{ "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": {} } ] }