# Vereschagin's rule

Vereschagin's Rule

Vereschagin's rule enables to easily calculate the integral

$\int_0^L M \overline{M} dx$

that is needed to solve statically indeterminate structures using the flexibility method.

The integral can be calculated as follows:

$\int_0^L M \overline{M} dx = A_M \overline{M}_{cg}$

where

• $A_M$ is the area under the curve M
• $\overline{M}_{cg}$ is value of $\overline{M}$ at the location of center of gravity of the area $A_M$

The value of $\overline{M}_{cg}$ must be determined for a constant or linear function.