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 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 adaptab ...

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 Plasticity may refer to: Science * Plasticity (physics), in engineering and physics, the propensity of a solid material to undergo permanent deformation under load * Neuroplasticity, in neuroscience, how entire brain structures, and the brain it ...

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 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 ...

in the structure.

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 l ...

s use limit states to define and check a structure's performance. Bounding Theorems of Plastic-Limit Load Analysis:

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 ...

provide a way to calculate limit loads without having to solve the

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 t ...

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 m ...

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 t ...

analysis provides an alternative way to estimate limit loads. They are: * The Upper Bound Plastic Collapse Theorem * The Lower Bound Plastic Collapse Theorem * The Lower Bound Shakedown Theorem * The Upper Bound Shakedown Theorem The Upper Bound Plastic Collapse Theorem states that an upper bound to the collapse loads can be obtained by postulating a

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 ** ...

and computing the ratio of its

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 adaptabi ...

to the work done by the applied loads.

References

Notes

Sources

Brown University Engineering Notes
Structural engineering Continuum mechanics {{standard-stub