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Neutral Axis
The neutral axis is an axis in the cross section of a beam (a member resisting bending) or shaft along which there are no longitudinal stresses or strains. If the section is symmetric, isotropic and is not curved before a bend occurs, then the neutral axis is at the geometric centroid. All fibers on one side of the neutral axis are in a state of tension, while those on the opposite side are in compression. Since the beam is undergoing uniform bending, a plane on the beam remains plane. That is: \gamma_=\gamma_=\tau_=\tau_=0 Where \gamma is the shear strain and \tau is the shear stress There is a compressive (negative) strain at the top of the beam, and a tensile (positive) strain at the bottom of the beam. Therefore by the Intermediate Value Theorem, there must be some point in between the top and the bottom that has no strain, since the strain in a beam is a continuous function. Let L be the original length of the beam (span) ε(y) is the strain as a function of coordinate on ... [...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 and loa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modulus Of Elasticity
An elastic modulus (also known as modulus of elasticity) is the unit of measurement of an object's or substance's resistance to being deformed elastically (i.e., non-permanently) when a stress is applied to it. The elastic modulus of an object is defined as the slope of its stress–strain curve in the elastic deformation region: A stiffer material will have a higher elastic modulus. An elastic modulus has the form: :\delta \ \stackrel\ \frac where stress is the force causing the deformation divided by the area to which the force is applied and strain is the ratio of the change in some parameter caused by the deformation to the original value of the parameter. Since strain is a dimensionless quantity, the units of \delta will be the same as the units of stress. Specifying how stress and strain are to be measured, including directions, allows for many types of elastic moduli to be defined. The three primary ones are: # ''Young's modulus'' (E) describes tensile and compressive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Second Moment Of Inertia
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 The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ..., is meters to the fourth power, metre, m4, or inches to the fourth power, inch, in4, when working in the Imperial units, I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neutral Plane
In mechanics, the neutral plane or neutral surface is a conceptual plane within a beam or cantilever. When loaded by a bending force, the beam bends so that the inner surface is in compression and the outer surface is in tension. The neutral plane is the surface within the beam between these zones, where the material of the beam is not under stress, either compression or tension. As there is no lengthwise stress force on the neutral plane, there is no strain or extension either: when the beam bends, the length of the neutral plane remains constant. Any line within the neutral plane parallel to the axis of the beam is called the deflection curve of the beam. To show that every beam must have a neutral plane, the material of the beam can be imagined to be divided into narrow fibers parallel to its length. When the beam is bent, at any given cross-section the region of fibers near the concave side will be under compression, while the region near the convex side will be under tension ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isambard Kingdom Brunel
Isambard Kingdom Brunel (; 9 April 1806 – 15 September 1859) was a British civil engineer who is considered "one of the most ingenious and prolific figures in engineering history," "one of the 19th-century engineering giants," and "one of the greatest figures of the Industrial Revolution, hochanged the face of the English landscape with his groundbreaking designs and ingenious constructions." Brunel built dockyards, the Great Western Railway (GWR), a series of steamships including the first propeller-driven transatlantic steamship, and numerous important bridges and tunnels. His designs revolutionised public transport and modern engineering. Though Brunel's projects were not always successful, they often contained innovative solutions to long-standing engineering problems. During his career, Brunel achieved many engineering firsts, including assisting in the building of the first tunnel under a navigable river (the River Thames) and the development of the , the first ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thomas Young (scientist)
Thomas Young FRS (13 June 177310 May 1829) was a British polymath who made notable contributions to the fields of vision, light, solid mechanics, energy, physiology, language, musical harmony, and Egyptology. He was instrumental in the decipherment of Egyptian hieroglyphs, specifically the Rosetta Stone. Young has been described as "The Last Man Who Knew Everything". His work influenced that of William Herschel, Hermann von Helmholtz, James Clerk Maxwell, and Albert Einstein. Young is credited with establishing the wave theory of light, in contrast to the particle theory of Isaac Newton. Young's work was subsequently supported by the work of Augustin-Jean Fresnel. Personal life Young belonged to a Quaker family of Milverton, Somerset, where he was born in 1773, the eldest of ten children. At the age of fourteen Young had learned Greek and Latin. Young began to study medicine in London at St Bartholomew's Hospital in 1792, moved to the University of Edinburgh Medical School i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Line Of Thrust
The line of thrust is the locus of the points, through which forces pass in a retaining wall or an arch. It is the line, along which internal forces flow In a stone structure, the line of thrust is a theoretical line that through the structure represents the path of the s of the compressive forces For a structure to be stable, the line of thrust must lie entirely inside the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arch
An arch is a vertical curved structure that spans an elevated space and may or may not support the weight above it, or in case of a horizontal arch like an arch dam, the hydrostatic pressure against it. Arches may be synonymous with vaults, but a vault may be distinguished as a continuous arch forming a roof. Arches appeared as early as the 2nd millennium BC in Mesopotamian brick architecture, and their systematic use started with the ancient Romans, who were the first to apply the technique to a wide range of structures. Basic concepts An arch is a pure compression form. It can span a large area by resolving forces into compressive stresses, and thereby eliminating tensile stresses. This is sometimes denominated "arch action". As the forces in the arch are transferred to its base, the arch pushes outward at its base, denominated "thrust". As the rise, i. e. height, of the arch decreases the outward thrust increases. In order to preserve arch action and prevent collapse ... [...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] |
First Moment Of Area
The first moment of area is based on the mathematical construct moments in metric spaces. It is a measure of the spatial distribution of a shape in relation to an axis. The first moment of area of a shape, about a certain axis, equals the sum over all the infinitesimal parts of the shape of the area of that part times its distance from the axis £''ad'' First moment of area is commonly used to determine the centroid of an area. Definition Given an area, ''A'', of any shape, and division of that area into ''n'' number of very small, elemental areas (''dAi''). Let ''xi'' and ''yi'' be the distances (coordinates) to each elemental area measured from a given ''x-y'' axis. Now, the first moment of area in the ''x'' and ''y'' directions are respectively given by: S_x = A \bar y = \sum_^n = \int_A y \, dA and S_y= A \bar x = \sum_^n = \int_A x \, dA. The SI unit for first moment of area is a cubic metre (m3). In the American Engineering and Gravitational systems the unit is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
First Moment
In mathematics, the moments of a function are certain quantitative measures related to the shape of the function's graph. If the function represents mass density, then the zeroth moment is the total mass, the first moment (normalized by total mass) is the center of mass, and the second moment is the moment of inertia. If the function is a probability distribution, then the first moment is the expected value, the second central moment is the variance, the third standardized moment is the skewness, and the fourth standardized moment is the kurtosis. The mathematical concept is closely related to the concept of moment in physics. For a distribution of mass or probability on a bounded interval, the collection of all the moments (of all orders, from to ) uniquely determines the distribution (Hausdorff moment problem). The same is not true on unbounded intervals (Hamburger moment problem). In the mid-nineteenth century, Pafnuty Chebyshev became the first person to think systematicall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pure Bending
Pure bending ( Theory of simple bending) is a condition of stress where a bending moment is applied to a beam without the simultaneous presence of Cylinder stress, axial, Shear stress, shear, or Deformation (mechanics), torsional forces. Pure bending occurs only under a constant bending moment (M) since the shear force (V), which is equal to \frac = V, has to be equal to zero. In reality, a state of pure bending does not practically exist, because such a state needs an absolutely weightless member. The state of pure bending is an approximation made to derive formulas. Kinematics of pure bending #In pure bending the axial lines bend to form circumference, circumferential lines and transverse lines remain straight and become radial lines. #Axial lines that do not extend or contract form a neutral surface. Assumptions made in the theory of Pure Bending #The material of the beam is homogeneous1 and isotropic2. #The value of Young's Modulus of Elasticity is same in tension and compressio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
