Vereschagin's rule

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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}


  • 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.

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