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diff --git a/Principles_Of_Foundation_Engineering/Chapter07_1.ipynb b/Principles_Of_Foundation_Engineering/Chapter07_1.ipynb
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-{


- "metadata": {


-  "name": "",


-  "signature": "sha256:6111670c8f96effbf1bc0bc29859353d67e53cd5b906d2b571173d1698f7ba9c"


- },


- "nbformat": 3,


- "nbformat_minor": 0,


- "worksheets": [


-  {


-   "cells": [


-    {


-     "cell_type": "heading",


-     "level": 1,


-     "metadata": {},


-     "source": [


-      "Chapter07:Lateral earth pressure"


-     ]


-    },


-    {


-     "cell_type": "heading",


-     "level": 2,


-     "metadata": {},


-     "source": [


-      "Ex7.1:Pg-319"


-     ]


-    },


-    {


-     "cell_type": "code",


-     "collapsed": false,


-     "input": [


-      "#example 7.1\n",


-      "\n",


-      "sigmao=48.0; # in KN/m^2\n",


-      "phi1=30*math.pi/180; # angle\n",


-      "phi2=36*math.pi/180; # angle\n",


-      "Ka1=(math.tan(math.pi/4.0-phi1/2))**2;\n",


-      "Ka2=(math.tan(math.pi/4.0-phi2/2))**2;\n",


-      "sigmaa1=Ka1*sigmao; # in KN/m^2\n",


-      "print round(sigmaa1,2),\"top soil pressure in kN/m**2\"\n",


-      "sigmaa2=Ka2*sigmao; # in KN/m^2\n",


-      "print round(sigmaa2,2),\"bottom soil pressure in kN/m**2\"\n",


-      "Po=1/2.0*3*16+3*12.48+1/3.0*3*(19.65-12.48)+1/2.0*3*29.43;\n",


-      "zbar=(24*(3+3/3.0)+37.44*(3/2.0)+10.76*3/3.0+44.1*3/3.0)/Po;\n",


-      "print round(zbar,2),\"resultant force acting from the bottom in m\"\n",


-      "\n",


-      "# The answers in the book are different due to approximation while here calculations are precise"


-     ],


-     "language": "python",


-     "metadata": {},


-     "outputs": [


-      {


-       "output_type": "stream",


-       "stream": "stdout",


-       "text": [


-        "16.0 top soil pressure in kN/m**2\n",


-        "12.46 bottom soil pressure in kN/m**2\n",


-        "1.84 resultant force acting from the bottom in m\n"


-       ]


-      }


-     ],


-     "prompt_number": 34


-    },


-    {


-     "cell_type": "heading",


-     "level": 2,


-     "metadata": {},


-     "source": [


-      "Ex7.2:Pg-321"


-     ]


-    },


-    {


-     "cell_type": "code",


-     "collapsed": false,


-     "input": [


-      "#example 7.2\n",


-      "\n",


-      "import math\n",


-      "c=14.36;\n",


-      "Gamma=17.4; #  in KN/m^3\n",


-      "H=6; # in m\n",


-      "phi=26*math.pi/180;\n",


-      "Ka=(math.tan(math.pi/4-phi/2))**2;\n",


-      "sigma0=Gamma*H*Ka-2*c*math.sqrt(Ka);\n",


-      "Pa=1/2.0*Gamma*H**2*Ka-2*c*H*math.sqrt(Ka);\n",


-      "print round(Pa,2),\"active force before which tensile crack appeared in kN/m\"\n",


-      "zbar=(244.32-323.1)/14.46;\n",


-      "print round(zbar,2),\"the line of action on which net force is acting in m\"\n",


-      "zc=2*c/Gamma/math.sqrt(Ka);\n",


-      "print round(zc,2),\"distance where tensile crack appeared in m\"\n",


-      "Pa=1/2.0*(H-zc)*(Gamma*H*Ka-2*c*math.sqrt(Ka));\n",


-      "print round(Pa,2),\"Active force in tensile crack in kN/m\"\n",


-      "zbar=(H-zc)/3;\n",


-      "print round(zbar,2),\"the line of action on which net force is acting in m\"\n",


-      "\n"


-     ],


-     "language": "python",


-     "metadata": {},


-     "outputs": [


-      {


-       "output_type": "stream",


-       "stream": "stdout",


-       "text": [


-        "14.62 active force before which tensile crack appeared in kN/m\n",


-        "-5.45 the line of action on which net force is acting in m\n",


-        "2.64 distance where tensile crack appeared in m\n",


-        "38.32 Active force in tensile crack in kN/m\n",


-        "1.12 the line of action on which net force is acting in m\n"


-       ]


-      }


-     ],


-     "prompt_number": 30


-    },


-    {


-     "cell_type": "heading",


-     "level": 2,


-     "metadata": {},


-     "source": [


-      "Ex7.3:Pg-322"


-     ]


-    },


-    {


-     "cell_type": "code",


-     "collapsed": false,


-     "input": [


-      "#example 7.3\n",


-      "import math\n",


-      "pi=math.pi\n",


-      "H=10.0; # in ft\n",


-      "Gamma=110.0; # in lb/ft^3\n",


-      "phi=35*math.pi/180.0; # angle\n",


-      "alpha=15*math.pi/180.0; # angle\n",


-      "theta=10*math.pi/180.0; # angle\n",


-      "zi=math.sin(math.sin(alpha)/math.sin(phi))-alpha+2*theta;\n",


-      "print round(zi*180.0/math.pi,2),\" is zi in degrees\"\n",


-      "Ka=math.cos(alpha-theta)*math.sqrt(1+(math.sin(phi))**2-2*math.sin(phi)*math.sin(zi))/((math.cos(theta))**2*(math.cos(alpha)+math.sqrt((math.sin(phi))**2+((math.sin(alpha))**2))));\n",


-      "Pa=1/2.0*Gamma*H**2*Ka;\n",


-      "print round(Pa,2),\" is rankine earth pressure in lb/ft\"\n",


-      "print \"there is slight error in answer due to rounding off error\"\n",


-      "Beta=math.tan(math.sin(phi)*math.sin(zi)/(1-math.sin(phi)*math.cos(zi)));\n",


-      "print round(Beta*180/pi,2),\" is angle in degrees\"\n",


-      "\n",


-      "# The answers in the book are different due to approximation while here calculations are precise"


-     ],


-     "language": "python",


-     "metadata": {},


-     "outputs": [


-      {


-       "output_type": "stream",


-       "stream": "stdout",


-       "text": [


-        "29.99  is zi in degrees\n",


-        "3078.61  is rankine earth pressure in lb/ft\n",


-        "there is slight error in answer due to rounding off error\n",


-        "36.7  is angle in degrees\n"


-       ]


-      }


-     ],


-     "prompt_number": 25


-    },


-    {


-     "cell_type": "heading",


-     "level": 2,


-     "metadata": {},


-     "source": [


-      "Ex7.4:Pg-326"


-     ]


-    },


-    {


-     "cell_type": "code",


-     "collapsed": false,


-     "input": [


-      "#example 7.4\n",


-      "\n",


-      "H=4.6; # in m\n",


-      "Gamma=16.5; # in KN/m^3\n",


-      "Ka=0.297;\n",


-      "Po=1/2.0*Gamma*H**2*Ka;\n",


-      "print round(Po,2),\"coulomb active force per unit length in kN/m\"\n",


-      "\n"


-     ],


-     "language": "python",


-     "metadata": {},


-     "outputs": [


-      {


-       "output_type": "stream",


-       "stream": "stdout",


-       "text": [


-        "51.85 coulomb active force per unit length in kN/m\n"


-       ]


-      }


-     ],


-     "prompt_number": 16


-    },


-    {


-     "cell_type": "heading",


-     "level": 2,


-     "metadata": {},


-     "source": [


-      "Ex7.5:Pg-331"


-     ]


-    },


-    {


-     "cell_type": "code",


-     "collapsed": false,


-     "input": [


-      "#example 7.5\n",


-      "\n",


-      "#part(a)\n",


-      "Gamma=105; # in lb/ft^3\n",


-      "H=10; #in ft\n",


-      "Kae=0.474;\n",


-      "k1=0;\n",


-      "Pae=1/2.0*Gamma*H**2*Kae*(1-k1) # in lb/ft\n",


-      "print Pae,\"active force in lb/ft\"\n",


-      "#part(b)\n",


-      "Ka=0.246;\n",


-      "Pa=1/2.0*Gamma*H**2*Ka; # in lb/ft\n",


-      "print Pa,\"active force in lb/ft\"\n",


-      "DPae=Pae-Pa;#deltaPae\n",


-      "zbar=(0.6*H*DPae+H/3*(Pa))/Pae;\n",


-      "print round(zbar,2),\"the distance of resultant force from bottom in ft\"\n",


-      "\n"


-     ],


-     "language": "python",


-     "metadata": {},


-     "outputs": [


-      {


-       "output_type": "stream",


-       "stream": "stdout",


-       "text": [


-        "2488.5 active force in lb/ft\n",


-        "1291.5 active force in lb/ft\n",


-        "4.44 the distance of resultant force from bottom in ft\n"


-       ]


-      }


-     ],


-     "prompt_number": 6


-    },


-    {


-     "cell_type": "heading",


-     "level": 2,


-     "metadata": {},


-     "source": [


-      "Ex7.6:Pg-337"


-     ]


-    },


-    {


-     "cell_type": "code",


-     "collapsed": false,


-     "input": [


-      "#example 7.6\n",


-      "\n",


-      "import math\n",


-      "import numpy\n",


-      "import matplotlib.pyplot as plt\n",


-      "\n",


-      "z=[0, 4, 8, 12, 16];\n",


-      "Gamma=110; # in lb/ft^3\n",


-      "phi=36*math.pi/180;\n",


-      "H=16; # in ft\n",


-      "Sa1=numpy.zeros(5);#sigma(1)\n",


-      "Sa2=numpy.zeros(5);#sigma(2)\n",


-      "Sztr=numpy.zeros(5);#sigma(z)translation\n",


-      "print \"z(ft)\\t sigma(1)(lb/ft**2)   \\t sigma(2)(lb/ft**2)    \\t sigma(z)translation (lb/ft**2)\\n\"\n",


-      "for i in range(0,5):\n",


-      "    Sa1[i]=Gamma*(math.tan(math.pi/4-phi*z[i]/2/H))**2*(z[i]-phi*z[i]**2/H/math.cos(phi*z[i]/H));\n",


-      "    Sa2[i]=Gamma*z[i]*(math.cos(phi)/(1+math.sin(phi)))**2;\n",


-      "    Sztr[i]=Sa1[i]/2.0+Sa2[i]/2.0;\n",


-      "    print  round(z[i],2),\"\\t \",round(Sa1[i],2),\"\\t\\t\\t \",round(Sa2[i],2),\"\\t\\t\\t \",round(Sztr[i],2),\"\\n\"\n",


-      "plt.plot(Sztr,z);\n",


-      "plt.title(\"sigma(z)translation vs z\")\n",


-      "plt.ylabel(\"z(ft)\")\n",


-      "plt.xlabel(\"sigma(z)translation (lb/ft**2)\")\n",


-      "plt.show()\n",


-      "\n",


-      "\n"


-     ],


-     "language": "python",


-     "metadata": {},


-     "outputs": [


-      {


-       "output_type": "stream",


-       "stream": "stdout",


-       "text": [


-        "z(ft)\t sigma(1)(lb/ft**2)   \t sigma(2)(lb/ft**2)    \t sigma(z)translation (lb/ft**2)\n",


-        "\n",


-        "0.0 \t  0.0 \t\t\t  0.0 \t\t\t  0.0 \n",


-        "\n",


-        "4.0 \t  269.92 \t\t\t  114.23 \t\t\t  192.07 \n",


-        "\n",


-        "8.0 \t  311.08 \t\t\t  228.46 \t\t\t  269.77 \n",


-        "\n",


-        "12.0 \t  233.53 \t\t\t  342.69 \t\t\t  288.11 \n",


-        "\n",


-        "16.0 \t  102.06 \t\t\t  456.92 \t\t\t  279.49 \n",


-        "\n"


-       ]


-      }


-     ],


-     "prompt_number": 13


-    },


-    {


-     "cell_type": "heading",


-     "level": 2,


-     "metadata": {},


-     "source": [


-      "Ex7.7:Pg-342"


-     ]


-    },


-    {


-     "cell_type": "code",


-     "collapsed": false,


-     "input": [


-      "#example 7.7\n",


-      "import math\n",


-      "Gammasat=18.86; # in KN/m^3\n",


-      "Gammaw=9.81; # in KN/m^3\n",


-      "phi1=math.pi/180*30;  # angle 1\n",


-      "phi2=math.pi/180*26; # angle 2\n",


-      "Kp1=(math.tan(math.pi/4+phi1/2))**2;\n",


-      "Kp2=(math.tan(math.pi/4+phi2/2))**2;\n",


-      "#for top soil\n",


-      "c=0;\n",


-      "sigma0=31.44; # in KN/m^2\n",


-      "sigmap=sigma0*Kp1+2*c*math.sqrt(Kp1);\n",


-      "print round(sigmap,2),\"passive pressure for top layer in kN/m**2\"\n",


-      "#for z=2\n",


-      "c=10;\n",


-      "sigma0=31.44; # in KN/m^2\n",


-      "sigmap=sigma0*Kp2+2*c*math.sqrt(Kp2);\n",


-      "print round(sigmap,2),\"passive pressure for z=2m in kN/m**2\"\n",


-      "#for z=3\n",


-      "c=10;\n",


-      "sigma0=15.72*2+(Gammasat-Gammaw)*1; # in KN/m^2\n",


-      "sigmap=sigma0*Kp2+2*c*math.sqrt(Kp2); # in KN/m^2\n",


-      "print round(sigmap,2),\" is passive pressure for z=3m in kN/m**2\"\n",


-      "\n"


-     ],


-     "language": "python",


-     "metadata": {},


-     "outputs": [


-      {


-       "output_type": "stream",


-       "stream": "stdout",


-       "text": [


-        "94.32 passive pressure for top layer in kN/m**2\n",


-        "112.53 passive pressure for z=2m in kN/m**2\n",


-        "135.7  is passive pressure for z=3m in kN/m**2\n"


-       ]


-      }


-     ],


-     "prompt_number": 3


-    }


-   ],


-   "metadata": {}


-  }


- ]


-}
\ No newline at end of file