Curved Structures and Their Applications in Buildings

Curved structures are being used in building design to create unique and functional spaces. They can be found in various types of buildings, including residential homes and commercial offices.

One notable example is the use of curved lines in the design of the Guggenheim Museum in Bilbao, Spain. This building's flowing curves create a sense of dynamism and visual interest.

The use of curved structures can also provide benefits in terms of natural light and ventilation. For instance, the curved roof of the Museum of Fine Arts in Boston allows for an abundance of natural light to enter the building.

Curved structures can be made using various materials, including steel and glass.

Curved structures can be generated from genetratrices that undergo geometrical operations like extrusion or revolution. This process allows for the creation of various types of curved structures.

An arch is generated by revolving a point or surface around a center, while a vault is created by extruding an arched surface. A dome, on the other hand, is formed by revolving an arched surface around an axis.

More complex shapes can be generated through boolean operations on a set of interacting volumes. These shapes include the Groin vault or Cross Vault, the Domical Vault, and the Umbrella Vault, among others.

Here are some examples of complex curved structures generated through boolean operations:

Curved structures are three-dimensional solids that can be generated from genetratrices through geometrical operations like extrusion or revolution. These operations are the same ones used in computer-aided design (CAD) software to create and analyze complex shapes.

An arch is created by revolving a point or surface around a center, while a vault is formed by extruding an arched surface. A dome, on the other hand, is generated by revolving an arched surface around an axis.

More complex shapes can be created by performing boolean operations on a set of interacting volumes. This can result in various shapes, such as the Groin vault or Cross Vault, which is formed by the intersection of two or more vaults.

Here are some examples of complex curved structures:

These complex shapes can be created using the same operations used in CAD software to analyze them, making it easier to design and understand curved structures.

Fabric dome shelters are a game-changer in the industrial, construction, and mining industries due to their exceptional design and durability.

They're engineered with precision, combining the lightweight nature of fabric materials with the stability of curved architecture, making them ideal for various applications.

These shelters possess the resilience to endure severe climatic conditions, providing a reliable and innovative solution that surpasses expectations.

Their aerodynamic shape ensures even distribution of external forces, minimising wind resistance and ensuring stability even in challenging weather conditions.

Fabric dome shelters are a modern evolution of steel dome structures, offering a lightweight and cost-effective solution for a range of purposes in industries such as mining, transport, and agriculture.

They're safe even in cyclonic wind conditions when engineered for Australian Wind Region D, and can be fully sealed with End Walls to give people and assets complete protection from the elements.

Fabric dome shelters are proven and effective, able to last decades with the correct care and maintenance, and can be moved from one location to another with little to no disturbance to the surrounding environment.

Curved structures have been used for centuries in various building types, including arches, vaults, and domes. These shapes were used to cover large rooms in buildings like the Domus Aurea of Emperor Nero and the Pantheon in Rome.

The Ancient Romans exploited curved structures for bridges, aqueducts, and sewage ducts, using materials like masonry and Roman concrete. They also built arch-dams, which were a type of curved structure used for infrastructure.

With the Industrial Revolution, the materials used for curved structures changed to wrought iron, cast iron, and later, reinforced concrete. This led to changes in the shape of infrastructures, such as the Garabit viaduct by Gustave Eiffel.

Architects have long employed curved shapes to create unique and functional structures. The Domus Aurea of Emperor Nero is an example of a building that utilized curved shapes to cover large rooms.

The Ancient Romans were skilled at using curved structures for various purposes, including bridges, aqueducts, and sewage ducts. They often used materials like masonry and Roman concrete.

The Industrial Revolution brought new materials like wrought iron and cast iron, which were used to create curved structures like the Palm House at Kew Gardens and The Crystal Palace. These buildings showcased the potential of curved architecture.

Reinforced concrete became a popular choice in the 20th century, thanks in part to the work of Pier Luigi Nervi. His ribbed hangars are a notable example of curved structures made from this material.

Curved surfaces have been used in a wide range of structures, from the Philips Pavilion in Brussels to the hyperbolic paraboloid-shaped L'Oceanogràfic in Valencia. These designs often blend seamlessly into their surroundings.

Curved structures have several advantages, including improved structural stability and resilience against external pressures. This is due in part to the absence of sharp angles, which can weaken a building's structure.

Curved structures, like vaults and arches, can't stand alone until they're completed. This is because they need a temporary supporting structure, called centring, to stay in place until the keystone is set.

Centring is almost always necessary, but there are some exceptions. Filippo Brunelleschi's domical vault in the Florence Cathedral is a famous example of a structure built without centring.

The vault was built using a massive, spherical dome-like structure with large ribs. The masonry herringbone bond helped to lean and fix each new layer on the previous one, creating a strong and stable structure.

The vault is also double-skin, with an intermediate hollow space that hosts staircases and allows air to flow, preventing humidity concentration. This design helped to resist parallel tensile stresses that could have separated the fuses of the vault.

Another example of a structure built without centring is the Global Vipassana Pagoda in Mumbai. Its massive masonry dome, with an inner diameter of about 85m, was made possible by the double curvature of the dome and the special shape of the carved sandstone blocks.

A curved structure's stability depends on its boundary conditions, with axial stress being the primary concern. In masonry curved structures, the funicolar polygon's position within the middle third of the cross section determines safety and stability.

Professor de:Jacques Heyman's assumptions about unlimited compressive resistance and null tensile and shear resistance are widely used in Gothic architecture. This method is still studied today, and has been adapted for three-dimensional cases.

The arrangement of single units in a curved structure plays a positive role in terms of stability, as seen in traditional masonry curved structures like vaults and domes. The double curvature of these structures helps distribute weight evenly.

In a hemispherical membrane, compressive stress occurs in the upper part, while hoop tensile stresses are present in the lower part. This leads to the formation of meridian cracks, dividing the dome into slices.

Curved structures can rely on their shape too, unlike post and lintel construction which depends on the resistance of single members.

Single curvature structures, such as simple vaults, show less capacity than double curvature ones like domes and cloisters.

A simple vault corresponds to a developable surface with null Gaussian curvature, making it possible to flatten to a planar surface with no distortion.

Dome-like and saddle structures have respectively positive and negative Gaussian curvature, making them shape-resistant structures par excellence.

This means that curved structures can distribute weight evenly and resist external forces like wind and snow, providing superior structural stability.

The curved shape of a structure can even deflect strong gusts, giving it greater wind resistance than other shaped structures.

Wood is a versatile material that can be bent to create complex curved shapes. With traditional and modern techniques, it's possible to achieve the desired curvature.

Steam Bending is a method that involves heating wood in a steambox until it becomes malleable, then securing it in a mold. This process allows wood to retain a curved shape after cooling.

Glued Laminated Wood is a popular method for bending large structural pieces. By gluing segments of wood following a curved mold, the material can be bent.

The Kerfing technique is used to curve large non-structural parts with spaced cuts. This method is often used for decorative elements.

Researchers have developed a new method that takes advantage of wood's natural swelling and contraction to make panels bend.

Concrete is not particularly known for its ability to bend, but traditional methods involve using curved formwork achieved by bending timber or plywood to the desired radius.

Curved formwork is still a viable option for creating complex geometries, and with more advanced technologies, it's possible to mass produce uniquely curved precast concrete using innovations like BIM, Computer Aided Manufacture (CAM), and robotically-reconfigurable molds.

3D construction printing also shows great promise in creating curved shapes through a computer-controlled process.

The Hongkun Art Gallery features a combination of rounded walls created using curved molds that guide visitors through the exhibition areas.

Cast from white concrete within CNC-cut and 3D-printed formwork, this structure acts as one dynamic unit with its continuous shape.

To build curved walls, architects can spray concrete onto a supporting structure made from layers of polystyrene sheets and mesh around a CNC-milled wooden frame, as seen in the Kouhsar Villa.

Recent innovations like Mesh Mould and Curvecrete are also making it easier to work with curved concrete, with Mesh Mould being a robotically-fabricated reinforced metal mesh that's filled with concrete, and Curvecrete using a parametric adjustable mold machine to manufacture curved concrete panels.

Curved glass is a game-changer in structural glazing applications, offering efficiency and resistance. It's surprising how far it's come in terms of complexity and time-consuming processes.

The main technologies used today are bending and tempering, hot bending, cold bending, and laminated bending. The bending and tempering process involves heating the glass to over 630°C in a glass bending oven to achieve the desired radius.

In hot bending, manufacturers use molds heated to 580-600°C, often with a mechanical bending press. This process is a significant improvement over traditional methods.

Cold bending is performed at natural temperatures, where the glass is glued or screwed into a frame to mechanically bend it. This method is surprisingly effective.

Bent laminated glass involves curving a glass sandwich with a mechanical fixture before the autoclave process. This creates a strong and durable result.

Curved glass can be used to maximize daylight and create a fluid, open living space, as seen in the Casa Kwantes property. The curved glass wall was integrated to avoid segmentation at its edges and provide a unique view of the space.

Transparent and curved glass can also be used to create a collaborative, dynamic space, such as in the Kering Offices. The interior partitions were constructed with curved glass at their corners to achieve this effect.