Flexure under Line Load

The graph below allows you to test the influence of different line loads/displacements and effective elastic thickness on the flexure of a plate. Just drag the sliders to modify the values. You find a short description of the governing equation below.

Plate Flexure due to Line Load

Flexure, $w$ , of an elastic plate due to a line load / end displacement, $w_0$ , is

$w = w_0{e^{ - x/\alpha }}\left( {\cos {x \over \alpha } + \sin {x \over \alpha }} \right)$

If the plate is broken then the sine term is dropped.

$x$ is the distance from the line load and $\alpha$ is

$\alpha = {\left( {{{4D} \over {\left( {{\rho_m} - {\rho_w}} \right)g}}} \right)^{1/4}}$

where $D$ is the flexural rigidity, which is related to Young’s modulus $E$ , Poisson’s ratio $\nu$ , and the effective elastic thickness $h$ through

$D = {{E{h^3}} \over {12\left( {1 - {\nu ^2}} \right)}}$

The other variables are the density of the mantle, $\rho_m$ , the density of water, $\rho_w$ , and the gravity acceleration, $g$ .

A more detailed derivation can be found in Geodynamics by Turcotte and Schubert.