# Flexural rigidity

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**Flexural rigidity** is defined as the force couple required to bend a non-rigid structure to a unit curvature or it can be defined as the resistance offered by a structure while undergoing bending.

## Contents

## Flexural rigidity of a bar

{{#invoke:main|main}} In a beam or rod, flexural rigidity (defined as EI) varies along the length as a function of x shown in the following equation:

where is the Young's modulus (in Pa), is the second moment of area (in m^{4}), is the transverse displacement of the beam at **x**, and is the bending moment at *x*.

Flexural rigidity has SI units of Pa·m^{4} (which also equals N·m²).

## Flexural rigidity of a plate (e.g. the lithosphere)

{{#invoke:main|main}} The thin lithospheric plates which cover the surface of the Earth are also subject to flexure, when a load or force is applied to them. On a geological timescale, the lithosphere behaves elastically (in first approach) and can therefore bend under loading by mountain chains, volcanoes and so on.

The flexure of the plate depends on:

- The plate thickness (usually referred to as mechanical thickness of the lithosphere).
- The elastic properties of the plate
- The applied load or force

As flexural rigidity of the plate is determined by the Young's modulus, Poisson's ratio and cube of the plate's elastic thickness, it is a governing factor in both (1) and (2).

= elastic thickness (~10–15 km)

Flexural rigidity of a plate has units of Pa·m^{3}, i.e. one dimension of length less from the one for the rod, as it refers to the moment per unit length per unit of curvature, and not the total moment.
I is termed as moment of inertia.J is denoted as 2nd moment of inertia/polar moment of inertia.

## See also

## References

- ↑ {{#invoke:citation/CS1|citation |CitationClass=book }}