In this article, we will show that the discipline of architecture is based on a complex set of elements, which evolve over the centuries depending on materials, construction techniques and mathematics. To fully understand the history and evolution of architecture, it is essential to integrate these 3 fundamental components and to know the constraints linked to the construction of architectural works. We will also give a wink to a French initiative started in 1997, which really deserves its place here.
Building materials: a history of stone, wood and innovations
The use of appropriate building materials is one of the pillars of architecture. Over the centuries, different materials have been used to meet architectural needs. Ancient Egypt, for example, used stone to build its famous pyramids, using mathematics to ensure the accuracy of dimensions and the stability of the structures.
Throughout history, new materials have appeared. Steel revolutionized construction in the 19th century, allowing architects to design more daring structures. The use of reinforced concrete in the 20th century gave rise to soaring skyscrapers and avant-garde buildings.
Construction techniques: from craftsmanship to digital technology
Construction techniques have also evolved in parallel with materials. In the Middle Ages, master builders used artisanal methods to build cathedrals. Mathematics, especially geometry, was essential for creating complex plans and designing magnificent vaults and arches.
With the advent of the industrial age, construction techniques evolved through the use of machines, cranes and prefabrication methods. Mathematics has been used to analyze constraints on structures, allowing the construction of ever more ambitious bridges and buildings.
Today, architecture incorporates advanced digital technologies based on mathematical principles that allow architects to design complex structures with unparalleled precision.
Mathematics: a timeless guide
In addition to basic measurements of the height or width of a building, mathematics also serves as a guide in choosing the use of certain types of materials and specific construction techniques to account for the force constraints with an essential role in architecture. They are an essential element to take into account because they determine the stability and durability of structures. Understanding these constraints is crucial to designing strong and safe buildings. Here is an overview of the main force constraints in architecture:
Compression: Compression is a force that pushes building materials inward. The elements that mainly experience compressive forces are pillars, columns and walls. Architects must ensure that these elements can support the load without excessive deformation.
Tension: Tension is the opposite of compression. It occurs when materials are stretched. Elements subject to tension forces include cables, chains and parts of suspended structures. It is crucial to choose materials that can withstand tension without breaking.
Shear: Shear force occurs when parts of a structure slide relative to each other. Areas subject to shear include joints, welds and fasteners. Design and materials must be chosen to resist these forces.
Bending: Bending is the deformation caused by the combination of compression and tension forces. Beams and lintels are elements commonly subjected to bending forces. The design of these elements must take into account their ability to resist these forces to avoid breakage or excessive deformation.
Cohesion: Cohesion refers to the ability of materials to resist rupture under internal forces. This is especially important for concrete, stone and brick materials. Engineers must ensure that these materials remain intact despite the stresses to which they are subjected.
Lateral compression: Lateral compression occurs when elements are compressed non-uniformly or obliquely. This can lead to deformation and structural failure. The design must minimize these forces to maintain stability.
Torsion: Torsion is a rotating force that acts on elements such as columns or posts. Architects and engineers must design these elements to resist twisting, using appropriate materials and shapes.
Earthquakes and winds: Seismic forces result from ground movements during an earthquake, while wind forces are caused by the pressure exerted by the wind on buildings. Buildings must be designed to resist these forces using techniques such as seismic isolation and wind resistance.
Understanding and managing these force constraints is essential to guarantee the safety and stability of buildings. Architects and engineers must take these forces into account when designing and choosing appropriate materials, structural forms and construction methods to ensure that structures can withstand the loads placed on them.
The Guédelon construction site: an example of returning to the fundamentals
The Guédelon site, located in Bourgogne, is an extraordinary example of the importance of these components in architecture. This project to reconstruct a 13th century medieval castle relies on fundamental mathematical knowledge to ensure precision in construction.
The craftsmen work in close collaboration with a scientific council, architects and other building specialists to guarantee that each element is designed and built with precision, in compliance with the standards of the time. The artisans of Guédelon work with local materials, such as stone, wood and metal, using period techniques, requiring mathematical skills for measurement, geometry and geodesy. Material strength calculations, proportions and measurements were crucial to the construction of castles, cathedrals and other monumental buildings of this period. This demonstrates how mathematics was central to the creation of monumental structures, even at a time when it was less formalized.
Architecture is constantly evolving as a reflection of the evolution of society. It results from the harmonious combination of materials, construction techniques and mathematics. Mathematics underpins the design principles, strength calculations and precise measurements needed to create exceptional buildings. Old buildings demonstrate the mastery of the craftsmen of the time, while modern achievements exploit technological innovations to create avant-garde structures.
Through this example, the Guédelon site reminds us of the importance of understanding and respecting the history of construction and remains a reflection of the mastery of materials, construction techniques and mathematics throughout the centuries. They are not just practical items but witnesses to the evolution of science, art and mathematics. They are at the heart of architecture, allowing architects to create works that reflect their times while preserving the know-how of the past.