Method of the moments of surfaces

The method of the “moments of surfaces” relates to the deformation of the beams in inflection, and consists in calculating the slope and the arrow of a beam.

The method of the Moment S of surfaces is a method a geometrical integration making it possible to calculate the deformed of a Poutre by connecting it to a diagram M/EI.

Method of the moments of surface

$\backslash \; frac\; \{1\}\; \{\backslash \; rho\}\; =\; \backslash \; frac\; \{D\; \backslash \; varphi\}\; \{D\; X\}\; =\; \backslash \; frac\; \{M\}\; \{E\; I\}$

$d\; \backslash \; varphi\; =\; \backslash \; frac\; \{M\}\; \{E\; I\}\; D\; x$

The variation of slope between two point has and B of the beam:

$\backslash \; varphi\_\; \{AB\}\; =\; \backslash \; int\_\; \{has\}\; ^\; \{B\}\; D\; \backslash \; varphi\; =\; \backslash \; int\_\; \{x\_A\}\; ^\; \{x\_B\}\; \backslash \; frac\; \{M\}\; \{E\; I\}\; D\; x$

That represents the surface, ranging between $x\_A$ and $x\_B$, under the curve $M/E\; I$:

$\backslash \; varphi\_\; \{AB\}\; =\; \backslash \; left\; \backslash \; lbrack\; \backslash \; text\; \{surface\; under\}\; \backslash \; \backslash \; frac\; \{M\}\; \{E\; I\}\; \backslash \; right\; \backslash \; rbrack\_\; \{has\}\; ^\; \{B\}$

Theorems of the method of the moments of surface

The method of the moments of surfaces is based on two theorems known as theorems of the moments of surfaces.

Theorem I: variation of the slope

Theorem II: tangential arrow

d*theta has as an expression -->

See too

• Method of Mohr
• Functions of singularities
• Method of superposition

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