In Herzogenried Park, Mannheim, Germany, there is a unique building: the Multihalle. It was designed by German architect Karl Friedrich Schinkel for the 1975 Federal Garden Exhibition in Germany; the renowned architect Frei Otto led the design of its most distinctive roof structure. This architectural masterpiece not only showcased its splendor at the garden exhibition but also left a significant mark in architectural history due to its pioneering structural concepts. Today, although it is no longer the world’s largest wooden gridshell building, it is undoubtedly considered a pioneer of large glass domes.
View from the main entrance of the Multihalle interior.
The gridshell (German: Gitterschale; Gridshell, Lattice shell) is a type of spatial grid structure. In a gridshell structure, the rod elements form a shell in a grid pattern, combining the advantages of good load-bearing thin shell structures and easy-to-process frame structures. It is worth noting that although the definitions are quite similar, gridshells are not equivalent to the lattice shell structures in the Chinese context. Domestic standards classify lattice shell structures based on whether their shapes are curved; in Germany, gridshell refers specifically to single-layer lattice shell structures, while multi-layer lattice shells and frame structures are classified under spatial trusses/rigid frames. This may be because the load-bearing characteristics of single-layer lattice shells are closer to those of thin shells rather than trusses.
Interior view of the main span.
Arches only experience compression and no bending under distributed vertical loads, fully utilizing the advantages of materials under compression. Thin shell structures are an extension of arches into three dimensions: the vertical loads distributed across the shell surface are converted into longitudinal forces evenly distributed along the shell direction. In gridshell structures, the grid replaces thin plates, and longitudinal forces manifest as axial forces in the grid rod elements. These rods experience almost no bending moments, thus achieving high material utilization efficiency and near-ideal load-bearing characteristics, making them particularly suitable for large-span buildings. The curved shape of the shell is determined by the transmission and flow of forces, resulting in a high degree of unity between the building’s shape and structural function, thus possessing natural elegance and beauty.
Several types of gridshell domes.
『Multihalle』
Frei Otto designed a new roof structure for the Multihalle, which features a smooth wooden gridshell top that seems to snuggle into the park landscape.The Multihalle consists of two spaces connected by pedestrian bridges, with the wooden shell covering all spaces, including the bridges.The entire building measures 160 × 115 m, with a maximum height of 20 m above the ground.Its maximum lateral span is 60 m, and the longitudinal span reaches up to 85 m.The shell structure is made of wooden strips from Canadian hemlock, arranged in two or four layers in a cross pattern, with a spacing of 50 cm between the strips.The cross-section of the wooden strips is a square with a side length of 5.5 cm.The surface shape was determined using the inverse hanging method; Otto created a small concept model using a fine mesh metal net and suspended it by fixing it to a wooden board with pushpins.This method is called the inverse hanging method. At that time, computer technology was not yet developed, and the digital model could only be obtained through photogrammetry of the hanging model.Complex structural calculations were later completed by the London firm Arup.
Hanging model of the Multihalle: the hanging points were designed at the supports, and the metal mesh naturally fell to form the optimal stress surface. Flipping it over yields the final building shape.
Note: The inverse hanging method mentioned above essentially utilizes the characteristic of flexible structures that only experience tensile forces under specific loads to determine the structural shape, and then the structure model is solidified and flipped to obtain a pure compression structure under gravitational load. The essence of the inverse hanging experiment is to achieve a zero-bending moment structure.
Inverse hanging method used for structure shaping.
In 1974, this commemorative building officially began construction.The construction process was also full of challenges:At that time, measurement technology was not as advanced as today, and total stations had not yet been invented;Three-dimensional models were also quite rough, lacking precise spatial coordinates.The construction method involved loosely assembling a planar grid with dowels, leaving sufficient displacement space with elongated holes.When the grid was hung to the designated position, several specific nodes were fixed to the corresponding height using scaffolding, causing the grid to deform into a curved surface, and finally, the dowels were tightened to fix the shape.Due to the low bending stiffness of the wooden strips and their strong ductility, they could still maintain good compressive capacity even after bending.
Standard nodes of the Multihalle.
It is worth noting that at the intersections of the wooden strips, elongated grooves were set, and the pre-compression between each layer of wooden rods created friction to fix the strips. After achieving the designed shape, it was necessary to trim the edges of the shell; additionally, diagonal cables were added to the rhomboid grid to make the soft grid a solid structure.
In January 1975, engineers conducted load tests for structural safety on the newly completed building: 205 water-filled garbage bins were suspended on the roof. The maximum deformation measured was 79 mm, which was 1 mm smaller than the theoretical calculation. After successfully conducting this static load test, the Multihalle opened as scheduled at the 1975 Federal Garden Exhibition in Germany.
Cross-section of the Multihalle.
Once exhibited, the Multihalle achieved great success, although it was originally designed as a temporary structure intended for use only during the garden exhibition.However, due to the building’s unique shape and construction, it was not dismantled as planned but was preserved.
Reinforcement of the Multihalle. Photo by Wu Chutian.
To this day, the Multihalle has been standing for 50 years and has undergone multiple repairs and maintenance, withstanding the test of time;however, its current health status is not optimistic:The building materials have reached their lifespan, wooden components have decayed due to moisture, and the main structure has deformed;the entire roof structure requires repair.It is currently in the major repair phase, with the renovation plan aiming to preserve the original structure’s appearance and stress principles as much as possible while implementing necessary repairs and reinforcement measures, allowing the hall to be reused.The goal of this repair is to extend its safety lifespan by 50 years, making the Multihalle a centennial building.
50×50 wooden strips matching a curvature radius of 12m. Photo by Wu Chutian.
The structural system and lightness of the Multihalle are of milestone significance, as wooden gridshell structures have been at their peak since their inception.After the Multihalle, a large number of similar gridshell roofs emerged in Western Europe and Japan, among which the EPFL multifunctional hall designed by Swiss architect J. Natterer and the wooden roof of the Hanover Expo are particularly well-known.
EPFL multifunctional hall.
Gridshell wooden pavilion at the Hanover Expo.
『Pompidou Metz Center』
The Pompidou Metz Center (also known as the Pompidou Center Metz branch, French: Centre Pompidou-Metz) is a contemporary art museum located in Metz, France. Due to the large collection at the Pompidou Center in Paris, many valuable works have not been displayed to the public since its opening in 1977. To increase the opportunity for displaying works and meet the growing demand for art treasures, the Pompidou Metz Center was born.
Exterior view of the Pompidou Metz Center.
Plan view of the wooden roof, with openings for the steel tower and flower column tubes.
The building’s most significant feature is its hexagonal wooden roof. The hexagon has special symbolic significance in France, as the country’s land shape resembles a hexagon. Additionally, this large hexagon consists of a series of hexagons and equilateral triangle patterns, constructed similarly to bamboo weaving techniques, allowing the wooden components to interlace and overlap. This concept was inspired by a traditional Chinese woven straw hat that Sanaa found in an antique shop in Paris in 1999.
The Chinese bamboo woven hat that inspired Sanaa.
Structural concept sketches provided to Sanaa by Arup (2004).
After determining the idea of weaving hexagonal wooden components, the structural design team established a structure system of wooden blocks + double-layer double-curved wooden rods, as the rectangular blocks clamped at the midpoint of the rods can be considered as altered rigid struts, and its structural force system has a strong implication of avoided truss.
The voided truss invented by a Belgian.
Once the structural system was determined, the next challenge was the shaping of the wooden roof, as Frei Otto’s previous work set a high standard, and with the advancement of computer technology (the first generation of Rhino design software was available in the early 21st century, and this project used that software for design), surface shaping no longer relied on the manual inverse hanging method but could be fully assisted by computers. The initial design team shaped the roof based on minimal surfaces but found that minimal surfaces interfered with the indoor steel structure; thus, the architects adjusted the shape based on minimal surfaces into a form they were satisfied with, submitting it to structural engineers.
Note:Minimal surfaces are surfaces where the average curvature at every point is 0. The study of such surfaces began with finding surfaces that minimize surface area under certain constraints (like fixed boundaries or accommodating volumes), hence the name “minimal surface.” Minimal surfaces possess physical significance and geometric properties that grant them excellent structural characteristics in engineering.Mathematically, handling minimal surfaces is quite challenging and can be solved using differential geometry, numerical methods, etc., to find minimal surfaces in three-dimensional space, which are then computed by software.In this project, we can understand the main steel tower and column feet as wire loops, with the soap film shape drawn out representing the corresponding minimal surface.
Soap film method for shaping.
The final roof surface was formed through 50 iterations using finite element software GSA.
This project was completed by Arup, and according to local French practices, contractors generally recheck the structure. The final deepening of the wooden structure was completed by the Swiss company SJB.Kempter.Fitze, which significantly optimized the node and processing schemes of the original structural plan. The curved glued wooden components at the junctions are connected by D24 prestressed threaded rods + hexagonal wooden dowels and disc springs, allowing shear force to be transmitted through friction at the joints. A long rectangular wooden clamp is set at the midpoint of the junction, and through positive nails and slanted wooden screws, it resists shear, resulting in a semi-rigid connection effect for the voided truss system.
Real scene of the tension end wooden beam dowel joint.
Tension end wooden beam dowel joint exploded view.
The double-curved wooden components posed significant challenges for the deepening design team, especially for components near the ground flower column area, where the components had a high degree of distortion. To improve the processing precision of the components, the production team ultimately chose to use CNC machines to “carve” the glued wooden blanks into finished products, although this method resulted in a very high waste rate, with approximately 50% of the glued wood being cut away. To reduce strength loss caused by cutting, the angle of the cutting process on the wooden components should be controlled to within 5°. For components near the ground, due to high pressure and bending moments, stronger European larch was ultimately used, and we can see in the following images that the lower wooden components are noticeably darker than the upper components.
Illustration of wooden rod joint extension nodes, dowel nodes, and semi-rigid voided truss nodes.
Structural analysis indicates that the hexagonal gridshell of this project does not behave like the Multihalle in terms of shell load-bearing, primarily due to the roof shape: the entire roof is relatively flat, and its structural force transmission exhibits a mixed force form of shell structure, cantilever structure, and significant bending. For gridshell structures whose roof shapes do not meet minimal surface conditions, their components may experience considerable bending moments, leading to cross-sections that are not as slender as those of the Multihalle.
Structural analysis model of the Pompidou Metz Center.
The bamboo weaving system of architect Sanaa allowed him to stand out among 153 competitors, and SJB’s excellent deepening and manufacturing capabilities presented the double-curved components with perfect smoothness, a level of craftsmanship that domestic manufacturers still find hard to match. Clearly, the completion of the Pompidou Metz Center enriched the expressive forms of wooden gridshell structures.
『Stockholm Wisdome Dome』
The expansion project of the Swedish National Museum of Technology consists of a dome, an immersive audiovisual experience spherical space, a café, and an exhibition hall. Architects Elding Oscarson and structural engineer Florian Kosche collaborated on the design, winning the architectural competition.
“Pearl and Shell”
LVL board strips and shear keys.
Note: LVL (laminated veneer lumber) is a material made by layering thick veneer in the direction of the grain, hot-pressing and gluing, and then sawing it. Its production process is similar to that of plywood, with the main difference in the assembly, hot-pressing, and post-treatment steps. The advantages of LVL compared to glued wood are its high strength; compared to glued wood of the same species, LVL’s strength is about twice as high, and its compressive strength can rival that of concrete.
Laminated veneer lumber (LVL).
The production of double-curved components is innovative; to achieve the dome effect, the rods are doubly curved and exhibit significant twisting. Due to the large number of rods, if each component were made using independent molds, the total cost would be unmanageable.The design unit innovatively utilized the advantage of single-layer LVL to freely deform, using preset curved molds on-site, layering 5 layers of LVL strips on the curved mold to present a natural micro-curve. Subsequently, wooden screws were used to secure the stacked LVL strips, allowing them to shape and combine under stress.
The architect did not pursue alignment of the overlapping LVL edges.
LVL board strips and shear key holes.
『Conclusion』
The wooden gridshell structure consists of continuous rod components forming a spatial wooden structure through multi-directional layering. Its construction principles involve layering and intertwining, forming a system through connections that are either flexible or rigid, resulting in a hybrid structural form; depending on geometric shapes or the strength of the nodes, gridshell structures can exhibit load-bearing as shell structures or local voided truss structures, with longitudinal rod components mainly bearing tension and compression while also accommodating some bending moments. The challenges of wooden gridshell structures lie in shaping, achieving twisted wooden components, and designing nodes, and the creative solutions to these challenges add a touch of charm to them.
In recent years, many wooden gridshell structures have emerged in China as well. Due to space limitations, other wooden gridshell projects will not be elaborated on here, but a brief introduction to some typical projects is provided for reader reference.
Taiyuan Botanical Garden Greenhouse.
The greenhouse at Taiyuan Botanical Garden is shaped like a “shell,” with the largest span of greenhouse #1 being 89.5m and a maximum height of 29.5m. It uses a two-way stacked glued wooden beam to form a gridshell structure system, with two-way cables set under the glued wooden beams, and the cables and glued wooden beams are connected through inverted quadrangular conical rods to form the entire greenhouse structure.
Restaurant at Taiyuan Botanical Garden.
The roof of the restaurant at Taiyuan Botanical Garden adopts a two-way crossed grid structure composed of layered wooden beams, with the wooden beams gradually reducing from 9 layers at the central skylight to 3 layers at the cantilevered end, relying on interlayer block nodes to form a staggered voided truss, achieving a maximum span of 25m. The design concept is based on traditional Chinese wooden structure roofs, reinterpreting their structure and geometric logic.
Yixing Ceramic Museum designed by Kengo Kuma.
The Yixing Ceramic Museum features a visually striking inverted shell-shaped roof, formed by multiple intersecting spherical surfaces, supported by four layers of wooden grid beams. These beams not only bear structural loads but also create a light and dynamic internal space. As the roof is made of local Yixing-produced purple clay tiles, the roof load is relatively large. Unlike conventional gridshell structures, the anti-overturning design of the top wooden rods deserves further study.
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