Reticulated shell is a kind of space truss structure similar to plane grid, which is a space frame based on members and arranged according to shell structure. It has the characteristics of truss and shell. Its force transmission characteristics are mainly through the pulling force, pressure or shear force in two directions in the shell. This kind of structure is a kind of spatial structure that attracts much attention at home and abroad, and has broad development prospects. Reticulated shells include single-layer reticulated shells, prestressed reticulated shells, plate-cone reticulated shells, ribbed ring cable-supported reticulated shells and single-layer bifurcated reticulated shells.

2. Development history of reticulated shells

The prototype of reticulated shell structure-dome structure. In the development of human society, long-span spatial structure is often the dream and goal pursued by architects. Among them, the development of reticulated shell structure has experienced a long historical evolution process. In order to have a better living space, ancient humans often used branches as skeletons and straw as skins, imitating eggshells, bird heads and caves to build dome structures, that is, primitive tents. With the development of building materials, the stone behind the dome is gradually replaced by masonry. Domes generally have a small span, ranging from 30m to 40m. The Roman Pantheon, built in 120 ~ 124, is a typical example of the early dome. By the19th century, the application of iron opened up a new era for the development of domes, and the appearance and application of modern reinforced concrete structure theory opened up a new field for long-span thin-shell domes. 1922, the first reinforced concrete thin shell planetarium in the history of civil engineering was built in Jena, Germany.

Jena planetarium

With the appearance and application of light and high-strength materials such as iron, steel and aluminum alloy, imaginative engineers began to apply various forms of bars to dome structures. Schwedler, a German engineer who is recognized as the "father of dome structure", played a key role in the birth and development of dome reticulated shells. On the basis of thin-shell dome, he put forward a new structural style, that is, the surface of the dome is divided into longitudinal ribs and latitudinal horizontal loop lines, which are connected together, and each trapezoidal grid is divided into two or four triangles with diagonal bars, so that the internal force distribution on the surface of the dome will be more uniform, and the weight of the structure itself will be further reduced, so that it can span more. This kind of dome structure is actually a real reticulated shell structure, that is, roughly the same grid or smaller units are regularly arranged along a certain surface, thus forming a spatial bar system structure.

Schwedler reticulated shell

3. Appreciation of completed reticulated shells

Fuller ball

1962165438+1October 13. After many twists and turns, Canada finally won the right to host the 1967 Montreal World Expo.

USA Pavilion of Montreal World Expo

At the Montreal World Expo, the most conspicuous design is a huge spherical building, which is Buckminster? The American Pavilion designed by Fuller (a great American artist, inventor and design scientist, 1895— 1983). The sphere of the USA Pavilion is 76 meters in diameter, and the triangular metal mesh structure is reasonably combined into a sphere. The whole design is simple and novel, without any redundant materials, and the building is like a delicate and beautiful crystal ball. The appearance of this globe venue not only makes the USA Pavilion a landmark building of this World Expo, but also makes the designer Buckminster? Fuller is famous.

Yasi Governor Hotel

YasViceroy Hotel (Abu Dhabi) is located in Abu Dhabi, United Arab Emirates. The chief architect is in charge, and Hani rashid+lise anne couture is in charge of structural design. Half of the hotel is built on land and half on water, and the seemingly separated two halves are integrated by a reticulated shell structure covering the outer layer. The whole building is not only elegant and dreamy at night, but also gives people a magnificent feeling during the day.

At the same time, the regular, symmetrical and gradual structural components make people's eyes flow continuously with the lines, and their thinking also diverges along the extension of the components.

Mur i.

Reticulated shells are not only suitable for long-span structures, but also can be used to build strange buildings similar to the artificial island of Moore Island, satisfying people's strong imagination. Mur Island was established to celebrate "Graz 2003 Cultural Capital", which was designed by Vito Acconci, a designer from new york, USA. The main structure of Moore Island is a spatial reticulated shell structure with bridges connected in series on both sides. Looking down from the river bank, the whole spiral island is like a huge silver shell, which is considered as a classic work integrating art and architecture, dream and reality.

shenzhen bay sports center

Reticulated shell structure is especially favored by large stadiums because of its reasonable stress, beautiful shape, satisfying complex free space and minimal interference between internal supports.

Known as the "Bird's Nest in the North and Spring Cocoon in the South", "Spring Cocoon" is the main venue of the 26th Universiade-Shenzhen Bay Sports Center 20 1 1. The whole project covers an area of about 3074 hectares with a total construction area of 256,000 square meters. It is a landmark building in Shenzhen.

The steel structure of Shenzhen Bay Sports Center is a long and complex spatial structure. Steel roof is composed of single-layer reticulated shell (public areas such as stadium and Dashu Square), double-layer curved grid (gymnasium and swimming pool) and vertical support system.

Layered reticulated shell is a complex spatial curved grid structure, with a plane length of 532.7m and a width of 240.4m, and the maximum height relative to the landing site is 42.3m (the landing site elevation is +6.0m). Except Dashu Square, the whole roof reticulated shell is composed of quadrilateral meshes directly woven by box-section members (700mm high and 450mm wide), and the average size of the mesh is about 4050 mm.

Hangzhou Olympic Sports Center Swimming Pool —— Unique Streamline of "Galaxy Phantom"

The shape of this sports swimming pool is unique. As can be seen from the picture, it is shaped like the wings of a butterfly. But when it is associated with swimming venues, it feels like a huge "bikini".

The roof of the swimming pool of Hangzhou Olympic Sports Center covers three units of the lower concrete structure, which is a complete steel reticulated shell structure and naturally extends to the 8m platform. The roof is a free-form surface.

The roofs of swimming pools and gymnasiums are inclined double-layer reticulated shells with variable thickness. The rhombic grid of reticulated shell is about 5m in side length and 6.3mx9.2m in diagonal length.

4. Form-finding of reticulated shell structure

Some architectural cases of reticulated shells are read, and the form-finding of reticulated shells is discussed from the structural aspect. There are many contents in structural form-finding, and there are usually three mainstream methods: force density method, dynamic relaxation method and nonlinear finite element method. Of these three methods, I usually prefer to use the third one, that is, the nonlinear finite element method. Here, I will focus on the nonlinear finite element method.

The basic principle of nonlinear finite element method is simply to use the method of upside-down hanging to complete form finding, and the text description is too boring, so I won't say much and give an example directly. If the building gives you a roof skin, such as a round skin, see the picture below.

Architectural epidermis

We assume that it is supported by a concrete roof, and the whole roof is a circular reticulated shell structure. We introduce it into ABAQUS, and because the roof usually bears uniform vertical surface load, we adopt the upside-down scheme to impose reverse surface load on it.

Abaqus finite element model

We use 5mm thick steel plate to simulate the shell, so that its bending stiffness can be ignored, and there is only tensile stress without bending moment in the shell. In this way, the shape we found has only pure pressure in the shell under uniform pressure, and there is no bending moment caused by span.

Because the shell structure is thin and the overall bending performance is poor, it is usually applied to long-span spatial structures, so it is necessary to find a shape to solve the bending moment caused by span, which is also one of the purposes of shape finding. The next step is to import the shell shape calculated by ABAQUS into rhinoceros, and then arrange the shell members on the plane and project them on the curved surface, and the space reticulated shell structure formed is the final structural calculation model we need. The whole process is relatively simple, so I won't demonstrate it in detail.

Form-finding result

The above form-finding method belongs to surface form-finding method. What Bian Xiao wants to mention in this paper is that the rod form-finding method can be directly used, that is, according to the skin of the building, the rods are directly arranged, and the nonlinear finite element analysis of the planar reticulated shell is carried out to get the final shape of the reticulated shell, and an example is given to illustrate it. If a single-layer Kewitt spherical reticulated shell is used to simulate the roof above, the shape of its components can be directly found by the toolbox compiled by Bian Xiao team, and then imported into SAP2000 (recognized analysis software), and a surface load of 5KN/m2 is applied on the opposite side. The calculation results are as follows. The 3KN.m in the figure is the additional bending moment on each member due to the double guiding load, while the bending moment formed by the long span is basically absent. The axial force of the bar seems to be the main force of each bar.

5. The little apple with structural imagination

Bian Xiao recently saw a photo of Apple's headquarters building, suddenly wanted to be an architect, and put forward some other modeling schemes. He can make a big atrium, with a large-span reticulated shell roof on the upper part of the atrium, and the shape of the reticulated shell is Apple's logo.

Apple headquarters building

Bian Xiao took this as a starting point and introduced the Apple logo into abaqus. Here, I want to explain that because the Apple logo is asymmetrical, I don't know who bit it, so the first step is to import abaqus for calculation and analysis, find out the principal stress flow of the shell structure, and provide ideas and guidance for us to arrange the shell bars in the future.

Abaqus model of apple logo

After calculation and analysis, the principal stress flow of the main structure is shown in the following figure, and then the reticulated shell members are arranged according to the boundary size of Apple logo. The principle of structural arrangement is that along the direction of principal stress flow, these stress flows will eventually become axial forces of shell members.

Form-finding results of apple logo reticulated shell

Principal stress flow obtained from form-finding analysis

In this paper, only the apple part is arranged, and the span of the leaf part is relatively small, so this paper will not analyze it. The maximum span of this structure is about 80m, and the initial camber is about 6m. After form-finding and calculation and analysis, it is found that the bending moment of shell members is about 1.3kN.m, which is basically a pure compression member.

Reticulated shell structure is simple, orderly and ultra-thin with its unique and beautiful shape, which is pleasing to the eye. However, as a structural engineer, it is necessary to calculate and analyze the long-span reticulated shell structure from many aspects, including its initial defects, overall stability, shell foot support thrust, construction simulation analysis and so on. However, with the more and more mature calculation software, reticulated shells will be more and more used in future projects.

I believe that after the above introduction, everyone has a certain understanding of the perfect design method of reticulated shell structure in structural design strategy. Welcome to Zhong Da for more information.

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