{
"metadata": {
"name": "",
"signature": "sha256:0405d0d7063a41d23ac6999d3522bb5dd0c6d2025222a87c1afa5e51af3425e8"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter13-Lateral Earth Pressure: \n",
"At-Rest, Rankine, and Coulomb"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex1-430"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#Calculate the lateral force Poper unit length of the wall. Also, determine the location ofthe resultant force. Assume that for sand OCR\u00012\n",
"OCR=2.\n",
"a=30.\n",
"Ko=(1.-math.sin(a/57.3))*(OCR)**math.sin(a/57.3)\n",
"##at z=0\n",
"To1=0.\n",
"Th1=0.\n",
"u1=0.\n",
"##at z=10\n",
"To2=10.*100.\n",
"Th2=Ko*To2\n",
"u2=0.\n",
"##at z=15\n",
"To3= 10.*100.+5.*(122.4-62.4)\n",
"Th3=Ko*To3\n",
"u3=5.*62.4\n",
"##Lateral force Po =Area 1 +\u0007 Area 2+\u0007 Area3+\u0007 Area 4\n",
"Po =(1./2.)*10.*707.+5.*707.+(1./2.)*5.*212.1+(1/2.)*5.*312.\n",
"z=((3535.)*(5.+10./3.)+3535.*(5./2.)+530.3*(5./3.)+780.*(5./3.))/Po\n",
"print'%s %.1f %s'%('z = ',z,' ft')\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"z = 4.8 ft\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex2-pg449"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#a.Rankine active force per unit length of the wall and the location of theresultant\n",
"#b.Rankine passive force per unit length of the wall and the location of the resultant\n",
"##c=0\n",
"a=36.\n",
"G=16.\n",
"Ka=(1.-math.sin(a/57.3))/(1.+math.sin(a/57.3))\n",
"##at z=0 Tp=0\n",
"z=6.\n",
"To=G*z\n",
"Ta=Ka*To\n",
"Pa=z*Ta/2.\n",
"\n",
"print'%s %.1f %s'%('a)Rankine active force per unit length of the wall = ',Pa,' kN/m')\n",
"print(' and the location of the resultant is z = 2m')\n",
"\n",
"\n",
"p=36.\n",
"G=16.\n",
"Kp=(1+math.sin(a/57.3))/(1-math.sin(a/57.3))\n",
"##at z=0 Tp=0\n",
"z=6.\n",
"To=G*z\n",
"Tp=Kp*To\n",
"Pp=z*Tp/2.\n",
"\n",
"print'%s %.1f %s'%(' b)Rankine passive force per unit length of the wall = ',Pp,' kN/m')\n",
"print (' and the location of the resultant is z = 2m')\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"a)Rankine active force per unit length of the wall = 74.8 kN/m\n",
" and the location of the resultant is z = 2m\n",
" b)Rankine passive force per unit length of the wall = 1109.2 kN/m\n",
" and the location of the resultant is z = 2m\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex3-pg450"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#Determine the active force Paperunit length of the wall as well as the location and direction of the resultant.\n",
"H=12.\n",
"a=20.\n",
"b=20.\n",
"G=115.\n",
"c=30.\n",
"Oa= math.asin(math.sin(a/57.3)/math.sin(c/57.3))*57.3-a+2.*b\n",
"Ka= (math.cos((a-b)/57.3)*math.sqrt(1.+(math.sin(c/57.3))**2.-2.*math.sin(c/57.3)*math.cos(Oa/57.3)))/((math.cos(b/57.3))**2.*(math.cos(a/57.3)+math.sqrt((math.sin(c/57.3))**2.-(math.sin(a/57.3))**2)))\n",
"Pa=G*H**2.*Ka/2.\n",
"B= math.atan((math.sin(c/57.3)*math.sin(Oa/57.3))/(1.-(math.sin(c/57.3)*math.cos(Oa/57.3))))*57.3\n",
"print'%s %.1f %s'%('The active force Pa per unit length of the wall = ',Pa,' lb/ft')\n",
"print'%s %.1f %s'%( ' The resultant will act a distance of 12/3 = 4 ft above the bottom of the wall with B = ',B,' degree')\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The active force Pa per unit length of the wall = 6423.5 lb/ft\n",
" The resultant will act a distance of 12/3 = 4 ft above the bottom of the wall with B = 30.0 degree\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex4-pg451"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#determine the force per unit length of the wall for Rankine\u2019s active state. Also find the location of the resultant.\n",
"a=30.\n",
"Ka1=(1.-math.sin(a/57.3))/(1.+math.sin(a/57.3))\n",
"a=35.\n",
"Ka2=(1-math.sin(a/57.3))/(1+math.sin(a/57.3))\n",
"##at z=0 so T0=0\n",
"##atz=3\n",
"To=3.*16.\n",
"Ta1=Ka1*To\n",
"Ta2=Ka2*To\n",
"\n",
"## At z=6\n",
"To=3.*16.+3.*(18.-9.81)\n",
"Ta2=Ka2*To\n",
"\n",
"Pa =(1/2.)*3.*16.+3.*13.0+ (1/2.)*3.*36.1\n",
"z= (24 *(3.+3./3.)+39.0*(3/2.)+54.15*(3/3.))/Pa\n",
"print'%s %.1f %s'%('The force per unit length of the wall = ',Pa,' kN/m')\n",
"print'%s %.1f %s'% (' The location of the resultant = ',z,'m ')\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The force per unit length of the wall = 117.2 kN/m\n",
" The location of the resultant = 1.8 m \n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex5-pg453"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#a.Maximum depth of the tensile crack\n",
"#b.Pabefore the tensile crack occurs\n",
"#c. Pa after the tensile crack occurs\n",
"Ka= (math.tan(1./57.3))**2.\n",
"G=16.5\n",
"cu=10.\n",
"H=6.\n",
"##at z=0\n",
"z=0.\n",
"Ta=G*z-2.*cu\n",
"##zt z=6\n",
"z=6.\n",
"Ta=G*z-2.*cu\n",
"\n",
"zo=2.*cu/G\n",
"## Before the tensile crack occurs\n",
"Pa= G*H**2./2. - 2.*cu*H\n",
"print'%s %.1f %s'%('Pa before the tensile crack occurs = ',Pa,' kN/m')\n",
"##After the tensile crack occurs\n",
"Pa=(H-zo)*Ta/2.\n",
"print'%s %.1f %s'%(' Pa after the tensile crack occurs = ',Pa,' kN/m')\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Pa before the tensile crack occurs = 177.0 kN/m\n",
" Pa after the tensile crack occurs = 189.1 kN/m\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex6-pg457"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#Determine the Rankine active force Paon the retaining wall after the tensile crack occurs.\n",
"H=15.\n",
"a=10.\n",
"G=118.\n",
"b=20.\n",
"C=250\n",
"Zo=2.*C*math.sqrt((1+math.sin(b/57.3))/(1.-math.sin(b/57.3)))/G\n",
"##at z=0 Ta=0\n",
"##at z=15 \n",
"z=15.\n",
"K=0.3\n",
"Ta=G*z*K*math.cos(a/57.3)\n",
"Pa=(H -Zo)*Ta/2.\n",
"print'%s %.1f %s'%('The Rankine active force Pa on the retaining wall after the tensile crack occurs = ',Pa,' lb/ft')\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The Rankine active force Pa on the retaining wall after the tensile crack occurs = 2339.8 lb/ft\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex7-pg459"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Estimate the active force,Pa , per unit length of the wall. Also, state the direction and location of the resultant force,Pa.\n",
"import math\n",
"c=30.\n",
"b=15.\n",
"a=10.\n",
"Ka=0.3872 ## from table 13.8\n",
"H=4.\n",
"G=15.\n",
"Pa=G*H**2.*Ka/2.\n",
"print'%s %.1f %s'%('The active force per unit length Pa = ',Pa,' kN/m')\n",
"print(' The resultant will act at a vertical distance equal to H/3 = 4/3 = 1.33 m above ' ' the bottom of the wall and will be inclined at an angle of 15\u0005to the back face of the wall.')\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The active force per unit length Pa = 46.5 kN/m\n",
" The resultant will act at a vertical distance equal to H/3 = 4/3 = 1.33 m above the bottom of the wall and will be inclined at an angle of 15\u0005to the back face of the wall.\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex9-pg478"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#Determine Pae.Also determine the location of the resultant line of action of Pae\u2014that is, .\n",
"kh=0.2\n",
"kv=0.\n",
"H=4.\n",
"a=0.\n",
"b=0.\n",
"c=15.\n",
"d=30.\n",
"G=15.5\n",
"B= math.atan(kh/(1-kv)/57.3)\n",
"b1=b+B\n",
"a1=a+B\n",
"Ka=0.452\n",
"Pa=G*H**2.*Ka/2.\n",
"Pae=Pa*(1.-kv)*((math.cos(b1/57.3))**2./((math.cos(b/57.3))**2.*(math.cos(B/57.3))**2.))\n",
"Ka=0.3014\n",
"Pa=G*H**2*Ka/2.\n",
"P1=Pae-Pa\n",
"z= ((Pa*H/3)+P1*0.6*H)/Pae\n",
"print'%s %.1f %s'%('Pae = ',Pae,' kN/m')\n",
"print'%s %.1f %s'%(' Z = ',z,' m')\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Pae = 56.0 kN/m\n",
" Z = 1.7 m\n"
]
}
],
"prompt_number": 15
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex10-pg479"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#Determine the magnitude of the active force,Pae.\n",
"H=28.\n",
"C=210.\n",
"b=10.\n",
"G=118.\n",
"c=20.\n",
"kh=0.1\n",
"Ka=math.tan(35./57.3)\n",
"zo=2.*C/(G*(Ka))\n",
"n=zo/(H-zo)\n",
"Nac=1.60\n",
"Nav=0.375\n",
"L=1.17\n",
"Pae= G*(H-zo)**2*(L*Nav)-C*(H-zo)*Nac\n",
"print'%s %.1f %s'%('The magnitude of the active force, Pae = ',Pae,' lb/ft')\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The magnitude of the active force, Pae = 19488.8 lb/ft\n"
]
}
],
"prompt_number": 16
}
],
"metadata": {}
}
]
}