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Euler Buckling
Euler's critical load or Euler's buckling load is the compressive load at which a slender column will suddenly bend or buckle. It is given by the formula: P_ = \frac where *P_, Euler's critical load (longitudinal compression load on column), *E, Young's modulus of the column material, *I, minimum second moment of area of the cross section of the column (area moment of inertia), *L, unsupported length of column, *K, column effective length factor This formula was derived in 1744 by the Swiss mathematician Leonhard Euler. The column will remain straight for loads less than the critical load. The ''critical load'' is the greatest load that will not cause lateral deflection (buckling). For loads greater than the critical load, the column will deflect laterally. The critical load puts the column in a state of unstable equilibrium. A load beyond the critical load causes the column to fail by buckling. As the load is increased beyond the critical load the lateral deflections increas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
FIG2
The fig is the edible fruit of ''Ficus carica'', a species of tree or shrub in the flowering plant family Moraceae, Native plant, native to the Mediterranean Basin, Mediterranean region, together with western and southern Asia. It has been cultivated since ancient times and is now widely grown throughout the world.''The Fig: its History, Culture, and Curing'', Gustavus A. Eisen, Washington, Govt. print. off., 1901 ''Ficus carica'' is the type species of the genus ''Ficus'', which comprises over 800 tropical and subtropical plant species. A fig plant is a deciduous tree or large shrub, growing up to tall, with smooth white bark. Its large leaves have three to five deep lobes. Its fruit (referred to as syconium, a type of is tear-shaped, long, with a green fruit that may ripen toward purple or brown, and sweet soft reddish flesh containing numerous crunchy seeds. The milky sap of the green parts is an Irritant (biology), irritant to human skin. In the Northern hemisphere, fres ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Material
A material is a matter, substance or mixture of substances that constitutes an Physical object, object. Materials can be pure or impure, living or non-living matter. Materials can be classified on the basis of their physical property, physical and chemical property, chemical properties, or on their geological origin or biological function. Materials science is the study of materials, their properties and their applications. Raw materials can be processed in different ways to influence their properties, by purification, shaping or the introduction of other materials. New materials can be produced from raw materials by Chemical synthesis, synthesis. In Industrial sector, industry, materials are inputs to list of manufacturing processes, manufacturing processes to produce products or more complex materials, and the nature and quantity of materials used may form part of the calculation for the cost of a product or delivery under contract, such as where contract costs are calculated ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bending Moment
In solid mechanics, a bending moment is the Reaction (physics), reaction induced in a structural element when an external force or Moment of force, moment is applied to the element, causing the element to bending, bend. The most common or simplest structural element subjected to bending moments is the Beam (structure), beam. The diagram shows a beam which is simply supported (free to rotate and therefore lacking bending moments) at both ends; the ends can only react to the Shear stress, shear loads. Other beams can have both ends fixed (known as encastre beam); therefore each end support has both bending moments and shear reaction loads. Beams can also have one end fixed and one end simply supported. The simplest type of beam is the cantilever, which is fixed at one end and is free at the other end (neither simple nor fixed). In reality, beam supports are usually neither absolutely fixed nor absolutely rotating freely. The internal reaction loads in a cross section (geometry), cr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deflection (engineering)
In structural engineering, deflection is the degree to which a part of a long structural element (such as Beam (structure), beam) is deformation (mechanics), deformed laterally (in the direction transverse to its longitudinal axis) under a Structural load, load. It may be quantified in terms of an angle (angular displacement) or a distance (linear displacement (geometry), displacement). A longitudinal deformation (in the direction of the axis) is called ''elongation (mechanics), elongation''. The deflection distance of a member under a load can be calculated by Integral, integrating the function that mathematically describes the slope of the deflected shape of the member under that load. Standard formulas exist for the deflection of common Beam (structure), beam configurations and load cases at discrete locations. Otherwise methods such as virtual work, Direct integration of a beam, direct integration, Castigliano's method, Macaulay's method or the direct stiffness method are use ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler–Bernoulli Beam Theory
Euler–Bernoulli beam theory (also known as engineer's beam theory or classical beam theory) is a simplification of the linear elasticity, linear theory of elasticity which provides a means of calculating the load-carrying and Deflection (engineering), deflection characteristics of Beam (structure), beams. It covers the case corresponding to small deflections of a beam (structure), beam that is subjected to lateral loads only. By ignoring the effects of shear deformation and rotatory inertia, it is thus a special case of Timoshenko–Ehrenfest beam theory. It was first enunciated circa 1750, but was not applied on a large scale until the development of the Eiffel Tower and the Ferris wheel in the late 19th century. Following these successful demonstrations, it quickly became a cornerstone of engineering and an enabler of the Second Industrial Revolution. Additional mathematical models have been developed, such as plate theory, but the simplicity of beam theory makes it an importa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Body Diagram
In physics and engineering, a free body diagram (FBD; also called a force diagram) is a graphical illustration used to visualize the applied forces, moments, and resulting reactions on a free body in a given condition. It depicts a body or connected bodies with all the applied forces and moments, and reactions, which act on the body(ies). The body may consist of multiple internal members (such as a truss), or be a compact body (such as a beam). A series of free bodies and other diagrams may be necessary to solve complex problems. Sometimes in order to calculate the resultant force graphically the applied forces are arranged as the edges of a polygon of forces or force polygon (see ). Free body A body is said to be "free" when it is singled out from other bodies for the purposes of dynamic or static analysis. The object does not have to be "free" in the sense of being unforced, and it may or may not be in a state of equilibrium; rather, it is not fixed in place and is thus " ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetry
Symmetry () in everyday life refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is Invariant (mathematics), invariant under some Transformation (function), transformations, such as Translation (geometry), translation, Reflection (mathematics), reflection, Rotation (mathematics), rotation, or Scaling (geometry), scaling. Although these two meanings of the word can sometimes be told apart, they are intricately related, and hence are discussed together in this article. Mathematical symmetry may be observed with respect to the passage of time; as a space, spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, including scientific model, theoretic models, language, and music. This article describes symmetry from three perspectives: in mathematics, including geometry, the m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radius Of Gyration
The 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. The radius of gyration has dimensions of distance or 0LT0and the SI unit is the metre (m). Formulation 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 ro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yield Strength
In materials science and engineering, the yield point is the point on a stress–strain curve that indicates the limit of elastic behavior and the beginning of plastic behavior. Below the yield point, a material will deform elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed, some fraction of the deformation will be permanent and non-reversible and is known as plastic deformation. The yield strength or yield stress is a material property and is the stress corresponding to the yield point at which the material begins to deform plastically. The yield strength is often used to determine the maximum allowable load in a mechanical component, since it represents the upper limit to forces that can be applied without producing permanent deformation. For most metals, such as aluminium and cold-worked steel, there is a gradual onset of non-linear behavior, and no precise yield point. In such a case, the offset yield p ... [...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] |
Cross Section (geometry)
In geometry and science, a cross section is the non-empty intersection (set theory), intersection of a solid body in three-dimensional space with a Plane (geometry), plane, or the analog in higher-dimensional spaces. Cutting an object into slices creates many parallel cross-sections. The boundary of a cross-section in three-dimensional space that is parallel to two of the Cartesian coordinate system, axes, that is, parallel to the plane determined by these axes, is sometimes referred to as a contour line; for example, if a plane cuts through mountains of a raised-relief map parallel to the ground, the result is a contour line in two-dimensional space showing points on the surface of the mountains of equal elevation. In technical drawing a cross-section, being a Planar projection, projection of an object onto a plane that intersects it, is a common tool used to depict the internal arrangement of a 3-dimensional object in two dimensions. It is traditionally crosshatched with th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. Types of friction include dry, fluid, lubricated, skin, and internal -- an incomplete list. The study of the processes involved is called tribology, and has a history of more than 2000 years. Friction can have dramatic consequences, as illustrated by the use of friction created by rubbing pieces of wood together to start a fire. Another important consequence of many types of friction can be wear, which may lead to performance degradation or damage to components. It is known that frictional energy losses account for about 20% of the total energy expenditure of the world. As briefly discussed later, there are many different contributors to the retarding force in friction, ranging from asperity deformation to the generation of charges and changes in local structure. When two bodies in contact move relative to each other, due to these variou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
