Centroides y Momentos de Inercia de Área para Formas 2D
- Page ID
- 83877
Se muestra la forma con área y ubicación centroide | Momentos de inercia de área rectangular | Momentos de inercia en el área polar |
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Rectángulo \(Area = bh\) |
\ begin {align*} i_x &=\ frac {1} {12} b h^3\\ [4pt] i_y &=\ frac {1} {12} b^3 h\ end {alinear*} |
\( J_z = \dfrac{1}{12} bh(b^2 + h^2) \) |
Triángulo Recto \(Area = \dfrac{1}{2} bh\) |
\ begin {align*} i_x &=\ frac {1} {36} bh^3\\ [4pt] i_y &=\ frac {1} {36} b^3 h\ end {alinear*} \ begin {align*} I_ {x'} &=\ frac {1} {12} bh^3\\ [4pt] I_ {y'} &=\ frac {1} {12} b^3 h\ end {alinear*} |
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Triángulo \(Area = \dfrac{1}{2} bh\) |
\(I_x = \dfrac{1}{36} bh^3\) \(I_{x'} = \dfrac{1}{12} bh^3\) |
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Círculo \(Area = \pi r^2\) |
\ begin {align*} i_x &=\ frac {\ pi} {4} r^4\\ [4pt] i_y &=\ frac {\ pi} {4} r^4\ end {alinear*} |
\(J_z = \dfrac{\pi}{2} r^4\) |
Anulo Circular \(Area = \pi (r_o^2 - r_i^2) \) |
\ begin {align*} i_x &=\ frac {\ pi} {4} (r_o^4 - r_i^4)\\ [4pt] i_y &=\ frac {\ pi} {4} (r_o^4 - r_i^4)\ end {align*} |
\(J_z = \dfrac{\pi}{2} (r_o^4 - r_i^4)\) |
Semicírculo \(Area = \dfrac{\pi}{2} r^2\) |
\(I_x = \left( \dfrac{\pi}{8} - \dfrac{8}{9 \pi} \right) r^4 \) \(I_y = \dfrac{\pi}{8} r^4\) \(I_{x'} = \dfrac{\pi}{8} r^4\) |
\(J_z = \left( \dfrac{\pi}{4} - \dfrac{8}{9 \pi} \right) r^4\) |
Cuarto de círculo \(Area = \dfrac{\pi}{4} r^2\) |
\ begin {align*} i_x &=\ left (\ frac {\ pi} {16} -\ frac {4} {9\ pi}\ derecha) r^4\\ [4pt] i_y &=\ left (\ frac {\ pi} {16} -\ frac {4} {9\ pi}\ derecha) r^4\ end {align*} \ begin {align*} I_ {x'} &=\ frac {\ pi} {16} r^4\\ [4pt] I_ {y'} &=\ frac {\ pi} {16} r^4\ end {alinear*} |
\( J_z = \left( \dfrac{\pi}{8} - \dfrac{8}{9 \pi} \right) r^4 \) |
Elipse \(Area = \pi ab\) |
\ begin {align*} i_x &=\ frac {\ pi} {4} ab^3\\ [4pt] i_y &=\ frac {\ pi} {4} a^3 b\ end {alinear*} |