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Funicular Curve
In architecture, the funicular curve (also funicular polygon, funicular shape, from the , "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 the basis of the ... [...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 is a comparison or correspondence between two things (or two groups of things) because of a third element that they are considered to share. In logic, it is an inference or an argument from one particular to another particular, as opposed to deduction, induction, and abduction. It is also used where at least one of the premises, or the conclusion, is general rather than particular in nature. It has the general form ''A is to B as C is to D''. In a broader sense, analogical reasoning is a cognitive process of transferring some information or meaning of a particular subject (the analog, or source) onto another (the target); and also the linguistic expression corresponding to such a process. 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 human thought processes. It has been argued that analogy lies ... [...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''. The force equal to the resultant force in magnitude, yet pointed in the opposite direction, is called an equilibrant force. Illustration The diagram illustrates simple graphical methods for finding the line of application of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sagrada Família
The Basílica i Temple Expiatori de la Sagrada Família, otherwise known as Sagrada Família, is a church under construction in the Eixample district of Barcelona, Catalonia, Spain. It is the largest unfinished Catholic church in the world. Designed by the Catalans, Catalan architect Antoni Gaudí (1852–1926), in 2005 his work on Sagrada Família was added to an existing (1984) UNESCO World Heritage Site, "Works of Antoni Gaudí". On 7 November 2010, Pope Benedict XVI consecrated the church and proclaimed it a minor basilica. On 19 March 1882, construction of Sagrada Família began under architect Francisco de Paula del Villar y Lozano, Francisco de Paula del Villar. In 1883, when Villar resigned, Gaudí took over as chief architect, transforming the project with his architectural and engineering style, combining Gothic architecture, Gothic and curvilinear Art Nouveau forms. Gaudí devoted the remainder of his life to the project, and he is buried in the church's crypt. At ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Church Of Colònia Güell
The Church of Colònia Güell (, ) is an unfinished work by Antoni Gaudí Antoni Gaudí i Cornet ( , ; ; 25 June 1852 – 10 June 1926) was a Catalans, Catalan architect and designer from Spain, widely known as the greatest exponent of Catalan ''Modernisme''. Gaudí's works have a style, with most located in Barc .... It was built as a place of worship for the people on a hillside in a manufacturing area in Santa Coloma de Cervelló, near Barcelona (Catalonia, Spain). Colònia Güell was the brainchild of Count Eusebi de Güell; who enlisted the help of architect Antoni Gaudí in 1898. However, work was not started until 1908, 10 years after commission. The plan for the building consisted of constructing two naves, an upper and a lower, two towers, and one forty-meter-high central dome. In 1914, the Güell family halted construction due to the death of Count Güell. At the time, the lower nave was almost complete so between the years of 1915 and 1917, it was completed and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dome
A dome () is an architectural element similar to the hollow upper half of a sphere. There is significant overlap with the term cupola, which may also refer to a dome or a structure on top of a dome. The precise definition of a dome has been a matter of controversy and there are a wide variety of forms and specialized terms to describe them. A dome can rest directly upon a Rotunda (architecture), rotunda wall, a Tholobate, drum, or a system of squinches or pendentives used to accommodate the transition in shape from a rectangular or square space to the round or polygonal base of the dome. The dome's apex may be closed or may be open in the form of an Oculus (architecture), oculus, which may itself be covered with a roof lantern and cupola. Domes have a long architectural lineage that extends back into prehistory. Domes were built in ancient Mesopotamia, and they have been found in Persian architecture, Persian, Ancient Greek architecture, Hellenistic, Ancient Roman architecture, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rotational Symmetry
Rotational symmetry, also known as radial symmetry in geometry, is the property a shape (geometry), shape has when it looks the same after some rotation (mathematics), rotation by a partial turn (angle), turn. An object's degree of rotational symmetry is the number of distinct Orientation (geometry), 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 -dimensional Euclidean space. Rotations are Euclidean group#Direct and indirect isometries, direct isometries, i.e., Isometry, isometries preserving Orientation (mathematics), orientation. Therefore, a symmetry group of rotational symmetry is a subgroup of (see Euclidean g ... [...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 Society of Jesus, Jesuit College and the University of Caen, where he received his Magister Artium, M.A. in 1682. He took Holy Orders the following year. Varignon gained his first exposure to mathematics by reading Euclid and then René Descartes, Descartes' ''La Géométrie''. He became professor of mathematics at the Collège des Quatre-Nations, 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 de France, Collège Royal. He was elected to the Prussian Academy of Sciences, 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 Isaa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Force Polygon
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 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 (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. 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 (see ). Free body A body is said to be "free" when it is singled out from other bodies for the purposes of dynamic or static analysis. The object does not have to be "free" in the sense of being unforced, and it may or may not be in a state of equilibrium; rather, it is not fixed in place and is thus "f ... [...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 p ... [...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 () is a geometric representation of how the force is applied. It is the straight line through the point at which the force is applied, and is in the same direction as the vector . The lever arm is the perpendicular distance from the axis of rotation to the line of action. 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 associated with a force \vec F directed at displacement \v ... [...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 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. 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 Robert Hooke's anal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
