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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter10-Stresses in a Soil Mass"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex1-pg257"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#principal stress and normal stresses and shear stresses\n",
      "##initialisation of variables\n",
      "sx= 2000. ##lb/ft^3\n",
      "sy= 2500. ##lb/ft^3\n",
      "T= 800. ##lb/ft^3\n",
      "t= 0.348##radians\n",
      "##calculations\n",
      "s1= (sx+sy)/2.+math.sqrt(((sy-sx)/2.)**2+T**2)\n",
      "s2= (sx+sy)/2.-math.sqrt(((sy-sx)/2.)**2+T**2)\n",
      "sn= (sx+sy)/2.+(sy-sx)*math.cos(2.*t)/2.-T*math.sin(2*t)\n",
      "Tn= (sy-sx)*math.sin(2.*t)/2.+T*math.cos(2*t)\n",
      "##results\n",
      "print'%s %.2f %s'% ('principle stress s1 = ',s1,' lb/ft^3 ')\n",
      "print'%s %.2f %s'% ('principle stress s2 = ',s2,' lb/ft^3 ')\n",
      "print'%s %.2f %s'% ('normal stress = ',sn,' lb/ft^3 ')\n",
      "print'%s %.2f %s'% ('shear stress = ',Tn,' lb/ft^3 ')\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "principle stress s1 =  3088.15  lb/ft^3 \n",
        "principle stress s2 =  1411.85  lb/ft^3 \n",
        "normal stress =  1928.93  lb/ft^3 \n",
        "shear stress =  774.22  lb/ft^3 \n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex3-pg262"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate vertical stress increase\n",
      "##initialisation of variables\n",
      "x= 3. ##m\n",
      "y= 4. ##m\n",
      "P= 5. ##kN\n",
      "z= 2. ##m\n",
      "##calculations\n",
      "r= math.sqrt(x**2+y**2)\n",
      "k= r/z\n",
      "I= 3./(2.*math.pi*((r/z)**2+1)**2.5)\n",
      "s= P*I/z**2\n",
      "##results\n",
      "print'%s %.4f %s'% ('verticle stress increase at 2m = ',s,' kN/m^3 ')\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "verticle stress increase at 2m =  0.0042  kN/m^3 \n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex6-pg270"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate the value of pressure and plot the graph\n",
      "import math\n",
      "%matplotlib inline\n",
      "import warnings\n",
      "warnings.filterwarnings('ignore')\n",
      "from math import log\n",
      "import numpy\n",
      "from math import tan\n",
      "import matplotlib\n",
      "from matplotlib import pyplot\n",
      "#given\n",
      "p=numpy.array([-9,-6,-3, 0,3,6,9])\n",
      "e=numpy.array([0.017,0.084,0.480,0.818,0.480,0.084,0.017])\n",
      "\n",
      "#calculations\n",
      "\n",
      "\n",
      "#results\n",
      "\n",
      "pyplot.plot(p,e)\n",
      "pyplot.xlabel('Pressure (ton/ft^2)')\n",
      "pyplot.ylabel('void ratio ,e')\n",
      "pyplot.title('Graph of pressure vs void ratio')\n",
      "pyplot.show()\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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VhzVrwnKoqfEmLntlbKSypMFm1knSlHKeNjOrtxlqPCFkr08/hdatw8Ls226b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\nOsFBB3kScM7VzA8/hOqkwYN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       "text": [
        "<matplotlib.figure.Figure at 0x54c4510>"
       ]
      }
     ],
     "prompt_number": 2
    }
   ],
   "metadata": {}
  }
 ]
}