Skip to main content\(\require{cancel}\let\vecarrow\vec
\renewcommand{\vec}{\mathbf}
\newcommand{\ihat}{\vec{i}}
\newcommand{\jhat}{\vec{j}}
\newcommand{\khat}{\vec{k}}
\DeclareMathOperator{\proj}{proj}
\newcommand{\kg}[1]{#1~\mathrm{kg} }
\newcommand{\lbm}[1]{#1~\mathrm{lbm} }
\newcommand{\slug}[1]{#1~\mathrm{slug}}
\newcommand{\m}[1]{#1~\mathrm{m}}
\newcommand{\km}[1]{#1~\mathrm{km}}
\newcommand{\cm}[1]{#1~\mathrm{cm}}
\newcommand{\mm}[1]{#1~\mathrm{mm}}
\newcommand{\ft}[1]{#1~\mathrm{ft}}
\newcommand{\inch}[1]{#1~\mathrm{in}}
\newcommand{\N}[1]{#1~\mathrm{N} }
\newcommand{\kN}[1]{#1~\mathrm{kN} }
\newcommand{\MN}[1]{#1~\mathrm{MN} }
\newcommand{\lb}[1]{#1~\mathrm{lb} }
\newcommand{\lbf}[1]{#1~\mathrm{lbf} }
\newcommand{\Nm}[1]{#1~\mathrm{N}\!\cdot\!\mathrm{m} }
\newcommand{\kNm}[1]{#1~\mathrm{kN}\!\cdot\!\mathrm{m} }
\newcommand{\ftlb}[1]{#1~\mathrm{ft}\!\cdot\!\mathrm{lb} }
\newcommand{\ftlbf}[1]{#1~\mathrm{ft}\!\cdot\!\mathrm{lbf} }
\newcommand{\inlb}[1]{#1~\mathrm{in}\!\cdot\!\mathrm{lb} }
\newcommand{\lbperft}[1]{#1~\mathrm{lb}/\mathrm{ft} }
\newcommand{\lbperin}[1]{#1~\mathrm{lb}/\mathrm{in} }
\newcommand{\Nperm}[1]{#1~\mathrm{N}/\mathrm{m} }
\newcommand{\kgperkm}[1]{#1~\mathrm{kg}/\mathrm{km} }
\newcommand{\psinch}[1]{#1~\mathrm{lb}/\mathrm{in}^2 }
\newcommand{\pqinch}[1]{#1~\mathrm{lb}/\mathrm{in}^3 }
\newcommand{\psf}[1]{#1~\mathrm{lb}/\mathrm{ft}^2 }
\newcommand{\pqf}[1]{#1~\mathrm{lb}/\mathrm{ft}^3 }
\newcommand{\Nsm}[1]{#1~\mathrm{N}/\mathrm{m}^2 }
\newcommand{\kgsm}[1]{#1~\mathrm{kg}/\mathrm{m}^2 }
\newcommand{\kgqm}[1]{#1~\mathrm{kg}/\mathrm{m}^3 }
\newcommand{\Pa}[1]{#1~\mathrm{Pa} }
\newcommand{\kPa}[1]{#1~\mathrm{kPa} }
\newcommand{\aSI}[1]{#1~\mathrm{m}/\mathrm{s}^2 }
\newcommand{\aUS}[1]{#1~\mathrm{ft}/\mathrm{s}^2 }
\newcommand{\unit}[1]{#1~\mathrm{unit} }
\newcommand{\ang}[1]{#1^\circ }
\newcommand{\second}[1]{#1~\mathrm{s} }
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
Section C.2 Moment of Inertia of Common Shapes
Table C.2.1. Moments of Inertia of Common Shapes
|
\((b/2, h/2)\) |
\(\bar{I}_{x'} = \dfrac{1}{12} b h^3\)
\(\bar{I}_{y'} = \dfrac{1}{12} b^3 h\)
|
\(I_{x} = \dfrac{1}{3} b h^3\)\(I_{y} = \dfrac{1}{3} b^3 h\)
|
|
\((b/3, h/3)\) |
\(\bar{I}_{x'} = \dfrac{1}{36} b h^3\)\(\bar{I}_{y'} = \dfrac{1}{36} b^3 h\)
|
\(I_x = \dfrac{1}{12} b h^3\)\(I_y = \dfrac{1}{12} b^3 h\)
|
|
\((r,r)\) |
\(\bar{I}_{x'}=\bar{I}_{y'}= \dfrac{\pi}{4} r^4\) |
\(I_{x}=I_{y}= \dfrac{5 \pi}{4} r^4\) |
|
\(\left (r, \dfrac{4r}{3\pi} \right)\) |
\(\bar{I}_{x'} = \left(\frac{\pi}{8} - \frac{8}{9\pi}\right) r^4\)
\(\bar{I}_{x'} \approx 0.1098\ r^4\)
\(\bar{I}_{y'} = \dfrac{\pi}{8} r^4 \)
|
\(I_x =\dfrac{\pi}{8} r^4\)
\(I_y =\dfrac{5 \pi}{8} r^4\)
|
|
\(\left (\dfrac{4r}{3\pi}, \dfrac{4r}{3\pi} \right)\) |
\(\bar{I}_{x'} = \frac{1}{2}\left(\frac{\pi}{8} - \frac{8}{9\pi}\right) r^4 \)
\(\bar{I}_{x'} = \bar{I}_{y'} \approx 0.0549\ r^4\)
|
\(I_x = I_y = \dfrac{\pi }{16}r^4\) |