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Bending Stiffness
The bending stiffness (K) is the resistance of a member against bending 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 = E I \frac{\mathrm{d} x^2} 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 In applied ... [...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) 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 infinitesimal element (which is viewed as a point) in an elastic body can occur along multiple DOF (maximum o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Young's Modulus
Young's modulus E, the Young modulus, or the modulus of elasticity in tension or compression (i.e., negative tension), is a mechanical property that measures the tensile or compressive stiffness of a solid material when the force is applied lengthwise. It quantifies the relationship between tensile/compressive stress \sigma (force per unit area) and axial strain \varepsilon (proportional deformation) in the linear elastic region of a material and is determined using the formula: E = \frac Young's moduli are typically so large that they are expressed not in pascals but in gigapascals (GPa). Example: * Silly Putty (increasing pressure: length increases quickly, meaning tiny E) * Aluminum (increasing pressure: length increases slowly, meaning high E) Higher Young's modulus corresponds to greater (lengthwise) stiffness. 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 exp ... [...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. 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 area ... [...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 *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 simulatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Curvature
In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane. 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 quantity, that is, it is expressed by a single real number. For surfaces (and, more generally for higher-dimensional manifolds), that are embedded in a Euclidean space, the concept of curvature is more complex, as it depends on the choice of a direction on the surfa ... [...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 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. 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''. The flexural rigidity (stiffness) of the beam is therefore related to both E, a material property, and I, the physical geometry of the beam. If the material exhibits Isotropic behavior then the Flexural Modulus is equal to the Modulus of Elasticity (You ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Applied Mechanics
Applied mechanics is the branch of science concerned with the motion of any substance that can be experienced or perceived by humans without the help of instruments. In short, when mechanics concepts surpass being theoretical and are applied and executed, general mechanics becomes applied mechanics. It is this stark difference that makes applied mechanics an essential understanding for practical everyday life. It has numerous applications in a wide variety of fields and disciplines, including but not limited to structural engineering, astronomy, oceanography, meteorology, hydraulics, mechanical engineering, aerospace engineering, nanotechnology, structural design, earthquake engineering, fluid dynamics, planetary sciences, and other life sciences. Connecting research between numerous disciplines, applied mechanics plays an important role in both science and engineering. Pure mechanics describes the response of bodies (solids and fluids) or systems of bodies to external behav ... [...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 *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 simulatio ... [...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 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. For example, a closet rod sagging under the weight of clothes on clothes hangers is an example of a beam experiencing bending. On the other hand, a 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 large diameter, but thin-walled, short tube supported at its ends an ... [...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) 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 infinitesimal element (which is viewed as a point) in an elastic body can occur along multiple DOF (maximum o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuum Mechanics
Continuum mechanics is a branch of mechanics that deals with the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such models in the 19th century. Explanation A continuum model assumes that the substance of the object fills the space it occupies. Modeling objects in this way ignores the fact that matter is made of atoms, and so is not continuous; however, on length scales much greater than that of inter-atomic distances, such models are highly accurate. These models can be used to derive differential equations that describe the behavior of such objects using physical laws, such as mass conservation, momentum conservation, and energy conservation, and some information about the material is provided by constitutive relationships. Continuum mechanics deals with the physical properties of solids and fluids which are independent of any particular coordinate sys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
