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Section C.2 Moment of Inertia of Common Shapes
Table C.2.1. Moments of Inertia of Common Shapes
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\((b/2, h/2)\) |
\(\bar{I}_{x'} = \dfrac{1}{12} b h^3\)
\(\bar{I}_{y'} = \dfrac{1}{12} b^3 h\)
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\(I_{x} = \dfrac{1}{3} b h^3\)\(I_{y} = \dfrac{1}{3} b^3 h\)
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\((b/3, h/3)\) |
\(\bar{I}_{x'} = \dfrac{1}{36} b h^3\)\(\bar{I}_{y'} = \dfrac{1}{36} b^3 h\)
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\(I_x = \dfrac{1}{12} b h^3\)\(I_y = \dfrac{1}{12} b^3 h\)
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\((r,r)\) |
\(\bar{I}_{x'}=\bar{I}_{y'}= \dfrac{\pi}{4} r^4\)
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\(I_{x}=I_{y}= \dfrac{5 \pi}{4} r^4\)
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\(\left (r, \dfrac{4r}{3\pi} \right)\) |
\(\bar{I}_{x'} = \left(\frac{\pi}{8} - \frac{8}{9\pi}\right) r^4\)
\(\bar{I}_{x'} \approx 0.1098\ r^4\)
\(\bar{I}_{y'} = \dfrac{\pi}{8} r^4\)
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\(I_x =\dfrac{\pi}{8} r^4\)
\(I_y =\dfrac{5 \pi}{8} r^4\)
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\(\left (\dfrac{4r}{3\pi}, \dfrac{4r}{3\pi} \right)\) |
\(\bar{I}_{x'} = \frac{1}{2}\left(\frac{\pi}{8} - \frac{8}{9\pi}\right) r^4\)
\(\bar{I}_{x'} = \bar{I}_{y'} \approx 0.0549\ r^4\)
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\(I_x = I_y = \dfrac{\pi }{16}r^4\)
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