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 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 limit ...
s 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 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 and computing the ratio of its
plastic dissipation to the work done by the applied loads.
References
Notes
Sources
Brown University Engineering Notes
Structural engineering
Continuum mechanics
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