Vereschagin's rule: Difference between revisions
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[[Image:Vereschagin rule.png|right|frame|Vereschagin's Rule]] | |||
Vereschagin's rule enables to easily calculate the integral | Vereschagin's rule enables to easily calculate the integral | ||
< | <math>\int_0^L M \overline{M} dx</math> | ||
that is needed to solve statically indeterminate structures using the [[flexibility method]]. | that is needed to solve statically indeterminate structures using the [[flexibility method]]. | ||
| Line 7: | Line 9: | ||
The integral can be calculated as follows: | The integral can be calculated as follows: | ||
< | <math>\int_0^L M \overline{M} dx = A_M \overline{M}_{cg}</math> | ||
where | where | ||
* < | * <math>A_M</math> is the area under the curve M | ||
* < | * <math>\overline{M}_{cg}</math> is value of <math>\overline{M}</math> at the location of center of gravity of the area <math>A_M</math> | ||
The value of < | The value of <math>\overline{M}_{cg}</math> must be determined for a constant or linear function. | ||
[ | == External Links == | ||
* [http://www.bridgeart.net/portal/node/67 Proof of Vereschagin's rule by hand calculations] (PDF) | |||
{{Traditional Analysis Methods}} | {{Traditional Analysis Methods}} | ||
[[Category:Hand Calculation]] | |||
Latest revision as of 02:24, 22 October 2024
Vereschagin's Rule
Vereschagin's rule enables to easily calculate the integral
that is needed to solve statically indeterminate structures using the flexibility method.
The integral can be calculated as follows:
where
- is the area under the curve M
- is value of at the location of center of gravity of the area
The value of must be determined for a constant or linear function.
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