created at May 1, 2021

Ring

Let's introduce a variable:

\alpha = \frac{d}{D}

Area:

A=\frac{\pi\cdot D^{2}}{4}(1-\alpha^{2})

I_{x}=I_{y}=\frac{\pi\cdot D^{4}}{64}(1-\alpha^{4});\quad I_{\rho}=\frac{\pi\cdot D^{4}}{32}(1-\alpha^{4})

W_{x}=W_{y}=\frac{\pi\cdot D^{3}}{32}(1-\alpha^{4});\quad W_{\rho}=\frac{\pi\cdot D^{3}}{16}(1-\alpha^{4})

i_{x}=i_{y}=\frac{D}{4}\sqrt{1 + \alpha^2}