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Section Modulus
Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. Other geometric properties used in design include area for tension and shear, radius of gyration for compression, and second moment of area and polar second moment of area for stiffness. Any relationship between these properties is highly dependent on the shape in question. Equations for the section moduli of common shapes are given below. There are two types of section moduli, the elastic section modulus and the plastic section modulus. The section moduli of different profiles can also be found as numerical values for common profiles in tables listing properties of such. Notation North American and British/Australian convention reverse the usage of ''S'' & ''Z''. Elastic modulus is ''S'' in North America, but ''Z'' in Britain/Australia, and vice versa for the plastic modulus. Eurocode 3 (EN 1993 - Steel Design) resolves this by using ''W'' for both, but distinguishe ...
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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 ...
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Area Moment Of Inertia Of A Circle
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 or planar lamina, while ''surface area'' refers to the area of an open surface or the boundary of a 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 curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept). The area of a shape can be measured by comparing the shape to squares of a fixed size. In the International System of Units (SI), the standard unit of area is the square metre (written as m2), which is the area of a square whose sides are one metre long. A shape with an area of three square metres would have the same area as three such squares. ...
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List Of Area Moments Of Inertia
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 unit of dimension of the second moment of area is length to fourth power, 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 (''d'') between the axes. I ...
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Beam Theory
Beam may refer to: Streams of particles or energy *Light beam, or beam of light, a directional projection of light energy **Laser beam *Particle beam, a stream of charged or neutral particles **Charged particle beam, a spatially localized group of electrically charged particles ***Cathode ray, or electron beam or e-beam, streams of electrons observed in discharge tubes ***X-ray beam, a penetrating form of high-energy electromagnetic radiation ** Molecular beam, a beam of particles moving at approximately equal velocities Arts, entertainment and media * Beam (music), a connection line in musical notation * Beam, to transport matter using the Transporter in the ''Star Trek'' fictional universe * Beam (rapper), American hip hop artist * BEAM.TV, an online digital delivery and content management platform * BEAM Channel 31, a Philippines television network * Beam (website), later Mixer, a former video game live streaming platform * BeamNG.drive, an open-world vehicle simulation v ...
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Section Modulus-C-channel
Section, Sectioning or Sectioned may refer to: Arts, entertainment and media * Section (music), a complete, but not independent, musical idea * Section (typography), a subdivision, especially of a chapter, in books and documents ** Section sign (§), typographical characters * Section (bookbinding), a group of sheets, folded in the middle, bound into the binding together * The Section (band), a 1970s American instrumental rock band * ''The Outpost'' (1995 film), also known as ''The Section'' * Section, an instrumental group within an orchestra * "Section", a song by 2 Chainz from the 2016 album ''ColleGrove'' * "Sectioning", a ''Peep Show'' episode * David "Section" Mason, a fictional character in '' Call of Duty: Black Ops II'' Organisations * Section (Alpine club) * Section (military unit) * Section (Scouting) Science, technology and mathematics Science * Section (archaeology), a view in part of the archaeological sequence showing it in the vertical plane * Section (bi ...
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Section Modulus-rectangular Tube
Section, Sectioning or Sectioned may refer to: Arts, entertainment and media * Section (music), a complete, but not independent, musical idea * Section (typography), a subdivision, especially of a chapter, in books and documents ** Section sign (§), typographical characters * Section (bookbinding), a group of sheets, folded in the middle, bound into the binding together * The Section (band), a 1970s American instrumental rock band * ''The Outpost'' (1995 film), also known as ''The Section'' * Section, an instrumental group within an orchestra * "Section", a song by 2 Chainz from the 2016 album ''ColleGrove'' * "Sectioning", a ''Peep Show'' episode * David "Section" Mason, a fictional character in '' Call of Duty: Black Ops II'' Organisations * Section (Alpine club) * Section (military unit) * Section (Scouting) Science, technology and mathematics Science * Section (archaeology), a view in part of the archaeological sequence showing it in the vertical plane * Section (bi ...
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Area Moment Of Inertia Of A Circular 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 or planar lamina, while ''surface area'' refers to the area of an open surface or the boundary of a 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 curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept). The area of a shape can be measured by comparing the shape to squares of a fixed size. In the International System of Units (SI), the standard unit of area is the square metre (written as m2), which is the area of a square whose sides are one metre long. A shape with an area of three square metres would have the same area as three such squares. ...
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Section Modulus-I-beam-weak Axis
Section, Sectioning or Sectioned may refer to: Arts, entertainment and media * Section (music), a complete, but not independent, musical idea * Section (typography), a subdivision, especially of a chapter, in books and documents ** Section sign (§), typographical characters * Section (bookbinding), a group of sheets, folded in the middle, bound into the binding together * The Section (band), a 1970s American instrumental rock band * ''The Outpost'' (1995 film), also known as ''The Section'' * Section, an instrumental group within an orchestra * "Section", a song by 2 Chainz from the 2016 album ''ColleGrove'' * "Sectioning", a ''Peep Show'' episode * David "Section" Mason, a fictional character in '' Call of Duty: Black Ops II'' Organisations * Section (Alpine club) * Section (military unit) * Section (Scouting) Science, technology and mathematics Science * Section (archaeology), a view in part of the archaeological sequence showing it in the vertical plane * Section (bi ...
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Radius Of Gyration
''Radius of gyration'' or gyradius of a body about the axis of rotation is defined as the radial distance to a point which would have a moment of inertia the same as the body's actual distribution of mass, if the total mass of the body were concentrated there. Mathematically the radius of gyration is the root mean square distance of the object's parts from either its center of mass or a given axis, depending on the relevant application. It is actually the perpendicular distance from point mass to the axis of rotation. One can represent a trajectory of a moving point as a body. Then radius of gyration can be used to characterize the typical distance travelled by this point. Suppose a body consists of n particles each of mass m. Let r_1, r_2, r_3, \dots , r_n be their perpendicular distances from the axis of rotation. Then, the moment of inertia I of the body about the axis of rotation is :I = m_1 r_1^2 + m_2 r_2^2 + \cdots + m_n r_n^2 : If all the masses are the same (m), then ...
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Section Modulus-I-beam-strong Axis
Section, Sectioning or Sectioned may refer to: Arts, entertainment and media * Section (music), a complete, but not independent, musical idea * Section (typography), a subdivision, especially of a chapter, in books and documents ** Section sign (§), typographical characters * Section (bookbinding), a group of sheets, folded in the middle, bound into the binding together * The Section (band), a 1970s American instrumental rock band * ''The Outpost'' (1995 film), also known as ''The Section'' * Section, an instrumental group within an orchestra * "Section", a song by 2 Chainz from the 2016 album ''ColleGrove'' * "Sectioning", a ''Peep Show'' episode * David "Section" Mason, a fictional character in '' Call of Duty: Black Ops II'' Organisations * Section (Alpine club) * Section (military unit) * Section (Scouting) Science, technology and mathematics Science * Section (archaeology), a view in part of the archaeological sequence showing it in the vertical plane * Section (bi ...
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I-beam
An I-beam, also known as H-beam (for universal column, UC), w-beam (for "wide flange"), universal beam (UB), rolled steel joist (RSJ), or double-T (especially in Polish language, Polish, Bulgarian language, Bulgarian, Spanish language, Spanish, Italian language, Italian and German language, German), is a beam (structure), beam with an or -shaped cross section (geometry), cross-section. The horizontal elements of the are flanges, and the vertical element is the "web". I-beams are usually made of structural steel and are used in construction and civil engineering. The web resists shear forces, while the flanges resist most of the bending moment experienced by the beam. The Euler–Bernoulli beam equation shows that the I-shaped section is a very efficient form for carrying both bending and shearing (physics), shear loads in the plane of the web. On the other hand, the cross-section has a reduced capacity in the transverse direction, and is also inefficient in carrying torsion ( ...
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