path: root/Strength_Of_Materials_by_B_K_Sarkar/chapter_12_som_1.ipynb

{
 "metadata": {
  "name": "chapter 12 som.ipynb"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 12:Propped Cantilever"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problem no 12.1,Page No.286"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "L=6 #m #Length of Beam\n",
      "L_1=4 #m #Length of Beam with udl Load\n",
      "w=10 #KN/m #u.d.l\n",
      "\n",
      "#Calculation\n",
      "\n",
      "#Deflection of cantileverat C due to udl on AB\n",
      "y_c=w*L_1**4*8**-1+w*L_1**3*6**-1*(L-L_1) \n",
      "\n",
      "#Deflection of cantileverat C due to prop reaction alone\n",
      "#y_c_2=R_c*L**3*3**-1\n",
      "\n",
      "#Since both Deflection are Equal\n",
      "#y_c=y_c_2\n",
      "\n",
      "R_c=y_c*(6**3)**-1*3 #Reaction at C\n",
      "\n",
      "#Result\n",
      "print\"The Reaction at End C is\",round(R_c,3),\"KN\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Reaction at End C is 7.407 KN\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problem no 12.2,Page No.286"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "L=10 #m #Length\n",
      "b=15 #cm #Width\n",
      "d=40 #cm #Depth\n",
      "y_c=1.5*10**-2 #m #Deflection\n",
      "E=120*10**9 \n",
      "y=0.2\n",
      "sigma=10*10**6 #Bending stress\n",
      "\n",
      "#Calculations\n",
      "\n",
      "I=b*d**3*12**-1*10**-8 #cm  #M.I\n",
      "\n",
      "#From Deflection at the centre of cantilever we get\n",
      "w=y_c*192*E*I*(L**4)**-1*10**-3 #udl distributed over the cantilever\n",
      "\n",
      "#From Bending Moment Equation we get\n",
      "w_2=sigma*I*y**-1*16*(L**2)**-1*10**-3    #udl distributed over the cantilever\n",
      "\n",
      "#Result\n",
      "print\"The safe uniformly Distributed Load is\",round(w_2,2),\"KN/m\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The safe uniformly Distributed Load is 6.4 KN/m\n"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problem no 12.3,Page No.287"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "L=6 #m #span of beam\n",
      "w=30*10**3 #KN/m #u.d.l\n",
      "P=160*10**3 #N #concentrated Load\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Consider a section at a distance x from the fixed end A and B.M at x\n",
      "#M_x=R_b*(6-x)-30*2**-1*(6-x)**2-160*(3-x)\n",
      "\n",
      "#E*I*d**2y*(dx**2)**-1=-M_x=-R_b*(6-x)+15*(6-x)+160*(3-x)\n",
      "\n",
      "#Now Integrating above term we get\n",
      "#E*I*dy*(dx)**-1=R_b*2**-1*(6-x)**2-5*(6-x)**3-80*(3-x)**2+C_1  (Equation 1)\n",
      "\n",
      "#Now on Integrating we get\n",
      "#E*I*y=-R_b*6**-1*(6-x)**3+5*4**-1*(6-x)**2+80*3**-1*(3-x)**3+C_1*x+C_2  (Equation 2)\n",
      "\n",
      "#At x=0,dy*dx**-1=0\n",
      "#substituting in equation 1 we get\n",
      "#C_1=1800-R_b\n",
      "\n",
      "#At x=0,y=0\n",
      "#substituting in equation 2 we get\n",
      "#C_2=36*R_b-2340\n",
      "\n",
      "#At x=6,y=0\n",
      "R_b=72**-1*(10800-2340)\n",
      "\n",
      "#At x=0\n",
      "x=0\n",
      "M_x=R_b*(6-x)-30*2**-1*(6-x)**2-160*(3-x)\n",
      "\n",
      "#Result\n",
      "print\"Bending Moment at A is\",round(M_x,2),\"KNm\"\n",
      "print\"The Reaction at B\",round(R_b,2),\"KN\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Bending Moment at A is -315.0 KNm\n",
        "The Reaction at B 117.5 KN\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problem no 12.4,Page No.288"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "L=4 #span of beam\n",
      "w_1=20*10**3 #Nm #u.d.l\n",
      "w_2=30*10**3 #Nm #u.d.l\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#consider a section at a distance x from A and B.M at this section is \n",
      "#M_x=R_b*(3-x)-10*x**2+90*x-195\n",
      "\n",
      "#Now integrating above equation we get\n",
      "#E*I*dy*(dx)**-1=-R_b(3*x-x**2*2**-1)+10*x**3*3**-1-45*x**2+195*x+C_1\n",
      "\n",
      "#again on Integrating we get\n",
      "#E*I*y=-R_b*(3*x**2*2**-1-x**3*6**-1)+10*x**4*12**-1-15*x**3+195*x**2*2**-1+C_1*x+C_2\n",
      "\n",
      "#At x=0,dy*(dx)**-1=0  Therefore C_1=0\n",
      "\n",
      "#At x=0,y=0  Therefore C_2=0\n",
      "\n",
      "#At x=3m, y=0\n",
      "x=3\n",
      "C_1=0\n",
      "C_2=0\n",
      "R_b=-(-10*x**4*12**-1+15*x**3-195*x**2*2**-1-C_1*x-C_2)*(3*x**2*2**-1-x**3*6**-1)**-1\n",
      "\n",
      "#result\n",
      "print\"Load taken by prop is\",round(R_b,2),\"KN\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Load taken by prop is 60.0 KN\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problem no 12.5,Page No.289"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "L=2 #m #Span of beam\n",
      "w=10 #KN/m #u.d.l\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Downward deflection at B(of Beam AB) due to u.d.l of 10 KN/m is\n",
      "Y_B_1=w*L**4*8**-1 \n",
      "\n",
      "#Upward deflection at B due to reaction at C alone is\n",
      "#Y_B_2=R_c*8*3**-1\n",
      "\n",
      "#Net downward deflection of cantilever at AB at B\n",
      "#Y_B=Y_B_1-Y_B_2\n",
      "\n",
      "#Downward Deflection of Beam CD at C due to the reaction\n",
      "#R_c=R_c*(3*E*I)**-1\n",
      "\n",
      "#since both deflection at C and B are equal\n",
      "R_c=20*(1*3**-1+8*3**-1)**-1\n",
      "\n",
      "#Result\n",
      "print\"Reaction at C is\",round(R_c,2),\"KN\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Reaction at C is 6.67 KN\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problem no 12.8,Page No.292"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "L=8 #m #span\n",
      "W=24*10**3 #N/m #U.D.L\n",
      "y=2*10**-2 #m #deflection\n",
      "E=20*10**9\n",
      "I=10**-5 #m**4\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#The Downward deflection at C Due to u.d.l\n",
      "#Y_c=5*W*L**3*(384*E*I)**-1\n",
      "\n",
      "#The Upward Deflection at C due to prop Reaction P \n",
      "#Y_c_1=P*L**3*(48*E*I)**-1\n",
      "\n",
      "#Since the prop is at the same level as end supports\n",
      "#Y_c_1=Y_c\n",
      "P_1=5*W*8**-1*10**-3 #KN\n",
      "\n",
      "#The reaction at A and B is equal\n",
      "R_a=R_b=(24-15)*2**-1\n",
      "\n",
      "#Shear Force at B\n",
      "V_B=4.5 #KN\n",
      "\n",
      "#Shear Force at C\n",
      "V_C1=4.5-24*2**-1\n",
      "V_C2=4.5-24*2**-1+15\n",
      "\n",
      "#Shea rForce at A\n",
      "V_A=-4.5 #KN\n",
      "\n",
      "#B.M at C due to u.d.l\n",
      "M_C1=W*L*8**-1*10**-3 #KN*m\n",
      "\n",
      "#B.M due to only prop reaction P=15 KN\n",
      "P=15\n",
      "M_C2=-P*L*4**-1 #KN*m\n",
      "\n",
      "#B.M at D\n",
      "M_D=4.5*1.5-24*8**-1*1.5**2*2**-1\n",
      "\n",
      "#In second case prop sinks by 2 cm\n",
      "#Y_c-Y_c_1=2 \n",
      "\n",
      "#So Further simplifying and sunstituting values in above equation we get\n",
      "P=-(2*100**-1-(5*W*L**3*(384*E*I)**-1))*(L**3*(48*E*I)**-1)**-1\n",
      "\n",
      "#Let Each end reaction be X\n",
      "X=(24-14.625)*2**-1\n",
      "\n",
      "#Result\n",
      "print\"prop reaction is\",round(P_1,2),\"KN\"\n",
      "print\"The End Reaction is\",round(X,2),\"KN\"\n",
      "\n",
      "#Plotting the SHear Force Diagram\n",
      "\n",
      "X1=[0,4,4,8,8]\n",
      "Y1=[V_B,V_C1,V_C2,V_A,0]\n",
      "Z1=[0,0,0,0,0]\n",
      "plt.plot(X1,Y1,X1,Z1)\n",
      "plt.xlabel(\"Length x in m\")\n",
      "plt.ylabel(\"Shear Force in kN\")\n",
      "plt.show()\n",
      "\n",
      "#Plotting the Bendimg Moment Diagram\n",
      "\n",
      "X2=[0,4,4]\n",
      "Y2=[0,M_C1,0]\n",
      "Z2=[0,0,0]\n",
      "plt.plot(X2,Y2)\n",
      "plt.xlabel(\"Lenght in m\")\n",
      "plt.ylabel(\"Bending Moment in kN.m\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "prop reaction is 15.0 KN\n",
        "The End Reaction is 4.69 KN\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAEPCAYAAACqZsSmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x56bdc90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEPCAYAAABP1MOPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xl0VOX9x/H3gIDFBHAjAYEmRZFskBB+oAKalK0skUVB\nEdSyqMWKUtAKWil6KoYKIlAVRFyhiFUxIIJgmwQIUAEDWEG0SCBAiAgnmARitvv7Y2SahAwzWe6d\n7fM6Zw7JzCT3e54D8+V57r3Px2YYhoGIiASsBp4uQEREPEuNQEQkwKkRiIgEODUCEZEAp0YgIhLg\n1AhERAKcaY0gOzubxMREoqKiiI6OZsGCBQDMnDmTNm3aEBcXR1xcHOvXrzerBBERcYPNrPsITpw4\nwYkTJ4iNjaWgoID4+Hg++ugj3nvvPYKDg5kyZYoZhxURkRq6xKxfHBoaSmhoKABBQUFERERw7Ngx\nAHQPm4iI97DkHEFWVhaZmZnccMMNACxcuJDOnTszfvx48vLyrChBREScML0RFBQUcPvttzN//nyC\ngoKYOHEihw4dYvfu3bRq1YqpU6eaXYKIiFyMYaLi4mKjX79+xrx586p9/dChQ0Z0dPQFz7dv394A\n9NBDDz30qMGjffv2tfqsNm1GYBgG48ePJzIyksmTJzuez8nJcXy9atUqYmJiLvjZgwcPYhiG1z/+\n/Oc/e7wG1ak6VadqPP84ePBgrT6vTTtZnJGRwbJly+jUqRNxcXEAzJo1ixUrVrB7925sNhvh4eEs\nXrzYrBJERMQNpjWCnj17Ul5efsHzAwYMMOuQIiJSC7qzuA4SEhI8XYJbVGf9Up31yxfq9IUa68K0\nG8rqwmaz4YVliYh4tdp+dmpGICIS4NQIREQCnBqBiIiPO3MGJk6s/c+rEYiI+LCUFIiKgv/8p/a/\nw7TLR0VExDw5OfDww7BnDyxfDoYBiYm1+12aEYiI+BDDgNdeg86doUMH2LsXbrmlbr9TMwIRER/x\n7bdw//1QWAiffQadOtXP79WMQETEy5WUQHIy3HgjDBkC27bVXxMAzQhERLzazp0wYQKEhtq/Dgur\n/2NoRiAi4oUKC2HqVBg0CB59FNatM6cJgBqBiIjX2bABYmLg++/tl4WOGQM2m3nH09KQiIiXOHUK\npkyB9HRYtAh+8xtrjqsZgYiIhxkG/P3v9hvDrrjCPguwqgmAZgQiIh51+LB9e4ijR+13CXfvbn0N\nmhGIiHhAWRksWADx8dCzJ+za5ZkmAJoRiIhY7j//sV8S2qQJZGTA9dd7th7NCERELFJUBDNm2PcE\nGjcOUlM93wRAMwIREUts3gz33QeRkfaN4lq39nRF/6NGICJiojNnYNo0WL0aFi6E4cM9XdGFtDQk\nImKS81kB5eXw1Vfe2QRAMwIRkXpXNSugrttEm00zAhGRemJGVoAVNCMQEakHZmUFWEEzAhGROjA7\nK8AKmhGIiNSSFVkBVtCMQESkhqzMCrCCGoGISA1YnRVgBS0NiYi4wVNZAVbQjEBE5CI8nRVgBc0I\nRESc8IasACtoRiAiUoU3ZQVYQTMCEZEKvC0rwAqaEYiI4L1ZAVbQjEBEAp43ZwVYwbQZQXZ2NomJ\niURFRREdHc2CBQsAOH36NH379qVDhw7069ePvLw8s0oQEbmoM2fsJ4PvvBNmzYIPPwy8JgAmNoJG\njRoxb948vvrqK7Zv385LL73E/v37SU5Opm/fvnzzzTf07t2b5ORks0oQEXHKV7ICrGDa0lBoaCih\noaEABAUFERERwbFjx1i9ejXp6ekA3HvvvSQkJKgZiIhlfC0rwAqWnCzOysoiMzOT7t27k5ubS0hI\nCAAhISHk5uZaUYKIBDhfzQqwgukniwsKCrjtttuYP38+wcHBlV6z2WzYnGzSMXPmTMfXCQkJJCQk\nmFiliPgzX84KuJi0tDTS0tIAyMqq/e+xGYZh1EtF1SgpKWHw4MEMGDCAyZMnA9CxY0fS0tIIDQ0l\nJyeHxMREvv7668pF2WyYWJaIBIiSEpg7F+bMgT/9CSZNgoYNPV2VOdLSIDGxdp+dpi0NGYbB+PHj\niYyMdDQBgFtvvZW33noLgLfeeouhQ4eaVYKIBLCdO+H//s/+AblzJ0ye7L9NoK5MmxFs2bKFm2++\nmU6dOjmWf5577jm6devGyJEjOXLkCGFhYbz33nu0aNGiclGaEYhILRUW2m8MW7bMPhsYPdr3t4l2\nR11mBKadI+jZsyfl5eXVvvbZZ5+ZdVgRCWAbNsDvfgc9eti3irj6ak9X5Bt0Z7GI+Dx/zgqwgstz\nBGvWrCEuLo7LL7+c4OBggoODadasmRW1iYhcVCBkBVjB5Yxg8uTJrFq1iujoaBo00B51IuIdAiUr\nwAouP9nbtGlDVFSUmoCIeIVAywqwgssZwezZsxkwYACJiYk0btwYsF/VM2XKFNOLExGpKBCzAqzg\n8r/5Tz31FEFBQRQVFVFQUEBBQQH5+flW1CYiAgR2VoAVXM4IcnJy2LhxoxW1iIhcINCzAqzgckYw\ncOBAPv30UytqERFxUFaAdVw2gpdffpkBAwZw6aWX6vJREbGEsgKs5XJpqKCgwIo6RESUFeAhuiZU\nRDxOWQGeVastJuLi4sjMzKzvWkQkAPlrVoAvqdWMQE1AROqqpASSk+HGG2HIENi2TU3AU7TpnIhY\nbudO+41hoaH2r8PCPF1RYHPaCMLDw53+kM1m47vvvjOlIBHxX4GaFeDtnDaCHTt2OL622WyUl5ez\ncuVK5syZQ5cuXSwpTkT8h7ICvJfTRnDVVVcBUF5ezttvv83zzz9PbGwsn3zyCZGRkZYVKCK+TVkB\n3s/pyeLi4mIWLVpEREQEmzdvJiUlheXLl6sJiIhblBXgO5zOCH71q19xySWX8Mgjj9CuXTv27t3L\n3r17MQwDm83GcN3qJyJOKCvAtzhtBH369AFwNICq1AhEpKqyMnjpJXjmGfty0GOPQaNGnq5KXHHa\nCN58800AioqKuPTSSyu9durUKVOLEhHfo6wA3+XyhrLhw4dTUlLi+D4nJ4e+ffuaWpSI+A5lBfg+\nl41g2LBhjBw5krKyMrKysujfvz/JyclW1CYiXm7zZoiNtc8G9uyxbxWhVFvf4/LO4vvuu4+ffvqJ\nIUOGcPjwYRYtWkSPHj2sqE1EvNSZMzBtGqxeDQsXaptoX+e0EcydOxew30xmGAbZ2dl07tyZ7du3\n8+9//1uZxSIBKiUFfv97GDTInhXQooWnK5K6ctoI8vPzsVW493vYsGHYbDblE4gEKGUF+C+bYRiG\np4uo6vwsREQ8zzBg6VJ44gl7dvBTT0GVCwnFC6SlQWJi7T47tfuoiDilrIDAoPP7InIBZQUEFs0I\nRKQSZQUEHpeN4Pvvv2fJkiVkZWVRWloK2NfwX3/9ddOLExHrKCsgcLlsBEOGDOHmm2+mb9++NPj5\nThGb/naI+BVlBQQ2l43g3LlzzJ4924paRMRiygoQcONk8eDBg1m7dq0VtYiIRZQVIBW5vI8gKCiI\ns2fP0rhxYxr9vJ+szWbjxx9/NK8o3UcgYpqKWQFLligrwF/U5T4ClzOCgoICysvLKSoqIj8/n/z8\nfLebwLhx4wgJCSEmJsbx3MyZM2nTpg1xcXHExcWxfv36GhctIjVXVgYLFkB8PPTsCbt2qQmIndNz\nBPv37yciIoIvvvii2tfdCbAfO3YskyZN4p577nE8Z7PZmDJlivYqErGQsgLkYpw2ghdeeIElS5Yw\nZcqUaq8SSk1NdfnLe/XqRVZW1gXPa9lHxBpFRTBrFrzyCjz7rL0ZaJtoqcppI1iyZAkAaWlp9X7Q\nhQsX8vbbb9O1a1fmzp1LC21fKFLvNm+27w0UGWnfKK51a09XJN7K8v8bTJw4kUOHDrF7925atWrF\n1KlTrS5BxK+dOWM/GXznnfbZwIcfqgnIxVm+xUTLli0dX0+YMIGkpKRq3zdz5kzH1wkJCSQkJJhc\nmYjvU1ZAYElLS3Os2lSzCu8207ehzsrKIikpiS+//BKwZx63atUKgHnz5rFjxw7+/ve/Vy5Kl4+K\n1EjFrIAlS5QVEIhMvXy0d+/ebj1XnVGjRnHTTTdx4MAB2rZty+uvv87jjz9Op06d6Ny5M+np6cyb\nN6/GRYuInWHAa69B587QoQPs3asmIDXndGno3LlznD17lpMnT3L69GnH8z/++CPHjh1z65evWLHi\ngufGjRtXizJFpCplBUh9cdoIFi9ezPz58zl+/Djx8fGO54ODg3nooYcsKU5ELlRSYt8ddM4c+NOf\nYNIkaNjQ01WJL3N5jmDBggU8/PDDVtUD6ByBiDMVswIWLVJWgPxPXc4RuHWyeOvWrZXyCIBKdwvX\nNzUCkcqUFSCumJpZPGbMGL777jtiY2NpWGH+aWYjEJH/UVaAmM1lI9i1axf79u1TGI2IxZQVIFZx\neflodHQ0OTk5VtQiIigrQKznckZw8uRJIiMj6datG02aNAHsa/irV682vTiRQFMxKyAlRdtEizVc\nNoLzWz1UPIGrZSKR+lVWBi+9BM88Y18Oeuwx+DkHSsR0LhtBQkICWVlZ/Pe//6VPnz6cPXu20tVD\nIlI3ygoQT3N5juDVV19lxIgRPPDAAwAcPXqUYcOGmV6YiL8rKrJfEpqYCOPGQWqqmoB4hstG8NJL\nL7FlyxaaNWsGQIcOHfj+++9NL0zEn23eDLGx9tnAnj32rSIUGCOe4nJpqEmTJo6TxAClpaU6RyBS\nS2fOwLRpsHo1LFwIw4d7uiIRN2YEt9xyC88++yxnz55l48aNjBgxwmmGgIg4l5JivyS0vNyeFaAm\nIN7C5RYTZWVlLF26lA0bNgDQv39/JkyYYOqsQFtMiD9RVoBYwfS9hqymRiD+wDBg6VJ44gl7dvBT\nT8Gll3q6KvFXpu41tGbNGmbMmFFp0zmbzcaPP/5Y44OJBAplBYgvcXmOYPLkybz11lucOnWK/Px8\n8vPz1QREnCgpgeRkuPFGGDIEtm1TExDv53JG0KZNG6Kiomiga9tELqpiVsDOncoKEN/hshHMnj2b\nAQMGkJiYSOPGjQH70tCUKVNML07EFygrQHydy0bw1FNPERwcTFFREcXFxVbUJOIzlBUg/sBlI8jJ\nyWHjxo1W1CLiM5QVIP7E5cL/wIED+fTTT62oRcTrKStA/JHL+wiCgoI4e/YsjRs3ptHP++Kaffmo\n7iMQb1QxK2DJEmUFiHepy30ELmcEBQUFlJeXU1RUpMtHJSCVlcGCBRAfDz17wq5dagLiX1yeIwBI\nSUlh06ZN2Gw2brnlFu01JAFDWQESCFzOCKZNm8aCBQuIiooiIiKCBQsWMH36dCtqE/EYZQVIIHF5\njiAmJobdu3fTsGFDwL4JXWxsLF9++aV5RekcgXjQ5s32vYEiI+Fvf4PWrT1dkYhrpu41ZLPZyMvL\n48orrwQgLy9PeQTil5QVIIHKZSOYPn06Xbp0ISEhAYD09HSSk5PNrkvEUikp8Pvfw6BB9qyAFi08\nXZGIddzahvr48ePs2LEDm81Gt27dCA0NNbcoLQ2JRZQVIP7ClKWhL774otL3bdq0AexN4fjx43Tp\n0qXGBxPxFlWzAt55R1kBEricNoKuXbsSHR3tODdQVWpqqmlFiZhJWQEilTltBC+88AL/+Mc/aNq0\nKXfccQfDhg0jODjYytpE6lVJiX130Dlz4E9/gkmT4OeL4UQCmstzBAcPHmTlypV89NFH/PKXv+TJ\nJ58kNjbW3KJ0jkDqWcWsgEWLlBUg/sfULSbat2/PkCFD6NevHzt27ODAgQO1qVHEIwoLYepU+9VA\njz4K69apCYhU5XRp6ODBg7z77rukpKTQrl077rjjDp588kl+8YtfWFmfSK0pK0DEPU6Xhho0aEBM\nTAxDhw6lWbNm9jf/vGTjbkLZuHHjWLt2LS1btnTciXz69GnuuOMODh8+TFhYGO+99x4tqly0raUh\nqQtlBUggMmVpaMaMGQwfPpwGDRpQUFBAQUEB+fn5jj/dMXbsWNavX1/pueTkZPr27cs333xD7969\ndXOa1BtlBYjUjls3lNVFVlYWSUlJjhlBx44dSU9PJyQkhBMnTpCQkMDXX39duSjNCKSGlBUggc7U\nk8X1LTc3l5CQEABCQkLIzc21ugTxI8oKEKk7t/IIzGKz2bSBndSasgJE6ofljeD8klBoaCg5OTm0\nbNmy2vfNnDnT8XVCQoJj0zuRoiKYNQteeQWefdbeDBpYPrcV8by0tDTS0tIAyMqq/e9xeY5g7ty5\nldbsbTYbzZs3Jz4+3q0by6qeI/jjH//IlVdeyeOPP05ycjJ5eXkXnDDWOQJxRlkBItWryzkCl43g\nrrvuYufOnSQlJWEYBmvXriUmJobDhw9z++238/jjjzv92VGjRpGens4PP/xASEgIzzzzDEOGDGHk\nyJEcOXJEl4+K25QVIHJxpjaCXr16sW7dOoKCggB7mP3AgQNZv3498fHx7N+/v1ZFX7QoNQKpoGJW\nwOzZygoQqY6pCWUnT56kcePGju8bNWpEbm4uTZs25VLt2ysmqpgVsHy5sgJEzOKyEYwePZru3bsz\ndOhQDMNgzZo13HXXXRQWFhIZGWlFjRJglBUgYi23bijbsWMHGRkZ2Gw2evToQdeuXc0tSktDAati\nVsBrrykrQMRdpi4NAXTp0oXWrVtTWlqKzWbjyJEjtGvXrsYHE3FGWQEinuOyESxcuJCnn36ali1b\n0rDCv8zzl4OK1FXFrICdO7VNtIjVXDaCF198kQMHDjiNrBSprcJCmDEDli2zzwZGjwbdaC5iPZf3\nY7Zr186xDbVIfdmwAWJi4Pvv7VtFjBmjJiDiKS5nBOHh4SQmJjJo0CDHZaTu5hGIVKWsABHv47IR\ntGvXjnbt2lFcXExxcbEjmEakJgwDVqywN4FRo+yzgJ/vURQRDzM9j6A2dPmofzlyxJ4VkJ2trAAR\ns5hy+egjjzzC/PnzSUpKuuA1m83G6tWra3wwCSxlZfDyy/DMM/CHP8Bjj0GjRp6uSkSqctoI7r77\nbgCmTp1qWTHiPypmBWzZoqwAEW+mpSGpVz/9ZM8IUFaAiLVMWRqKiYlx+kM2m429e/fW+GDi37Zs\nse8NFBFh3yhOWQEivsFpI1izZg0AL7/8MmBfKjIMg+XLl1tTmfiMM2dg+nT7dtHKChDxPS6XhmJj\nY9m9e3el5+Li4sjMzDSvKC0N+YyUFHjoIRg4UFkBIp5k6qZzhmGwZcsWevbsCUBGRoY+pIUTJ+wb\nw+3ZY98iQlkBIr7LZSN4/fXXGTt2LGfOnAGgRYsWvPHGG6YXJt7JMOD11+1LQcoKEPEPLhtBfHw8\ne/fudTSC5s2bm16UeKdvv4UHHoCCAvjsM2UFiPgLl42gqKiIDz74gKysLEpLSwH7Gv6MGTNML068\ng7ICRPyby0YwZMgQWrRoQXx8vDKKA5CyAkT8n8tGcOzYMT799FMrahEvUlgIf/6z/UTwnDnKChDx\nZy7v+bzpppt081iA2bjRnhWQmwtffqmsABF/53JGsHnzZt544w3Cw8Np0qQJoDuL/ZWyAkQCk8tG\nsG7dOivqEA8yDHj3XXsTuPNOZQWIBBqXS0NhYWFkZ2eTmppKWFgYl112mW4o8yNHjsDgwfDcc/DR\nRzBvnpqASKBx2QhmzpzJX//6V5577jkAiouLGTNmjOmFibnKyuz7AsXHQ48esGuXAmNEApXLpaFV\nq1aRmZlJfHw8ANdccw35+fmmFybmUVaAiFTkckbQpEkTGlTYUL6wsNDUgsQ8P/0EM2ZAYiKMGwep\nqWoCIuJGIxgxYgQPPPAAeXl5vPrqq/Tu3ZsJEyZYUZvUoy1bIDbWPhvYswfuv1+BMSJi51ZC2YYN\nG9iwYQMA/fv3p2/fvuYWpW2o642yAkQCg6nbUAP069ePfv36cfLkSa666qoaH0Q8o2JWwFdfKStA\nRKrndHFg27ZtJCQkMHz4cDIzM4mOjiYmJoaQkBDdW+DlTpyAESPgscfsW0QsXqwmICLOOW0EDz30\nEE888QSjRo0iMTGR1157jRMnTrBp0yamT59uZY3iJsOApUvt20N36AB79yowRkRcc7o0VFZWRr9+\n/QCYMWMGN9xwAwAdO3bEpo1nvI6yAkSktpzOCCp+2Gv7ae9VUgLJyXDjjXDrrbBtm5qAiNSM0xnB\n3r17CQ4OBuDcuXOOr89/X1dhYWE0a9aMhg0b0qhRIz7//PM6/85Ao6wAEakPF10aMpPNZiMtLY0r\nrrjC1OP4I2UFiEh98ugtRbpXoOaUFSAi9c1jjcBms9GnTx+6du3KkiVLPFWGzzh1Cu69F+67D15+\nGd55B66+2tNViYg/cOuGMjNkZGTQqlUrTp48Sd++fenYsSO9evVyvD5z5kzH1wkJCSQkJFhfpBdQ\nVoCIOJOWlkZaWhoAWVm1/z1ubTFhtqeffpqgoCCmTp0KaIuJ844cgYkTITsblizRNtEi4lxdtpjw\nyNLQ2bNnHVtZFxYWsmHDBmJiYjxRildSVoCIWMkjS0O5ubkMGzYMgNLSUkaPHu24eS3QKStARKzm\nkUYQHh7O7t27PXFor/XTT/Dss/DKK/Y/J0zQNtEiYg2PnSyW/9myxX41UESEPSugdWtPVyQigUSN\nwIOUFSAi3kCLDx6SkgLR0fYTw199pSYgIp6jGYHFTpyASZPsS0DLlmmbaBHxPM0ILKKsABHxVpoR\nWEBZASLizTQjMJGyAkTEF2hGYBJlBYiIr9CMoJ4VFsKjj8LgwfY/161TExAR76ZGUI+UFSAivkhL\nQ/Xg1Cn7NtHp6bBoEfzmN56uSETEfZoR1IFhwIoV9hvDrrjCvmGcmoCI+BrNCGqpYlbARx9pm2gR\n8V2aEdSQsgJExN9oRlADygoQEX+kGYEbfvoJZsyAxEQYNw5SU9UERMR/aEbggrICRMTfqRE4oawA\nEQkUWhqqhrICRCSQaEZQgbICRCQQaUaAsgJEJLAF/IxAWQEiEugCdkagrAAREbuAnBEoK0BE5H8C\nakagrAARkQsFTCNQVoCISPX8fmlIWQEiIhfntzMCZQWIiLjHL2cEygoQEXGfX80IlBUgIlJzfjMj\nUFaAiEjt+PyMQFkBIiJ149MzAmUFiIjUnU82AmUFiIjUH59bGlJWgIhI/fJII1i/fj0dO3bkuuuu\nY/bs2W79zIkTMGIEPPaYPStg8WJo0cLkQkVEAoDljaCsrIyHHnqI9evXs2/fPlasWMH+/fudvt+b\nswLS0tI8XYJbVGf9Up31yxfq9IUa68LyRvD5559z7bXXEhYWRqNGjbjzzjtJSUmp9r3ffgu9e9v/\n9//ZZ/Dss3DppRYXfBG+8pdDddYv1Vm/fKFOX6ixLixvBMeOHaNt27aO79u0acOxY8cueJ+yAkRE\nrGH5VUM2N7f8TE1VVoCIiCUMi23bts3o37+/4/tZs2YZycnJld7Tvn17A9BDDz300KMGj/bt29fq\nc9lmGIaBhUpLS7n++uv55z//SevWrenWrRsrVqwgIiLCyjJERORnli8NXXLJJfztb3+jf//+lJWV\nMX78eDUBEREPsnxGICIi3sWjdxa7c2PZww8/zHXXXUfnzp3JzMy0uEI7V3WmpaXRvHlz4uLiiIuL\n4y9/+YvlNY4bN46QkBBiYmKcvscbxtJVnd4wlgDZ2dkkJiYSFRVFdHQ0CxYsqPZ9nh5Td+r09JgW\nFRXRvXt3YmNjiYyMZPr06dW+z9Nj6U6dnh7LisrKyoiLiyMpKana12s0nrU+61tHpaWlRvv27Y1D\nhw4ZxcXFRufOnY19+/ZVes/atWuNAQMGGIZhGNu3bze6d+/ulXWmpqYaSUlJltdW0aZNm4wvvvjC\niI6OrvZ1bxhLw3BdpzeMpWEYRk5OjpGZmWkYhmHk5+cbHTp08Mq/n+7U6Q1jWlhYaBiGYZSUlBjd\nu3c3Nm/eXOl1bxhLw3BdpzeM5Xlz58417rrrrmrrqel4emxG4M6NZatXr+bee+8FoHv37uTl5ZGb\nm+t1dQIYHl5h69WrF5dffrnT171hLMF1neD5sQQIDQ0lNjYWgKCgICIiIjh+/Hil93jDmLpTJ3h+\nTJs2bQpAcXExZWVlXHHFFZVe94axdKdO8PxYAhw9epRPPvmECRMmVFtPTcfTY43AnRvLqnvP0aNH\nLavRWQ1V67TZbGzdupXOnTszcOBA9u3bZ2mN7vCGsXSHN45lVlYWmZmZdK8Sd+dtY+qsTm8Y0/Ly\ncmJjYwkJCSExMZHIyMhKr3vLWLqq0xvGEuAPf/gDzz//PA0aVP8RXtPx9FgjcPfGsqrdzt2fqy/u\nHK9Lly5kZ2ezZ88eJk2axNChQy2orOY8PZbu8LaxLCgo4Pbbb2f+/PkEBQVd8Lq3jOnF6vSGMW3Q\noAG7d+/m6NGjbNq0qdotG7xhLF3V6Q1j+fHHH9OyZUvi4uIuOjupyXh6rBFcc801ZGdnO77Pzs6m\nTZs2F33P0aNHueaaayyrsboaqqszODjYMaUcMGAAJSUlnD592tI6XfGGsXSHN41lSUkJt912G2PG\njKn2H7y3jKmrOr1pTJs3b86gQYPYuXNnpee9ZSzPc1anN4zl1q1bWb16NeHh4YwaNYp//etf3HPP\nPZXeU9Px9Fgj6Nq1K99++y1ZWVkUFxezcuVKbr311krvufXWW3n77bcB2L59Oy1atCAkJMTr6szN\nzXV0388//xzDMKpdW/QkbxhLd3jLWBqGwfjx44mMjGTy5MnVvscbxtSdOj09pj/88AN5eXkAnDt3\njo0bNxIXF1fpPd4wlu7U6emxBJg1axbZ2dkcOnSId999l1//+teOsTuvpuPpsYQyZzeWLV68GIAH\nHniAgQMH8sknn3Dttddy2WWX8cYbb3hlne+//z6vvPIKl1xyCU2bNuXdd9+1vM5Ro0aRnp7ODz/8\nQNu2bXn66acpKSlx1OgNY+lOnd4wlgAZGRksW7aMTp06OT4MZs2axZEjRxy1esOYulOnp8c0JyeH\ne++9l/LycsrLy7n77rvp3bu31/1bd6dOT49ldc4v+dRlPHVDmYhIgPO5qEoREalfagQiIgFOjUBE\nJMCpEYhl9CF0AAADEElEQVSIBDg1AhGRAKdGICIS4NQIxKdVt+1DfQoLC6v2ztH09HS2bdtW7c+s\nWbPG6bbqIt7IYzeUidQHs/ejsdls1e7nkpqaSnBwMDfeeOMFryUlJTndI17EG2lGIH7n4MGDDBgw\ngK5du3LzzTdz4MABAH7729/yyCOP0KNHD9q3b88HH3wA2HecfPDBB4mIiKBfv34MGjTI8RrAwoUL\niY+Pp1OnThw4cICsrCwWL17MvHnziIuLY8uWLZWO/+abbzJp0qSLHrOirKwsOnbsyNixY7n++usZ\nPXo0GzZsoEePHnTo0IEdO3aYNVQigBqB+KH777+fhQsXsnPnTp5//nkefPBBx2snTpwgIyODjz/+\nmGnTpgHw4YcfcvjwYfbv388777zDtm3bKs00rr76anbt2sXEiROZM2cOYWFh/O53v2PKlClkZmbS\ns2fPSsevOkup7phVHTx4kEcffZSvv/6aAwcOsHLlSjIyMpgzZw6zZs2qr6ERqZaWhsSvFBQUsG3b\nNkaMGOF4rri4GLB/QJ/fnTMiIsIR1LFlyxZGjhwJ4NiHvqLhw4cD9i2IP/zwQ8fz7uzO4uyYVYWH\nhxMVFQVAVFQUffr0ASA6OpqsrCyXxxGpCzUC8Svl5eW0aNHCaUZr48aNHV+f/yCveh6g6gd8kyZN\nAGjYsCGlpaU1rqm6Y1Z1/hhg3xP//M80aNCgVscUqQktDYlfadasGeHh4bz//vuA/YN37969F/2Z\nHj168MEHH2AYBrm5uaSnp7s8TnBwMPn5+dW+pn0cxdeoEYhPO3v2LG3btnU8XnzxRZYvX87SpUuJ\njY0lOjqa1atXO95fcf3+/Ne33XYbbdq0ITIykrvvvpsuXbrQvHnzC45ls9kcP5OUlMSqVauIi4sj\nIyPD6fucHbO63+3se29MkhP/om2oRYDCwkIuu+wyTp06Rffu3dm6dSstW7b0dFkiltA5AhFg8ODB\n5OXlUVxczIwZM9QEJKBoRiAiEuB0jkBEJMCpEYiIBDg1AhGRAKdGICIS4NQIREQCnBqBiEiA+3+K\nzqsRe/u3SQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5651370>"
       ]
      }
     ],
     "prompt_number": 12
    }
   ],
   "metadata": {}
  }
 ]
}