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Robert Maillart的“强结构”设计策略:建筑设计的工程化 | “强结构”系列讲座实录

Robert Maillart的“强结构”设计策略:建筑设计的工程化 | “强结构”系列讲座实录
主讲人:Denis Zastavni | 编辑:原源 | 2022.10.21 11:30


Robert Maillart的“强结构”设计策略:建筑设计的工程化
Robert Maillart's design approaches to “Strong Structures”: the engineering of architectural designs

主讲人:Denis Zastavni(鲁汶大学 UCLouvain)




今晚讲座的主题是关于瑞士工程师Robert Maillart,他在20世纪初革新了混凝土结构设计的方法。他设计的结构十分特别,在今天讲座的后面部分,我会更详细地介绍他的作品。

The topic of this lecture is about the Swiss engineer Robert Maillart, who renewed totally the way to design concrete structures in the beginning of the 20th century. As one can see on pictures of his works, some of his structures are very particular.



Graphic Statics is a graphical technique to analyze structures. Maillart used it to analyse, but also to design his structures so its use is totally meaningful to explain the work of Robert Maillart.  Maillart is a pioneer in using this special technique for design purposes, as well for inventing suited geometry and construction techniques fitting the real nature of concrete as a structural material.


我会以一些作品的图片对Robert Maillart展开介绍,为了向大家展示,相比之下在他那个时代的普遍建造是怎样的——这有助于理解他的作品和结构设计方法的智慧与创新之处。

I will first introduce Robert Maillart with a few pictures of his work, just to show you, by contrast, what was constructed at his time: This should help to understand how smart and innovative was his work and his approach for structural design.



Robert Maillart 1898至1940年间的设计作品介绍
Introduction to Robert Maillart's Design 1898-1940

Robert Maillart(图1)居住在瑞士,出生于1872年,于1940年去世。直到生命的尽头他都在工作,所以向大家介绍的他最后一个作品就建于他去世那年。在他有生之年,他自己的公司建造了约50座桥,为300多座楼宇设计或者建造了结构。他建造的桥梁使用了六种不同的结构系统。桥梁会更有趣些,从桥梁衍生出的一些技术也在一些有趣的建筑上实现了:例如Chiasso shed,与设计蘑菇状楼板的技术。

Robert Maillart (fig. 1) lived in Switzerland; he is born in 1872 and died in 1940. He worked until the very end of his life, so the last work one can show is from 1940. During his life, he built about 50 bridges and designed or built the structure of 300 buildings with his own company. There are six different structural systems used for his bridges. The bridges are more interesting, but they are also some interesting realisation around buildings: for instance the Chiasso shed, as well the technique to design continuous mushroom-slabs.


△ Robert Maillart(1872—1940),著名瑞士工程师,他在20世纪初彻底改变了钢筋混凝土结构的思考和设计方式。他的影响力至今仍然存在,其许多设计都是无与伦比的。

Robert Maillart [1872-1940], the famous Swiss engineer who revolutionised the way reinforced concrete structures were considered and designed in the early 20th century. His influence is still alive today and many of his designs are unequaled.

图源 Credits:ETH‐Bibliothek Zurich,Image Archive


Maillart 1929年建造的Salginatobel桥(图2)是世界上、也是工程史上最重要的20个结构之一。这是一个非常智慧的设计,我也乐意在接下来的介绍当中谈谈我的看法。

Robert Mailart's Salginatobel Bridge from 1929 is hold to be one of the 20 most important structural works in the world in the history of engineering (fig. 2). This is a very smart design that I will have the pleasure to comment below.


△ 瑞士Salginatobel桥(1930),由Robert Maillart于1928至1929年设计。这个杰作被认为是工程史上最重要的20个结构之一。

The Salginatobel Bridge [1930], Switzerland, designed by Robert Maillart in 1928-1929. This masterpice is hold to be one of the 20 most important structures in the history of engineering.

图源 Credits:D. Zastavni,2012


图解静力学的原理与图形设计相关。在Salginatobel桥左侧支撑的近距离视角中,它呈现出了不常见的形式(图3)。这些都是非常具有“塑性”的形式,将激励在他之后的许多建筑师和工程师。Maillart的作品Chiasso Shed(图4)是“加劲拱桥”的一种变体,与其原理类似,也是采用图解静力学设计(图5),我们会在下一页中详细介绍。仓库后面的棚屋使用了他的蘑菇板结构体系,是通过对真实比例模型进行荷载测试来进行设计的。

Graphical design rules are linked to Graphic Statics. A close point of view of the left support of the Salginatobel Bridge shows uncommon forms (fig. 3).  These are very 'plastic' forms that will inspire a lot of architects and engineers after him. Maillart's Chiasso Shed (fig.4) is another example of a structure presenting uncommon forms. The structure is a kind of smart variation of the principle of what will be called 'stiffened arch bridge', designed with Graphic Statics (fig. 5)., that we will detail in the next pages. The warehouse building behind the shed uses his structural system of mushroom-slabs, designed with real-scale testing.


△ Salginatobel桥的细部(Robert Maillart,1930设计)

The Salginatobel Bridge, detail (Robert Maillart, 1930)

图源 Credits:D. Zastavni,2012


△ Chiasso Shed的平、立面(Robert Maillart,1924)

The Chiasso Shed plan and elevation(Robert Maillart,1924)

图源 Credits:D. Zastavni,2012


△ 使用图解静力学对Chiasso Shed(1924)的几何设计进行综合分析

Synthetic insight in the geometric design of the Chiasso Shed [1924], using Graphic Statics

图源 Credits:D. Zastavni,2012



More images presenting close views of this structure all reveal the accuracy of the detailing work made on it: the funicular central part; side part as a cantilever triangle of forces, or the connections between the two. Another mechanism more similar to a Vierendeel system appears in the perpendicular direction:  perpendicular horizontal bars connecting some of the vertical members of the structure to each other, and then to the massive building sitting behind. This structural mechanism is against axial wind forces (fig. 6).


△ 图名:Chiasso Shed的细部设计(Robert Maillart,1924)

The Chiasso Shed, detail (Robert Maillart, 1924)

图源 Credits:D. Zastavni,2008



Concrete & structural design ca.1900


Now we have a first idea of how interesting and amazing are Maillart's structures. I remind you that this was built 120 years ago. So that's a long time, and these are very progressive forms for that time.



What about concrete? We have to know that at that time reinforced concrete was quite a new material. So now we just introduce the state of the knowledge around concrete as a structural material, for us to understand what makes a difference in Maillart's designs compared to what happened elsewhere at that time.



Concrete is material that come from roman times: this means 2,000 years ago. The technique was then to fill carvings in the ground or the void between two masonries with stones. And then to pour on the stones a mortar made of sand and lime, to fill the space between them and form a massive concrete from that roman time. Using a reactive sand in the mortar gave a kind of cement, but cement did not exist at that time: Only lime was available.


这种著名的罗马混凝土叫做Opus Caementicum(这是拉丁名,是当时意大利使用的语言)。那个时代使用这种罗马混凝土的一个著名例子是罗马万神殿。之后,一些相关工程师在1890年左右奠定了现代混凝土结构设计的基础:Lambot,Hennebique,Mesnager,Tetmajer……以及Robert Maillart!他们各自的贡献将会在接下来向大家展示。

This famous Roman concrete was named Opus Caementicum (This is the latin name, the language that was spoken at that time in Italy). A famous example built with this technique is the Pantheon in Rome at that time. Some later, several people laid down the theoretical basis of the modern concrete around 1890: Lambot, Hennebique, Mesnager, Tetmajer… and Robert Maillart! Their respective contributions will be presented below.



Lambot is the first: he built a small boat made of concrete in 1848 and this will change totally the meaning of what this material is. Concrete was a massive masonry, cracked and sinking. When using the association of steel and concrete, you suddenly have a new material that is able to be light, thin, elastic, floating, and without cracks. This is the very beginning of a story that will finish in this paper with the explanation of Maillart's work.



An insight of the steel reinforcement pattern of such a boat in 1887 would show features similar to a continuous light mesh.



At that time, in 1854, people began to use steel as reinforcement in building. The patterns of steel reinforcement were quite peculiar: at that time, according to Wilkinson, reinforcements for slabs will have kinds of funicular forms along the slab.



This is the time of 'systems', that are the proposals of a specific positioning of steel reinforcements to constitute a construction system for concrete. Monier's System and Hennebique's System of 1892 are examples of this. Hennebique devised the right way to put a steel reinforcement in concrete and, for this, invented stirrups that can resist shear forces in concrete. Stirrups – vertical steel frames connecting the top and bottom longitudinal reinforcements of the beam – made the system complete and turn it fully efficient.



Hennebique patented his system in 1892, and Maillart built his first bridge in 1894. So just 2 years later.



Mesnager invented a kind of hinge for concrete through crossing reinforcement steel bars. Such concrete hinges as proposed by Mesnager-Feysinnet will be used in Maillart's works from 1929.



Tetmajer expressed a very contemporary idea: if concrete cracks under bending forces while covering a steel reinforcement that secures the continuity in a structure, the result will be the creation of a kind of hinge that will reorganize forces in the whole structure. His idea gives a measure of how this engineer perceived cracks in concrete, that will also be part of the way that Maillart was looking at concrete structures.



And then we will see Maillart summarising these contributions and himself bringing a revolution about concrete design with his own approaches.



Looking at construction systems for buildings, we see the global arrangement as proposed by Hennebique looking very similar to what was made with other materials (timber and iron e.g.). Since it had columns supporting beams, and then beams themselves supporting other beams, and the other direction there will be a slab on these, this is very close to what was made with masonry, iron and timber. These are not creative forms. On the contrary, Maillart proposed the principle of continuous mushroom-slabs, in which we see the beams totally disappearing and a very creative way to manage the reinforcement system in the thickness of the slab.



About bridges: a bridge of 1899 designed and build by Hennebique, just mentioned above, shows a thick arch (between 90 and 120 cm thick) supporting columns, that are supporting beams again and the deck's slab. So this is a very traditional design that contrasts heavily with Maillart's design of stiffened arch bridges (with supporting arch with thickness of between 18 to 23 cm) that will be presented below. Other examples of such bridges follow for you to understand what was built at that time. The Risorgimento Bridge of 1911 in Italy has been long considered to be the first bridge that was using a concrete box for the section of the arch. Actually, the first box section in concrete ever used in the history is from Maillart in 1901, ten years before: a smaller bridge that presented the invented solution of a concrete box under the name: "Systeme Maillart".  



Other examples of bridges made of concrete have exactly the same form than bridges made of masonry, with clay bricks. And as shown above, in the beginning of a new material, this is a very common phenomenon that forms in the new material look to structures made with previous other materials. For concrete, new relevant forms were still to be invented and Maillart will be part of this adventure. Maillart's design will show elegant bridges with thickness less than ever seen before him.



Robert Maillart的结构设计:1898至1940
Robert Maillart's Structural Design: 1898-1940


The Tavanasa bridge (fig. 7) is built in 1905. This is really early. This is the first, let's say "consistent" structure that Maillart would be proposing. And this is actually a concrete bridge that works as a three-hinged arch: two side hinges at supports and a central hinge. And you see a kind of evolving inertia between hinges along these bridges, corresponding to the variation of bending forces, giving him these very particular forms. You have to keep in mind at that time that was something that people have never seen before. People were just building plain concrete bridge with stone facades in front of each side just to give them a look of what people were doing for the previous 100 years. So, Maillart's new forms were quite uncommon.


△ Tavanasa桥(Robert Maillart,1905年设计)

The Tavanasa Bridge (Robert Maillart, 1905)

图源 Credits:D. Zastavni,2008



If you look at his bridge, it appears to us a full rational structure. As the Salginatobel Bridge (1929), or the Vessy Bridge (1936) or the Lachen Bridge (1940).



The Salginatobel bridge (fig. 2) is this example that you have already seen. This is also a three-hinged arch bridge. This is a kind of evolution of the bridge just shown before.



The Vessy bridge came 6 years later (fig. 8). The line of the arch is not a circle anymore. The form of  his supporting arch is uncommon, but fully rational. The centers of the arches are box sections; on both sides, these are U-shape sections. This is really new in the design, when people are just building thick arches totally filled with concrete.


△ Vessy桥(Robert Maillart,1936设计)

The Vessy Bridge (Robert Maillart, 1936)

图源 Credits:D. Zastavni,2022



Lachen Bridge is the last bridges built by Maillart in 1940 (the year he dies). The form is still rational, becoming sharp and very particular. This design is very interesting, since very contemporary, but the structure is 80 years old!



Looking at a timeline of Maillart's three-hinged arch shows that that kind of bridge was used all his career along, with a break between 1905 end 1929. Maillart developed other systems also: stiffened arch bridges are based on massive arch bridges and hinged classical arch bridges, but including a stiffening system in the deck (fig. 9). This is the inversion – made of concrete – of suspended bridges.


△ Maillart的加劲拱桥原理

The principle of Maillart's stiffened arch bridge

图源 Credits:D. Zastavni,2008



The very thin arch is the inversion of the suspension funicular cable of suspended bridge, whose form is obtained with Graphic Statics. The arch of the Valtschielbach Bridge (1925) is about 23cm thick at the center and 26cm thick on both sides: thicknesses never seen before Maillart's bridge. The line is circular, close to the thrust line remaining in his thickness.



Along time, Maillart's stiffened arch bridges evolve: the general form of the arch is purer, corresponding to a true funicular arch, its thickness becoming constant at 20 cm only as in the Schwandbach Bridge (fig. 10).


△ Schwandbach桥(Robert Maillart,1933)

The Schwandbach Bridge (Robert Maillart, 1933)

图源 Credits:D. Zastavni,2022


Chiasso Shed(1924年)(图5)建于Valtschielbach桥之前,在Maillart最早设计的两座加劲拱桥之后。它的几何形状非常特殊,但它基于相同的理性方法,即再次使用图解静力学设计:在均布荷载下达到平衡的悬链,均布荷载等于屋顶自重的静荷载与雪荷载之和。

The Chiasso Shed (1924) (fig. 5)is built before the Valtschielbach Bridge, but after Maillart's two first stiffened arch bridges of that kind. Its geometry is very particular, but it comes from the same full rational approach of a funicular line equilibrating a constant uniformly distributed load corresponding to the dead load of the roof slab and the snow loading, obtained again with Graphic Statics.



With a thickness of about 24 cm X 24 cm, each member of the supporting structure can only resist a symmetrical uniformly distributed loading on the roof, with a funicular action. This seems very thin for a span of about 24 meters, contrasting strongly with everything that was made with concrete at that time (fig. 6).


回到时间轴上来看,在Maillart的作品中有8个不同的结构系统,其中7个系统仅用于桥梁(加上大跨度的Chiasso Shed)。在这些系统的基础上,蘑菇板的原理出现在了仓库和工厂建筑中,因为它适合重载。

Examining the chronology of Maillart's works, we discover a series of 8 different structural systems, among which 7 systems only for bridges (+ the large span of the Chiasso Shed). Behind this, the principle of mushroom-slabs appears for warehouse and factory buildings since it is suited for heavy loading.



Mailarts works demonstrate the variety of design for each of such other bridges. It can be demonstrated that each of these bridges is very specialized for its function, that cannot be exchanged: you cannot replace one bridge by another system on which you have to carefully take over the analysis to make the right decision. About this, we developed years ago a kind of decision tree leading to the choice of the suited type of bridge, depending on the external and internal conditions acting on it (fig. 11).


△ Maillart桥梁设计的决策树

Typological decision-making tree for Robert Maillart's bridges systems

图源 Credits:D. Zastavni,2013


还有一个时间方面的问题:三个系统一直存在于Maillart的一生中—— 一是三铰链拱桥,二是加劲拱桥及其6种演变,三是蘑菇板,三者一直持续到1940年Maillart生命结束。

So just one more thing about chronology: three systems exist together all-along Maillart's life: 1/three-hinged arch bridges, 2/ stiffened arch bridges and their 6 variations or evolutions and 3/mushroom-slabs, up to the end of Maillart's life in 1940.



Graphical statics will be required to explain the definition of the majority of Maillart's structural forms. You can go more in a detail in the series of papers which references are given below. There are a PhD dissertation and 19 papers deepening the subject for 15 years. The next step will be a book: the amount of content is form now sufficiently important to require such a written synthesis.


参考文献 References

D. Zastavni. "La conception chez Robert Maillart: Morphogenèse des Structures Architecturales," Ph.D. dissertation, LOCI/SST, UCLouvain, Louvain-la-Neuve, 2007.

D. Zastavni. "The structural design of Maillart's Chiasso Shed (1924): a graphic procedure," Structural Engineering International, vol. 18(3), 2008, pp. 247-25.

D. Zastavni. Robert Maillart's Design - Morphogenesis for architectural structures : At the occasion of the delivery of the Edoardo Benvenuto Prize 2008. Conference in commemoration of Edoardo Benvenuto (1940-1998) on the tenth anniversary, Rome, (2008).

D. Zastavni. "What was truly innovative about Maillart's designs using reinforced concrete?," in Proceedings of the Third International Congress on Construction History, Berlin: Neunplus1, 2009, pp. 1539-1546.

D. Zastavni, J.-F. Cap. What ideas does Maillart's eighty-year-old approach give us about how a concrete structure could be designed in the 21th century? FIB conference, London (2009).

D. Zastavni, J.-F. Cap. What ideas does Maillart's eighty-year-old approach give us about how a concrete structure could be designed in the 21th century? Evolution and trends in design, analysis and construction of shell and spatial structures : proceedings of the IASS Symposium 2009, Valencia (2009).

D. Zastavni. Maillart's design methods and sustainable design: 33rd IABSE International Symposium Bangkok 2009: "Sustainable Infrastructure: Environment Friendly, Safe and Resource Efficient", Bangkok, du 09/09/2009 au 11/09/2009. IABSE Congress Report — Vol. 96, no. 1, pp. 17-18 (2009).

D. Zastavni. Robert Maillart's Innovative use of Concrete. DOCOMOMO Journal — Vol. 45, no. 2011/2, pp. 12-21.

D. Zastavni. Maillart's practices for structural design : (ETH-Bibliothek's virtual exhibition). in Carvais R., Guillerme A., Nègre V., Sakarovitch J. ; "Nuts & Bolts of Construction History". Paris : A. et J. Picard, 2012.

D. Zastavni, C. Fivet. Conception en béton : à la recherche des fondamentaux. Le béton, matière en devenir - Edition 3 : Lausanne, Learning Center, EPFL. 2012.

D. Zastavni. Géométrie et conception de la dalle en béton chez Maillart : une simplicité toute relative. in R. Gargiani: L'architrave le plancher la plate-forme (collectif) : Nouvelle histoire de la construction. Lausanne : Presses polytechniques et universitaires romande. 2012.

D. Zastavni. Conception des ouvrages en béton armé au début du 20e siècle : approches visionnaires de R. Maillart (1872-1940). In Denoël J.F., Espion B., Hellebois A., Provost M. ; "Histoires de Béton Armé - Patrimoine, Durabilité, Innovations". Bruxelles : FABI, 2013. pp. 82-87, 99.

D. Zastavni. Typological decision-making tree for the design of arch bridges from historical studies. In Radic, J. ; Kuster, M ; Savor, S ; "ARCH'13", Zagreb: Secon-CSSE, 2013. pp. 325-332.

D. Zastavni, J.-F. Cap, J.-P. Jasienski. Load path and prestressing in conceptual design related to Maillart's Vessy Bridge.  IASS-SLTE 2014 Symposium "Shells, Membranes and Spatial Structures: Footprints". Brasilia, Brazil (2014).

C. Fivet, D. Zastavni. Robert Maillart's key methods from the Salginatobel bridge design process (1928). Journal of IASS — Vol. 53, no. 171, p. 39-47 (1 March 2012).

D. Zastavni, C. Fivet. "Purely geometrical considerations during the design of bridges in the early 20th century – The case of R. Maillart," in Proceedings of the Fifth International Congress on Construction History, B. Bowen and Al., & Donald Friedman, Thomas Leslie, and John Ochsendorf Eds, First Edition, 2015,  Vol.3, pp.  637-644.

D. Zastavni. "Maillart's design approach: Where graphic statics and geometry start... and end." Research Workshop, Chair of Structural Design – Prof. Dr. Joseph Schwartz, - Villa Garbald, Castasegna, 28-30 August 2017.

D. Zastavni. Structural concepts and artisanal construction in R. Maillart's design principles. In: P. Cassinello, A. Blázquez, M. SÁnchez Rojas, Á Sorlí ; "Architecture, Engineering, Concrete / AEC 2018. Where do we come from? Where are we going?". Madrid: Fundacion Edurado Torroja, 2018. pp. 737 – 744.

D. Zastavni, Robert Maillart's innovative views in using concrete. In: DOCOMOMO PRESERVATION TECHNOLOGY DOSSIER 10, Concrete - Conservation Challenges, 2021 [on press].

Allan McRobie, Cameron Millar, Denis Zastavni, Bill Baker. Graphical Stability Analysis of Maillart's Roof at Chiasso. In: Structural Engineering International [on press], 2022.










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