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    "# Cross sectional quantitites"
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    "## Definition section parameters\n",
    "| Surface      |Static moment of area| Moment of Inertia            | Polar moment of inertia                 | Steiner's rule |\n",
    "|--------------|---------------------|------------------------------|-----------------------------------------|----------------|\n",
    "|$A=\\int_A\\,dA$|$S_y = \\int_A y\\, dA$|$I_{yy}=I_z=\\int_A y^2\\,dA$   |$I_p = \\int_A r^2\\, dA = I_{yy} + I_{zz}$|$I_{\\overline{yy}}=I_{yy(own)}+\\bar{y}_c^2 \\cdot A$|  \n",
    "|              |$S_z = \\int_A z\\, dA$|$I_{yz}=I_{zy}=\\int_A y*z\\,dA$|                                         |$I_{\\overline{yz}}=I_{\\overline{zy}}=I_{yz(own)}+\\bar{y}_c \\cdot \\bar{z}_c \\ A$|\n",
    "|              |                     |$I_{zz}=I_{y}=\\int_A z^2\\,dA$ |                                         |$I_{\\overline{zz}}=I_{zz(own)}+\\bar{z}_c^2 \\cdot A$"
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    "## Section parameters\n",
    "\n",
    "```{figure} Images/Rectangle shape.jpg\n",
    "---\n",
    "scale: 100%\n",
    "---\n",
    "```\n",
    "\n",
    "### Square\n",
    "|Area, centre of gravity| Moments of intertia own | other                       |\n",
    "|-----------------------|-------------------------|-----------------------------|\n",
    "|$A=bh$                 |$I_{yy}=\\frac{1}{12}*b^3*h$      |$I_{\\overline{yy}}=1/3b^3h$  | \n",
    "|$\\bar{y}_C=\\frac{1}{2}b$         |$I_{zz}=\\frac{1}{12}bh^3$        |$I_{\\overline{zz}}=\\frac{1}{3}bh^3$  |\n",
    "|$\\bar{z}_C=\\frac{1}{2}b$         |$I_{yz}=\\frac{1}{12}bh^3$        |$I_{\\overline{yz}}=\\frac{1}{4}b^2h^2$|\n",
    "\n",
    "```{figure} Images/Parallelogram shape.jpg\n",
    "---\n",
    "scale: 100%\n",
    "---\n",
    "```\n",
    "\n",
    "### Parallelogram\n",
    "|Area, centre of gravity    | Moments of intertia own       | other                         |\n",
    "|---------------------------|-------------------------------|-------------------------------|\n",
    "|$A=bh$                     |$I_{yy}=\\frac{1}{12}(a^2+b^2)$|$I_{\\overline{yy}}=1/3bh^3$  | \n",
    "|$\\bar{y}_C=\\frac{1}{2}(a+b)$ |$I_{zz}=\\frac{1}{12}bh^3$      |                               |\n",
    "|$\\bar{z_C}=\\frac{1}{2}h$     |$I_{yz}=\\frac{1}{12}abh^2$   |                               |\n",
    "\n",
    "```{figure} Images/Triangle shape.jpg\n",
    "---\n",
    "scale: 100%\n",
    "---\n",
    "```\n",
    "\n",
    "### Triangle\n",
    "|Area, centre of gravity       | Moments of intertia own          | other                           |\n",
    "|------------------------------|----------------------------------|---------------------------------|\n",
    "|$A=\\frac{1}{2}bh$             |$I_{yy}=\\frac{1}{36}*(a^2-ab+b^2)$|$I_{\\overline{zz}}=\\frac{1}{3}bh^3$      | \n",
    "|$\\bar{y}_C=\\frac{1}{3}(2a-b)$ |$I_{zz}=\\frac{1}{36}bh^3$         |$I_{\\overline{yz}}=\\frac{1}{8}(2a-b)bh^2$|\n",
    "|$\\bar{z}_C=\\frac{2}{3}h$      |$I_{yz}=\\frac{1}{72}abh^2$        |$I_{\\overline{\\overline{zz}}}=\\frac{1}{12}bh^3$     |\n",
    "\n",
    "```{figure} Images/Trapezoid shape.jpg\n",
    "---\n",
    "scale: 100%\n",
    "---\n",
    "```\n",
    "\n",
    "### Trapezoid\n",
    "|Area, centre of gravity                  | Moments of intertia own                       | other                                              | \n",
    "|-----------------------------------------|-----------------------------------------------|----------------------------------------------------|\n",
    "|$A=\\frac{1}{2}(a+b)h$                    |$I_{zz}=\\frac{1}{36}\\frac{a^2+4ab+b^2}{a+b}h^3$|$I_{\\overline{zz}}=\\frac{1}{3}bh^3$                 | \n",
    "|$\\bar{y}_C=\\frac{1}{3}\\frac{a+2b}{a+b}h$ |                                               |$I_{\\overline{\\overline{zz}}}=\\frac{1}{12}(a+3b)h^3$|\n",
    "|$\\bar{z}_C=\\frac{2}{3}h$                 |                                               |                                                    |\n",
    "\n",
    "```{figure} Images/Circle shape.jpg\n",
    "---\n",
    "scale: 100%\n",
    "---\n",
    "```\n",
    "\n",
    "### Circle\n",
    "|Area, centre of gravity | Moments of intertia own      | other                                               | \n",
    "|------------------------|------------------------------|-----------------------------------------------------|\n",
    "|$A=πR^2$                |$I_{yy}=I_{zz}=\\frac{1}{4}R^4$|$I_{\\overline{yy}}=I_{\\overline{zz}}=\\frac{5}{4}πR^4$| \n",
    "|                        |$I_{yz}=0$                    |$I_{\\overline{\\overline{yz}}}=πR^4$                  |\n",
    "|                        |$I_p=\\frac{1}{2}πR^4$         |                                                     |\n",
    "\n",
    "```{figure} Image/Thick walled ring shape.jpg\n",
    "---\n",
    "scale: 100%\n",
    "---\n",
    "```\n",
    "\n",
    "### Thick-walled ring\n",
    "|Area, centre of gravity | Moments of intertia own                 | other           | \n",
    "|------------------------|-----------------------------------------|-----------------|\n",
    "|$A=πR_0^2R_i^2$         |$I_{yy}=I_{zz}=\\frac{1}{4}π(R_0^4-R_i^4)$|                 | \n",
    "|                        |$I_{yz}=0$                               |                 |\n",
    "|                        |$I_p=\\frac{1}{2}π(R_0^4-R_i^4)$          |                 |\n",
    "\n",
    "```{figure} Images/Thin walled ring shape.jpg\n",
    "---\n",
    "scale: 100%\n",
    "---\n",
    "```\n",
    "\n",
    "### Thin-walled ring\n",
    "|Area, centre of gravity | Moments of intertia own      | other                                      | \n",
    "|------------------------|------------------------------|--------------------------------------------|\n",
    "|$A=2πRt$                |$I_{yy}=I_{zz}=πR^3t$         |$I_{\\overline{yy}}=I_{\\overline{zz}}=3πR^3t$| \n",
    "|                        |$I_{yz}=0$                    |                                            |\n",
    "|                        |$I_p=\\frac{1}{2}πR^3t$        |                                            |\n",
    "\n",
    "```{figure} Images/Half circle shape.jpg\n",
    "---\n",
    "scale: 100%\n",
    "---\n",
    "```\n",
    "\n",
    "### Half circle\n",
    "|Area, centre of gravity   | Moments of intertia own              | other                                               | \n",
    "|--------------------------|--------------------------------------|-----------------------------------------------------|\n",
    "|$A=\\frac{1}{2}πR^2$       |$I_{yy}=\\frac{1}{8}πR^4$              |$I_{\\overline{yy}}=I_{\\overline{zz}}=\\frac{1}{8}πR^4$| \n",
    "|$\\bar{y}_C=0$             |$I_{zz}=(\\frac{π}{8}-\\frac{8}{9π})R^4$|$I_{\\overline{\\overline{yz}}}=0$                     |\n",
    "|$\\bar{z}_C=\\frac{4}{3π}R$ |$I_{yz}=0$                            |                                                     |\n",
    "\n",
    "```{figure} Images/Half thin walled ring shape.jpg\n",
    "---\n",
    "scale: 100%\n",
    "---\n",
    "```\n",
    "\n",
    "### Half thin-walled ring\n",
    "|Area, centre of gravity | Moments of intertia own       | other                                                | \n",
    "|------------------------|-------------------------------|------------------------------------------------------|\n",
    "|$A=πRt$                 |$I_{yy}=I_{zz}=\\frac{1}{2}R^3t$|$I_{\\overline{yy}}=I_{\\overline{zz}}=\\frac{1}{2}πR^3t$| \n",
    "|$\\bar{y}_C=0$           |$I_{zz}=0$                     |$I_{\\overline{yz}}=0$                                 |\n",
    "|$\\bar{z}_C=0$           |$I_{yz}=0$                     |                                                      |"
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    "## Centre of gravity for moment diagrams\n",
    "\n",
    "```{figure} Images/Centre of gravity 1.jpg\n",
    "---\n",
    "scale: 100%\n",
    "---\n",
    "```\n",
    "\n",
    "```{figure} Images/Centre of gravity 2.jpg\n",
    "---\n",
    "scale: 100%\n",
    "---\n",
    "```\n",
    "\n",
    "```{figure} Images/Centre of gravity 3.jpg\n",
    "---\n",
    "scale: 100%\n",
    "---\n",
    "```\n",
    "\n",
    "```{figure} Images/Centre of gravity 4.jpg\n",
    "---\n",
    "scale: 100%\n",
    "---\n",
    "```"
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