Moments of area ring

20.3
Moments of area ring
Fig. 1
pipe cross-section
d a outside diameter di inside diameter
Eqn. 1
\require{color}\definecolor{myred}{RGB}{255,0,0} A=\frac{\mathrm\pi}4\cdot\left(d_{\color{myred}a}^{\color{myred}2}-d_{\color{myred}i}^{\color{myred}2}\right)
Eqn. 2
\require{color}\definecolor{myred}{RGB}{255,0,0} I=\frac{\mathrm\pi}{64}\cdot\left(d_{\color{myred}a}^{\color{myred}4}-d_{\color{myred}i}^{\color{myred}4}\right)
Eqn. 3
\require{color}\definecolor{myred}{RGB}{255,0,0} i=\frac14\cdot\left(d_{\color{myred}a}^{\color{myred}2}+d_{\color{myred}i}^{\color{myred}2}\right)
Eqn. 4
\require{color}\definecolor{myred}{RGB}{255,0,0} W=\frac{\mathrm\pi}{32}\cdot\frac{\left(d_{\color{myred}a}^{\color{myred}4}-d_{\color{myred}i}^{\color{myred}4}\right)}{d_{\color{myred}a}}
Cross sectional areaA=490.6mm2 
Moment of areaI=78,970.1mm4 
Radius of gyrationi=643.83mm 
Moment of resistanceW=3,948.5mm3 
Outer Diameterda = 40mm
Inner diameterdi = 31.23mm
Calc 1
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