Thank you ma’am.
@@ibelieveicansoar You're most welcome!
Thank you so much for this , it really did help
Great video👍
I have yet to see a buttress fly, to me they are just buttresses and fliers. Later high French Gothic Cathedrals also used (hidden) iron elements such as links, rods, and chains to resolve the forces in the walls and fliers, for instance, at Amiens. The most famous collapse of an HF Gothic Cathedral did not come in the earlier period but in the later period, a flamboyant period of ever-increasing asperations. When Beauvois cathedral's choir ceiling crashed down so did the confidence and flamboyance of gothic designers and builders, in many ways, it was the end of an era. Beauvois Cathedral had the highest ceiling of any gothic structure at over 150 ft. It is far too complex to discuss here, but even today the reasons for the collapse of the choir ceiling are contested , but like many disasters, there were probably a number of contributing factors combining together, including high order modal resonance of the fliers caused by high winds, Tacoma Narrows anyone It still exists, unfinished, and damaged, but about to undergo a major preservation project. It is extraordinary, visit it if you can.
BTW.
The name gothic was an insult bestowed on these great structures during later periods.
Hello! I'm an architecture student. i have a question, can flying buttress be used to hold weights of a building or a castle second floor? the whole point is to avoid using columns on the inside and using neo gothic and baronial style architecture elements
Didn't have math?!?! They had a very high understanding of higher math. They had a very good understanding of math a thousand years or more before the construction of these flying buttresses. Capernacus,Newton, Pythagoras,and on and on
Thanks Sir
Simply good and good
Thanks a lot 😊
can you elaborate the point you said at 7:00 about reaction force … Thanks for your videos
The myth that cathedrals took centuries to build is really a... myth... They did take a long time to build, around 60 years, which was about the lifespan of the average adult at that time. Why some of them took so long to build was because construction had to be sometimes halted for a multitude of reasons. For example the cathedral at Köln Germany was officialy under construction for 632 years, but it includes a lot of dismantling and rebuilding, and a 300 year pause.
Thank you for the homework help :)
Have you read Pillars of the Earth by Ken Follet? my favourite book.
I recently bought it, Hows it?
Hehe butt