created at April 25, 2021



A=abA=a\cdot b


L=2(a+b)L=2\cdot (a + b)

Moments of inertia:

Ix=ba312;Iy=ab312;Ixy=0;Iρ=Ix+IyI_{x}=\frac{b\cdot a^{3}}{12};\quad I_{y}=\frac{a\cdot b^{3}}{12};\quad I_{xy}=0;\quad I_{\rho}=I_{x} + I_{y}

Moments of resistance:

Wx=ba26;Wy=ab26;W_{x}=\frac{b\cdot a^{2}}{6};\quad W_{y}=\frac{a\cdot b^{2}}{6};

Radius of inertia:

ix=a23;iy=b23;i_{x}=\frac{a}{2\cdot \sqrt{3}};\quad i_{y}=\frac{b}{2\cdot \sqrt{3}};

Moments of inertia for rotated axis

Consider axis Ox1y1, rotated relative to Oxy by angle α (see figure above). Then moments of inertia relative to these rotated axis can be found as:

Ix1=Ixcos2(α)+Iysin2(α)Ixysin(2α)I_{x1}=I_{x}\cdot cos^{2}(\alpha) + I_{y}\cdot sin^{2}(\alpha) - I_{xy}\cdot sin(2\cdot \alpha)
Iy1=Ixsin2(α)+Iycos2(α)Ixycos(2α)I_{y1}=I_{x}\cdot sin^{2}(\alpha) + I_{y}\cdot cos^{2}(\alpha) - I_{xy}\cdot cos(2\cdot \alpha)
Ix1y1=IxIy2sin(2α)+Ixycos(2α)I_{x1y1}=\frac{I_{x} - I_{y}}{2}\cdot sin(2\cdot \alpha) + I_{xy}\cdot cos(2\cdot \alpha)