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20
Buckling
20.6
Rotation 2nd order moments of area
203 Articles  2254 Elements

Rotation 2nd order moments of area

20.6
Eqn. 1
\require{color}\definecolor{myred}{RGB}{255,0,0} I_{\color{myred}\eta}=\frac{I_{\color{myred}y}+I_{\color{myred}z}}2+\frac{I_{\color{myred}y}-I_{\color{myred}z}}2\cdot\cos\left(2\cdot\varphi\right)-I_{\color{myred}yz}\cdot\sin\left(2\cdot\varphi\right)
Eqn. 2
\require{color}\definecolor{myred}{RGB}{255,0,0} I_{\color{myred}\zeta}=\frac{I_{\color{myred}y}+I_{\color{myred}z}}2-\frac{I_{\color{myred}y}-I_{\color{myred}z}}2\cdot\cos\left(2\cdot\varphi\right)+I_{\color{myred}yz}\cdot\sin\left(2\cdot\varphi\right)
Eqn. 3
\require{color}\definecolor{myred}{RGB}{255,0,0} I_{\color{myred}\eta\zeta}=\frac{I_{\color{myred}y}-I_{\color{myred}z}}2\cdot\sin\left(2\cdot\varphi\right)+I_{\color{myred}yz}\cdot\cos\left(2\cdot\varphi\right)
Moment of areaIη=0mm4 
Iζ=200mm4 
Mixed moment of areaIηζ=0mm4 
Angleφ = 45°
Moment of areaIy = 100mm4
Iz = 100mm4
Mixed moment of areaIyz = 100mm4
45
Calc 1

Moments of area after rotation of the coordinate system by the angle of rotation φ 62

62
Holzmann, Meyer, Schumpich / Technische Mechanik, Teil 3 Festigkeitslehre / Teubner / Stuttgart / 1986 / 6. Auflage
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