Flexural rigidity

Flexural rigidity is defined as the force couple required to bend a fixed non-rigid structure by one unit of curvature, or as the resistance offered by a structure while undergoing bending.
Flexural rigidity of a beam.
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 formula_2 is the flexural modulus (in Pa), formula_3 is the second moment of area (in m4), formula_4 is the transverse displacement of the beam at x, and formula_5 is the bending moment at "x". If the material exhibits Isotropic behavior then the Flexural Modulus is equal to the Modulus of Elasticity (Young's Modulus).
Flexural rigidity has SI units of Pa·m4 (which also equals N·m²).
Flexural rigidity of a plate (e.g. the lithosphere).
In the study of geology, lithospheric flexure affects the thin lithospheric plates covering the surface of the Earth 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 other heavy objects. Isostatic depression caused by the weight of ice sheets during the last glacial period is an example of the effects of such loading.
The flexure of the plate depends on:
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).
Flexural Rigidity
formula_6
formula_2 = Young's Modulus
formula_8 = elastic thickness (~5–100 km)
formula_9 = Poisson's Ratio
Flexural rigidity of a plate has units of Pa·m3, i.e. one dimension of length less than the same property 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.