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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 is based on experimental results by J. B. Johnson from around 1900 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 y ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler Johnson Crit NEW
Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in many other branches of mathematics such as analytic number theory, complex analysis, and infinitesimal calculus. He introduced much of modern mathematical terminology and Mathematical notation, notation, including the notion of a function (mathematics), mathematical function. He is also known for his work in mechanics, fluid dynamics, optics, astronomy and music theory. Euler is held to be one of the greatest mathematicians in history and the greatest of the 18th century. A statement attributed to Pierre-Simon Laplace expresses Euler's influence on mathematics: "Read Euler, read Euler, he is the master of us all." Carl Friedrich Gauss remarked: "The study of Euler's works will remain the best school for the different fields of mathematics, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structural Engineering
Structural engineering is a sub-discipline of civil engineering in which structural engineers are trained to design the 'bones and muscles' that create the form and shape of man-made structures. Structural engineers also must understand and calculate the stability, strength, rigidity and earthquake-susceptibility of built structures for buildings and nonbuilding structures. The structural designs are integrated with those of other designers such as architects and building services engineer and often supervise the construction of projects by contractors on site. They can also be involved in the design of machinery, medical equipment, and vehicles where structural integrity affects functioning and safety. See glossary of structural engineering. Structural engineering theory is based upon applied physical laws and empirical knowledge of the structural performance of different materials and geometries. Structural engineering design uses a number of relatively simple structural c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Buckling
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 in slender columns. 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 ... [...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 featur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler's Critical Load
Euler's critical 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 area moment of inertia of the cross section of the column (second moment of area), *L, unsupported length of column, *K, column effective length factor This formula was derived in 1757 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 increase, until it may fail in oth ... [...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 buckle. It is defined as l/k where l is the effective length of the column and k is the 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 height:width ratio exceeds 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radius Of Gyration
''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. 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 rotation is :I = m_1 r_1^2 + m_2 r_2^2 + \cdots + m_n r_n^2 : If all the masses are the same (m), then ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interpolates
In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points. In engineering and science, one often has a number of data points, obtained by sampling or experimentation, which represent the values of a function for a limited number of values of the independent variable. It is often required to interpolate; that is, estimate the value of that function for an intermediate value of the independent variable. A closely related problem is the approximation of a complicated function by a simple function. Suppose the formula for some given function is known, but too complicated to evaluate efficiently. A few data points from the original function can be interpolated to produce a simpler function which is still fairly close to the original. The resulting gain in simplicity may outweigh the loss from interpolation error and give better performance in ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yield Stress
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. In some materials, such as aluminium, there is a gradual onset of non-linear behavior, making the precise yield point difficult to determine. In such a case, the offset yiel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mode Of Failure
Failure causes are defects in design, process, quality, or part application, which are the underlying cause of a failure or which initiate a process which leads to failure. Where failure depends on the user of the product or process, then human error must be considered. Component failure / failure modes A part failure mode is the way in which a component failed "functionally" on the component level. Often a part has only a few failure modes. For example, a relay may fail to open or close contacts on demand. The failure mechanism that caused this can be of many different kinds, and often multiple factors play a role at the same time. They include corrosion, welding of contacts due to an abnormal electric current, return spring fatigue failure, unintended command failure, dust accumulation and blockage of mechanism, etc. Seldom only one cause (hazard) can be identified that creates system failures. The real root causes can in theory in most cases be traced back to some kind of huma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Critical Stress Vs Slenderness Ratio For Al 2024
Critical or Critically may refer to: *Critical, or critical but stable, medical states **Critical, or intensive care medicine *Critical juncture, a discontinuous change studied in the social sciences. *Critical Software, a company specializing in mission and business critical information systems *Critical theory, a school of thought that critiques society and culture by applying knowledge from the social sciences and the humanities * Critically endangered, a risk status for wild species *Criticality (status), the condition of sustaining a nuclear chain reaction Art, entertainment, and media * ''Critical'' (novel), a medical thriller written by Robin Cook * ''Critical'' (TV series), a Sky 1 TV series * "Critical" (''Person of Interest''), an episode of the American television drama series ''Person of Interest'' *"Critical", a 1999 single by Zion I People *Cr1TiKaL (born 1994), an American YouTuber and Twitch streamer See also *Critic *Criticality (other) *Critical Conditi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elasticity (physics)
In physics and materials science, elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate loads are applied to them; if the material is elastic, the object will return to its initial shape and size after removal. This is in contrast to ''plasticity'', in which the object fails to do so and instead remains in its deformed state. The physical reasons for elastic behavior can be quite different for different materials. In metals, the atomic lattice changes size and shape when forces are applied (energy is added to the system). When forces are removed, the lattice goes back to the original lower energy state. For rubbers and other polymers, elasticity is caused by the stretching of polymer chains when forces are applied. Hooke's law states that the force required to deform elastic objects should be directly proportional to the distance of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
