Diferencia entre revisiones de «Cálculo de materiales»

Línea 44: Línea 44:


<math>
<math>
\sin \alpha = \dfrac{\dfrac{\color{Green}{h}}{2}}{\color{Green}{h}} = \dfrac{1}{2}; \alpha = 30^\circ
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{s_h}{2}\right)^2} \right)
 
\sin \alpha = \dfrac{\dfrac{\color{Green}{s_h}}{2}}{\color{Green}{s_h}} = \dfrac{1}{2}; \alpha = 30^\circ


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\begin{align}
\begin{align}
A_{saco} & = \left(\color{Green}{L_v} - \dfrac{\pi \color{Green}{h}}{3} \right) \times \color{Green}{h} + 2 \left(\pi \color{Green}{h}^2 \times \dfrac{2\alpha}{360} - \dfrac{1}{2} \times \color{Green}{h} \sqrt{\color{Green}{h}^2 - \left(\dfrac{\color{Green}{h}}{2} \right)^2} \right) \\
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) \\
& = \color{Green}{L_v} \color{Green}{h} - \dfrac{\pi \color{Green}{h}^2}{3} + 2 \left(\pi \color{Green}{h}^2 \times \dfrac{1}{6} - \dfrac{1}{2} \times \dfrac{\color{Green}{h}^2 \sqrt{3}}{2} \right) \\
& = \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) \\
& = \color{Green}{L_v} \color{Green}{h} - \dfrac{\pi \color{Green}{h}^2}{3} + \dfrac{\pi \color{Green}{h}^2}{3} - \dfrac{\color{Green}{h}^2 \sqrt{3}}{2} \\
& = \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} \\
& = \color{Green}{L_v} \color{Green}{h} - \color{Green}{h}^2 \dfrac{\sqrt{3}}{2}
& = \color{Green}{L_v} \color{Green}{s_h} - \color{Green}{s_h}^2 \dfrac{\sqrt{3}}{2}
\end{align}
\end{align}
</math>
</math>
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