|
Bending Stiffness
The bending stiffness (K) is the resistance of a member against bending deflection/deformation. It is a function of the Young's modulus E, the second moment of area I of the beam cross-section about the axis of interest, length of the beam and beam boundary condition. Bending stiffness of a beam can analytically be derived from the equation of beam deflection when it is applied by a force. :K = \frac where \mathrm is the applied force and \mathrm is the deflection. According to elementary beam theory, the relationship between the applied bending moment M and the resulting curvature \kappa of the beam is: :M = E I \kappa \approx E I \frac where w is the deflection of the beam and x is the distance along the beam. Double integration of the above equation leads to computing the deflection of the beam, and in turn, the bending stiffness of the beam. Bending stiffness in beams is also known as Flexural rigidity. See also * Applied mechanics * Beam theory * Bending *Stiffness ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stiffness
Stiffness is the extent to which an object resists deformation in response to an applied force. The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is. Calculations The stiffness, k, of a body is a measure of the resistance offered by an elastic body to deformation. For an elastic body with a single degree of freedom (DOF) (for example, stretching or compression of a rod), the stiffness is defined as k = \frac where, * F is the force on the body * \delta is the displacement produced by the force along the same degree of freedom (for instance, the change in length of a stretched spring) Stiffness is usually defined under quasi-static conditions, but sometimes under dynamic loading. In the International System of Units, stiffness is typically measured in newtons per meter (N/m). In Imperial units, stiffness is typically measured in pounds (lbs) per inch. Generally speaking, deflections (or motions) of an infinitesima ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Young's Modulus
Young's modulus (or the Young modulus) is a mechanical property of solid materials that measures the tensile or compressive stiffness when the force is applied lengthwise. It is the modulus of elasticity for tension or axial compression. Young's modulus is defined as the ratio of the stress (force per unit area) applied to the object and the resulting axial strain (displacement or deformation) in the linear elastic region of the material. Although Young's modulus is named after the 19th-century British scientist Thomas Young, the concept was developed in 1727 by Leonhard Euler. The first experiments that used the concept of Young's modulus in its modern form were performed by the Italian scientist Giordano Riccati in 1782, pre-dating Young's work by 25 years. The term modulus is derived from the Latin root term '' modus'', which means ''measure''. Definition Young's modulus, E, quantifies the relationship between tensile or compressive stress \sigma (force per unit ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Second Moment Of Area
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 or the US customary system. 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 * Radio 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 People * Beam (rapper) (born 1995), American hip hop artist * Anong Beam, Canadian Ojibwe artist and curator * Carl Beam (1943–2005), Indigenous Canadian artist Arts, entertainment and media * Beam (music), a connection line in musical notation * ''Beam'' (single album), by Hoshi X Woozi, 2025 * ''The Beam'' (fairy tale), the Brothers Grimm tale 149 * BEAM.TV, an online digital delivery and content management platform * BEAM Channel 31, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Curvature
In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane. If a curve or surface is contained in a larger space, curvature can be defined ''extrinsically'' relative to the ambient space. Curvature of Riemannian manifolds of dimension at least two can be defined ''intrinsically'' without reference to a larger space. For curves, the canonical example is that of a circle, which has a curvature equal to the reciprocal of its radius. Smaller circles bend more sharply, and hence have higher curvature. The curvature ''at a point'' of a differentiable curve is the curvature of its osculating circle — that is, the circle that best approximates the curve near this point. The curvature of a straight line is zero. In contrast to the tangent, which is a vector quantity, the curvature at a point is typically a scalar q ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flexural Rigidity
Flexural rigidity is defined as the force couple required to bend a fixed non- rigid structure by one unit of curvature, or as the resistance offered by a structure while undergoing bending. Flexural rigidity of a beam Although the moment M(x) and displacement y generally result from external loads and may vary along the length of the beam or rod, the flexural rigidity (defined as EI) is a property of the beam itself and is generally constant for prismatic members. However, in cases of non-prismatic members, such as the case of the tapered beams or columns or notched stair stringers, the flexural rigidity will vary along the length of the beam as well. The flexural rigidity, moment, and transverse displacement are related by the following equation along the length of the rod, x: :\ EI \ = \int_^ M(x) dx + C_1 where E is the flexural modulus (in Pa), I is the second moment of area (in m4), y is the transverse displacement of the beam at x, and M(x) is the bending moment at ''x' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 * Radio 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 People * Beam (rapper) (born 1995), American hip hop artist * Anong Beam, Canadian Ojibwe artist and curator * Carl Beam (1943–2005), Indigenous Canadian artist Arts, entertainment and media * Beam (music), a connection line in musical notation * ''Beam'' (single album), by Hoshi X Woozi, 2025 * ''The Beam'' (fairy tale), the Brothers Grimm tale 149 * BEAM.TV, an online digital delivery and content management platform * BEAM Channel 31, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bending
In applied mechanics, bending (also known as flexure) characterizes the behavior of a slender structural element subjected to an external Structural load, load applied perpendicularly to a longitudinal axis of the element. The structural element is assumed to be such that at least one of its dimensions is a small fraction, typically 1/10 or less, of the other two.Boresi, A. P. and Schmidt, R. J. and Sidebottom, O. M., 1993, Advanced mechanics of materials, John Wiley and Sons, New York. When the length is considerably longer than the width and the thickness, the element is called a Beam (structure), beam. For example, a closet rod Deflection (engineering), sagging under the weight of clothes on clothes hangers is an example of a beam experiencing bending. On the other hand, a wikt:shell, shell is a structure of any geometric form where the length and the width are of the same order of magnitude but the thickness of the structure (known as the 'wall') is considerably smaller. A l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stiffness
Stiffness is the extent to which an object resists deformation in response to an applied force. The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is. Calculations The stiffness, k, of a body is a measure of the resistance offered by an elastic body to deformation. For an elastic body with a single degree of freedom (DOF) (for example, stretching or compression of a rod), the stiffness is defined as k = \frac where, * F is the force on the body * \delta is the displacement produced by the force along the same degree of freedom (for instance, the change in length of a stretched spring) Stiffness is usually defined under quasi-static conditions, but sometimes under dynamic loading. In the International System of Units, stiffness is typically measured in newtons per meter (N/m). In Imperial units, stiffness is typically measured in pounds (lbs) per inch. Generally speaking, deflections (or motions) of an infinitesima ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuum Mechanics
Continuum mechanics is a branch of mechanics that deals with the deformation of and transmission of forces through materials modeled as a ''continuous medium'' (also called a ''continuum'') rather than as discrete particles. Continuum mechanics deals with ''deformable bodies'', as opposed to rigid bodies. A continuum model assumes that the substance of the object completely fills the space it occupies. While ignoring the fact that matter is made of atoms, this provides a sufficiently accurate description of matter on length scales much greater than that of inter-atomic distances. The concept of a continuous medium allows for intuitive analysis of bulk matter by using differential equations that describe the behavior of such matter according to physical laws, such as mass conservation, momentum conservation, and energy conservation. Information about the specific material is expressed in constitutive relationships. Continuum mechanics treats the physical properties of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
