{
 "metadata": {
  "name": "chapter 14 som.ipynb"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 14:Dams and Retaining Walls"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problem no 14.1,Page No.325"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Initilization of variables\n",
      "b=2 #m #width \n",
      "FOS=1.5 #Factor of safety\n",
      "#rho_mason=2.5*rho_w\n",
      "mu=0.5 #coeffeicient of friction\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let L=1 m (length of dam)\n",
      "L=1\n",
      "#W=b*H*L*rho\n",
      "#After substituting values and Further simplifying we get\n",
      "#W=2*H*rho\n",
      "\n",
      "#Total Pressure\n",
      "#P=W*H**2*2**-1\n",
      "\n",
      "x_bar=b*2**-1 #Distance of Line of action of W from waterface\n",
      "\n",
      "#Distance of pt where resultant cuts the base measured from Line of action\n",
      "#x=P*W**-1*H*3**-1\n",
      "#After substituting values and Further simplifying we get\n",
      "#x=H**2*30**-1\n",
      "\n",
      "#x_bar+x=2*b*3**-1\n",
      "#After substituting values and Further simplifying we get\n",
      "#1+H**2*30**-1=2*b*3**-1\n",
      "H=(30*(2*b*3**-1-1))**0.5 #height of dam\n",
      "\n",
      "#Frictional Resistance offered at the base\n",
      "#F=mu*W\n",
      "#After substituting values and Further simplifying we get\n",
      "#F=3.16*rho\n",
      "\n",
      "#Total Lateral Pressure\n",
      "#P=W*H**2*2**-1\n",
      "#P=4.99*W\n",
      "\n",
      "#Factor of safety against sliding\n",
      "#FOS1=F*P**-1=3.16*4.99**-1*rho_mason*rho_w**-1\n",
      "FOS1=3.16*4.99**-1*2.5\n",
      "\n",
      "#FOS1>FOS\n",
      "\n",
      "#Result\n",
      "print\"Dam is safe against sliding\",round(FOS1,2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Dam is safe against sliding 1.58\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problem no 14.2,Page No.327"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Initilization of variables\n",
      "D=2 #m #External Diameter\n",
      "d=1.5 #m #Internal Diameter\n",
      "P=1600 #N/m**2 #N/m**2 #Wind Pressure\n",
      "W=19200 #N/m**2 #Weight of masonry\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let H be max height of dam\n",
      "\n",
      "#W2=pi*4**-1*(D**2-d**2)*H*W #weight of chimney\n",
      "#W2=26400*H\n",
      "\n",
      "#Eccentricrty\n",
      "x=(D**2+d**2)*(8*D)**-1\n",
      "\n",
      "#P2=H*D*P #Lateral thrust of wind on chimney\n",
      "#P2=3200*H\n",
      "\n",
      "#Now by using the relation we get P*W**-1=x*(H*2**-1)**-1\n",
      "#After substituting values and Further simplifying we get\n",
      "H=0.39*2*26400*3200**-1\n",
      "\n",
      "#result\n",
      "print\"The Height of Dam is\",round(H,2),\"m\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Height of Dam is 6.44 m\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problem no 14.3,Page No.327"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Initilization of variables\n",
      "rho_w=10 #KN/m**3 #Density of water\n",
      "rho_mason=22.4 #KN/m**3 #Density of mason\n",
      "H=6 #m #height of dam\n",
      "a=1 #m #width of top\n",
      "b=4 #m #bottom width\n",
      "h=5.5 #m #Weight of water depth \n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let L=1 m (length of dam)\n",
      "L=1\n",
      "\n",
      "#weight of dam\n",
      "W=(a+b)*2**-1*H*a*rho_mason\n",
      "\n",
      "#Lateral thrust\n",
      "P=rho_w*h**2*a*2**-1\n",
      "\n",
      "#distance of Line of action of W measured from vertical face\n",
      "x_bar=(b**2+b*a+a**2)*(3*(b+a))**-1\n",
      "\n",
      "#distance of pt where resultant cuts the base\n",
      "x=P*W**-1*h*3**-1\n",
      "\n",
      "#Eccentricity\n",
      "e=x_bar+x-b*2**-1\n",
      "\n",
      "#Stress at Pt B\n",
      "sigma1=W*b**-1*(1-6*e*b**-1)\n",
      "\n",
      "#stress at Pt C\n",
      "sigma2=W*b**-1*(1+6*e*b**-1)\n",
      "\n",
      "#Result\n",
      "print\"Max stress intensities at the base is\",round(sigma2,2),\"KN/m**2\"\n",
      "print\"Min stress intensities at the base is\",round(sigma1,2),\"KN/m**2\"\n",
      "\n",
      "#Plotting the Shear Force Diagram\n",
      "\n",
      "X1=[0,L,L]\n",
      "Y1=[sigma2,sigma1,0]\n",
      "Z1=[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"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Max stress intensities at the base is 112.38 KN/m**2\n",
        "Min stress intensities at the base is 55.62 KN/m**2\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ptUB4uHHfnRYPiH379mHUqFHo37+//jLSsmXLMGTIEMTGxuLChQvw8PDAxo0b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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x55942b0>"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problem no 14.4,Page No.329"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Initilization of variables\n",
      "H=10 #m #height od dam\n",
      "a=2 #m #top width\n",
      "b=5 #m #bottom width\n",
      "W=25 #KN/m**3 #weight of mason\n",
      "rho_w=10 #KN/m**3 #density of water\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let L=1 m (length of dam)\n",
      "L=1\n",
      "\n",
      "#weight of dam\n",
      "W2=(b+a)*H*L*W*2**-1\n",
      "\n",
      "##Lateral thrust\n",
      "P=rho_w*H**2*L*2**-1 \n",
      "\n",
      "#Resultant thrust\n",
      "R=(P**2+W**2)**0.5\n",
      "\n",
      "#Distance of Line of action from vertical base\n",
      "x_bar=(b**2+b*a+a**2)*(3*(b+a))**-1\n",
      "\n",
      "##distance of pt where resultant cuts the base\n",
      "x=P*W2**-1*H*3**-1\n",
      "\n",
      "#Eccentricity\n",
      "e=x_bar+x-b*2**-1\n",
      "\n",
      "#Stress at Pt B\n",
      "sigma1=W2*b**-1*(1-6*e*b**-1)\n",
      "\n",
      "#stress at Pt C\n",
      "sigma2=W2*b**-1*(1+6*e*b**-1)\n",
      "\n",
      "#Result\n",
      "print\"The Resultant Thrust on the base is\",round(R,2),\"KN\"\n",
      "\n",
      "#Plotting the Shear Force Diagram\n",
      "\n",
      "X1=[0,L,L]\n",
      "Y1=[-sigma2,-sigma1,0]\n",
      "Z1=[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"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Resultant Thrust on the base is 500.62 KN\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KXKQmq9IxEH+lBHJ5p05Zc1W98AJMmACPPgpXXml3VCJiN69MZSKBwRhrXY4H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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5657d50>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problem no 14.5,Page No.330"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Initilization of variables\n",
      "H=30 #m #height of Dam\n",
      "h=29 #m #height of water\n",
      "rho_w=9810 #N/m**3 \n",
      "rho_mason=22560 #N/m**3\n",
      "sigma1=0 #KN/m**3\n",
      "sigma2=880 #KN/m**3\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let L=1 m (length of dam)\n",
      "L=1\n",
      "\n",
      "#weight of dam\n",
      "#W=(a+b)*2**-1*L*H*rho_mason*10**-3\n",
      "#After substituting values and Further simplifying we get\n",
      "#W=338.4*(a+b) #equation1\n",
      "\n",
      "#Pressure at B=0, Sinc etension at base has just been avoided\n",
      "\n",
      "#Eccentricity\n",
      "e=b*6**-1  #as sigma1=0\n",
      "\n",
      "#Pressure at C\n",
      "#sigma2=W2*b**-1*(1+6*e*b**-1)\n",
      "#After substituting values and Further simplifying we get\n",
      "#W=440*b\n",
      "\n",
      "#From equation1,440*b=338*(a+b)\n",
      "#b=3.33*a\n",
      "\n",
      "#the distance of C.Gof dam\n",
      "#x_bar=(b**2+b*a+a**2)*(3*(b+a))**-1\n",
      "#After substituting values and Further simplifying we get\n",
      "#x_bar=1.187*a\n",
      "\n",
      "#distance of pt where resultant cuts the base\n",
      "#x=P*W2**-1*H*3**-1\n",
      "#After substituting values and Further simplifying we get\n",
      "#x=27.214*a**-1\n",
      "\n",
      "#Now x_bar+x=2*3**-1*b\n",
      "#After substituting values and Further simplifying we get\n",
      "a=(27.17*(2.22-1.187)**-1)**0.5\n",
      "b=3.33*a\n",
      "\n",
      "#Result\n",
      "print\"The top width dam is\",round(a,2),\"m\"\n",
      "print\"The bottom width dam is\",round(b,2),\"m\"\n",
      "\n",
      "\n",
      "#Plotting the Shear Force Diagram\n",
      "\n",
      "X1=[0,L,L]\n",
      "Y1=[sigma2,sigma1,0]\n",
      "Z1=[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"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The top width dam is 5.13 m\n",
        "The bottom width dam is 17.08 m\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KSrDb7QDY7XZKSkoAKCwsZPDgwY7j/f39KSgouPDMJ2536aUwbx7ccovZhnzpUvjrX6F7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\nhIiI1EhJQkREavT/G7kEgAv8kjUAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5650490>"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problem no 14.6,Page No.332"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Initilization of variables\n",
      "H= 4 #m #height of dam\n",
      "a=1 #m #Top width\n",
      "b=3 #m #bottom width\n",
      "rho1=9810 #N/m**3 #weight of water\n",
      "rho2=19620 #n/m**3 #Weight of mason\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let L=1 m (length of dam)\n",
      "L=1\n",
      "\n",
      "#weight of dam\n",
      "W=(a+b)*2**-1*L*H*rho2*10**-3\n",
      "\n",
      "##Lateral thrust\n",
      "P=rho1*H**2*L*2**-1*10**-3 \n",
      "\n",
      "#Distance of Line of action from vertical base\n",
      "x_bar=(b**2+b*a+a**2)*(3*(b+a))**-1\n",
      "\n",
      "#distance of pt where resultant cuts the base\n",
      "x=P*W**-1*H*3**-1\n",
      "\n",
      "#Eccentricity\n",
      "e=x_bar+x-b*2**-1\n",
      "\n",
      "#Stress at Pt B\n",
      "sigma1=W*10**3*b**-1*(1-6*e*b**-1)\n",
      "\n",
      "#stress at Pt C\n",
      "sigma2=W*10**3*b**-1*(1+6*e*b**-1)\n",
      "\n",
      "#Stresses at the base when resorvoir is empty\n",
      "\n",
      "e2=x_bar-b*2**-1\n",
      "\n",
      "#Minus sign indicates sigma_b>sigma_c\n",
      "\n",
      "#Stress at C\n",
      "sigma2_2=W*10**3*b**-1*(1+6*round(e2,2)*b**-1)\n",
      "\n",
      "#Stress at Pt B\n",
      "sigma1_2=W*10**3*b**-1*(1-6*round(e2,2)*b**-1)\n",
      "\n",
      "#result\n",
      "print\"When the Reservoir is full :sigma1\",round(sigma1,2),\"KN/m**2\"\n",
      "print\"                           :sigma2\",round(sigma2,2),\"KN/m**2\"\n",
      "print\"When the Reservoir is empty:sigma1_2\",round(sigma1_2,2),\"KN/m**2\"\n",
      "print\"                           :sigma2_2\",round(sigma2_2,2),\"KN/m**2\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "When the Reservoir is full :sigma1 26160.0 KN/m**2\n",
        "                           :sigma2 78480.0 KN/m**2\n",
        "When the Reservoir is empty:sigma1_2 96268.8 KN/m**2\n",
        "                           :sigma2_2 8371.2 KN/m**2\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problem no 14.7,Page No.333"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Initilization of variables\n",
      "H=8 #m #height of dam\n",
      "h=7.5 #m #Height of water\n",
      "a=1 #m #top width\n",
      "mu=0.6 #Coeffeicient of friction\n",
      "rho_mason=22.4 #KN/m**3 #weight of mason\n",
      "rho_w=9.81 #KN/m**3 #density of water\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#weight of dam\n",
      "#W=(a+b)*2**-1*L*H*rho2*10**-3\n",
      "#After substituting values and further simplifying we get\n",
      "#W=89600*(b+1)\n",
      "\n",
      "#Distance of Line of action from vertical base\n",
      "#x_bar=(b**2+b*a+a**2)*(3*(b+a))**-1\n",
      "#After substituting values and further simplifying we get\n",
      "#x_bar=(1+b+b**2)*(3*(1+b))**-1\n",
      "\n",
      "#Lateral thrust\n",
      "P=rho_w*h**2*2**-1\n",
      "\n",
      "#Min width to avoid tension at base\n",
      "#Z=x_bar+P*W**-1*h*3**-1\n",
      "#Z=2*3**-1*b\n",
      "#After substituting values and further simplifying we get\n",
      "#b**2+b-24.09=0\n",
      "a=1\n",
      "b=1\n",
      "c=-24.09\n",
      "\n",
      "X=b**2-4*a*c\n",
      "\n",
      "b1=(-b+X**0.5)*(2*a)**-1\n",
      "b2=(-b-X**0.5)*(2*a)**-1\n",
      "\n",
      "#Thus width cannot be negative,b1 is considered\n",
      "\n",
      "#Min width to avoid sliding\n",
      "#mu*W>P\n",
      "#After substituting values and further simplifying we get\n",
      "b=P*10**3*(mu*89600)**-1-1\n",
      "\n",
      "#Result\n",
      "print\"The Min bottom width is\",round(b,2),\"m\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Min bottom width is 4.13 m\n"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problem no 14.8,Page No.334"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Initilization of variables\n",
      "H=10 #m #height of dam\n",
      "a=1 #m #top width\n",
      "b=7 #m #Bottom width\n",
      "rho_mason=19620 #N/m**3 #weight of mason\n",
      "rho_w=9810 #N/m**3 #density of water\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Lateral thrust\n",
      "P=rho_w*H**2*2**-1\n",
      "\n",
      "#weight of dam\n",
      "W=(rho_w*H*2**-1*a)+(rho_mason*(a+b)*2**-1*H)\n",
      "\n",
      "#Taking Moment at B,M_B=0\n",
      "x_bar=((rho_w*H*2**-1*1*3**-1)+(rho_mason*H*2**-1*2*3**-1)+(rho_mason*H*1.5)+(rho_mason*H*5*11*2**-1*3**-1))*W**-1\n",
      "\n",
      "#Now using relation we get\n",
      "x=P*W**-1*H*3**-1\n",
      "\n",
      "#Eccentricity\n",
      "e=x_bar+x-b*2**-1\n",
      "\n",
      "#Max stress\n",
      "sigma_max=W*b**-1*(1+6*round(e,2)*b**-1)\n",
      "\n",
      "#Min stress\n",
      "sigma_min=W*b**-1*(1-6*round(e,2)*b**-1)\n",
      "\n",
      "#Result\n",
      "print\"The Max stresses on the base is\",round(sigma_max,2),\"N/m**2\"\n",
      "print\"The Min stresses on the base is\",round(sigma_min,2),\"N/m**2\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Max stresses on the base is 228372.8 N/m**2\n",
        "The Min stresses on the base is 9870.06 N/m**2\n"
       ]
      }
     ],
     "prompt_number": 47
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problem no 14.10,Page No.337"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Initilization of variables\n",
      "H=6 #m #height of dam\n",
      "a=1 #m #top width\n",
      "b=3 #m #Bottom width\n",
      "rho_mason=22 #KN/m**3 #weight of mason\n",
      "rho_earth=16 #KN/m**3 #density of water\n",
      "phi=30 #Degree #angle of repose\n",
      "mu=0.5 #Coeffecient of friction\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let Length of dam ,L=1 m\n",
      "L=1 #m\n",
      "\n",
      "#weight of dam\n",
      "W=(a+b)*2**-1*L*H*rho_mason\n",
      "\n",
      "#Lateral thrust\n",
      "P=rho_earth*H**2*L*2**-1*((1-sin(30*pi*180**-1))*(1+sin(phi*pi*180**-1))**-1)\n",
      "\n",
      "#Distance of Line of action from vertical base\n",
      "x_bar=(b**2+b*a+a**2)*(3*(b+a))**-1\n",
      "\n",
      "#distance of pt where resultant cuts the base\n",
      "x=P*W**-1*H*3**-1\n",
      "\n",
      "#Eccentricity\n",
      "e=x_bar+x-b*2**-1\n",
      "e_max=b*6**-1\n",
      "\n",
      "#stress at toe\n",
      "sigma2=W*10**3*b**-1*(1+6*round(e,2)*b**-1)*10**-3\n",
      "\n",
      "#Safe agaainst bearing\n",
      "\n",
      "#Frictional Resistance \n",
      "F=mu*W\n",
      "\n",
      "#Hence F>P,so it is safe against sliding\n",
      "\n",
      "#Result\n",
      "print\"Safe against bearing as well as sliding\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Safe against bearing as well as sliding\n"
       ]
      }
     ],
     "prompt_number": 69
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problem no 14.11,Page No.338"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Initilization of variables\n",
      "H=8 #m #height of dam\n",
      "a=1 #m #top width\n",
      "b=4.5 #m #Bottom width\n",
      "rho_mason=24 #KN/m**3 #weight of mason\n",
      "rho_earth=20 #KN/m**3 #density of water\n",
      "phi=30 #Degree #angle of repose\n",
      "mu=0.5 #Coeffecient of friction\n",
      "BC=120 #KN/m**2\n",
      "\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let Length of dam ,L=1 m\n",
      "L=1 #m\n",
      "\n",
      "#weight of dam\n",
      "W=(a+b)*2**-1*L*H*rho_mason\n",
      "\n",
      "#Rankine's coeff earth pressure\n",
      "K=((1-sin(30*pi*180**-1))*(1+sin(phi*pi*180**-1))**-1)\n",
      "\n",
      "#Lateral thrust\n",
      "P=rho_earth*H**2*L*2**-1*round(K,2)\n",
      "\n",
      "#Distance of Line of action from vertical base\n",
      "x_bar=(b**2+b*a+a**2)*(3*(b+a))**-1\n",
      "\n",
      "#distance of pt where resultant cuts the base\n",
      "x=P*W**-1*H*3**-1\n",
      "\n",
      "#Eccentricity\n",
      "e=x_bar+x-b*2**-1\n",
      "\n",
      "#Pressure at heel B\n",
      "sigma1=W*b**-1*(1-6*round(e,2)*b**-1)\n",
      "\n",
      "#Pressure at heel C\n",
      "sigma2=W*b**-1*(1+6*round(e,2)*b**-1)\n",
      "\n",
      "#sigma2>120 #KN/m**2,so it is unsafe against bearing capacity of the soil\n",
      "\n",
      "#result\n",
      "print\"Unsafe against the bearing capacity of soil\" \n",
      "\n",
      "#Plotting the Shear Force Diagram\n",
      "\n",
      "X1=[0,L,L]\n",
      "Y1=[sigma2,sigma1,0]\n",
      "Z1=[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"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Unsafe against the bearing capacity of soil\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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pKYm4uDj8/PwICQkhLCyM1NTUS892ImUQHAyJibBnj1lL8cADphbUm2+anfBEqpoiK+23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\nzhxISzMrtrt3h75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tfv75Z7edv3HjxmzYsIH69et75Hoi3kAtCKm0du3aRZ8+fbjhhhu4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\nJSUIERFxSQlCRERc+v9brQ7wu4yTKgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x54faf90>"
       ]
      }
     ],
     "prompt_number": 86
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problem no 14.12,Page No.340"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Initilization of variables\n",
      "H=6 #m #height of dam\n",
      "a=1.5 #m #top width\n",
      "b=3.5 #m #Bottom width\n",
      "rho_s=16 #KN/m**3 #density of soil\n",
      "rho_mason=22.5 #KN/m**3 #density of mason\n",
      "phi=30 #Degree #angle of repose\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let Length of dam ,L=1 m\n",
      "L=1 #m\n",
      "\n",
      "#weight of dam\n",
      "W=(a+b)*2**-1*L*H*rho_mason\n",
      "\n",
      "#Rankine's coeff earth pressure\n",
      "K=((1-sin(30*pi*180**-1))*(1+sin(phi*pi*180**-1))**-1)\n",
      "\n",
      "#Lateral thrust\n",
      "P=rho_s*H**2*L*2**-1*K\n",
      "\n",
      "#Distance of Line of action from vertical base\n",
      "x_bar=(b**2+b*a+a**2)*(3*(b+a))**-1\n",
      "\n",
      "#distance of pt where resultant cuts the base\n",
      "x=P*W**-1*H*3**-1\n",
      "\n",
      "#Eccentricity\n",
      "e=x_bar+x-b*2**-1\n",
      "\n",
      "#Pressure at heel B\n",
      "sigma1=W*b**-1*(1-6*round(e,3)*b**-1)\n",
      "\n",
      "#Pressure at heel C\n",
      "sigma2=W*b**-1*(1+6*round(e,3)*b**-1)\n",
      "\n",
      "#Result\n",
      "print\"The Max Intensities of soil at the wall is\",round(sigma2,2),\"KN/m**2\"\n",
      "print\"The Min Intensities of soil at the wall is\",round(sigma1,2),\"KN/m**2\"\n",
      "\n",
      "#Plotting the Shear Force Diagram\n",
      "\n",
      "X1=[0,L,L]\n",
      "Y1=[sigma2,sigma1,0]\n",
      "Z1=[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"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Max Intensities of soil at the wall is 118.91 KN/m**2\n",
        "The Min Intensities of soil at the wall is 73.95 KN/m**2\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ffVXHjh1TbGysxowZY3/9J598UgMHDlR0dLT++9//XrH8Rx55RM8995wk6dNP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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x555a0f0>"
       ]
      }
     ],
     "prompt_number": 113
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problem no 14.13,Page No.341"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Initilization of variables\n",
      "H=6 #m #height of dam\n",
      "a=1 #m #top width\n",
      "b=3 #m #Bottom width\n",
      "rho_s=18 #KN/m**3 #density of soil\n",
      "rho_mason=24 #KN/m**3 #density of mason\n",
      "alpha=20\n",
      "phi=30\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Let Length of dam ,L=1 m\n",
      "L=1 #m\n",
      "\n",
      "a2=cos(alpha*pi*180**-1)\n",
      "b2=(cos(alpha*pi*180**-1)-((cos(alpha*pi*180**-1)**2-cos(phi*pi*180**-1)**2))**0.5)\n",
      "c2=(cos(alpha*pi*180**-1)+((cos(alpha*pi*180**-1)**2-cos(phi*pi*180**-1)**2)**0.5))\n",
      "\n",
      "X=a2*b2*c2**-1\n",
      "\n",
      "#Total Pressue on the wall\n",
      "P=rho_s*H**2*2**-1*X\n",
      "\n",
      "#The Horizontal component of pressure\n",
      "P_H=P*cos(20*pi*180**-1)\n",
      "\n",
      "#The Vertical component of pressure\n",
      "P_V=P*sin(20*pi*180**-1)\n",
      "\n",
      "#weight of wall\n",
      "W=(a+b)*H*rho_mason*2**-1\n",
      "\n",
      "#TotaL Weight \n",
      "W1=W+P_V\n",
      "\n",
      "#Taking moment of vertical Loads about B,M_B=0\n",
      "x_bar=(rho_mason*a*H*0.5+rho_mason*H*2)*W1**-1\n",
      "\n",
      "x=P_H*W1**-1*H*3**-1\n",
      "\n",
      "#eccentricity\n",
      "e=x_bar+x-b*2**-1\n",
      "\n",
      "#Stress at the toe at C\n",
      "sigma_max=W1*b**-1*(1+6*round(e,2)*b**-1)\n",
      "\n",
      "#Stress at the heel at B\n",
      "sigma_min=W1*b**-1*(1-6*round(e,2)*b**-1)\n",
      "\n",
      "#Result\n",
      "print\"Pressure at the base of the wall:Pressure at the heel\",round(sigma_min,2),\"KN/m**2\"\n",
      "print\"                                :Pressure at the toe\",round(sigma_max,2),\"KN/m**2\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Pressure at the base of the wall:Pressure at the heel 37.84 KN/m**2\n",
        "                                :Pressure at the toe 184.76 KN/m**2\n"
       ]
      }
     ],
     "prompt_number": 155
    }
   ],
   "metadata": {}
  }
 ]
}