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.
See main article: Euler–Bernoulli beam equation. Although the moment
M(x)
y
EI
x
EI{dy\overdx} =
| x | |
| \int | |
| 0 |
M(x)dx+C1
E
I
y
M(x)
E
I
Flexural rigidity has SI units of Pa·m4 (which also equals N·m2).
See main article: Plate theory. 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[1]
D=
| 3}{12(1-\nu | |
| \dfrac{Eh | |
| e |
2)}
E
he
\nu
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.