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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": {}
}
]
}
|
