主讲人：David Lopez Lopez, Marta Domènech Rodríguez / 加泰罗尼亚理工
整理翻译：吴庆宜、汪勇 / 哈尔滨工业大学（深圳）
校对：曹婷 / 哈尔滨工业大学（深圳）
Our lecture today will be about the design and construction of masonry shells! We would like to begin with this structure and share it with you because of how inspiring it is.
As you can see, it is an ancient drawing. It has more than one hundred years and it belongs to the collection of drawings by the Guastavinos at the archives of the Columbia university Avery Library.
△ 图1：圣约翰大教堂，瓦拱的剖面，Rafael Guastavino Jr., 1909 图源：Guastavino Vaulting, The Art of Structural Tile
The drawing is the cross section of a dome. It is a dome with a span of around 30 meters. Please take a look at the impressive slenderness of the cross-section. We are inspired by this picture because it is the efficiency we want to achieve. This structure can span really long and can cover a huge amount of space with very little material.
This dome was designed by the Guastavinos and it is the crossing dome of the Cathedral of Saint John the Divine in New York. When they built it, they knew they could congratulate themselves to have built one of the thinnest and more efficient masonry domes so far worldwide. They could compare their work with the domes of the Pantheon in Rome, the Hagia Sophia in Istanbul or the Florence Cathedral, to conclude that they were doing it much better in terms of material efficiency.
They could build this fantastic dome, first, because they knew how it worked structurally, but also because they used an appropriate construction technique to do it. With this technique they could build such structures in a cheap way, which allowed them to attract a lot of commissions in the US at that time. This technique allowed them to build without formwork. The cable system that you see on the image and the minimal guide-work were the only things that they were using as provisional support for their dome.
△ 图2：圣约翰大教堂穹顶建造过程中的拉索与导向装置 图源：Guastavino Vaulting, The Art of Structural Tile
They used a construction technique called tile vaulting or Catalan vaulting. This is an ancient technique that has its origins in the Spanish Mediterranean regions. And one of the many advantages that we think it has is that, as said, it can be built without formwork, like you can see in the picture.
△ 图3：加泰罗尼亚拱的建造不需要木模板 图源：Guastavino Vaulting, The Art of Structural Tile
And how is it done? On the one hand, light bricks for the first layer are required, either tiles (thin bricks) or hollow bricks. On the other hand, the binder should be fast-setting, either a fast-setting cement or a fast-setting gypsum. As you can see in the picture, the mason is building the vault without any formwork. He is applying a fast-setting binder to the light brick and then sticking it to the wall, then waiting only for some seconds for the cement or gypsum to harden to then release. The brick stays temporarily cantilevering in the air, and once the first row is finished resulting in a stable arch, then he can build the contiguous row. The first layer serves as formwork for the next one.
Something interesting from this traditional technique is its refinement through the years, which makes it very efficient. Different solutions can be found using Catalan vaulting, from small-scale, self-constructed spaces to long-span structures.
Going back to the Guastavinos, we can explain now who they were. Normally, you will hear about Rafael Guastavino, but, as mentioned before, in fact, they were two. They were father and son. Rafael Guastavino Sr was an architect from Spain who emigrated at the ending of the nineteenth century from Spain to the United States. There, he patented the tile vault. In fact, it was weird that he patented something that had been used for ages in Spain.
The Guastavinos did many innovations in the technique. One of them was related to the order in building the layers of the tile vault. They built the first layer with tiles and fast-setting gypsum, and then they put the second one on top. What they did afterwards is sticking a third layer from underneath, having the freedom to create any kind of pattern and finishing with the bricks and the joints.
Father and son, they built incredible examples in the United States, many of them in New York, where they built around three hundred buildings. Maybe you have visited them and did not know that these structures were unreinforced Catalan vaults built without formwork, like the one in the image, which is the Oyster Bar at the Grand Central Terminal in New York, the market under the Queensboro bridge, also in New York, or the City Hall Subway station, which features a perfectly-done brick pattern, placed from underneath by sticking the bricks to the intrados of the vaults, and having a double function: structural and decorative.
△ 图4：纽约中央车站的牡蛎酒吧 图源：Guastavino Vaulting, The Art of Structural Tile
△ 图5：Queensboro桥下的市场 摄影：David Lopez Lopez
Speaking again about efficient structures, these images are wonderful examples to show how they mastered this technique to build such slender and geometrically-complex structures. As you can see in the image, the stairs are being load-tested. They could resist this load because they were very well designed and very well built. The Guastavinos mastered construction and knew geometry was extremely important to achieve a proper structural behavior. In many of their buildings, the geometry and the structural analysis were obtained and performed thanks to graphic statics.
△ 图6：Guastavino父子建造的瓦拱曲线楼梯 图源：Guastavino Vaulting, The Art of Structural Tile
A very famous architect who also used graphic statics to design and analyze structures was Antoni Gaudí. This method was always used in 2D, because it was still not developed in 3D. Graphic statics in 3D is much more complex, so Gaudí had to explore funicular structures using his famous hanging models to figure out how they worked in 3d. With the help of these physical models, he could design and start the construction of the Basilica of Sagrada Familia (still in construction).
△ 图7：高迪制作的悬链模型 图源：Structural Deisgn III&IV, ETH Zurich
The hanging models, although quite inspiring, took Gaudí a lot of time to build them, and then there was the problem of “flipping” them, or translating the geometry from a tension-only to a compression-only structure (which is the way masonry structures need to work). Nowadays, it would be a waste of time to build such a complex physical model, as we have other means and tools that allow us to computationally design compression-only structures.
△ 图8：使用RhinoVault设计的纯受压曲面 图源：Block Research Group, ETH
这些软件中RhinoVault是ETH (瑞士联邦理工学院）的BLOCK研究组（Block Research Group）为设计创新者开发的一款软件。我们用它来设计后面将向大家展示的建筑案例。这个软件可以帮助你设计受压结构，砌块结构正符合这样一种受力模式。这个软件通过力流以及力的平衡来灵活地控制结构。图8最上方那一排是推力线，同时也是受压的结构形式。中间是对应的形图解，表现的是悬链平衡形式在水平方向上的投影。最下面是力图解，它们展示的是力在水平方向上的分布情况。设计师可以通过改变这些图解来探索不同的悬链形结构形式。
One of them is RhinoVault, a plug-in for Rhinoceros developed at the Block Research Group at the ETH Zurich. RhinoVault is the software that we used to design the buildings or prototypes that will be shown later in the presentation. It features a flexible geometry control by modifying the force flow and equilibrium in the structure. The Figure 8 shows thrust networks on the top, which would be the shape of the compression-only structures, the corresponding form diagrams in the middle, which shows the vertical projection in the horizontal plane of the funicular equilibrium solution, and the force diagram at the bottom, which represents the horizontal equilibrium of the structure. The user can modify these diagrams to explore different funicular solutions.
Combining the flexibility of RhinoVault with the versatility of tile vaulting, we designed and built the pavilion that we are going to show next: BRICK-TOPIA.
This pavilion was the first free-form tile vault at a human-scale. The use of this construction technique was appropriate in that context taking into account the surrounding masonry buildings and considering that tile vaulting is rooted in the Spanish building tradition and knowledge.
△ 图9：使用Rhinovault设计的项目BRICK-TOPIA 图源：Map13 Barcelona
As previously mentioned, Brick-topia was designed using RhinoVault. You can see the form diagram, force diagram and thrust network in the image.
△ 图10：纸板、钢筋构成的脚手架系统作为BRICK-TOPIA建造的导向装置 图源：Manuel de Lózar and Paula López Barba
We used a system of scaffolding, cardboard and steel rods to build a guidework. It was mainly made by architects or architecture students volunteering to learn about the traditional construction technique and its combination with contemporary computational tools.
The guidework is required to help the masons build the correct geometry, which is crucial to achieve a correct compression-only structural behaviour.
The cardboard was cut and placed on the scaffolding platforms to mark the general shape of the pavilion. The steel rods were then placed on top of the edges of the cardboard to create a stable three-dimensional net. The cardboard was then removed to allow the masons to move on the scaffoldings’ platforms. The images show the expert masons building the vault using the net of steel rods as guidework.
The entire guidework system is removed once the tile vault is finished, having a completely unreinforced masonry structure.
△ 图11：工匠使用钢筋作为导向装置来建造曲面 图源：Manuel de Lózar and Paula López Barba
△ 图12：工匠使用钢筋作为导向装置来建造曲面 图源：Map13 Barcelona
The unreinforced tile-vaulted structure had two or three layers of brick depending on the spot of the vault and according to the results of the structural analysis. The part of the pavilion with two layers of bricks was 6.5 cm thick, while the part with three layers, featuring the bigger and higher vault, was 11.5 cm thick.
The image shows the finished pavilion, which, as previously mentioned, was the result of the combination of current form-finding computational tools with this ancient and efficient construction technique, that allowed us to build such a complex geometry.
△ 图13：最终建成的展馆BRICK-TOPIA 图源：Map13 Barcelona
△ 图14：最终建成的展馆BRICK-TOPIA 图源：Manuel de Lózar and Paula López Barba
Following a similar design logic, we also designed some other projects. If you have interest, you can find more detailed information in the links below: