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Funicular Polygon
In architecture, the funicular curve (also funicular polygon, funicular shape, from the la, fūniculus, "of rope") is an approach used to design the compression-only structural forms (like masonry arches) using an equivalence between the rope with hanging weights and standing arch with its load. This duality was noticed by Robert Hooke in 1675 ("as hangs the flexible line, so, but inverted, will stand the rigid arch"). If the hanging rope carries just its own weight (in this case it is usually called a "chain" and is equivalent to a free-standing arch with no external load), the resulting curve is a catenary. In graphic statics, a ''funicular polygon'' is a graphic method of finding out the line of action for a combination of forces applied to a solid body at different points, a complement to the force polygon used to obtain the value and direction of the resultant force. Both polygons were introduced by Pierre Varignon (''Nouvelle Mecanique ou Statique'', 1725) and became ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analogy Between An Arch And A Hanging Chain And Comparison To The Dome Of St Peter's Cathedral In Rome
Analogy (from Greek ''analogia'', "proportion", from ''ana-'' "upon, according to" lso "against", "anew"+ ''logos'' "ratio" lso "word, speech, reckoning" is a cognitive process of transferring information or meaning from a particular subject (the analog, or source) to another (the target), or a linguistic expression corresponding to such a process. In a narrower sense, analogy is an inference or an argument from one particular to another particular, as opposed to deduction, induction, and abduction, in which at least one of the premises, or the conclusion, is general rather than particular in nature. The term analogy can also refer to the relation between the source and the target themselves, which is often (though not always) a similarity, as in the biological notion of analogy. Analogy plays a significant role in problem solving, as well as decision making, argumentation, perception, generalization, memory, creativity, invention, prediction, emotion, explanation, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structural Form (engineering)
Simultaneous equations models are a type of statistical model in which the dependent variables are functions of other dependent variables, rather than just independent variables. This means some of the explanatory variables are jointly determined with the dependent variable, which in economics usually is the consequence of some underlying equilibrium mechanism. Take the typical supply and demand model: whilst typically one would determine the quantity supplied and demanded to be a function of the price set by the market, it is also possible for the reverse to be true, where producers observe the quantity that consumers demand ''and then'' set the price. Simultaneity poses challenges for the estimation of the statistical parameters of interest, because the Gauss–Markov assumption of strict exogeneity of the regressors is violated. And while it would be natural to estimate all simultaneous equations at once, this often leads to a computationally costly non-linear optimization ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Masonry
Masonry is the building of structures from individual units, which are often laid in and bound together by mortar; the term ''masonry'' can also refer to the units themselves. The common materials of masonry construction are bricks, building stone such as marble, granite, and limestone, cast stone, concrete blocks, glass blocks, and adobe. Masonry is generally a highly durable form of construction. However, the materials used, the quality of the mortar and workmanship, and the pattern in which the units are assembled can substantially affect the durability of the overall masonry construction. A person who constructs masonry is called a mason or bricklayer. These are both classified as construction trades. Applications Masonry is commonly used for walls and buildings. Brick and concrete block are the most common types of masonry in use in industrialized nations and may be either load-bearing or non-load-bearing. Concrete blocks, especially those with hollow cores, offer va ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arch
An arch is a vertical curved structure that spans an elevated space and may or may not support the weight above it, or in case of a horizontal arch like an arch dam, the hydrostatic pressure against it. Arches may be synonymous with vaults, but a vault may be distinguished as a continuous arch forming a roof. Arches appeared as early as the 2nd millennium BC in Mesopotamian brick architecture, and their systematic use started with the ancient Romans, who were the first to apply the technique to a wide range of structures. Basic concepts An arch is a pure compression form. It can span a large area by resolving forces into compressive stresses, and thereby eliminating tensile stresses. This is sometimes denominated "arch action". As the forces in the arch are transferred to its base, the arch pushes outward at its base, denominated "thrust". As the rise, i. e. height, of the arch decreases the outward thrust increases. In order to preserve arch action and prevent collapse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Hooke
Robert Hooke FRS (; 18 July 16353 March 1703) was an English polymath active as a scientist, natural philosopher and architect, who is credited to be one of two scientists to discover microorganisms in 1665 using a compound microscope that he built himself, the other scientist being Antoni van Leeuwenhoek in 1676. An impoverished scientific inquirer in young adulthood, he found wealth and esteem by performing over half of the architectural surveys after London's great fire of 1666. Hooke was also a member of the Royal Society and since 1662 was its curator of experiments. Hooke was also Professor of Geometry at Gresham College. As an assistant to physical scientist Robert Boyle, Hooke built the vacuum pumps used in Boyle's experiments on gas law, and himself conducted experiments. In 1673, Hooke built the earliest Gregorian telescope, and then he observed the rotations of the planets Mars and Jupiter. Hooke's 1665 book ''Micrographia'', in which he coined the term "cell", ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Catenary
In physics and geometry, a catenary (, ) is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends in a uniform gravitational field. The catenary curve has a U-like shape, superficially similar in appearance to a parabola, which it is not. The curve appears in the design of certain types of arches and as a cross section of the catenoid—the shape assumed by a soap film bounded by two parallel circular rings. The catenary is also called the alysoid, chainette,MathWorld or, particularly in the materials sciences, funicular. Rope statics describes catenaries in a classic statics problem involving a hanging rope. Mathematically, the catenary curve is the graph of the hyperbolic cosine function. The surface of revolution of the catenary curve, the catenoid, is a minimal surface, specifically a minimal surface of revolution. A hanging chain will assume a shape of least potential energy which is a catenary. Galileo Galil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graphic Statics
In a broad sense, the term graphic statics is used to describe the technique of solving particular practical problems of statics using graphical means. 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 frame, 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 the architects to instantly visualize form and forces. History Markou and Ruan 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 Rober ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Line Of Action
In physics, the line of action (also called line of application) of a force ''(F)'' is a geometric representation of how the force is applied. It is the line through the point at which the force is applied in the same direction as the vector .Mungan, Carl E. "Acceleration of a pulled spool." The Physics Teacher 39.8 (2001): 481-485. https://www.usna.edu/Users/physics/mungan/_files/documents/Publications/TPT.pdf The concept is essential, for instance, for understanding the net effect of multiple forces applied to a body. For example, if two forces of equal magnitude act upon a rigid body along the same line of action but in opposite directions, they cancel and have no net effect. But if, instead, their lines of action are not identical, but merely parallel, then their effect is to create a moment on the body, which tends to rotate it. Calculation of torque For the simple geometry associated with the figure, there are three equivalent equations for the magnitude of the torque ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Force Polygon
A free body diagram consists of a diagrammatic representation of a single body or a subsystem of bodies isolated from its surroundings showing all the forces acting on it. In physics and engineering, a free body diagram (FBD; also called a force diagram) is a graphical illustration used to visualize the applied forces, moments, and resulting reactions on a 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 (such as a truss), or be a compact body (such as a beam). A series of free bodies and other diagrams may be necessary to solve complex problems. Purpose Free body diagrams are used to visualize forces and moments applied to a body and to calculate reactions in mechanics problems. These diagrams are frequently used both to determine the loading of individual structural components and to calculate internal forces within a stru ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Resultant Force
In physics and engineering, a resultant force is the single force and associated torque obtained by combining a system of forces and torques acting on a rigid body via vector addition. The defining feature of a resultant force, or resultant force-torque, is that it has the same effect on the rigid body as the original system of forces. Calculating and visualizing the resultant force on a body is done through computational analysis, or (in the case of sufficiently simple systems) a free body diagram. The point of application of the resultant force determines its associated torque. The term ''resultant force'' should be understood to refer to both the forces and torques acting on a rigid body, which is why some use the term ''resultant force–torque''. Illustration The diagram illustrates simple graphical methods for finding the line of application of the resultant force of simple planar systems. #Lines of application of the actual forces and \scriptstyle \vec_ in the leftmost ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre Varignon
Pierre Varignon (1654 – 23 December 1722) was a French mathematician. He was educated at the Jesuit College and the University of Caen, where he received his M.A. in 1682. He took Holy Orders the following year. Varignon gained his first exposure to mathematics by reading Euclid and then Descartes' ''La Géométrie''. He became professor of mathematics at the Collège Mazarin in Paris in 1688 and was elected to the Académie Royale des Sciences in the same year. In 1704 he held the departmental chair at Collège Mazarin and also became professor of mathematics at the Collège Royal. He was elected to the Berlin Academy in 1713 and to the Royal Society in 1718. Many of his works were published in Paris in 1725, three years after his death. His lectures at Mazarin were published in Elements de mathematique' in 1731. Varignon was a friend of Newton, Leibniz, and the Bernoulli family. Varignon's principal contributions were to graphic statics and mechanics. Except for l'H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rotational Symmetry
Rotational symmetry, also known as radial symmetry in geometry, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which it looks exactly the same for each rotation. Certain geometric objects are partially symmetrical when rotated at certain angles such as squares rotated 90°, however the only geometric objects that are fully rotationally symmetric at any angle are spheres, circles and other spheroids. Formal treatment Formally the rotational symmetry is symmetry with respect to some or all rotations in ''m''-dimensional Euclidean space. Rotations are direct isometries, i.e., isometries preserving orientation. Therefore, a symmetry group of rotational symmetry is a subgroup of ''E''+(''m'') (see Euclidean group). Symmetry with respect to all rotations about all points implies translational symmetry with respect to all translations, so space is homo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
