The Italian approach: ribs, coffers, and The Spanish ... · 2014 SRA took out Dieste to give him...
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THEMES The German approach: analysis and geometry The Italian approach: ribs, coffers, and buttresses The "Spanish" approach: double curvature and thinness Concrete shells and stiffness Economy of labor vs. efficiency of materials Complexity of analysis vs. complexity of form
Transcript of The Italian approach: ribs, coffers, and The Spanish ... · 2014 SRA took out Dieste to give him...
THEMES
The German approach: analysis and geometryThe Italian approach: ribs, coffers, and buttressesThe "Spanish" approach: double curvature and thinnessConcrete shells and stiffnessEconomy of labor vs. efficiency of materialsComplexity of analysis vs. complexity of form
2014 SRA took out Dieste to give him more attention in place of Maillarts buidlings in with Isler.
Edited by SRA Sp06, should be expanded back to two Eladio Dieste added and Candela-Torroja/Gaudi church comparison deletedConsider making into two.Also, don’t denigrate analysis, denigrate being trapped by analysis.Add intro. to explain why “roof vaults” is a sep. category. i.e., long-span roofs are more like long-span bridges in their necessity to be pure structure (as opposed to buildings) and “roof vaults” begins the evolution of modern stadiums, convention centers, etc.Consider pulling Dieste, or putting him right after Gaudi – his forms though later in time speak more to a time before Torroja and Candela’s RC forms..Sanjay discussion – consider pulling Gaudi or doign only the school house and getting right into spanish forms...
Sp 2008This lecture is still pretty disorganized but I propose taking it back to 2 lectures. Lecture 1 German and Italian, Lecture 2 Spanish.I have integrated back in the best of DPB lecture material (earlier we cut some nice Nervi discussions)This is still very much a work in progress.
SP 09Some structural themes to perhaps focus on:1. The edge of the dome. This has similarity to the transfer girder problem in tall buildings and has two parts. First, how is force transferred and second how is stiffness provided.2. Gaudi is able to make highly asymmetric forms that are nonetheless responsive to the structural forces.
Agree that this should be split for next year. Too many important characters crammed into one lecture. This will take real work. This year I have trimmed out some material to put some think, pair, share exercises in.
11-01 san diego hangar_150dpi.jpg
Illustration of the german national style where forms, such as the barrel vault, are derived from scientific-type theories.
11-03 nathaniel leverone field house_150dpi.jpg
Illustration of the Italian style derived from the ribbed vaulting in Roma and Renaissance domes and vaults.
11-02 xochimilco restaurant_150dpi.jpg
Illustration of the Spanish style derived from an old tradition of Catalonian tile vaulting and strong forms with double curvature
The German tradition, best illustrated at the firm of Dycherhoff and Widmann would develop practical construction techniques in-line with mathematical advances to produce new and lighter domes. Three generations of engineers would show the way for the German tradition of thin shell construction.
11-09 dome force distribution_150dpi.jpg
illustration of meridian and hoop forces in a dome under gravity loading. Note meridians are in compression, but hoops vary from compression in the top to tension hoops near the bottom.
11-11 jena planetarium construction_150dpi.jpg
Dischinger preferred relatively simple forms that could be analyzed using membrane theory and the advanced of the time (by Geckler) to understand the bending that invariably developed near the supports.
(membrane theory is a specialized version of shell theory that provides the solution for internal forces in shells when due to loading, and/or shape, and/or boundary conditions only forces in the plane of the shell exist – no bending – such membrane forces can readily be designed with a minimum of material, as opposed to bending which requires significnat material to be resisted).
Built after WW I, Dischinger devised a way of building concrete domes (for Planetaria with the Zeiss Optimical Company) by spraying concrete on a reinforcing cage already erected. In this dome the steel takes the tensile stresses that develop. This was an efficient and profitable system widely used in Germany.
11-12 leipzig market halls_150dpi.jpg
Dischinger’s first large domes were the leipzig market hall. Polygonal in shape with slender ribs stiffening the junctions of the pie-shaped sectors.The market hall, Leipzig Germany 1929, Franz Dischinger. Each of these 76m span polygonal domes was only 1/3 the weight of the 67m span Breslau dome of 1913 – then the longest spanning concrete dome. The lightness was possible because they were designed as thin shell surfaces. The shape came from the math.
Billington says Centennial Hall in Breslau in his Thin Shell book, but the archiotect was from Breslau and the dome is actually in Poland. Further clarification: Breslau is the Germanized version of the city name Wroclaw, which has a very odd pronunciation, kind of like ‘vruswav’ Poland was probably under German control when the dome was designed and built, so Billington uses Breslau, but it is certainly correct, and better sounding to Poles, to call is Wroclaw today.
11-12 leipzig market halls_150dpi.jpg
Dischinger’s first large domes were the leipzig market hall. Polygonal in shape with slender ribs stiffening the junctions of the pie-shaped sectors.The market hall, Leipzig Germany 1929, Franz Dischinger. Each of these 76m span polygonal domes was only 1/3 the weight of the 67m span Breslau dome of 1913 – then the longest spanning concrete dome. The lightness was possible because they were designed as thin shell surfaces. The shape came from the math.
Billington says Centennial Hall in Breslau in his Thin Shell book, but the archiotect was from Breslau and the dome is actually in Poland.
Excerpts on Centennial hall from unesco world heritage web site: (http://whc.unesco.org/en/list/1165/)
Brief DescriptionThe Centennial Hall (Jahrhunderthalle in German and Hala Ludowa in Polish), a landmark in the history of reinforced concrete
architecture, was erected in 1911-1913 by Max Berg, at the time municipal architect in Breslau, as the Polish city of Wrocław was called at the time, when it was part of Germany. The Centennial Hall, a multi-purpose recreational building, is a centrally-planned structure situated on the Exhibition Grounds. The structure of the Centennial Hall is a symmetrical quatrefoil form with a vast circular central space (65m diameter, 42m high) that can seat some 6,000 persons. The 23m-high dome is topped with a lantern in steel and glass. The windows are made of exotic hardwood and, in order to improve the acoustics, the walls are covered with an insulating layer of concrete mixed with wood or cork. The elevations have no decoration or ornament, but the exposed concrete texture is marked with the imprints of the wooden formwork. ...The Centennial Hall is a pioneering work of modern engineering and architecture, which exhibits an important interchange of influences in the early 20th century, becoming a key reference in the later development of reinforced concrete structures.
11-19 frankfurt market hall_150dpi.jpgLine drawing from Billington Thin Shell Concrete Structures pg 15 2nd ed. fig. 1-9 Wholesale Market in Frankfurt
Finsterwalder, whom we met earlier as pioneering cantilever construction methods in pre-stressed concrete designed some of the first reinforced concrete barrel shells. He actually was one of the pioneers (subject of his PhD) in the mathematics that extended thin shell theory to barrel vaults.
He used deep longitudinal beams and deep transverse diaphragms to transfer loads to the corner columns.
Membrane theory demanded that the ending edge be vertical or severe bending would ensue.
11-20 barrel shell geometry_150dpi.jpg
The Germans (e.g., Dischinger, and Finsterwalder) focused on simple shapes, like domes and barrels with stiff supports (e.g., the diaphragms) designed specifically such that mathematical theories could be used.
I cut the following slide that showed the governing equations because I don’t think it adds much other than some ‘wow that is complicated’ factor, and I can’t explain it except in the most general terms.
11-21 barrel shell mathematical formulation_150dpi.jpg
“German” mathematical formulation for barrel shell. Here we see the membrane theory a simplified shell theory that ignores bending. The solution has been assumed, and a function (a geometry) is sought that separates x,phi,z.
11-22 us army warehouse barrel shells_150dpi.jpg
Tedesko with the dome and barrel vault would bring thin shell construction, in the German style, to the U.S.Such mathematical ideas when brought to life suggest somewhat unintegrated and strange forms. Here we see Tedesko’s 1941 US army columbus warehouse. The top equation in the previous slide suggested a solution using separation of variables that is brought to life in the structure above. The barrel carries loads long., and then the frame carries the loads horizontally. Note the four transverse units and MANY long unites.
11-23 ribless barrel shell tests_150dpi.jpg
Tedesko would go beyond the German tradition, and in the best traditions of structural artists learn from his earlier works and training and evolve his own style. Tedesko’s dis-satisfaction lead him to load test a roof that eliminated the heavy frames, and instead gradually thickened the shell where necessary – here shown in a 1950 load test.
11-23 ribless barrel shell tests_150dpi.jpg
Tedeskos ribless vaults are also much flatter than the true barrels of Finsterwalder
11-24 ribless barrel shell warehouse, middletown, pa_150dpi.jpg
Tedesko in the mid-1950’s went on to build a ribless warehouse that was both economical and efficient, demonstrating a clear improvement in form from his earlier solution.
11-25 barrel shell hangar, san diego_150dpi.jpgTedesko showed a similar evolution of form – from heavy arches such as that shown here in the 1941 San Digo hangar to 11-26 barrel shell hangar, rapid city_150dpi.jpgTedesko’s 1948 Rapid City Hangar shows arches that are much reduced because the shell roof is now carrying much more of the load. The underlying point here is that Tedesko achieved a better form be understanding how the shell could behave physically if the design was not restriced to fulfilling just those conditions which meet a mathematical solution.The German tradition may fail to provide a tight integration of form raising it to the level of high class structural art, but it is economic and efficient and should still be considered successful – especially compared to shell structures which follow no tradition.
11-25 barrel shell hangar, san diego_150dpi.jpgTedesko showed a similar evolution of form – from heavy arches such as that shown here in the 1941 San Digo hangar to 11-26 barrel shell hangar, rapid city_150dpi.jpgTedesko’s 1948 Rapid City Hangar shows arches that are much reduced because the shell roof is now carrying much more of the load. The underlying point here is that Tedesko achieved a better form be understanding how the shell could behave physically if the design was not restriced to fulfilling just those conditions which meet a mathematical solution.The German tradition may fail to provide a tight integration of form raising it to the level of high class structural art, but it is economic and efficient and should still be considered successful – especially compared to shell structures which follow no tradition.
Think pair share on this.
The approach is mathematically determined geometric forms.
It could (falsely?) provide great confidence to the designer since exact expressions for the response are available.
It is limiting because there are a fairly small number of forms that can be analyzed exactly.
The Italian tradition, in part, traces to the Pantheon and other structures and the use of ribbing in the dome structure.
11-36 nervi hangar_150dpi.jpg
Nervis barrel vaults for the Italian air force direct the forces by ribs which make a lighter roof structure and one which is more expressive.
Nervi was a builder as well as a designer – just like Maillart, Finsterwalder, Freyssinet and others. His airport hangars were made from prefabricated pieces.The prefabricated pieces could then be assembled on site, and a simple roof added – in this case tile.
As Nervi put it, his early experiences “had formed in me a habit of searching for solutions that were intrinsically constructionally the most economic, a habit which the many succeeding competition tenders (almost the totality
of my projects) have only succeeded in strengthening.” T&B pg 178
I have removed the following three slides of Nervi’s Florence stadium roof. They don’t seem to fit with the dicussion of his ribbed domes, even though they are very nice shells. They get shown very briefly in comparison to Candela later on. SRA 2009.
11-28 italian air force hangar_150dpi.jpg
Italian style. Nervi is designining airplane hangars as well. (Nervi above, Tedesko below) Nervi would say structures “can only be solved correctly through a superior and purely intuitive re-elaboration of the mathematical results” – Nervi clearly intends to contrast himself with the Germans.
The key visual/structural difference is how few supports are needed for the Nervi roof, in which the structure is a cohesive whole instead of a repeated unit cell
photo by ArwadeNervi’s predisposition for ribbing comes, in part, from the ancient Roman tradition such as in the Basilica of Constantine25m barrels 50m high!
AD 313
11-45 little sports palace _150dpi.jpg11-43 little sports palace supports_150dpi.jpg
Nervis purest dome structure is the 1937 Little Sports Palace in Rome
11-44 little sports palace_150dpi.jpg
Nervi’s little sports palace was built out of precast diamond shaped pans
11-46 little sports palace construction_150dpi.jpg
Note the precast diamond shapes pans
11-47 little sports palace construction_150dpi.jpg
Pans used to form the underside of the Little Sports Palace
11-35 nervi hangar construction_150dpi.jpg
Molds for making the prefabricated RC pieces that would form the structure for Nervi’s hangars.
11-49 little sports palace construction_150dpi.jpg
The diamnod shapes pans were placed on scaffolding and then a smooth roof was cast on top
11-51 little sports palace interior_150dpi.jpg11-73 small sports palace skylight_150dpi.jpg
Inside we get a sense of the structure Nervi was creating.Nervi would say structures “can only be solved correctly through a superior and purely intuitive re-elaboration of the mathematical results” – Nervi clearly intends to contrast himself with the Germans.As Nervi put it, his early experiences “had formed in me a habit of searching for solutions that were intrinsically constructionally the most economic, a habit which the many succeeding competition tenders (almost the totality of my projects) have only succeeded in strengthening.” T&B pg 178
12-01 little sports palace roof interior_150dpi.jpg
the diamond shapes form together to provide the appearance of two way ribbing and provide a nice pattern as well.
Nervi structures at Dartmouth, photos by Arwadeice arena
Nervi structures at Dartmouth, photos by Arwadeice arena
Nervi structures at Dartmouth, photos by Arwadeice arena
TPS on this.
1. Diamonds v. triangles, curved v/. straight lines2. It would be great if someone came up with 2-way v. one way action.
11-60 saint mary's cathedral_150dpi.jpg
At the Saint Mary’s Cathedral in San Francisco Nervi was the structural engineering consultant, but here his ribs will not express structure.
11-61 saint mary's cathedral_150dpi.jpg
The interior of the cathedral shows the ribs as a sort of decoration.
The thin ribs just stop as they run into a massive wall. Nervi, outside of Italy, has much less expressive possibilities – partly because of different labor conditions and partly because of architectural opinions – where designers make the form first and then get Nervi to make the stand up (I.e., those on the opposite side from Viollet-le-Duc)
11-13 basel market hall_150dpi.jpg
Here we see another market hall, the inside of Basel, note that the roof is supported by colums and heavy horizontal transfer beams. This is reminiscent of F Kahn’s first attempt to deal with the column demand at Plaza level (Brinswick) where he used a deep transfer beam.
11-14 column-supported dome stress trajectories_150dpi.jpg
Need for deep transfer beams at the base can be overcome by internal reinforcement based on the trajectory of forces – but it is lifeless because we see no transition visually.
11-15 los angeles dome_150dpi.jpg
The result of using only internal reinforcement to handle the flow of forces are illustrated in this small dome in LA – with its “lifeless” appearance.
11-16 little sports palace_150dpi.jpg
Contrast this with Pier Luigi Nervi’s Little Sports Palace which (1) use Y-shaped buttresses and (2) small undulations in the dome edge to express the transition between the dome forces and the concentrated, isolated, support reactions.
TPS
1. wwrinkling at dome edge, Y-shaped buttresses, colors2. wrinkling provides stiffness, Y-shape provides redundant load paths
The German ribs are gone, as are the Italian’s more subtle ribs, buttresses are removed too.
12-06 stone and tile vaults_150dpi.jpg
Catalan tile vaulting styles can be much lighter than traditional brick vaulting (A above)
12-24 sagrada familia school_150dpi.jpg
the doubly curbed surface is stiffer than the signly curved barrel vaults. T&B 1984 – this doubly curved form was “of a higher order and greater complexity than [usual forms] of the midle ages whih were being revived at the time.”
12-22 sagrada familia school roof_150dpi.jpg
Gaudi’s most approachable structure is a little parochial school house next to the towers at Sagrad Familia which Gaudi designed with a doubly curved saddle shape roof in tile!
12-23 sagrada familia school diagrams_150dpi.jpg
it can be erected using straight lines (important for tile!) easier for concrete too.
www.structurae.deExpiatory Church of the Sagrada Familia Photo by Nicolas Janberg Gaudi’s most monumental work was the Sagrad Familia,Towers at the Church for the holy family, Barcelona. only very partially completed. To have any hope of understanding these forms we should back up to Gaudi’s earlier work/training ground.
12-08 colonia guell chapel_150dpi.jpg
Between 1908 and 1915 Antonio Gaudi completed the crypt and porch of the Church of the Colonia Guell, just outside Barcelona, where he used a tile roof in the ceiling in the form of hyperbolic parabaloids. He also designed the columns to line up with the internal forces so that they could be built of stone without bending.
12-11 colonia guell chapel interior sketch_150dpi.jpg
method used by Gaudi for exploring formsHe then drew his design from the photo – on both the inside
12-13 colonia guell chapel_150dpi.jpg
Thusly he gave his designs their form – here we seen to colonia guell chapel
12-14 colonia guell chapel_150dpi.jpg
Gauid’s model design gives a good approximation of the correct for, but is not purely the right direction for reinforced concrete – as we shall visit in later lectures.The church was never completed only the crypt and the porch.
12-17 colonia guell chapel_150dpi.jpg
structural support comes from leaning columns
12-18 colonia guell chapel_150dpi.jpgstructural support comes from leaning columns the undulating walls are also in tile and are hyperbolic paraboloid.12-19 colonia guell chapel_150dpi.jpgstructural support comes from leaning columns
Gaudi wished to build something that looked like a part of nature in the sense of materials and forms.
Gaudi designed in stone – those taking up his tradition in modern materials would provide similarly striking solutions – first with Torroja
12-27 zarzuella racecourse_150dpi.jpg
Torroja explored vaulting using RC and created his masterpiece in 1935 the Zarzuela Hippodrome roof cantilever roof shells for the dog racing track outside of Madrid.The shell is 2 in. thick at the free end! 5.5 in. thick at the crown. Roof suffered 26 holes in the Spanish Civil War, without collapse.
Torroja v NerviHippodrome v Florence Municipal
12-32 zarzuella conoid shell_150dpi.jpgThen he began to study the cantilever shell – he found a pure conoid with a horizontal edge to be unappealing
12-33 zarzuella hyperboloid shell_150dpi.jpgA partial conoid gave a curved free surface at the edge
12-34 zarzuella roof_150dpi.jpg
Torroja presented his design evolution – but wanted it known that it was neither purely rational or purely imaginative “but rather both togetehr”
Photo credit Albert Sanchez, UMass student
And a note on durability of concrete.
Stadium outside Tikrit Iraq, 2004
12-36 tachira club model_150dpi.jpg
Torroja had quite a nice lab where he tested his different vaulting ideas.
His careful testing would greatly influence Isler (that waits for a nother day)
12-40 algeciras market_150dpi.jpgThe Algeciras Market Hall is another of Torroja’s famous works., this dome, supported on only 8 columnsMeridonal forces within the shell are carried to the columns through separate edge barrel shells.which transfer nearby horizontal forces to the column topsThese horizontal forces must be taken by polygonal tension ties
12-40 algeciras market_150dpi.jpgThe Algeciras Market Hall is another of Torroja’s famous works., this dome, supported on only 8 columnsMeridonal forces within the shell are carried to the columns through separate edge barrel shells.which transfer nearby horizontal forces to the column topsThese horizontal forces must be taken by polygonal tension ties
12-45 algeciras market_150dpi.jpg
Torroja used extra edge shells and tension ties to carry the forces that Nervi put directly into his butresses.Both solutions are efficient and economical, both meet our criteria for contemplation and affirmation as structural art, but they are VERY different.
12-45 algeciras market_150dpi.jpg12-46 xochimilco restaurant diagram_150dpi.jpg
12-03 xochimilco restaurant_150dpi.jpg
Spaniard, Candela, ribless – single form integrated right down to the foundation
12-47 xochimilco restaurant construction_150dpi.jpg
Felix Candela continued the Spanish tradition after being forced to leave Spain after the civil war.Candela’s structures are mostly in Mexico, here we see his favorite the his favorit at Xochimilico (1958), made of eight hyperbolic-paraboloid vaults. 1 5/8 in. thick shell.In 1954 he was invited to an MIT conference on thin shells (Kresge would be complete in 1955), Candela from T&B pg 189 “having arrived with a complex about the prestige of the place and the numerous experts gathered there, I suddently found that I was somewhat ahead of the experts myself.”
12-52 hyperboloid paraboloid_150dpi.jpg
Candela’s discovery of the joys of the hyperbolic parabolid lead him to make many of these structures.
12-60 hyperbolic paraboloid sections_150dpi.jpg
From the hyperbolic paraboloid one can isolate other shells – such as the cantilevered shell and the warped plate
12-53 cuernavaca chapel_150dpi.jpg
12-54 cuernavaca chapel_150dpi.jpg
One shape he used is the saddle here for the Cuernavaca Chapel
12-60 hyperbolic paraboloid sections_150dpi.jpg
From the hyperbolic paraboloid one can isolate other shells – such as the cantilevered shell and the warped plate
12-55 oslo hypar_150dpi.jpg
Another shape is the groined vault – such as one on three supports here in Oslo
12-60 hyperbolic paraboloid sections_150dpi.jpg
From the hyperbolic paraboloid one can isolate other shells – such as the cantilevered shell and the warped plate
12-61 umbrella warehouse diagram_150dpi.jpg
The warped plate can easily be built on straight line form boards.
12-62 umbrella diagram_150dpi.jpg
Four such plates put together form an inverted umbrella
12-63 experimental umbrella_150dpi.jpg
Tested by workers such a structure proved quite strong.
12-64 great southwest corporation insignia_150dpi.jpg
This shape was Candela’s bread and butter serving for sculpture
12-65 umbrella construction_150dpi.jpg
Mostly though, serving as a very inexpensive industrial roof
12-66 umbrella construction_150dpi.jpg
TPS
1. Gaudi used model building, Candela used mathematical forms and repeated, but relied on two way action unlike the Germans. (Did Candela have exact solutions for the response? I.e., was he mathematical in form choice but not in analysis? Or both?)
2. Gaudi was forced to avoid all tension since he built in unreinforced masonry. Candela’s shells also necessary must be compression structures but could be dramatically thin since small amounts of reinforcement were available for local bending (hmm, is this true? Aren’t the Guastavino vaults very very thin without reinforcement? Gaudi’s school roof also? need to think about this more.
11-62 kresge auditorium, mit_150dpi.jpg
The Kresge auditorium at MIT – where a sphere was designed to be supported at 3 points is the best known US shell design built in the spirit of Viollet-le-Duc’s detractors. The from came neither from mathematical solution of simplified membrane theory for shells, nor from experiments, models, and experience of a designer. Rather the idea is to just have a nice shape in disregard of structure.Architect: Eero Saarinen, Engineer: Amman and Whitney
11-63 kresge auditorium construction _150dpi.jpg
Looking at the construction we can already see how the stiffening rings, or hoops, are effectively cut off everywhere except at the top. Therefore, the resistance of the roof to bending is largely lost in the large triangular segments below the hoop termination.
11-64 kresge auditorium, mit_150dpi.jpg
The roof has moved, broken up roofing, and even before completion heavy struts had to be added to carry the weight so now
11-65 kresge auditorium, mit_150dpi.jpg
the ungainly hinges serve really only as drainage, and a convenient location for the leaching out materials from the concrete.
11-67 cnit_150dpi.jpg
The form did not come from any manner of structural ideas or traditions. Coming purely as a geometric form it is an abject structural failure and a nice reminder that even at MIT things don’t always go as planned.Contrast to this, consider the CNIT dome in Paris. Here is a dome supported at 3 points – with over 6 times the span of Kresge.
www.structurae.netID Number 17362DescriptionSydney Opera HouseTaken in 2004PhotographerIan G. Bowie
http://www.powerhousemuseum.com/imageservices/tag/sailing/ - example of the type of sails thought to motivate Utzon
http://www.smh.com.au/ftimages/2008/11/30/1227979824216.html Utzon dies article, sketch for original design
earlier structurae image
http://www.powerhousemuseum.com/imageservices/tag/sailing/ - example of the type of sails thought to motivate Utzon
http://www.smh.com.au/ftimages/2008/11/30/1227979824216.html Utzon dies article, sketch for original design
THEMES
The German approach: analysis and geometryThe Italian approach: ribs, coffers, and buttressesThe "Spanish" approach: double curvature and thinnessConcrete shells and stiffnessEconomy of labor vs. efficiency of materialsComplexity of analysis vs. complexity of form
Edited by SRA Sp06, should be expanded back to two Eladio Dieste added and Candela-Torroja/Gaudi church comparison deletedConsider making into two.Also, don’t denigrate analysis, denigrate being trapped by analysis.Add intro. to explain why “roof vaults” is a sep. category. i.e., long-span roofs are more like long-span bridges in their necessity to be pure structure (as opposed to buildings) and “roof vaults” begins the evolution of modern stadiums, convention centers, etc.Consider pulling Dieste, or putting him right after Gaudi – his forms though later in time speak more to a time before Torroja and Candela’s RC forms..Sanjay discussion – consider pulling Gaudi or doign only the school house and getting right into spanish forms...
Sp 2008This lecture is still pretty disorganized but I propose taking it back to 2 lectures. Lecture 1 German and Italian, Lecture 2 Spanish.I have integrated back in the best of DPB lecture material (earlier we cut some nice Nervi discussions)This is still very much a work in progress.
SP 09Some structural themes to perhaps focus on:1. The edge of the dome. This has similarity to the transfer girder problem in tall buildings and has two parts. First, how is force transferred and second how is stiffness provided.2. Gaudi is able to make highly asymmetric forms that are nonetheless responsive to the structural forces.
Agree that this should be split for next year. Too many important characters crammed into one lecture. This will take real work. This year I have trimmed out some material to put some think, pair, share exercises in.
