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.

External Links

• Proof of Vereschagin's rule by hand calculations (PDF)