In a broad sense, the term graphic statics is used to describe the technique of solving particular practical problems of statics using graphical means. [1] Actively used in the architecture of the 19th century, the methods of graphic statics were largely abandoned in the second half of the 20th century, primarily due to widespread use of frame structures of steel and reinforced concrete that facilitated analysis based on linear algebra. The beginning of the 21st century was marked by a "renaissance" of the technique driven by its addition to the computer-aided design tools thus enabling engineers to instantly visualize form and forces. [2]
Markou and Ruan [2] trace the origins of the graphic statics to da Vinci and Galileo who used the graphical means to calculate the sum of forces, Simon Stevin's parallelogram of forces and the 1725 introduction of the force polygon and funicular polygon by Pierre Varignon. Giovanni Poleni used the graphical calculations (and Robert Hooke's analogy between the hanging chain and standing structure) while studying the dome of the Saint Peter's Basilica in Rome (1748). Gabriel Lamé and Émile Clapeyron studied of the dome of the Saint Isaac's Cathedral with the help of the force and funicular polygons (1823). [2]
Finally, Carl Culmann had established the new discipline (and gave it a name) in his 1864 work Die Graphische Statik. Culmann was inspired by preceding work by Jean-Victor Poncelet on earth pressure and Lehrbuch der Statik by August Möbius. The next twenty years saw rapid development of methods that involved, among others, major physicists like James Clerk Maxwell and William Rankine. In 1872 Luigi Cremona introduced the Cremona diagram to calculate trusses, [3] in 1873 Robert H. Bow established the "Bow's notation" [4] that is still in use. [2] It fell out of use, especially since construction methods, such as concrete post and beam, allowed for familiar numerical calculations. Access to powerful computation gave structural engineers new tools to compute stresses for shell structures such as Finite element method.
While the method is not commonly used for construction today, graphic statics was proposed as an educational tool to teach intuition in engineering education. [5] It is employed in classes at MIT [6] and ETH. [7] for architecture and structural engineering students.
To graphically determine the resultant force of multiple forces, the acting forces can be arranged as edges of a polygon by attaching the beginning of one force vector to the end of another in an arbitrary order. Then the vector value of the resultant force would be determined by the missing edge of the polygon. [8] In the diagram, the forces P1 to P6 are applied to the point O. The polygon is constructed starting with P1 and P2 using the parallelogram of forces (vertex a). The process is repeated (adding P3 yields the vertex b, etc.). The remaining edge of the polygon O-e represents the resultant force R.
In the case of two applied forces, their sum (resultant force) can be found graphically using a parallelogram of forces.
With the advent of computational tools and parametric design, graphic statics has undergone significant evolution, transitioning from manual drawing techniques to digital workflows. These adaptations have enhanced its precision, accessibility, and integration into modern architectural and engineering practices. [9]
Several software platforms have integrated graphic statics principles, enabling designers to explore equilibrium-based forms and optimize structures efficiently. A few examples include:
Digital adaptations have expanded the scope of graphic statics, making it a valuable tool for:
The digitization of graphic statics has also influenced its role in education. Many universities such as MIT now teach graphic statics through interactive software, enabling students to experiment with equilibrium concepts in a hands-on manner.
Despite its advantages, digital graphic statics faces challenges such as scalability for highly complex systems and integration with advanced analytical tools like Finite Element Method (FEM). However, ongoing research continues to address these limitations.
Statics is the branch of classical mechanics that is concerned with the analysis of force and torque acting on a physical system that does not experience an acceleration, but rather is in equilibrium with its environment.
The unified modeling language (UML) is a general-purpose visual modeling language that is intended to provide a standard way to visualize the design of a system.
Computer-aided design (CAD) is the use of computers to aid in the creation, modification, analysis, or optimization of a design. This software is used to increase the productivity of the designer, improve the quality of design, improve communications through documentation, and to create a database for manufacturing. Designs made through CAD software help protect products and inventions when used in patent applications. CAD output is often in the form of electronic files for print, machining, or other manufacturing operations. The terms computer-aided drafting (CAD) and computer-aided design and drafting (CADD) are also used.
Autodesk 3ds Max, formerly 3D Studio and 3D Studio Max, is a professional 3D computer graphics program for making 3D animations, models, games and images. It is developed and produced by Autodesk Media and Entertainment. It has modeling capabilities and a flexible plugin architecture and must be used on the Microsoft Windows platform. It is frequently used by video game developers, many TV commercial studios, and architectural visualization studios. It is also used for movie effects and movie pre-visualization. 3ds Max features shaders, dynamic simulation, particle systems, radiosity, normal map creation and rendering, global illumination, a customizable user interface, and its own scripting language.
A truss is an assembly of members such as beams, connected by nodes, that creates a rigid structure.
The parallelogram of forces is a method for solving the results of applying two forces to an object. When more than two forces are involved, the geometry is no longer a parallelogram, but the same principles apply to a polygon of forces. The resultant force due to the application of a number of forces can be found geometrically by drawing arrows for each force. The parallelogram of forces is a graphical manifestation of the addition of vectors.
In physics and engineering, a free body diagram is a graphical illustration used to visualize the applied forces, moments, and resulting reactions on a free body in a given condition. It depicts a body or connected bodies with all the applied forces and moments, and reactions, which act on the body(ies). The body may consist of multiple internal members, or be a compact body. A series of free bodies and other diagrams may be necessary to solve complex problems. Sometimes in order to calculate the resultant force graphically the applied forces are arranged as the edges of a polygon of forces or force polygon.
A beam is a structural element that primarily resists loads applied laterally across the beam's axis. Its mode of deflection is primarily by bending, as loads produce reaction forces at the beam's support points and internal bending moments, shear, stresses, strains, and deflections. Beams are characterized by their manner of support, profile, equilibrium conditions, length, and material.
Christian Otto Mohr was a German civil engineer. He is renowned for his contributions to the field of structural engineering, such as Mohr's circle, and for his study of stress.
Robert Maillart was a Swiss civil engineer who revolutionized the use of structural reinforced concrete with such designs as the three-hinged arch and the deck-stiffened arch for bridges, and the beamless floor slab and mushroom ceiling for industrial buildings. His Salginatobel (1929–1930) and Schwandbach (1933) bridges changed the aesthetics and engineering of bridge construction dramatically and influenced decades of architects and engineers after him. In 1991 the Salginatobel Bridge was declared an International Historic Civil Engineering Landmark by the American Society of Civil Engineers.
The Cremona diagram, also known as the Cremona-Maxwell method, is a graphical method used in statics of trusses to determine the forces in members. The method was developed by the Italian mathematician Luigi Cremona. However, recognizable Cremona diagrams appeared as early as 1725, in Pierre Varignon's posthumously published work, Nouvelle Méchanique ou Statique.
Shear force and bending moment diagrams are analytical tools used in conjunction with structural analysis to help perform structural design by determining the value of shear forces and bending moments at a given point of a structural element such as a beam. These diagrams can be used to easily determine the type, size, and material of a member in a structure so that a given set of loads can be supported without structural failure. Another application of shear and moment diagrams is that the deflection of a beam can be easily determined using either the moment area method or the conjugate beam method.
An architectural drawing or architect's drawing is a technical drawing of a building that falls within the definition of architecture. Architectural drawings are used by architects and others for a number of purposes: to develop a design idea into a coherent proposal, to communicate ideas and concepts, to convince clients of the merits of a design, to assist a building contractor to construct it based on design intent, as a record of the design and planned development, or to make a record of a building that already exists.
Generative design is an iterative design process that uses software to generate outputs that fulfill a set of constraints iteratively adjusted by a designer. Whether a human, test program, or artificial intelligence, the designer algorithmically or manually refines the feasible region of the program's inputs and outputs with each iteration to fulfill evolving design requirements. By employing computing power to evaluate more design permutations than a human alone is capable of, the process is capable of producing an optimal design that mimics nature's evolutionary approach to design through genetic variation and selection. The output can be images, sounds, architectural models, animation, and much more. It is, therefore, a fast method of exploring design possibilities that is used in various design fields such as art, architecture, communication design, and product design.
VisualFEA is a finite element analysis software program for Microsoft Windows and Mac OS X. It is developed and distributed by Intuition Software, Inc. of South Korea, and used chiefly for structural and geotechnical analysis. Its strongest point is its intuitive, user-friendly design based on graphical pre- and postprocessing capabilities. It has educational features for teaching and learning structural mechanics, and finite element analysis through graphical simulation. It is widely used in college-level courses related to structural mechanics and finite element methods.
Parametric design is a design method in which features, such as building elements and engineering components, are shaped based on algorithmic processes rather than direct manipulation. In this approach, parameters and rules establish the relationship between design intent and design response. The term parametric refers to the input parameters that are fed into the algorithms.
C3D Toolkit is a proprietary cross-platform geometric modeling kit software developed by Russian C3D Labs. It's written in C++. It can be licensed by other companies for use in their 3D computer graphics software products. The most widely known software in which C3D Toolkit is typically used are computer aided design (CAD), computer-aided manufacturing (CAM), and computer-aided engineering (CAE) systems.
In manufacturing, freeform surface machining refers to the machining of complex surfaces that are not uniformly planar. The industries which most often manufactures free-form surfaces are basically aerospace, automotive, die mold industries, biomedical and power sector for turbine blades manufacturing. Generally 3- or 5-axis CNC milling machines are used for this purpose. The manufacturing process of freeform surfaces is not an easy job, as the tool path generation in present CAM technology is generally based on geometric computation so tool path are not optimum. The geometry can also be not described explicitly so errors and discontinuities occurrence in the solid structure cannot be avoided. Free-form surfaces are machined with the help of different tool path generation method like adaptive iso-planar tool path generation, constant scallop tool path generation, adaptive iso-parametric method, iso-curvature, isophote and by other methods. The different methods are chosen based on the parameters which is needed to be optimized.
Eleni Chatzi is a Greek civil engineer, researcher, and a professor and Chair of Structural Mechanics and Monitoring at the Department of Civil, Environmental and Geomatic Engineering of the Swiss Federal Institute of Technology in Zurich.
In architecture, the funicular curve is an approach used to design the compression-only structural forms using an equivalence between the rope with hanging weights and standing arch with its load. This duality was noticed by Robert Hooke in 1675. If the hanging rope carries just its own weight, the resulting curve is a catenary.