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Limit Loads
Limit load is the maximum load that a structure can safely carry. It's the load at which the structure is in a state of incipient plastic collapse. As the load on the structure increases, the displacements increases linearly in the elastic range until the load attains the yield value. Beyond this, the load-displacement response becomes non-linear and the plastic or irreversible part of the displacement increases steadily with the applied load. Plasticity spreads throughout the solid and at the limit load, the plastic zone becomes very large and the displacements become unbounded and the component is said to have collapsed. Any load above the limit load will lead to the formation of plastic hinge in the structure. Engineers use limit states to define and check a structure's performance. Bounding Theorems of Plastic-Limit Load Analysis: Plastic limit theorems provide a way to calculate limit loads without having to solve the boundary value problem in continuum mechanics. Finite e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plastic Deformation
In engineering, deformation refers to the change in size or shape of an object. ''Displacements'' are the ''absolute'' change in position of a point on the object. Deflection is the relative change in external displacements on an object. Strain is the ''relative'' internal change in shape of an infinitesimally small cube of material and can be expressed as a non-dimensional change in length or angle of distortion of the cube. Strains are related to the forces acting on the cube, which are known as stress, by a stress-strain curve. The relationship between stress and strain is generally linear and reversible up until the yield point and the deformation is elastic. The linear relationship for a material is known as Young's modulus. Above the yield point, some degree of permanent distortion remains after unloading and is termed plastic deformation. The determination of the stress and strain throughout a solid object is given by the field of strength of materials and for a structure ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plasticity (physics)
In physics and materials science, plasticity, also known as plastic deformation, is the ability of a solid material to undergo permanent Deformation (engineering), deformation, a non-reversible change of shape in response to applied forces. For example, a solid piece of metal being bent or pounded into a new shape displays plasticity as permanent changes occur within the material itself. In engineering, the transition from Elasticity (physics), elastic behavior to plastic behavior is known as Yield (engineering), yielding. Plastic deformation is observed in most materials, particularly metals, soils, Rock (geology), rocks, concrete, and foams. However, the physical mechanisms that cause plastic deformation can vary widely. At a crystalline scale, plasticity in metals is usually a consequence of dislocations. Such defects are relatively rare in most crystalline materials, but are numerous in some and part of their crystal structure; in such cases, plastic crystallinity can res ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plastic Hinge
In the structural engineering beam theory, the term "plastic hinge" is used to describe the deformation of a section of a beam where plastic bending occurs. In earthquake engineering plastic hinge is also a type of energy damping device allowing plastic rotation eformationof an otherwise rigid column connection. Plastic behaviour In plastic limit analysis of structural members subjected to bending, it is assumed that an abrupt transition from elastic to ideally plastic behaviour occurs at a certain value of moment, known as plastic moment (Mp). Member behaviour between Myp and Mp is considered to be elastic. When Mp is reached, a plastic hinge is formed in the member. In contrast to a friction Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction: *Dry friction is a force that opposes the relative lateral motion of t ...less hinge permitting free rotation, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Engineer
Engineers, as practitioners of engineering, are professionals who invent, design, analyze, build and test machines, complex systems, structures, gadgets and materials to fulfill functional objectives and requirements while considering the limitations imposed by practicality, regulation, safety and cost. "Science is knowledge based on our observed facts and tested truths arranged in an orderly system that can be validated and communicated to other people. Engineering is the creative application of scientific principles used to plan, build, direct, guide, manage, or work on systems to maintain and improve our daily lives." The word ''engineer'' (Latin ) is derived from the Latin words ("to contrive, devise") and ("cleverness"). The foundational qualifications of an engineer typically include a four-year bachelor's degree in an engineering discipline, or in some jurisdictions, a master's degree in an engineering discipline plus four to six years of peer-reviewed professiona ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plastic Limit Theorems
Plastic limit theorems in continuum mechanics provide two bounds that can be used to determine whether material failure is possible by means of plastic deformation for a given external loading scenario. According to the theorems, to find the range within which the true solution must lie, it is necessary to find both a stress field that balances the external forces and a velocity field or flow pattern that corresponds to those stresses. If the upper and lower bounds provided by the velocity field and stress field coincide, the exact value of the collapse load is determined. Limit theorems The two plastic limit theorems apply to any elastic-perfectly plastic body or assemblage of bodies. Lower limit theorem: If an equilibrium distribution of stress can be found which balances the applied load and nowhere violates the yield criterion, the body (or bodies) will not fail, or will be just at the point of failure. Upper limit theorem: The body (or bodies) will collapse if ther ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boundary Value Problem
In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions. Boundary value problems arise in several branches of physics as any physical differential equation will have them. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems. A large class of important boundary value problems are the Sturm–Liouville problems. The analysis of these problems involves the eigenfunctions of a differential operator. To be useful in applications, a boundary value problem should be well posed. This means that given the input to the problem there exists a unique solution, which depends continuously on the input. Much theoretical work in the field of partial differential ... [...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 sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Element
The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems). To solve a problem, the FEM subdivides a large system into smaller, simpler parts that are called finite elements. This is achieved by a particular space discretization in the space dimensions, which is implemented by the construction of a mesh of the object: the numerical domain for the solution, which has a finite number of points. The finite element method formulation of a boundary value problem finally results in a system of algebraic equations. The method approximates the unknown function over the domain. The simple ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Collapse Mechanism
Collapse or its variants may refer to: Concepts * Collapse (structural) * Collapse (topology), a mathematical concept * Collapsing manifold * Collapse, the action of collapsing or telescoping objects * Collapsing user interface elements ** Accordion (GUI) -- collapsing list items ** Code folding -- collapsing subsections of programs or text ** Outliner -- supporting folding and unfolding subsections * Ecosystem collapse or Ecological collapse * Economic collapse * Gravitational collapse creating astronomical objects * Societal collapse ** Dissolution of the Soviet Union, the collapse of Soviet federalism ** State collapse * Wave function collapse, in physics Medicine and biology In medicine, collapse can refer to various forms of transient loss of consciousness such as syncope, or loss of postural muscle tone without loss of consciousness. It can also refer to: * Circulatory collapse * Lung collapse * Hydrophobic collapse in protein folding Art, entertainment and m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plastic Dissipation
Plastics are a wide range of synthetic or semi-synthetic materials that use polymers as a main ingredient. Their plasticity makes it possible for plastics to be moulded, extruded or pressed into solid objects of various shapes. This adaptability, plus a wide range of other properties, such as being lightweight, durable, flexible, and inexpensive to produce, has led to its widespread use. Plastics typically are made through human industrial systems. Most modern plastics are derived from fossil fuel-based chemicals like natural gas or petroleum; however, recent industrial methods use variants made from renewable materials, such as corn or cotton derivatives. 9.2 billion tonnes of plastic are estimated to have been made between 1950 and 2017. More than half this plastic has been produced since 2004. In 2020, 400 million tonnes of plastic were produced. If global trends on plastic demand continue, it is estimated that by 2050 annual global plastic production will reach over 1,10 ... [...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] |
