Mekanika Bahan

1. Mekanika Bahan Menurunkan rumus luas penampang persegi, segitiga dan lingkaran

Monday, December 20, 2021

Hai hai Engineer, Berikut ini menurunkan rumus Luas Penampang, Sbb :

Penampang Persegi

$dA=h.dx$

$A=\int_{0}^{b}dA$

$A=\int_{0}^{b}h.dx$

$A=\left [ h.dx \right ]_{0}^{b}$

$A=\left [ h.b \right ]-\left [h.0\right ]$

$A=h.b$

Penampang Lingkaran

$dA=dr.r.d\theta$

$A=\int_{}^{} dA$

$dA=\int_{}^{}dr.r.d\theta$

$A=\int_{0}^{R}r.dr.\int_{0}^{\pi /2} d\theta$

$A=\tfrac{1}{2}.R^{2}.\frac{\pi }{2}$

$A_{\frac{1}{4}lingkaran}=\frac{1}{4}.\pi.R^{2}$

$A=\pi .R^{2}$

Penampang Segitiga

$dA=b^{'}.dy$

$A=\int_{0}^{b}dA$

$A=\int_{0}^{h}.b^{'}$

$dA=\int_{0}^{h}.\frac{b}{h}\left ( h-y \right ).dy$

$A=\frac{b}{h}.\left [ \int_{0}^{h}h.dy-\int_{0}^{h}y.dy \right ]$

$A=\frac{b}{h}.\left [ h^{2}-\frac{1}{2}.h^{2} \right ]$

$A=\frac{1}{2}.b.h$

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