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The second moment of area, or second area moment, or quadratic moment of area and also known as the area moment of inertia, is a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis. The second moment of area is typically denoted with either an I (for an axis that lies in the plane of the area) or with a J (for an axis perpendicular to the plane). In both cases, it is calculated with a multiple integral over the object in question. Its dimension is L (length) to the fourth power. Its unit of dimension, when working with the International System of Units, is meters to the fourth power, m4, or inches to the fourth power, in4, when working in the Imperial System of Units. In structural engineering, the second moment of area of a beam is an important property used in the calculation of the beam's deflection and the calculation of stress caused by a moment applied to the beam. In order to maximize the second moment of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Area
Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or ''plane area'' refers to the area of a shape A shape or figure is a graphics, graphical representation of an object or its external boundary, outline, or external Surface (mathematics), surface, as opposed to other properties such as color, Surface texture, texture, or material type. A pl ... or planar lamina, while ''surface area'' refers to the area of an open surface or the boundary (mathematics), boundary of a solid geometry, three-dimensional object. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat. It is the two-dimensional analogue of the length of a plane curve, curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept). The area of a shape can be measured by com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structural Load
A structural load or structural action is a force, deformation, or acceleration applied to structural elements. A load causes stress, deformation, and displacement in a structure. Structural analysis, a discipline in engineering, analyzes the effects of loads on structures and structural elements. Excess load may cause structural failure, so this should be considered and controlled during the design of a structure. Particular mechanical structures—such as aircraft, satellites, rockets, space stations, ships, and submarines—are subject to their own particular structural loads and actions. Engineers often evaluate structural loads based upon published regulations, contracts, or specifications. Accepted technical standards are used for acceptance testing and inspection. Types Dead loads are static forces that are relatively constant for an extended time. They can be in tension or compression. The term can refer to a laboratory test method or to the normal usage of a material ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moment Of Area Of A Rectangle Through The Centroid
Moment or Moments may refer to: * Present time Music * The Moments, American R&B vocal group Albums * ''Moment'' (Dark Tranquillity album), 2020 * ''Moment'' (Speed album), 1998 * ''Moments'' (Darude album) * ''Moments'' (Christine Guldbrandsen album) * ''Moments'' (Mark Holden album), 1995 * ''Moments'' (Leo Ku album) * ''Moments'' (Barbara Mandrell album) * ''Moments'' (Andrew Rayel album) * ''Moments'' (Boz Scaggs album) Songs * "Moment" (Blanche song) (2018) * "Moment" (SMAP song) (2012) * "Moment", a song by Aiden from ''Conviction'' * "Moment", a 2014 song by Young Money from '' Young Money: Rise of an Empire'', featuring Lil Wayne * "Moments" (Hans Bollandsås song) (2010) * "Moments" (Emerson Drive song) (2007) * "Moments" (Ayumi Hamasaki song) (2004) * "Moments" (Tove Lo song) (2014) * "Moments" (One Direction song) (2011) * "Moments" (Freddy Verano song) * "Moments", a song by Westlife from ''Westlife'' Film and television * ''Moment'' (film), a 1978 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Second Moments Of Area
The following is a list of second moments of area of some shapes. The second moment of area, also known as area moment of inertia, is a geometrical property of an area which reflects how its points are distributed with respect to an arbitrary axis. The physical unit, unit of dimension of the second moment of area is length to fourth power, unit of length, L4, and should not be confused with the mass moment of inertia. If the piece is thin, however, the mass moment of inertia equals the area density times the area moment of inertia. Second moments of area Please note that for the second moment of area equations in the below table: I_x = \iint_A y^2 \, dx \, dy and I_y = \iint_A x^2 \, dx \, dy. Parallel axis theorem The parallel axis theorem can be used to determine the second moment of area of a rigid body about any axis, given the body's second moment of area about a parallel axis through the body's centroid, the area of the cross section, and the perpendicular distance ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linearity Of Integration
In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with differentiation, integration is a fundamental, essential operation of calculus,Integral calculus is a very well established mathematical discipline for which there are many sources. See and , for example. and serves as a tool to solve problems in mathematics and physics involving the area of an arbitrary shape, the length of a curve, and the volume of a solid, among others. The integrals enumerated here are those termed definite integrals, which can be interpreted as the signed area of the region in the plane that is bounded by the graph of a given function between two points in the real line. Conventionally, areas above the horizontal axis of the plane are positive while areas below are negative. Integrals also refer to the concept of an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pythagorean Theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation relating the lengths of the sides ''a'', ''b'' and the hypotenuse ''c'', often called the Pythagorean equation: :a^2 + b^2 = c^2 , The theorem is named for the Greek philosopher Pythagoras, born around 570 BC. The theorem has been proven numerous times by many different methods – possibly the most for any mathematical theorem. The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years. When Euclidean space is represented by a Cartesian coordinate system in analytic geometry, Euclidean distance satisfies the Pythagorean relation: the squared dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parallel Axis Theorem
The parallel axis theorem, also known as Huygens–Steiner theorem, or just as Steiner's theorem, named after Christiaan Huygens and Jakob Steiner, can be used to determine the moment of inertia or the second moment of area of a rigid body about any axis, given the body's moment of inertia about a parallel axis through the object's center of gravity and the perpendicular distance between the axes. Mass moment of inertia Suppose a body of mass is rotated about an axis passing through the body's center of mass. The body has a moment of inertia with respect to this axis. The parallel axis theorem states that if the body is made to rotate instead about a new axis , which is parallel to the first axis and displaced from it by a distance , then the moment of inertia with respect to the new axis is related to by : I = I_\mathrm + md^2. Explicitly, is the perpendicular distance between the axes and . The parallel axis theorem can be applied with the stretch rule and perpe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartesian Coordinates
A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length. Each reference coordinate line is called a ''coordinate axis'' or just ''axis'' (plural ''axes'') of the system, and the point where they meet is its ''origin'', at ordered pair . The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin. One can use the same principle to specify the position of any point in three-dimensional space by three Cartesian coordinates, its signed distances to three mutually perpendicular planes (or, equivalently, by its perpendicular projection onto three mutually perpendicular lines). In general, ''n'' Cartesian coordinates (an element of real ''n''-space) specify the point in an ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moment Of Area Of An Arbitrary Shape
Moment or Moments may refer to: * Present time Music * The Moments, American R&B vocal group Albums * ''Moment'' (Dark Tranquillity album), 2020 * ''Moment'' (Speed album), 1998 * ''Moments'' (Darude album) * ''Moments'' (Christine Guldbrandsen album) * ''Moments'' (Mark Holden album), 1995 * ''Moments'' (Leo Ku album) * ''Moments'' (Barbara Mandrell album) * ''Moments'' (Andrew Rayel album) * ''Moments'' (Boz Scaggs album) Songs * "Moment" (Blanche song) (2018) * "Moment" (SMAP song) (2012) * "Moment", a song by Aiden from ''Conviction'' * "Moment", a 2014 song by Young Money from '' Young Money: Rise of an Empire'', featuring Lil Wayne * "Moments" (Hans Bollandsås song) (2010) * "Moments" (Emerson Drive song) (2007) * "Moments" (Ayumi Hamasaki song) (2004) * "Moments" (Tove Lo song) (2014) * "Moments" (One Direction song) (2011) * "Moments" (Freddy Verano song) * "Moments", a song by Westlife from ''Westlife'' Film and television * ''Moment'' (film), a 1978 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, with its main goal being to understand how the universe behaves. "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Moments Of Inertia
Moment of inertia, denoted by , measures the extent to which an object resists rotational acceleration about a particular axis, it is the rotational analogue to mass (which determines an object's resistance to ''linear'' acceleration). The moments of inertia of a mass have units of dimension ML2( ass× engthsup>2). It should not be confused with the second moment of area, which is used in beam calculations. The mass moment of inertia is often also known as the rotational inertia, and sometimes as the angular mass. For simple objects with geometric symmetry, one can often determine the moment of inertia in an exact closed-form expression. Typically this occurs when the mass density is constant, but in some cases the density can vary throughout the object as well. In general, it may not be straightforward to symbolically express the moment of inertia of shapes with more complicated mass distributions and lacking symmetry. When calculating moments of inertia, it is useful to rememb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
