MASONRY SHELLS
Researching and Understanding through Experimentation
HD 0314, SK 0814, JP 1814, KS 2414, NT 2714, YR 3014, AL 3114, TM 4214 Indubhai Parekh School of Architecture
Preface
This paper presents the study on Catalan Vault construction technique and its execution methods and learnings. It shows how this construction technique is more economical as well as structurally efficient than conventional techniques . This paper is primarily addressed to educators as well as pupils of architecture. An understanding of this technique, as one of the means to construct shell will help them provide for better solution to address their design problems in an innovative manner. Grateful acknowledgment is here made to those who helped this group during the site work, namely batch mates, juniors of batch 17 and last but not least to various faculties for their invaluable advice . Batch mate Bhumit Savsaviya’s contribution is especially acknowledged. We are indebted to Mr. Raj Hadvani of Gopal Industries for his support in this research. This work would not have reached its present form without their invaluable help.
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Contents Preface ...................................................................................................................................................................... 1 Table of Figure ............................................................................................................................................................ 3 Definition ...................................................................................................................................................................... 4 History .......................................................................................................................................................................... 5 Egypt ......................................................................................................................................................................... 5 Assyrians ................................................................................................................................................................ 5 Greeks and Romans ............................................................................................................................................. 6 Middle Ages............................................................................................................................................................. 6 Renaissance ........................................................................................................................................................... 7 Secondary Case Study - Brick-topia, the thin-tile vaulted pavilion ............................................................. 7 Intention ................................................................................................................................................................... 7 Introduction ............................................................................................................................................................ 7 Materials.................................................................................................................................................................. 8 Concrete slab..................................................................................................................................................... 8 Bricks ................................................................................................................................................................... 9 Binders ................................................................................................................................................................ 9 Form-finding method..........................................................................................................................................10 Structural analysis .............................................................................................................................................. 11 Construction .......................................................................................................................................................... 12 Formwork .......................................................................................................................................................... 12 Decentring ........................................................................................................................................................ 14 Conclusions .......................................................................................................................................................... 14 Sampling .....................................................................................................................................................................15 Intention .............................................................................................................................................................15 Sampling 1 ..............................................................................................................................................................15 Sampling 2.............................................................................................................................................................. 16 Sampling 3.............................................................................................................................................................. 17 Sampling 4 ............................................................................................................................................................ 18 Stage1: Foundation and Piers ...................................................................................................................... 18 Stage 2: Edge Arches ...................................................................................................................................... 19 Stage 3: Dome .................................................................................................................................................. 23
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Learnings ...............................................................................................................................................................31 Final Proposal............................................................................................................................................................31 Architectural and Tectonic requirements.................................................................................................31 Structural requirements .............................................................................................................................. 32 Fabrication requirements ............................................................................................................................ 32 Form Finding ........................................................................................................................................................ 33 References............................................................................................................................................................38
Table of Figure Figure 1. Timbrel Vault .............................................................................................................................................. 4 Figure 2. Timbrel Vault of multiple tiles ............................................................................................................... 4 Figure 3. Egyptian Elliptical Vault .......................................................................................................................... 5 Figure 4. Assyrians’ Corbelled Vault .................................................................................................................... 6 Figure 5.General view of the project. ................................................................................................................... 8 Figure 6. Building Brick-topia’s first layer of bricks: (a) applying fast-setting cement and placing the brick, (b) cleaning the joint. .............................................................................................................................. 8 Figure 7. Detail of the support................................................................................................................................10 Figure 8. Panoramic view showing some features of the design. ............................................................... 11 Figure 9. Compressive stresses for the most unfavorable load combination. ........................................ 12 Figure 10. Formwork scheme: (a) axonometric, (b) construction................................................................13 Figure 11. Grid of bent steel rods. Manuel de Lózar and Paula López Barba.............................................13 Figure 12. Opening of the pavilion. Manuel de Lózar and Paula López Barba.......................................... 14 Figure 13. Sampling 1 ................................................................................................................................................15 Figure 14. Sampling 2 ............................................................................................................................................... 16 Figure 15. Sampling 3 ............................................................................................................................................... 17 Figure 16. Sampling 4 Plan ..................................................................................................................................... 18 Figure 17. Edge Arch Photo plate .......................................................................................................................... 19 Figure 18. Course 1 ................................................................................................................................................... 20 Figure 19. Course 2 – Tile at 55O ............................................................................................................................ 20 Figure 20. Course 3 .................................................................................................................................................. 20 Figure 21. Photo showing all the three course .................................................................................................. 21 Figure 22. Edge Arch Photo plate 1 ...................................................................................................................... 22 Figure 23. Gaussian Curvature Analysis of Isometric view of 3D Model................................................... 23 Figure 24. Gaussian Curvature Analysis - Plan............................................................................................... 23 Figure 25. Metal Guide ............................................................................................................................................24 Figure 26. Pendentive ............................................................................................................................................. 25 Figure 27. Dome - First Layer ............................................................................................................................... 25
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Figure 28. Tile bonded using POP......................................................................................................................... 26 Figure 29. Vertical Band as starting point for second layer.......................................................................... 26 Figure 30. Second Layer Dome Photo plate ...................................................................................................... 27 Figure 31. Completed Dome Photo plate ............................................................................................................ 28 Figure 32. Expenses Chart ....................................................................................................................................30 Figure 33. Interdependent Constraints .............................................................................................................. 32 Figure 34. Digital Workflow Steps ....................................................................................................................... 33 Figure 35. Form Diagram .......................................................................................................................................34 Figure 36. Force Diagram ......................................................................................................................................34 Figure 37. Functional Shell (Before) ................................................................................................................... 35 Figure 38. Catenary Shell (After) ......................................................................................................................... 35 Figure 39. Plan .......................................................................................................................................................... 36 Figure 40. Catenary Curve Graph for Section A ............................................................................................... 36 Figure 41. Gaussian Curvature Analysis Isometric view ............................................................................... 37 Figure 42. Rendered Views of Proposed Shell ................................................................................................ 37
Definition A "Timbrel Vault" of a single thickness of brick or tile (Fig. I) has no more resistance than an arch or vault built on the "Gravity System"; because, no matter how good the mortar may be, there is only one vertical joint, and the bricks or tiles are working as voussoirs. Consequently, this form of arch belongs to the "Gravity System."
Figure 1. Timbrel Vault
But if we put another course over the first (Fig. 2), breaking joints, and laici with hydraulic material, we will have the action of cohesive force. In this way the mortar laid over the first course, or extrados, takes bond with it, and also with the course Iaid on top.
Figure 2. Timbrel Vault of multiple tiles
As soon as the cement sets, we will have shearing resistance. In this way, we introduce a new additional strength to the arch which is a peculiarity of the Timbrel Arch System. In the Gravity System, the strength of gravity alone is the only force keeping the voussoirs in place by pressure against each other in the joints. These joints are not protected, and any reduction in the width of the joints in consequence of pressure, or weight on the arch, comprises the setting of the mortar. For
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this reason, in the "Gravity System" the mortar serves only as a cushion, even if cement mortar, because of bad setting, and adds no strength to the arch. Constructing vaults in brick was mastered by the Romans, who use arched structure to strengthen their buildings and constructions. This technique was then improved by Catalan people with layers of thinner, lighter bricks to create a ceiling not only light but also very strong for which it is named “Volta Catalana�. Other names for this technique are Catalan arch, Catalan turn or Timbrel vault.
History The first step performed has been to investigate the historical aspect in order to frame the vaults and its construction technique all along the history of architecture and to understand the reasons of its great success. "Cohesive System" is as ancient as the "Gravity System." But although the "Cohesive System," including the application of timbrel arches, was frequently practiced by the ancients, after reaching the height of its splendor in the Middle Ages it gradually disappeared, in proportion as modern civilization and the Renaissance approached.
Egypt City of Sepulchres, near Thebes, there is an elliptical vault constructed of unburned brick. It is 2.50 m. in length, by 1.42 m. in height, measured from the springing.
Figure 3. Egyptian Elliptical Vault
Assyrians The Assyrians improved the manufacture of brick. Encamped between the rivers Tigris and Euphrates, and with abundance of clay at their disposal, as well as asphalts and mineral oils, which
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they used as fuel, they carne to the practical idea of burning the clay, and instead of using raw brick, they used burnt bricks.
Figure 4. Assyrians’ Corbelled Vault
The gardens of Semiramis, at Babylon, and the subterranean passages under the Euphrates, were nothing else but vaults built with very large bricks.
Greeks and Romans Their facilities for obtaining clay and fuel were not favorable, and they were therefore more devoted to stone construction. The Romans, in particular, had a marked fondness for stone and concrete, of which they made very good use, not only in triumphal arches and bridges, but also in military and urban constructions, such as sewers, etc. The aqueduct of Segovia and the city walls of Tarragona are other specimens, again showing their predilection for stone and concrete. The former is a wonderfully magnificent structure and a model of static equilibrium.
Middle Ages The true epoch of the development of the " Cohesive System " and the dome was in the Middle Ages, but no important specimens of the "Timbrel Vault," or with the brick set flat against the center, are left. The cupola was the dominant line of their monuments and as the Oriental civilization had great influence in the antique Byzantium, not only did it give to the Byzantines the richness of their colors and decorations, but it gave also the foundation for new ideas in the architectural arts; to such an extent, that it founded the classical] examples of the " Cohesive System." From the building of the cupola of St. Sophia to the period of the Renaissance several cupolas on the cohesive principle were constructed. The principal of these cupolas were the Mosques of Solyman II., Sultan Ahmet, and the Holy Apostles, of Constantinople; ¡Santa Maria of Ravenna; St. Mark, Venice, and the Cathedral of Zamora, whose cupola is one of the most beautiful in Europe.
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Renaissance After this epoch, in the Renaissance, the most remarkable are those in the Santa Maria del Fiore, and the Medici Chapel and Baptistery of Florence; St. Augustine's and St. Peter's in the Vatican, Rome; the Madonna de la Salute, Venice; Ste. Geneviève, Paris; St. Paul' s, London; La Real capilla de los Desemparados, Valencia.
Secondary Case Study - Brick-topia, the thin-tile vaulted pavilion Intention The project ‘‘Brick-topia’’ was based on a combination of the latest structural analysis and formfinding computational tools with traditional, cheap and effective construction techniques. It is the result of innovation to fight against budget and time. The initial budget was 3000 euros and only seven weeks was the time to look for sponsors, design the pavilion, plan the construction phases and build it. The whole process of designing, decision on the materials, structural analysis and construction is presented in the paper, including exploration on new form-finding methods. Catalan/thin-tile vault to redesign a project in situ and research on a new formwork system using scaffolding, cardboard, wire and steel rods and having a cutter as main tool.
Introduction The building was a vaulted unreinforced masonry structure made with the traditional technique of thin-tile vaulting (also known as ‘‘Catalan vault’’). It reached a maximum height of 4 m, had spans between 5 and 7 m and the shell had a surface of 150 m2 (Fig. 5). ‘‘Catalan vaults’’ are masonry structures made with bricks and binder. The bricks are placed flat setting up two, three or more layers. Traditionally thin bricks – or thin tiles – are used because of their lightness, which is a necessary condition to build the first layer ‘‘in space’’ (without a continuous formwork, Fig. 6) using gypsum or fast setting cement. The aim of using these binders for the first layer is the quick adhesion achieved so that the bricks get attached within seconds to the edge walls or to the previous arcs or stable sections already finished, cantilevering for some time and avoiding the necessity of cantering [1]. The second and subsequent
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layers can be set with lime or Portland cement mortar. The ‘‘Brick-topia’’ pavilion takes as reference and inspiration the prototype built by the Block Research Group at the ETH in Zürich [2].
Figure 5.General view of the project.
Figure 6. Building Brick-topia’s first layer of bricks: (a) applying fast -setting cement and placing the brick, (b) cleaning the joint.
Materials There were three main elements composing the building: the concrete slab, the bricks and the binders (Fig. 6).
Concrete slab As no perforations on the ground were permitted, superficial foundations had to be implemented. The slab was made of reinforced concrete and served as foundation for the entire structure. The surface of the concrete slab was 285 m2 and 120 mm thick. The reinforcement consisted of 8 mm
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diameter steel bars in both directions every 150 mm. Steel reinforcement was placed where needed depending on the horizontal thrusts in each support.
Bricks o
The first layer is built ‘‘in space’’ using light bricks, which will be cantilevering for some moments depending only on the fast-setting mortar capacity to hold it from its edges. Traditionally thin bricks approximately 15 mm thick are used, but also hollow bricks of 40 mm are suitable, as they are also light and have more surface at the edge, improving the adherence during the construction process. The bricks used in the project for the first layer were traditional handmade bricks, 280 140 150 mm. Their weights may vary, but it was approximately 1 kg per piece.
o
The second layer was made with hollow industrialized bricks, 280x140x40 still light (1.5 kg per piece) to prevent an excess of weight on the first layer. The price of these pieces was also a reason for its election as the budget was tight and the sponsorship of the companies offering bricks could not cover every layer.
o
The third and final layer was not applied to the whole construction. It was only built over the biggest vault, with the rest of the building only two layers thick (a thickness of 65 mm in total). Solid bricks were used, with dimensions 280x140x43 mm, 3 kg weight each and a handmade texture. The weight of the third layer, instead of being a handicap, helps reaching the stability against possible destabilizing punctual loads. Approximately 4100 bricks were used for each of the first two layers and 1400 for the third one.
Binders The two binders that can be used to build the first layer of a ‘‘Catalan vault’’ are plaster of Paris (gypsum) or fast-setting cement. In this case, a ‘‘natural rapid cement’’ was chosen because of its resistance to exterior conditions, its strength and the quickness of this strength to be achieved. Due to the weather conditions with temperatures over 30 C at the worksite, ice cubes were used to obtain cold water to make the mix and slow down the setting process.
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Figure 7. Detail of the support.
o
For the first layer only rapid cement was used as binder.
o
For the second layer a mix of rapid cement and washed thin sand (1:1) was applied. This mix is more difficult to work with than Portland cement mortar as the rapidity of setting makes it more unworkable, especially for a second layer, in which more binder is used than in the first one because of the necessity to have also binding material between layers.
o
For the third layer grey dry Portland cement mortar was used. An already mixed mortar was selected to speed up the production. The thickness of the joints varies between 5 mm and 10 mm, with the joints between layers slightly wider than the joints between bricks in the same layer.
Form-finding method The shape of the pavilion is the result of a thorough design process using the software Rhino Vault. This tool is a plug-in of Rhinoceros developed at the Block Research Group in the Institute of Technology in Architecture at the ETH in ZĂźrich. It allows the design of compression-only vaulted structures with a high formal complexity.
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Figure 8. Panoramic view showing some features of the design.
The design had two principal goals: (1) fulfil the requirements specified by the client making a functional pavilion for the site with a clear intention when defining the openings and closed spaces, (2) explore the possibilities of the construction technique providing the building with different features that would take the structure to the limit (Fig. 8). Some of the features that were incorporated in the design are inclined thin supports, arches that cannot be inscribed in a plane, a twisting support where arches in perpendicular directions land, different heights of the vaults, different degrees of curvature and a big hole in the shell.
Structural analysis Rhino Vault guarantees a shape working in compression when it is only subjected to self-weight loads. The building should be able to resist the applicable wind and snow. The exposition of the specific points of the building depending on its height and location and the wind coefficient depending on the shape and orientation of the specific surface. The safety factors are 1.35 for dead loads and 1.5 for live loads [6]. To perform the structural analysis, the Finite Element Method was used [7].
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Figure 9. Compressive stresses for the most unfavorable load combination.
Masonry structures have usually low compressive stresses comparing to the compressive strength of the material. The application of the different load combinations to the model resulted in the development of tensile stresses. The thickness of the vault was then increased in the needed places until the tensile stress was admissible. The most unfavourable situation was caused by punctual loads at the two inclined supports, almost independently of the wind and snow load cases. The analysis applying this load combination with a thickness of 65 mm – two layers of bricks – in the whole vault showed non-admissible tensile stresses at these supports reaching 0.48 N/mm2. Increasing the thickness to 118 mm – three layers of bricks – was enough to reach acceptable values (maximum tensile stresses reported were 0.13 N/ mm2).
Construction Apart from the intrinsic limitations of the material, two parameters were the main constraints during construction: time and budget. Fast and economical construction systems needed to be implemented in order to achieve the proposed goals.
Formwork The combination between the computational tool Rhino Vault and the use of the Catalan vault as construction technique, already put into practice by the Block Research Group [2],
Traditionally, no load bearing false work is needed, as the geometry of the vault is normally reached by building stable portions of the structure during the construction process. False work used in free-form Catalan vaults needs to have load bearing capacity to support the self-weight of parts of the structure until stable arches or portions of the structure are built. However, as the self-weight of thin-tile vaults is low in comparison to other masonry structures, the false work does not have to support high stresses.
The solution adopted had three main elements or materials: scaffolding, cardboard and steel rods. The final shape and load bearing capacity of the false work is given by a grid of bent steel rods.
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Figure 10. Formwork scheme: (a) axonometric, (b) construction.
The scaffolding was composed by 2 m by 2 m modules at different levels depending on the height of the vault at the specific area. Cardboard panels, 2 m by 2 m, were cut on site following the shape of the sections. Each module of the scaffolding served as the base for a system of four stable intersecting cardboard panels (Fig. 10). When the whole shape had been defined by the cardboard panels, 6m-long steel rods were placed on the top edges of the cardboard shaping the vault. First, £10 mm steel rods were placed in one direction and secondly, £8 mm rods were disposed in the perpendicular direction. They were tied together with wire where they intersect. (Fig. 11).
The expected error between the designed shell and the final shape of the false work, due to the manual process of building, does not affect the stability of the vault. Even in very slender vaults, thrust lines are normally inscribed within the thickness of the vault.
Figure 11. Grid of bent steel rods. Manuel de Lózar and Paula López Barba.
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Decentring
The formwork in ‘‘Brick-topia’’ could only support the self-weight of the first layer of bricks and some occasional loads that the workers may accidentally apply. Therefore, the vault itself already started to work when the second layer was being built and tools, construction material and workers were standing on the two-layered vault to continue the construction process.
The decentring consisted of cutting the wire that connected the steel bars to each other and by detaching them from the scaffolding and slab.
Figure 12. Opening of the pavilion. Manuel de Lózar and Paula López Barba.
Conclusions
One of the most remarkable features of this project was the success of the formwork system. The initial idea came from the scheme developed for the prototype in the ETH Zurich [2], it worked well in this project, some improvements could be made to avoid movements on the net of steel rods that could cause cracking, such as more points fixing the spatial net to the scaffolding, which would have helped to reach a higher stiffness on the net. A big improvement could also be done providing the formwork with a thicker edge at the arches so that the bricks would lay on it and would not slide while the arch is not yet completed.
More research needs to be done in order to optimize timing and construction processes.
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Sampling Intention Sampling is done using several materials to test and understand the behavior of brick and the binding agent and their relationship. It enabled us to understand the behavior of the system, form and its execution. Material used and its form are the principal governing factors that determines the failure or the success of the system.
Sampling 1 Inquiry Material Binding Agent Form Formwork Result
Will it work? Hollow Terracotta Block – Plaster of Paris Rampant Arch Wooden Formwork as Guide Failure due to shifting of springing point
Figure 13. Sampling 1
The first sampling was done to understand the working of the binding agent, Plaster of Paris with the Terracotta block. It was the first rudimentary attempt to understand the basic execution methods. The wooden formwork was used just as a guide to achieve the correct form. The sample failed when
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additional load was applied, due to the shifting of the springing point. Due to failure, the study of the behavior of the system under load was left incomplete.
Sampling 2 Inquiry Material Binding Agent Form Formwork Result
Behavior of vault Hollow Terracotta Blocks – Plaster of Paris Rampant Arch No formwork Successful
Figure 14. Sampling 2
The second sampling was done to experiment and execute the vault without a guide, using terracotta hollow blocks and POP. The aim was to examine the binding strength of POP. The vault was made up of two bays of arches. The form achieved without using any guide did not follow the desired curvature. In spite of this, the vault withstood self-weight. This attempt still classified as “Gravity System” and not “Timbrel System”.
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Sampling 3 Inquiry Material Binding Agent Form Formwork Result
Can slender Kota Stone arch work? Kota stone – Plaster of Paris Freestanding Shell No formwork Failure due to execution fault
Figure 15. Sampling 3
The third sampling was done with thin Kota stone tiles with POP as binding agent. The Kota stone tiles, since not as permeable as terracotta, was not able to bind properly as per earlier arrangement. Hence an alternating course arrangement (Fig. 14) was carried out. This changed the form of shell. The principle reason of failure was due to the its inability to withstand the vibration and movement caused by hand during the execution. Since this was a free standing shell, we felt that had both the end of the shell been supported, failure would have been avoided. We also felt the need of a guide, which would have assisted in achieving correct catenary curve that might have avoided the failure as well.
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Sampling 4 Stage1: Foundation and Piers Inquiry Material Binding Agent Form Formwork Result
Pre-Final scaled sample Brick (foundation and piers Portland Cement, POP Shallow Foundation and 1.5 Brick Course No Formwork Successful
Learning from the previous sampling attempts, the 3 course deep foundation was carried out at the four springing points of the cross vault. The distance between the piers is 2.21m and the internal diagonal distance is and the internal diagonal distance is 3.22m (Fig. 16). The piers, extending from the foundation level, terminated two courses above ground level. To deal with side thrust, buttresses were introduced at the side of pier for providing further stability.
Figure 16. Sampling 4 Plan All dimensions are in meter
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Stage 2: Edge Arches Inquiry Material Binding Agent Form Formwork Result
Pre-Final scaled sample Terracotta tiles (Arch) POP, Portland Cement Catenary Shallow arch Metal Sheet Guide of Shallow arch Successful
Figure 17. Edge Arch Photo plate
The formwork was placed into position keeping it raised over the ground. The formwork, made out of 2mm metal sheet acts as guides and is not capable to take any load. Another formwork used is made out of 5mm plywood sheet, it again is not equipped to take up any load. Each arch is comprised of 3 layers as shown in Fig. 18-20.
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Figure 18. Course 1
Here, 1.
Course 1 is binded by using Plaster of Paris, having proportion of 1 part water and 3 parts of Plaster of Paris.
Figure 19. Course 2 – Tile at 55 O
2. Course 2 is built with tiles arranged at 55o. This arrangement will help in staggering the bond line of dome.
Figure 20. Course 3
3. Course 3 is arranged in tiles arranged along the length of the arch for the aesthetic purposes. It is important to note that course 2 and 3 are binded with Portland Cement mortar, having proportion 1 part Cement 3 part finely filtered sand and 2 bottle caps of plasticiser.
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Figure 21. Photo showing all the three course
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Figure 22. Edge Arch Photo plate 1
The total material used in making these arches are: 1.
Tiles: 124, 104 and 128 in courses 1,2 and 3 respectively.
2. POP: 15kgs 3. Cement: 10kgs
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Stage 3: Dome Inquiry Material Binding Agent Form Formwork Result
Pre-Final scaled sample Terracotta tiles POP, Portland Cement Catenary Shallow Dome Metal Bar Guide at diagonals Successful
The length and curvature of metal bars that will be used as guides were first calculated with the help of Rhino.
Figure 23. Gaussian Curvature Analysis of Isometric view of 3D Model
Figure 24. Gaussian Curvature Analysis - Plan
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With the generous help of owners of Gopal Industries, these bars were curved into the desired form at their factory workshop. These rods had to be distorted to a certain extend on site to compensate for the minor error in the execution.
Figure 25. Metal Guide
Metal Rods were attached to the piers with the help of POP and secondary rod were attached to help in maintaining the form. The center, marked by sturdy bar, is used to tie one end of string. This string is used to maintain the courses of dome and directions of tile. Hence, string acts as a second guide.
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Figure 26. Pendentive
Each tile at the pendentive, up to 6 courses, were tailored and cut to achieve the perfect curvature. The rest of the courses followed the above procedure to achieve desired form.
Figure 27. Dome - First Layer
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Figure 28. Tile bonded using POP
The second layer for the dome, bonded using Portland Cement, was started with the vertically arranged tile to gesture and accentuate the curvature of the dome.
Figure 29. Vertical Band as starting point for second layer
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The courses above and the below the vertical band were carried out simultaneously to achieve the finished dome. Again the string was used as a guide to arrange the tiles. The first dome layer acts as lost formwork for the second layer. Decentering of the guides was carried out by using hand grinders to cut off the bond between rods and POP when there was only 3 layers left to the oculus.
Figure 30. Second Layer Dome Photo plate
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The oculus is finished up with a circular ring made out of terracotta with white mud plaster applied to it to highlight it from the rest of the masonry.
Figure 31. Completed Dome Photo plate
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The total material used in making this dome was: 1.
Tiles: 387 (not inclusive of failed tiles) in each course of dome.
2. POP: 45kgs 3. Cement: 35kgs Total cost of the sampling can be broken down as following
Expenses
13% 18% 8%
Terracotta tile 6%
Transportation Plaster of Paris Portland Cement Miscellaneous
55%
Figure 32. Expenses Chart
Breakdown of Expenses Terracotta Tile
4250/-
Transportation
1450/-
Plaster of Paris
995/-
Portland Cement
600/-
Miscellaneous
480/-
Total
7775/-
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Key facts and properties of executed Dome
Total surface area
5.504 m2
Total covered area
5.062 m2
Total number of voussoirs
387 tiles
Average size of voussoirs
20 x 7 x 1 cm
Maximum span
3.22 m
Total surface area of contact faces
2.089 m2
Total surface area of upper and lower faces
5.418 m2
Volume stone
0.5418 m3
Learnings The learning is divided on many levels. The first major learning curve was the translation from single curved surface(arch) to double curved surface (dome) i.e. pendentive. Its construction technique was immense learning. Secondly, the process of making a dome and its complexities, on-site adjustments and working with material. The whole sampling process instilled skill, faith in the system and above all team spirit that can help push the final proposal into reality.
Final Proposal Architectural and Tectonic requirements From all aspects that influence the desired overall shape of the vault, the architectural and tectonic intents, which include contextual, functional and visual considerations, are the least restrictive ones. Even though the shape generation has to follow structural requirements, structural design approaches have been implemented in the presented digital model that allow balancing of the constraints of structural form with our intents, by giving the designer careful and explicit control over all parameters of the form finding. (Fig. 33)
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Figure 33. Interdependent Constraints
Structural requirements The thickness of the vault and thus the local offset values for the voussoirs generation should be sufficient to provide stability under live loading and to reduce the danger of buckling. The ideal orientation of the tessellation is aligned to the local force vector field.
Fabrication requirements The guides that will act as formwork were the primary concerned parameters and the bending process that will determine the design. Another governing factor is the dimension of the masonry unit i.e. terracotta tile – 0.2 x 0.07 x 0.01 m.
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Form Finding The brief was to design an auxiliary functional shell in the canteen area of Indubhai Parekh School of Architecture which shelters from the environment in the site area of 28.44 m2. The free-form shell was conceived for this, here ‘free-form’ refers to the complexity of the doublecurved, often unexpected forms of compression-only structures. This shell was modelled in Rhinoceros based on the following sketched sections that caters to just the architectural requirements. The functional shell model was processed into the RhinoVAULT plugin developed by ETH Zurich. (Fig. 34)
Figure 34. Digital Workflow Steps
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The form diagram defines the perimeter and force pattern, representing the predefined “flow of forces�, of the vault design in plan. The force diagram defines the horizontal force components in the structure, and how they are proportionally distributed/related. The form and force diagrams, as shown in Fig. 35-36, were produced to study the forces acting on the shell.
Figure 35. Form Diagram
Figure 36. Force Diagram
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The Horizontal and Vertical force vectors acting on the shell, were modified and manipulated in such a way that the shell acts purely in compression. This resulted in a changed into a Catenary shell.
Figure 37. Functional Shell (Before)
Figure 38. Catenary Shell (After)
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The resultant form is more of a “saddled� form with pinched ridge and broadened base. The shell covers an area of 28.443 m2 having largest span of 6.32m and highest ridge height of 2.89m.
Figure 39. Plan
This catenary shell is crosschecked at different intervals with Catenary Curve Analysis tool to authenticate its precision. The following table is the calculation graph for curve at Section A.
Figure 40. Catenary Curve Graph for Section A
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The results of graph correlates with the curve generated by RhinoVAULT. The shell is then subjected to Gaussian Curve analysis to determine its curvature range (Fig. 41). The Gaussian graph range shows that there is not much variation except at the ridge. The oculi will play a major role in determining the tile tessellation geometries.
Figure 41. Gaussian Curvature Analysis Isometric view
Figure 42. Rendered Views of Proposed Shell
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Key facts and properties of Proposed Shell
Total surface area
37.440 m2
Total covered area
28.443 m2
Total number of voussoirs
5264 tiles (Two Layers)
Average size of voussoirs
20 x 7 x 1 cm
Maximum span
6.32 m
Total surface area of contact faces
56.872 m2
Total surface area of upper and lower faces
73.696 m2
Volume stone
0.7369 m3
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Thank You
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