Limit load (physics)

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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.

Plasticity (physics) The deformation of a solid material undergoing non-reversible changes of shape in response to applied forces

In physics and materials science, plasticity describes the deformation of a (solid) material undergoing non-reversible changes 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 elastic behavior to plastic behavior is called yield.

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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.

Plastic hinge

In the structural engineering beam theory 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 [deformation] of an otherwise rigid column connection.

Engineer professional practitioner of engineering and its sub classes

Engineers, as practitioners of engineering, are professionals who invent, design, analyze, build, and test machines, systems, structures and materials to fulfill objectives and requirements while considering the limitations imposed by practicality, regulation, safety, and cost. The word engineer is derived from the Latin words ingeniare and ingenium ("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 professional practice and passage of engineering board examinations.

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 element analysis provides an alternative way to estimate limit loads. They are:

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.

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.

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.

The Upper Bound Plastic Collapse Theorem states that an upper bound to the collapse loads can be obtained by postulating a collapse mechanism and computing the ratio of its plastic dissipation to the work done by the applied loads.

Related Research Articles

A fracture is the separation of an object or material into two or more pieces under the action of stress. The fracture of a solid usually occurs due to the development of certain displacement discontinuity surfaces within the solid. If a displacement develops perpendicular to the surface of displacement, it is called a normal tensile crack or simply a crack; if a displacement develops tangentially to the surface of displacement, it is called a shear crack, slip band, or dislocation.

In physics, 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 forces are applied to them. If the material is elastic, the object will return to its initial shape and size when these forces are removed.

Strength of materials, also called mechanics of materials, is a subject which deals with the behavior of solid objects subject to stresses and strains. The complete theory began with the consideration of the behavior of one and two dimensional members of structures, whose states of stress can be approximated as two dimensional, and was then generalized to three dimensions to develop a more complete theory of the elastic and plastic behavior of materials. An important founding pioneer in mechanics of materials was Stephen Timoshenko.

Solid mechanics also known as Mechanics of solids is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation under the action of forces, temperature changes, phase changes, and other external or internal agents.

Stress–strain analysis is an engineering discipline that uses many methods to determine the stresses and strains in materials and structures subjected to forces. In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other, while strain is the measure of the deformation of the material.

Viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist shear flow and strain linearly with time when a stress is applied. Elastic materials strain when stretched and immediately return to their original state once the stress is removed.

In science, buckling is an instability that leads to structural failure. The failure modes can in simple cases be found by simple mathematical solutions. For complex structures the failure modes are found by numerical tools.

Fracture mechanics

Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material's resistance to fracture.

In continuum mechanics, elastic shakedown behavior is one in which plastic deformation takes place during running in, while due to residual stresses or strain hardening the steady state is perfectly elastic.

In materials science, fracture toughness is a property which describes the ability of a material to resist fracture, and is one of the most important properties of any material for many design applications. The linear-elastic fracture toughness of a material is determined from the stress intensity factor at which a thin crack in the material begins to grow. It is denoted KIc and has the units of or . Plastic-elastic fracture toughness is denoted by JIc, with the unit of J/cm2 or lbf-in/in2, and is a measurement of the energy required to grow a thin crack.

Structural mechanics

Structural mechanics or Mechanics of structures is the computation of deformations, deflections, and internal forces or stresses within structures, either for design or for performance evaluation of existing structures. It is one subset of structural analysis. Structural mechanics analysis needs input data such as structural loads, the structure's geometric representation and support conditions, and the materials' properties. Output quantities may include support reactions, stresses and displacements. Advanced structural mechanics may include the effects of stability and non-linear behaviors.

Failure theory is the science of predicting the conditions under which solid materials fail under the action of external loads. The failure of a material is usually classified into brittle failure (fracture) or ductile failure (yield). Depending on the conditions most materials can fail in a brittle or ductile manner or both. However, for most practical situations, a material may be classified as either brittle or ductile. Though failure theory has been in development for over 200 years, its level of acceptability is yet to reach that of continuum mechanics.

Discontinuity layout optimization

Discontinuity layout optimization (DLO) is an engineering analysis procedure which can be used to directly establish the amount of load that can be carried by a solid or structure prior to collapse. Using DLO the layout of failure planes, or 'discontinuities', in a collapsing solid or structure are identified using mathematical optimization methods. It is assumed that failure occurs in a ductile or 'plastic' manner.

A finite element limit analysis (FELA) uses optimisation techniques to directly compute the upper or lower bound plastic collapse load for a mechanical system rather than time stepping to a collapse load, as might be undertaken with conventional non-linear finite element techniques. The problem may be formulated in either a kinematic or equilibrium form.

Smoothed finite element methods (S-FEM) are a particular class of numerical simulation algorithms for the simulation of physical phenomena. It was developed by combining meshfree methods with the finite element method. S-FEM are applicable to solid mechanics as well as fluid dynamics problems, although so far they have mainly been applied to the former.

Weakened weak form is used in the formulation of general numerical methods based on meshfree methods and/or finite element method settings. These numerical methods are applicable to solid mechanics as well as fluid dynamics problems.

Crack closure is a phenomenon in fatigue loading, during which the crack remains in a closed position even though some external tensile force is acting on the material. During this process the crack opens only at stress above a particular stress. This is due to factors such as plastic deformation or phase transformation during crack propagation, corrosion of crack surfaces, presence of fluids in the crack, or roughness at cracked surfaces. This provides a longer life for fatigued material than expected, by slowing the crack growth rate.


Concrete is widely used construction material all over the world. It is composed of aggregate, cement and water. Composition of concrete varies to suit for different applications desired. Even size of the aggregate can influence mechanical properties of concrete to a great extent.

Scott W. Sloan Laureate Professor of Civil Engineering, University of Newcastle (Australia)

Scott William Sloan FRS FREng FAA FTSE is laureate Professor of Civil Engineering at the University of Newcastle.

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Notes

  1. 1 2 3 4 Bower, Allan F. "Analytical techniques and solutions for plastic solids". Applied Mechanics of Solids. Retrieved 14 February 2016.

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