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qstruct:teoria:qsection:sezioni_compatte_generiche

Sezioni compatte generiche

Ci riferiamo a sezione compatte generiche delimitate da spezzate chiuse.

$$\iint \limits_{S} \mathrm{d}y \mathrm{d}z = \frac{ y_{2} - y_{1} }{2} \left( z_{2} + z_{1} \right)$$

$$\iint \limits_{S} y \; \mathrm{d}y \mathrm{d}z = \frac{y_{2} - y_{1}}{6} \left[ y_1 \left( 2 z_1 + z_{2} \right) + y_{2} \left( z_1 + 2 z_{2} \right) \right]$$

$$\iint \limits_{S} z \; \mathrm{d}y \mathrm{d}z = \frac{y_{2} - y_1}{6} \left( z_{2}^2+z_{2} \cdot z_{1} + z_{1}^2 \right)$$

$$\iint \limits_{S} y^2 \; \mathrm{d}y \mathrm{d}z = \frac{y_{2} - y_1}{12} \left[ y_1^2 \left( 3 z_1 + z_{2} \right) + 2 y_1 \, y_{2} \left( z_1 + z_{2} \right) + y_{2}^2 \left( z_1 + 3 z_{2} \right) \right]$$

$$\iint \limits_{S} z^2 \; \mathrm{d}y \mathrm{d}z = \frac{y_{2} - y_1}{12} \left( z_{2}^3 + z_{2}^2 z_1 + z_{2} z_{1}^2 + z_{1}^3 \right) $$

$$\iint \limits_{S} y \, z \; \mathrm{d}y \mathrm{d}z = \frac{y_{2} - y_1}{24} \left[ z_{1}^2 \left( 3y_{1} + y_{2} \right) + 2 z_{1} z_{2} \left(y_{1} + y_{2} \right) + z_{2}^2 \left( 3 y_{2} + y_{1} \right) \right]$$

$$\iint \limits_{S} y^3 \; \mathrm{d}y \mathrm{d}z = \frac{y_{2} - y_1}{20} \left[ y_1^3 \left( 4 z_{1} + z_{2} \right) + y_1^2 \, y_{2} \left( 3 z_{1} + 2 z_{2} \right) + y_{1} \, y_{2}^2 \left( 2 z_{1} + 3 z_{2} \right) + y_{2}^3 \left( z_1 + 4 z_{2} \right) \right]$$

$$\iint \limits_{S} z^3 \; \mathrm{d}y \mathrm{d}z = \frac{y_{2} - y_1}{20} \left( z_{2}^4 + z_{2}^3 z_{1} + z_{2}^2 z_{1}^2 + z_{2} z_{1}^3 + z_{1}^4 \right)$$

$$\iint \limits_{S} y^2 \, z \; \mathrm{d}y \mathrm{d}z = \frac{y_{2} - y_1}{60} \left[ y_1^2 \left( 6 z_{1}^2 + 3 z_1 \, z_{2} + z_{2}^2 \right) + y_1 \, y_{2} \left( 3 z_1^2 + 4 z_1 \, z_{2} + 3 z_{2}^2 \right) + y_{2}^2 \left( 6 z_{2}^2 + 3 z_1 \, z_{2} + z_1^2 \right) \right]$$

$$\iint \limits_{S} y \, z^2 \; \mathrm{d}y \mathrm{d}z = \frac{y_{2} - y_1}{60} \left[ z_1^3 \left( 4 y_1 + y_{2} \right) + z_1^2 \, z_{2} \left( 3 y_1 + 2 y_{2} \right) + z_1 \, z_{2}^2 \left( 2 y_1 + 3 y_{2} \right) + z_{2}^3 \left( y_1 + 4 y_{2} \right) \right]$$


qstruct/teoria/qsection/sezioni_compatte_generiche.txt · Ultima modifica: 2012/12/02 19:16 (modifica esterna)

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