List Of Second Moments Of Area - Wikipedia

For thin tubes, r ≡ r 1 ≈ r 2 {\displaystyle r\equiv r_{1}\approx r_{2}} and r 2 ≡ r 1 + t {\displaystyle r_{2}\equiv r_{1}+t} and so to first order in t {\displaystyle t} , r 2 4 = r 1 4 + 4 r 1 3 t + ⋯ {\displaystyle r_{2}^{4}=r_{1}^{4}+4r_{1}^{3}t+\cdots } . So, for a thin tube, I x = I y ≈ π r 3 t {\displaystyle I_{x}=I_{y}\approx \pi r^{3}t} and I z ≈ 2 π r 3 t {\displaystyle I_{z}\approx 2\pi r^{3}t} .

I z {\displaystyle I_{z}} is the second polar moment of area.