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| Línea 365: |
Línea 365: |
| s_h = 0,275 \times \color{Green}{L_v} \text{— altura del saco lleno y compactado} \\ | | s_h = 0,275 \times \color{Green}{L_v} \text{— altura del saco lleno y compactado} \\ |
| s_w = 0,725 \times \color{Green}{L_v} \text{— anchura del saco lleno y compactado} | | s_w = 0,725 \times \color{Green}{L_v} \text{— anchura del saco lleno y compactado} |
| </math>
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| ===== Sección con laterales como segmentos circulares =====
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| [[Archivo:sección_saco_arco.png|none|frame|Sección con laterales como segmentos circulares]]
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| <math>
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| s_w = \color{Green}{L_v} - \dfrac{\pi \color{Green}{s_h}}{3} + 2 \left(\color{Green}{s_h} - \sqrt{\color{Green}{s_h}^2 - \left(\dfrac{\color{Green}{s_h}}{2} \right)^2} \right)
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| = \color{Green}{L_v} - \dfrac{\pi \color{Green}{s_h}}{3} + 2 \left(\color{Green}{s_h} - \color{Green}{s_h} \dfrac{\sqrt{3}}{2} \right)
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| = \color{Green}{L_v} + \color{Green}{s_h} \left( 2 - \dfrac{\sqrt{3}}{2} - \dfrac{\pi}{3} \right)
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| = \color{Green}{L_v} + \dfrac{\color{Green}{s_h}}{3} \left( 6 - 3\sqrt{3} - {\pi} \right)
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| \\
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| \sin \alpha = \dfrac{\dfrac{\color{Green}{s_h}}{2}}{\color{Green}{s_h}} = \dfrac{1}{2}; \alpha = 30^\circ
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| \\
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| \begin{align}
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| A_{saco} & = \left(\color{Green}{L_v} - \dfrac{\pi \color{Green}{s_h}}{3} \right) \times \color{Green}{s_h} + 2 \left(\pi \color{Green}{s_h}^2 \times \dfrac{2\alpha}{360} - \dfrac{1}{2} \times \color{Green}{s_h} \sqrt{\color{Green}{s_h}^2 - \left(\dfrac{\color{Green}{s_h}}{2} \right)^2} \right) \\
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| & = \color{Green}{L_v} \color{Green}{s_h} - \dfrac{\pi \color{Green}{s_h}^2}{3} + 2 \left(\pi \color{Green}{s_h}^2 \times \dfrac{1}{6} - \dfrac{1}{2} \times \dfrac{\color{Green}{s_h}^2 \sqrt{3}}{2} \right) \\
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| & = \color{Green}{L_v} \color{Green}{s_h} - \dfrac{\pi \color{Green}{s_h}^2}{3} + \dfrac{\pi \color{Green}{s_h}^2}{3} - \dfrac{\color{Green}{s_h}^2 \sqrt{3}}{2} \\
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| & = \color{Green}{L_v} \color{Green}{s_h} - \color{Green}{s_h}^2 \dfrac{\sqrt{3}}{2}
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| \end{align}
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| </math> | | </math> |
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