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   "source": [
    "# Chapter 4 Centroid Centre of mass and Centre of Gravity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example 4.8 Centroid of a composite plane figure"
   ]
  },
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   "execution_count": 1,
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     "text": [
      "The centroid of the un equal I-section is 10.961538 cm \n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Initilization of variables\n",
    "b1=20 #cm # width of top flange\n",
    "t1=5 #cm # thickness of top flange\n",
    "b2=5 #cm # width of web\n",
    "t2=15 #cm # thickness or height of the web\n",
    "b3=30 #cm # width of bottom flange\n",
    "t3=5 #cm # thickness of bottom flange\n",
    "# Calculations\n",
    "A1=b1*t1 #cm**2 # area of bottom flange\n",
    "A2=b2*t2 #cm**2 # area of the web\n",
    "A3=b3*t3 #cm**2 # area of top flange\n",
    "y1=t3+t2+(t1/2) #cm # y co-ordinate of the centroid of top flange\n",
    "y2=t3+(t2/2) #cm #  y co-ordinate of the centroid of the web\n",
    "y3=t3/2 #cm #  y co-ordinate of the centroid of the bottom flange\n",
    "y_c=((A1*y1)+(A2*y2)+(A3*y3))/(A1+A2+A3) #cm # where y_c is the centroid of the un-symmetrical I-section\n",
    "# Results\n",
    "print('The centroid of the un equal I-section is %f cm \\n'%y_c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example 4.9 Centroid of a composite plane figure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The centroid of the cross-sectional area of a Z-section about x-axis is 13.557692 cm \n",
      "\n",
      "The centroid of the cross-sectional area of a Z-section about y-axis is 7.692308 cm \n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Initilization of variables\n",
    "# The given section is Z-section which is un-symmetrycal about both the axis\n",
    "b1=20 #cm # width of bottom flange \n",
    "t1=5 #cm # thickness of the bottom flange\n",
    "b2=2.5 #cm # thickness of the web of the flange\n",
    "t2=15 #cm # depth of the web\n",
    "b3=10 #cm # width of the top flange\n",
    "t3=2.5 #cm # thickness of the top flange\n",
    "# Calculations\n",
    "# Respective areas\n",
    "A1=b1*t1 # cm**2 # area of the bottom flange\n",
    "A2=b2*t2 # cm**2 # area of the web\n",
    "A3=b3*t3 # cm**2 # area of the top-flange\n",
    "# first we calculate the x co-ordinate of the centroid\n",
    "x1=b3-b2+(b1/2) #cm # for the bottom flange\n",
    "x2=b3-(b2/2) #cm # for the web\n",
    "x3=b3/2 #cm # for the top flange\n",
    "x_c=((A1*x1)+(A2*x2)+(A3*x3))/(A1+A2+A3) #cm\n",
    "# secondly we calculate the y co-ordinate of the centroid\n",
    "y1=t1/2 #cm # for the bottom flange\n",
    "y2=t1+(t2/2) #cm # for the web\n",
    "y3=t1+t2+(t3/2) #cm # for the top flange\n",
    "y_c=((A1*y1)+(A2*y2)+(A3*y3))/(A1+A2+A3) # cm\n",
    "# Results\n",
    "print('The centroid of the cross-sectional area of a Z-section about x-axis is %f cm \\n'%x_c)\n",
    "print('The centroid of the cross-sectional area of a Z-section about y-axis is %f cm \\n'%y_c)"
   ]
  }
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