面積・重心・断面二次モーメントの計算

各種形状の断面積、重心の距離、断面二次モーメント、断面係数についての公式表を掲載しています。
断面A：断面積e：重心の距離I：断面二次モーメントZ＝I/e：断面係数
\[bh\]\[\frac{h}{2}\]\[\frac{bh^{3}}{12}\]\[\frac{bh^{2}}{6}\]
\[h^{2}\]\[\frac{h}{2}\]\[\frac{h^{4}}{12}\]\[\frac{h^{3}}{6}\]
\[h^{2}\]\[\frac{h}{2}\sqrt{2}\]\[\frac{h^{4}}{12}\]\[0.1179h^{3}=\frac{\sqrt{2}}{12}h^{3}\]
\[\frac{bh}{2}\]\[\frac{2}{3}h\]\[\frac{bh^{3}}{36}\]\[\frac{bh^{2}}{24}\]
\[(2b+b_{1})\frac{h}{2}\]\[\frac{1}{3}\times\frac{3b+2b_{1}}{2b+b_{1}}h\]\[\frac{6b^{2}+6bb_{1}+{b_1}^{_2}}{36(2b+b_{1})}h^{3}\]\[\frac{6b^{2}+6bb_{1}+{b_1}^{2}}{12(3b+2b_1)}h^{2}\]
\[\frac{3\sqrt{3}}{2}r^{2}\\
=2.598r^{2}\]		\[\sqrt{\frac{3}{4}}r=0.886r\]\[\frac{5\sqrt{3}}{16}r^{4}＝0.5413r^{4}\]\[\frac{5}{8}r^{3}\]
\[r\]\[\frac{5\sqrt{3}}{16}r^{3}＝0.5413r^{3}\]
\[2.828r^{2}\]\[0.924r^{2}\]\[\frac{1+2\sqrt{2}}{6}r^{4}\\
=0.6381r^{4}\]		\[0.6906r^{3}\]
\[0.8284a^{2}\]\begin{align}
b&=\frac{a}{1+\sqrt{2}}\\
&=0.4142a
\end{align}		\[0.0547a^{4}\]\[0.1095a^{3}\]
\[\pi r^{2}=\frac{\pi d^{2}}{4}\]\[\frac{d}{2}\]\[\frac{\pi d^{4}}{64}=\frac{\pi r^{4}}{4}
\begin{align}
&=0.0491d^{4}\\
&≒0.05d^{4}\\
&=0.7854r^{4}
\end{align}\]		\[\frac{\pi d^{3}}{32}=\frac{\pi r^{3}}{4}
\begin{align}
&=0.0982d^{3}\\
&≒0.1d^{3}\\
&=0.7854r^{3}
\end{align}\]
\[r^{2}\left(1-\frac{\pi}{4}\right)\\
＝0.2146r^{2}\]		\begin{align}
e_{1} &= 0.2234r \\
e_{2} &= 0.7766r
\end{align}		\[0.0075r^{4}\]\[\frac{0.0075r^{4}}{e_2}
\begin{align}
&=0.00966r^{3}\\
&≒0.01r^{3}
\end{align}\]
\[\pi ab\]\[a\]\[\frac{\pi}{4}ba^{3}＝0.7854ba^{3}\]\[\frac{\pi}{4}ba^{2}＝0.7854ba^{2}\]
\[\frac{\pi}{2}r^{2}\]\begin{align}
e_{1} &= 0.4244r \\
e_{2} &= 0.5756r
\end{align}		\[\left(\frac{\pi}{8}-\frac{8}{9\pi}\right)r^{4}\\
＝0.1098r^{4}\]		\begin{align}
Z_{1} &= 0.2587r^{3} \\
Z_{2} &= 0.1908r^{3}
\end{align}
\[\frac{\pi}{4}r^{2}\]\begin{align}
e_{1} &= 0.4244r \\
e_{2} &= 0.5756r
\end{align}		\[0.055r^{4}\]\begin{align}
Z_{1} &= 0.1296r^{3} \\
Z_{2} &= 0.0956r^{3}
\end{align}
\[b(H-h)\]\[\frac{H}{2}\]\[\frac{b}{12}(H^{3}-h^{3})\]\[\frac{b}{6H}(H^{3}-h^{3})\]
\[A^{2}-a^{2}\]\[\frac{A}{2}\]\[\frac{A^{4}-a^{4}}{12}\]\[\frac{1}{6}\frac{A^{4}-a^{4}}{A}\]
\[A^{2}-a^{2}\]\[\frac{A}{2}\sqrt{2}\]\[\frac{A^{4}-a^{4}}{12}\]\[\frac{A^{4}-a^{4}}{12A}\sqrt{2}\\
=\frac{0.1179(A^{4}-a^{4})}{A}\]
\[\frac{\pi}{4}({d_{2}}^{2}-{d_{1}}^{2})\]\[\frac{d_{2}}{2}\]\[\frac{\pi}{64}({d_{2}}^{4}-{d_{1}}^{4})\\
=\frac{\pi}{4}(R^{4}-r^{4})\]		\[\frac{\pi}{32}\left(\frac{{d_{2}}^{4}-{d_{1}}^{4}}{d_{2}}\right)\\
=\frac{\pi}{4}\times\frac{R^{4}-r^{4}}{R}\]
\[a^{2}-\frac{\pi{d}^{2}}{4}\]\[\frac{a}{2}\]\[\frac{1}{12}\left(a^{4}-\frac{3\pi}{16}d^{4}\right)\]\[\frac{1}{6a}\left(a^{4}-\frac{3\pi}{16}d^{4}\right)\]
\[2b(h-d)\\
+\frac{\pi}{4}d^{2}\]		\[\frac{h}{2}\]\[\frac{1}{12}\left\{\frac{3\pi}{16}d^{4}\\
+b(h^{3}-d^{3})\\
+b^{3}(h-d)\right\}\]		\[\frac{1}{6h}\left\{\frac{3\pi}{16}d^{4}\\
+b(h^{3}-d^{3})\\
+b^{3}(h-d)\right\}\]
\[2b(h-d)+\\
\frac{\pi}{4}({d_1}^{2}-d^{2})\]		\[\frac{h}{2}\]\[\frac{1}{12}\left\{\frac{3\pi}{16}({d_1}^{4}-d^{4})\\
+b(h^{3}-{d_1}^{3})\\
+b^{3}(h-d_1)\right\}\]		\[\frac{1}{6h}\left\{\frac{3\pi}{16}({d_1}^{4}-d^{4})\\
+b(h^{3}-{d_1}^{3})\\
+b^{3}(h-d_1)\right\}\]
最新更新年月日：　2023年6月23日
※ 本稿は21年6月時点の最新情報を掲載しています。

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