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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] |
Statics
Statics is the branch of classical mechanics that is concerned with the analysis of force and torque (also called moment) acting on physical systems that do not experience an acceleration (''a''=0), but rather, are in static equilibrium with their environment. The application of Newton's second law to a system gives: : \textbf F = m \textbf a \, . Where bold font indicates a vector that has magnitude and direction. \textbf F is the total of the forces acting on the system, m is the mass of the system and \textbf a is the acceleration of the system. The summation of forces will give the direction and the magnitude of the acceleration and will be inversely proportional to the mass. The assumption of static equilibrium of \textbf a = 0 leads to: : \textbf F = 0 \, . The summation of forces, one of which might be unknown, allows that unknown to be found. So when in static equilibrium, the acceleration of the system is zero and the system is either at rest, or its center of mas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Saint Peter's Basilica
The Papal Basilica of Saint Peter in the Vatican ( it, Basilica Papale di San Pietro in Vaticano), or simply Saint Peter's Basilica ( la, Basilica Sancti Petri), is a church built in the Renaissance style located in Vatican City, the papal enclave that is within the city of Rome, Italy. It was initially planned by Pope Nicholas V and then Pope Julius II to replace the aging Old St. Peter's Basilica, which was built in the fourth century by Roman emperor Constantine the Great. Construction of the present basilica began on 18 April 1506 and was completed on 18 November 1626. Designed principally by Donato Bramante, Michelangelo, Carlo Maderno and Gian Lorenzo Bernini, St. Peter's is the most renowned work of Renaissance architecture and the largest church in the world by interior measure. While it is neither the mother church of the Catholic Church nor the cathedral of the Diocese of Rome (these equivalent titles being held by the Archbasilica of Saint John Lat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edge (geometry)
In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope. In a polygon, an edge is a line segment on the boundary, and is often called a polygon side. In a polyhedron or more generally a polytope, an edge is a line segment where two faces (or polyhedron sides) meet. A segment joining two vertices while passing through the interior or exterior is not an edge but instead is called a diagonal. Relation to edges in graphs In graph theory, an edge is an abstract object connecting two graph vertices, unlike polygon and polyhedron edges which have a concrete geometric representation as a line segment. However, any polyhedron can be represented by its skeleton or edge-skeleton, a graph whose vertices are the geometric vertices of the polyhedron and whose edges correspond to the geometric edges. Conversely, the graphs that are skeletons of three-dimensional polyhedra can be characterized by Steinitz's theore ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polygon Of Forces
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 struct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truss
A truss is an assembly of ''members'' such as beams, connected by ''nodes'', that creates a rigid structure. In engineering, a truss is a structure that "consists of two-force members only, where the members are organized so that the assemblage as a whole behaves as a single object". A "two-force member" is a structural component where force is applied to only two points. Although this rigorous definition allows the members to have any shape connected in any stable configuration, trusses typically comprise five or more triangular units constructed with straight members whose ends are connected at joints referred to as ''nodes''. In this typical context, external forces and reactions to those forces are considered to act only at the nodes and result in forces in the members that are either tensile or compressive. For straight members, moments (torques) are explicitly excluded because, and only because, all the joints in a truss are treated as revolutes, as is necessary for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cremona Diagram
The Cremona diagram, also known as the Cremona-James Clerk Maxwell, Maxwell method, is a graphical method used in statics of trusses to determine the forces in members (graphic statics). 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''.. See also . In the Cremona method, first the external forces and reactions are drawn (to scale (ratio), scale) forming a vertical line in the lower right side of the picture. This is the net force, sum of all the force Vector (geometric), vectors and is equal to zero as there is mechanical equilibrium. Since the static equilibrium, equilibrium holds for the external forces on the entire truss construction, it also holds for the internal forces acting on each joint. For a joint to be ''at rest'' the sum of the forces on a joint must also be equal to zero. Starting at joint ''Aor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Luigi Cremona
Antonio Luigi Gaudenzio Giuseppe Cremona (7 December 1830 – 10 June 1903) was an Italian mathematician. His life was devoted to the study of geometry and reforming advanced mathematical teaching in Italy. He worked on algebraic curves and algebraic surfaces, particularly through his paper ''Introduzione ad una teoria geometrica delle curve piane'' ("Introduction to a geometrical theory of the plane curves"), and was a founder of the Italian school of algebraic geometry. Biography Luigi Cremona was born in Pavia (Lombardy), then part of the Austrian-controlled Kingdom of Lombardy–Venetia. His youngest brother was the painter Tranquillo Cremona. In 1848, when Milan and Venice rose against Austria, Cremona, then only seventeen, joined the ranks of the Italian volunteers. He remained with them, fighting on behalf of his country's freedom, until, in 1849, the capitulation of Venice put an end to the campaign. He then returned to Pavia, where he pursued his studies at the univer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Rankine
William John Macquorn Rankine (; 5 July 1820 – 24 December 1872) was a Scottish mechanical engineer who also contributed to civil engineering, physics and mathematics. He was a founding contributor, with Rudolf Clausius and William Thomson (Lord Kelvin), to the science of thermodynamics, particularly focusing on the first of the three thermodynamic laws. He developed the Rankine scale, an equivalent to the Kelvin scale of temperature, but in degrees Fahrenheit rather than Celsius. Rankine developed a complete theory of the steam engine and indeed of all heat engines. His manuals of engineering science and practice were used for many decades after their publication in the 1850s and 1860s. He published several hundred papers and notes on science and engineering topics, from 1840 onwards, and his interests were extremely varied, including, in his youth, botany, music theory and number theory, and, in his mature years, most major branches of science, mathematics and engineering. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Clerk Maxwell
James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician and scientist responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism and light as different manifestations of the same phenomenon. Maxwell's equations for electromagnetism have been called the " second great unification in physics" where the first one had been realised by Isaac Newton. With the publication of "A Dynamical Theory of the Electromagnetic Field" in 1865, Maxwell demonstrated that electric and magnetic fields travel through space as waves moving at the speed of light. He proposed that light is an undulation in the same medium that is the cause of electric and magnetic phenomena. (This article accompanied an 8 December 1864 presentation by Maxwell to the Royal Society. His statement that "light and magnetism are affections of the same substance" is at page 499.) The unification of light and electrical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
August Möbius
August is the eighth month of the year in the Julian calendar, Julian and Gregorian calendars, and the fifth of seven months to have a length of 31 days. Its zodiac sign is Leo (astrology), Leo and was originally named ''Sextilis'' in Latin because it was the 6th month in the original ten-month Roman calendar under Romulus and Remus, Romulus in 753 BC, with March being the first month of the year. About 700 BC, it became the eighth month when January and February were added to the year before March by King Numa Pompilius, who also gave it 29 days. Julius Caesar added two days when he created the Julian calendar in 46 BC (708 Ab urbe condita, AUC), giving it its modern length of 31 days. In 8 BC, it was renamed in honor of Emperor Augustus. According to a Senatus consultum quoted by Macrobius, he chose this month because it was the time of several of his great triumphs, including the conquest of Egypt. Commonly repeated lore has it that August has 31 days because Augustus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jean-Victor Poncelet
Jean-Victor Poncelet (; 1 July 1788 – 22 December 1867) was a French engineer and mathematician who served most notably as the Commanding General of the École Polytechnique. He is considered a reviver of projective geometry, and his work ''Traité des propriétés projectives des figures'' is considered the first definitive text on the subject since Gérard Desargues' work on it in the 17th century. He later wrote an introduction to it: ''Applications d'analyse et de géométrie''. As a mathematician, his most notable work was in projective geometry, although an early collaboration with Charles Julien Brianchon provided a significant contribution to Feuerbach's theorem. He also made discoveries about projective harmonic conjugates; relating these to the poles and polar lines associated with conic sections. He developed the concept of parallel lines meeting at a point at infinity and defined the circular points at infinity that are on every circle of the plane. These discoverie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carl Culmann
Carl Culmann (10 July 1821 – 9 December 1881) was a German structural engineer. Born in Bad Bergzabern, Palatinate region, Rhenish Palatinate, in modern-day Germany, Culmann's father, a pastor, tutored him at home before enrolling him at the military engineering school at Metz to prepare for entry to the École Polytechnique. Culmann's ambitions were frustrated by an attack of typhoid and, after a long convalescence, he attended the University of Karlsruhe, Karlsruhe Polytechnic School. He joined the Bavarian civil service in 1841 as an apprentice engineer in the design of railroad bridges.Hartenberg (1981) Continuing his mathematical studies, in particular under L. C. Schnürlein, in 1847 Culmann transferred to Munich so that he could improve his English language, English in anticipation of a study tour to the United Kingdom and the United States. His tour lasted from 1849 to 1851, studying the comparative designs of truss bridges and developing new analytical techniques to fa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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