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20
Buckling
20.4
Area moment of circle segment
203 Articles  2254 Elements

Area moment of circle segment

20.4
Circle section
Fig. 1
Circle section
α angle r radius y 0 center of gravity coordinate

The second-order moment of area with respect to the y-axis is obtained by shifting according to Steiner's theorem to the center of gravity y 0 .6061

Eqn. 1
\require{color}\definecolor{myred}{RGB}{255,0,0} A=\frac{r^{\color{myred}2}}2\cdot\left(2\cdot\alpha-\sin\;\left(2\cdot\alpha\right)\right)
Eqn. 2
\require{color}\definecolor{myred}{RGB}{255,0,0} y_{\color{myred}0}=\frac{\left(2\cdot r\cdot\sin\;\alpha\right)^{\color{myred}3}}{12\cdot A}
Eqn. 3
\require{color}\definecolor{myred}{RGB}{255,0,0} I_{\color{myred}x}=\frac{r^{\color{myred}4}}{144}\cdot\left(36\cdot\alpha-9\cdot\sin\left(4\cdot\alpha\right)-\frac{128\cdot\sin^{\color{myred}6}\left(\alpha\right)}{2\cdot\alpha-\sin\left(2\cdot\alpha\right)}\right)
Eqn. 4
\require{color}\definecolor{myred}{RGB}{255,0,0} I_{\color{myred}y}=\frac{r^{\color{myred}4}}4\cdot\left(\alpha-\frac23\cdot\sin\left(2\cdot\alpha\right)+\frac1{12}\cdot\sin\left(4\cdot\alpha\right)\right)
Eqn. 5
\require{color}\definecolor{myred}{RGB}{255,0,0} I_{\color{myred}xy}=0
Cross sectional areaA=0.9cm2 
Centroid y-coordinatey0=6.14mm 
Radiusr = 10mm
Angleα = 70°
10
Calc 1
Moments of area circle segment
60
Böge, A. / Arbeitshilfen und Formeln für das technische Studium / Vieweg / Braunschweig / 1985 / 6. Auflage
61
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