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20
Buckling
20.5
Moments of area triangle
203 Articles  2254 Elements

Moments of area triangle

20.5
Any triangle
Fig. 1
Any triangle
a 1& a 2   Lengths h a height x 0 & y 0 center of mass coordinates

The triangle is advantageously broken down into two right-angled triangles.606263

Eqn. 1
\require{color}\definecolor{myred}{RGB}{255,0,0} A=\frac{h_{\color{myred}a}\cdot\left(a_{\color{myred}1}+a_{\color{myred}2}\right)}2
Eqn. 2
\require{color}\definecolor{myred}{RGB}{255,0,0} x_{\color{myred}0}=\frac13\cdot\left(2\cdot a_{\color{myred}1}+a_{\color{myred}2}\right)
Eqn. 3
\require{color}\definecolor{myred}{RGB}{255,0,0} y_{\color{myred}0}=\frac13\cdot h_{\color{myred}a}
Eqn. 4
\require{color}\definecolor{myred}{RGB}{255,0,0} I_{\color{myred}x}=\frac{h_{\color{myred}a}^{\color{myred}3}}{36}\cdot\left(a_{\color{myred}1}+a_{\color{myred}2}\right)
Eqn. 5
\require{color}\definecolor{myred}{RGB}{255,0,0} I_{\color{myred}y}=\frac{h_{\color{myred}a}}{36}\cdot\left(a_{\color{myred}2}^{\color{myred}3}+2\cdot a_{\color{myred}1}^{\color{myred}2}\cdot a_{\color{myred}2}+a_{\color{myred}1}^{\color{myred}3}+2\cdot a_{\color{myred}2}^{\color{myred}2}\cdot a_{\color{myred}1}\right)
Eqn. 6
\require{color}\definecolor{myred}{RGB}{255,0,0} I_{\color{myred}xy}=\frac{h_{\color{myred}a}^{\color{myred}2}}{72}\cdot\left(a_{\color{myred}2}^{\color{myred}2}-a_{\color{myred}1}^{\color{myred}2}\right)
Cross sectional areaA=2,700mm2 
Centroid x-coordinatex0=40mm 
Centroid y-coordinatey0=20mm 
Moment of areaIx=54dm4 
Iy=94.5dm4 
Mixed moment of areaIxy=-13.5dm4 
Heightha = 60mm
Lengtha1 = 30mm
a2 = 60mm
60
Calc 1
Moments of area triangle
60
Böge, A. / Arbeitshilfen und Formeln für das technische Studium / Vieweg / Braunschweig / 1985 / 6. Auflage
62
Holzmann, Meyer, Schumpich / Technische Mechanik, Teil 3 Festigkeitslehre / Teubner / Stuttgart / 1986 / 6. Auflage
63
Dankert, J.; Dankert, H. / Technische Mechanik / Springer Vieweg / Wiesbaden / 2013 / 7. Auflage
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