|
Buckling
In structural engineering, buckling is the sudden change in shape (Deformation (engineering), deformation) of a structural component under Structural load, load, such as the bowing of a column under Compression (physics), compression or the wrinkling of a plate under Shearing (physics), shear. If a structure is subjected to a gradually increasing load, when the load reaches a critical level, a member may suddenly change shape and the structure and component is said to have ''buckled''. Euler's critical load and Johnson's parabolic formula are used to determine the buckling stress of a column. Buckling may occur even though the Stress (mechanics), stresses that develop in the structure are well below those needed to cause Catastrophic failure, failure in the material of which the structure is composed. Further loading may cause significant and somewhat unpredictable deformations, possibly leading to complete loss of the member's load-carrying capacity. However, if the deformation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler's Critical Load
Euler's critical load or Euler's buckling load is the compressive Structural load, load at which a slender column will suddenly bend or Buckling , 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, :File:ColumnEffectiveLength.png, column effective length factor This formula was derived in 1744 by the Switzerland, 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 Instability, unstable equilibrium. A load beyond the critical load causes the column to Structural inte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johnson's Parabolic Formula
In structural engineering, Johnson's parabolic formula is an empirically based equation for calculating the critical buckling stress of a column. The formula was developed by John Butler Johnson in 1893 as an alternative to Euler's critical load formula under low slenderness ratio (the ratio of radius of gyration to effective length) conditions. The equation interpolates between the Yield Stress, yield stress of the material to the critical buckling stress given by Euler's formula relating the slenderness ratio to the stress required to buckle a column. ''Buckling'' refers to a mode of failure in which the structure loses stability. It is caused by a lack of structural stiffness. Placing a load on a long slender bar may cause a buckling failure before the specimen can fail by compression. Johnson parabola Eulers formula for buckling of a slender column gives the critical stress level to cause buckling but doesn't consider material failure modes such as yield which has been sho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Buckling Beam Element
In structural engineering, buckling is the sudden change in shape ( deformation) of a structural component under load, such as the bowing of a column under compression or the wrinkling of a plate under shear. If a structure is subjected to a gradually increasing load, when the load reaches a critical level, a member may suddenly change shape and the structure and component is said to have ''buckled''. Euler's critical load and Johnson's parabolic formula are used to determine the buckling stress of a column. Buckling may occur even though the stresses that develop in the structure are well below those needed to cause failure in the material of which the structure is composed. Further loading may cause significant and somewhat unpredictable deformations, possibly leading to complete loss of the member's load-carrying capacity. However, if the deformations that occur after buckling do not cause the complete collapse of that member, the member will continue to support the load ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Slenderness Ratio
In architecture, the slenderness ratio, or simply slenderness, is an aspect ratio, the quotient between the height and the width of a building. In structural engineering, slenderness is used to calculate the propensity of a column to Buckling, buckle. It is defined as l/k where l is the effective length of the column and k is the radius of gyration, least radius of gyration, the latter defined by k^2=I/A where A is the area of the cross-section of the column and I is the second moment of area of the cross-section. The effective length is calculated from the actual length of the member considering the rotational and relative translational boundary conditions at the ends. Slenderness captures the influence on buckling of all the geometric aspects of the column, namely its length, area, and second moment of area. The influence of the material is represented separately by the material's modulus of elasticity E. Structural engineers generally consider a skyscraper as slender if the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Column
A column or pillar in architecture and structural engineering is a structural element that transmits, through compression, the weight of the structure above to other structural elements below. In other words, a column is a compression member. The term ''column'' applies especially to a large round support (the shaft of the column) with a capital and a base or pedestal, which is made of stone, or appearing to be so. A small wooden or metal support is typically called a '' post''. Supports with a rectangular or other non-round section are usually called '' piers''. For the purpose of wind or earthquake engineering, columns may be designed to resist lateral forces. Other compression members are often termed "columns" because of the similar stress conditions. Columns are frequently used to support beams or arches on which the upper parts of walls or ceilings rest. In architecture, "column" refers to such a structural element that also has certain proportional and decorative f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compression (physics)
In mechanics, compression is the application of balanced inward ("pushing") forces to different points on a material or Structural system, structure, that is, forces with no Net force, net sum or torque directed so as to reduce its size in one or more directions.Ferdinand Pierre Beer, Elwood Russell Johnston, John T. DeWolf (1992), "Mechanics of Materials". (Book) McGraw-Hill Professional, It is contrasted with tension (physics), tension or traction, the application of balanced outward ("pulling") forces; and with shear stress, shearing forces, directed so as to displace layers of the material parallel to each other. The compressive strength of materials and structures is an important engineering consideration. In uniaxial compression, the forces are directed along one direction only, so that they act towards decreasing the object's length along that direction. The compressive forces may also be applied in multiple directions; for example inwards along the edges of a plate or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mechanical Equilibrium
In classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero. By extension, a physical system made up of many parts is in mechanical equilibrium if the net force on each of its individual parts is zero. In addition to defining mechanical equilibrium in terms of force, there are many alternative definitions for mechanical equilibrium which are all mathematically equivalent. * In terms of momentum, a system is in equilibrium if the momentum of its parts is all constant. * In terms of velocity, the system is in equilibrium if velocity is constant. * In a rotational mechanical equilibrium the angular momentum of the object is conserved and the net torque is zero. More generally in conservative systems, equilibrium is established at a point in Configuration space (physics), configuration space where the gradient of the potential energy with respect to the generalized coordinates is zero. If a particle in equilibrium has zero velocity, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stress (physics)
In continuum mechanics, stress is a physical quantity that describes Force, forces present during Deformation (physics), deformation. For example, an object being pulled apart, such as a stretched elastic band, is subject to Tension (physics), ''tensile'' stress and may undergo Elongation (materials science), elongation. An object being pushed together, such as a crumpled sponge, is subject to Compression (physics), ''compressive'' stress and may undergo shortening. The greater the force and the smaller the cross-sectional area of the body on which it acts, the greater the stress. Stress has Dimension (physics), dimension of force per area, with SI Units, SI units of newtons per square meter (N/m2) or Pascal (unit), pascal (Pa). Stress expresses the internal forces that neighbouring particles of a continuous material exert on each other, while Strain (mechanics), ''strain'' is the measure of the relative deformation (mechanics), deformation of the material. For example, when a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Species
A species () is often defined as the largest group of organisms in which any two individuals of the appropriate sexes or mating types can produce fertile offspring, typically by sexual reproduction. It is the basic unit of Taxonomy (biology), classification and a taxonomic rank of an organism, as well as a unit of biodiversity. Other ways of defining species include their karyotype, DNA sequence, morphology (biology), morphology, behaviour, or ecological niche. In addition, palaeontologists use the concept of the chronospecies since fossil reproduction cannot be examined. The most recent rigorous estimate for the total number of species of eukaryotes is between 8 and 8.7 million. About 14% of these had been described by 2011. All species (except viruses) are given a binomial nomenclature, two-part name, a "binomen". The first part of a binomen is the name of a genus to which the species belongs. The second part is called the specific name (zoology), specific name or the specific ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leonhard Euler
Leonhard Euler ( ; ; ; 15 April 170718 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer. He founded the studies of graph theory and topology and made influential discoveries in many other branches of mathematics, such as analytic number theory, complex analysis, and infinitesimal calculus. He also introduced much of modern mathematical terminology and Mathematical notation, notation, including the notion of a mathematical function. He is known for his work in mechanics, fluid dynamics, optics, astronomy, and music theory. Euler has been called a "universal genius" who "was fully equipped with almost unlimited powers of imagination, intellectual gifts and extraordinary memory". He spent most of his adult life in Saint Petersburg, Russia, and in Berlin, then the capital of Kingdom of Prussia, Prussia. Euler is credited for popularizing the Greek letter \pi (lowercase Pi (letter), pi) to denote Pi, th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
B52-buckling
B5, B05, B-5 may refer to: Biology * ATC code B05 (''Blood substitutes and perfusion solutions''), a therapeutic subgroup of the Anatomical Therapeutic Chemical Classification System * Cytochrome ''b''5, ubiquitous electron transport hemoproteins ** Cytochrome b5, type A, a human microsomal cytochrome b5 * HLA-B5, an HLA-B serotype * Pantothenic acid (a.k.a. vitamin B5), a water-soluble vitamin * Procyanidin B5, a B type proanthocyanidin Entertainment * Alekhine's Defence (ECO code B5), a chess opening beginning with the moves e4 Nf6 * B5 (band), an R&B boy band ** ''B5'' (album), B5's self-titled debut album * ''Babylon 5'', an American science fiction television series * The Be Five, a band formed by castmembers of Babylon 5 Transport * Amadeus (airline) (IATA code: B5), an airline based in Germany (1996–2004) * B5 and B5 DOHC, models of the Mazda B engine series * B-5, the manufacturer's model number for the Blackburn Baffin biplane * B5 platform, the series de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Force
In physics, a force is an influence that can cause an Physical object, object to change its velocity unless counterbalanced by other forces. In mechanics, force makes ideas like 'pushing' or 'pulling' mathematically precise. Because the Magnitude (mathematics), magnitude and Direction (geometry, geography), direction of a force are both important, force is a Euclidean vector, vector quantity. The SI unit of force is the newton (unit), newton (N), and force is often represented by the symbol . Force plays an important role in classical mechanics. The concept of force is central to all three of Newton's laws of motion. Types of forces often encountered in classical mechanics include Elasticity (physics), elastic, frictional, Normal force, contact or "normal" forces, and gravity, gravitational. The rotational version of force is torque, which produces angular acceleration, changes in the rotational speed of an object. In an extended body, each part applies forces on the adjacent pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
