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+{
+"cells": [
+ {
+		   "cell_type": "markdown",
+	   "metadata": {},
+	   "source": [
+       "# Chapter 12: Moment of Inertia"
+	   ]
+	},
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 12.10: Moment_of_Inertia_of_a_Composite_area_or_hollow_section.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"// Initilization of variables\n",
+"b1=120 // mm // width of the flange pate of L-section\n",
+"d1=20 // mm // depth of the flange plate\n",
+"b2=20 // mm // width/thickness of the web\n",
+"d2=130 // mm // depth of the web\n",
+"// Calculations\n",
+"// (a) Location of the centroid of the composite area\n",
+"A_1=b1*d1 // mm^2 // area of the flange plate\n",
+"A_2=b2*d2 // mm^2 // area of the web\n",
+"y_1=d2+(d1/2) // mm // y-coordinate of the centroid\n",
+"y_2=d2/2 // mm // y-coordinate of the centroid\n",
+"x_1=60 // mm // x-coordinate of the centroid\n",
+"x_2=110 // mm // x-coordinate of the centroid\n",
+"y_c=((A_1*y_1)+(A_2*y_2))/(A_1+A_2) // mm // from the bottom edge\n",
+"x_c=((A_1*x_1)+(A_2*x_2))/(A_1+A_2) // mm // from the bottom edge\n",
+"// (b) Moment of Inertia of the composite area about the centroidal x-axis\n",
+"// Area (A_1) M.I of area A_1 about x-axis\n",
+"I_x1=(b1*(d1^3))/12 // mm^4\n",
+"// M.I of the area A_1 about the centroidal x-axis of the composite area (By parallel-axis theorem)\n",
+"OC_1=d2+(d1/2) // mm // from the bottom edge\n",
+"OC_2=d2/2 // mm // from the bottom edge\n",
+"OC=y_c // mm // from the bottom edge\n",
+"d_1=(d2-y_c)+(d1/2) // mm\n",
+"d_2=y_c-OC_2 // mm \n",
+"I_X1=(I_x1)+(A_1*d_1^2) // mm^4\n",
+"// Area(A_2) M.I of area A_2 about x-axis\n",
+"I_x2=(b2*d2^3)/12 // mm^4\n",
+"// M.I of the area A_2 about the centroidal x-axis of the composite area (By parallel-axis theorem)\n",
+"I_X2=(I_x2)+(A_2*d_2^2) // mm^4\n",
+"// COMPOSITE AREA:M.O.I of the composite area about the centroidal x-axis\n",
+"I_x=(I_X1)+(I_X2) // mm^4\n",
+"// (c) Moment of Inertia of the composite area about the centroidal y-axis\n",
+"// Area (A_1) M.I of area A_1 about y-axis\n",
+"I_y1=(d1*(b1^3))/12 // mm^4\n",
+"// M.I of the area A_1 about the centroidal y-axis of the composite area (By parallel-axis theorem)\n",
+"d_3=x_c-(b1/2) // mm // distance between c &c1 along x axis\n",
+"I_Y1=(I_y1)+(A_1*d_3^2) // mm^4\n",
+"// Area(A_2) M.I of area A_2 about y-axis\n",
+"I_y2=(d2*b2^3)/12 // mm^4\n",
+"// M.I of the area A_2 about the centroidal y-axis of the composite area (By parallel-axis theorem)\n",
+"d_4=b1-x_c-(b2/2) // mm // distance between c &c2 along x axis\n",
+"I_Y2=(I_y2)+(A_2*d_4^2) // mm^4\n",
+"// COMPOSITE AREA:M.O.I of the composite area about the centroidal y-axis\n",
+"I_y=(I_Y1)+(I_Y2) // mm^4\n",
+"// Results\n",
+"clc\n",
+"printf('The M.O.I of the composite area about the centroidal x-axis is %f mm^4 \n',I_x)\n",
+"printf('The M.O.I of the composite area about the centroidal Y-axis is %f mm^4 \n',I_y)\n",
+"// NOTE: The answer for I_x given in text book is 0.76*10^6 insted of 10.76*10^6"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 12.14: Product_of_Inertia.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"// Initilization of variables\n",
+"b=1 // cm // smaller side of the L-section\n",
+"h=4 // cm // larger side of the L-section\n",
+"// Calculations\n",
+"// (A) RECTANGLE A_1: Using the paralel axis theorem\n",
+"Ixy=0\n",
+"I_xy1=(Ixy)+((h*b)*(b/2)*(h/2)) // cm^4\n",
+"// (B) RECTANGLE A_2: Using the paralel axis theorem\n",
+"I_xy2=(Ixy)+((b*(h-1))*(1+(3/2))*(b/2)) // cm^4\n",
+"// Product of inertia of the total area\n",
+"I_xy=I_xy1+I_xy2 // cm^4\n",
+"// Calculations\n",
+"clc\n",
+"printf('The Product of inertia of the L-section is %f cm^4 \n',I_xy)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 12.15: Principal_Moment_of_Inertia.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"// Initilization of variables\n",
+"I_x=1548 // cm^4 // M.O.I of the Z-section about X-axis\n",
+"I_y=2668 // cm^4 // M.O.I of the Z-section about Y-axis\n",
+"b=12 // cm // width of flange of the Z-section\n",
+"d=3 // cm // depth of flange of the Z-section\n",
+"t=2 // cm // thickness of the web of the Z-section\n",
+"h=6 // cm // depth of the web of the Z-section\n",
+"//Calculations\n",
+"A_1=b*d // cm^2 // area of top flange\n",
+"x_1=-5 // cm // distance of the centroid from X-axis for top flange\n",
+"y_1=4.5 // cm // distance of the centroid from Y-axis for top flange\n",
+"A_2=t*h // cm^2 // area of web\n",
+"x_2=0 // cm // distance of the centroid from X-axis for the web\n",
+"y_2=0 // cm // distance of the centroid from Y-axis for the web\n",
+"A_3=b*d // cm^2 // area of bottom flange\n",
+"x_3=5 // cm // distance of the centroid from X-axis for top flange\n",
+"y_3=-4.5 // cm // distance of the centroid from Y-axis for top flange\n",
+"// Product of Inertia of the total area is,\n",
+"I_xy=((A_1*x_1*y_1)+(A_3*x_3*y_3)) // cm^4\n",
+"// The direction of the principal axes is,\n",
+"theta_m=(atand((2*I_xy)/(I_y-I_x)))/2 // degree\n",
+"// Principa M.O.I\n",
+"I_max=((I_x+I_y)/2)+(sqrt(((I_x-I_y)/2)^2+(I_xy)^2)) // cm^4\n",
+"I_mini=((I_x+I_y)/2)-(sqrt(((I_x-I_y)/2)^2+(I_xy)^2)) // cm^4\n",
+"// Results\n",
+"clc\n",
+"printf('The principal axes of the section about O is %f degree \n',theta_m)\n",
+"printf('The Maximum value of principal M.O.I is %f cm^4 \n',I_max)\n",
+"printf('The Minimum value of principal M.O.I is %f cm^4 \n',I_mini)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 12.7: EX12_7.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"// Initilization of variables\n",
+"A= 50 // cm^2 // area of the shaded portion\n",
+"J_A=22.5*10^2 // cm^4 // polar moment of inertia of the shaded portion\n",
+"d=6 // cm\n",
+"// Calculations\n",
+"J_c=J_A-(A*d^2) \n",
+"// substuting the value of I_x from eq'n 2 in eq'n 1 we get,\n",
+"I_y=J_c/3 // cm^4 // M.O.I about Y-axis\n",
+"// Now from eq'n 2,\n",
+"I_x=2*I_y // cm^4 // M.O.I about X-axis\n",
+"// Results\n",
+"clc\n",
+"printf('The centroidal moment of inertia about X-axis (I_x) is %f cm^4 \n',I_x)\n",
+"printf('The centroidal moment of inertia about Y-axis (I_y) is %f cm^4 \n',I_y)"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 12.8: Moment_of_Inertia_of_a_Composite_area_or_hollow_section.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"// Initilization of variables\n",
+"b=20 // cm // width of the pate\n",
+"d=30 // cm // depth of the plate\n",
+"r=15 // cm // radius of the circular hole\n",
+"h=20 // cm // distance between the centre of the circle & the x-axis\n",
+"// Calculations\n",
+"// (a) Location of the centroid of the composite area\n",
+"A_1=b*d // cm^2 // area of the plate\n",
+"y_1=d/2 // cm // y-coordinate of the centroid\n",
+"A_2=(%pi*r^2)/4 // cm^2 // area of the circle removed (negative)\n",
+"y_2=h // cm // y-coordinate of the centroid\n",
+"y_c=((A_1*y_1)-(A_2*y_2))/(A_1-A_2) // cm // from the bottom edge\n",
+"// (b) Moment of Inertia of the composite area about the centroidal x-axis\n",
+"// Area (A_1) M.I of area A_1 about x-axis\n",
+"I_x1=(b*(d^3))/12 // cm^4\n",
+"// M.I of the area A_1 about the centroidal x-axis of the composite area (By parallel-axis theorem)\n",
+"OC_1=15 // cm // from the bottom edge\n",
+"OC_2=20 // cm\n",
+"OC=12.9 // cm // from the bottom edge\n",
+"d_1=OC_1-OC // cm\n",
+"d_2=OC_2-OC // cm \n",
+"I_X1=(I_x1)+(A_1*d_1^2) // cm^4\n",
+"// Area(A_2) M.I of area A_2 about x-axis\n",
+"I_x2=(%pi*r^4)/64 // cm^2\n",
+"// M.I of the area A_2 about the centroidal x-axis of the composite area (By parallel-axis theorem)\n",
+"I_X2=(I_x2)+(A_2*d_2^2) // cm^4\n",
+"// COMPOSITE AREA:M.O.I of the composite area about the centroidal x-axis\n",
+"I_x=(I_X1)-(I_X2) // cm^4\n",
+"// Results\n",
+"clc\n",
+"printf('The M.O.I of the composite area about the centroidal x-axis is %f cm^4 \n',I_x)\n",
+"// There may be a small error in the answer due to decimal point discrepancy"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 12.9: Moment_of_Inertia_of_a_Composite_area_or_hollow_section.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"// Initilization of variables\n",
+"b1=80 // mm // width of the flange pate\n",
+"d1=20 // mm // depth of the flange plate\n",
+"b2=40 // mm // width/thickness of the web\n",
+"d2=60 // mm // depth of the web\n",
+"// Calculations\n",
+"// (a) Location of the centroid of the composite area\n",
+"A_1=b1*d1 // mm^2 // area of the flange plate\n",
+"y_1=d2+(d1/2) // mm // y-coordinate of the centroid\n",
+"A_2=b2*d2 // mm^2 // area of the web\n",
+"y_2=d2/2 // mm // y-coordinate of the centroid\n",
+"y_c=((A_1*y_1)+(A_2*y_2))/(A_1+A_2) // mm // from the bottom edge\n",
+"// (b) Moment of Inertia of the composite area about the centroidal x-axis\n",
+"// Area (A_1) M.I of area A_1 about x-axis\n",
+"I_x1=(b1*(d1^3))/12 // mm^4\n",
+"// M.I of the area A_1 about the centroidal x-axis of the composite area (By parallel-axis theorem)\n",
+"OC_1=70 // mm // from the bottom edge\n",
+"OC_2=30 // mm // from the bottom edge\n",
+"OC=y_c // mm // from the bottom edge\n",
+"d_1=(d2-y_c)+(d1/2) // mm\n",
+"d_2=y_c-OC_2 // mm \n",
+"I_X1=(I_x1)+(A_1*d_1^2) // mm^4\n",
+"// Area(A_2) M.I of area A_2 about x-axis\n",
+"I_x2=(b2*d2^3)/12 // mm^4\n",
+"// M.I of the area A_2 about the centroidal x-axis of the composite area (By parallel-axis theorem)\n",
+"I_X2=(I_x2)+(A_2*d_2^2) // mm^4\n",
+"// COMPOSITE AREA:M.O.I of the composite area about the centroidal x-axis\n",
+"I_x=(I_X1)+(I_X2) // mm^4\n",
+"// Results\n",
+"clc\n",
+"printf('The M.O.I of the composite area about the centroidal x-axis is %f mm^4 \n',I_x)\n",
+"// NOTE: The answer given in the text book is 2.31*10^3 insted of 2.31*10^6."
+   ]
+   }
+],
+"metadata": {
+		  "kernelspec": {
+		   "display_name": "Scilab",
+		   "language": "scilab",
+		   "name": "scilab"
+		  },
+		  "language_info": {
+		   "file_extension": ".sce",
+		   "help_links": [
+			{
+			 "text": "MetaKernel Magics",
+			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+			}
+		   ],
+		   "mimetype": "text/x-octave",
+		   "name": "scilab",
+		   "version": "0.7.1"
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+}