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diff --git a/Principles_Of_Foundation_Engineering/Chapter09_1.ipynb b/Principles_Of_Foundation_Engineering/Chapter09_1.ipynb new file mode 100755 index 00000000..8264fd98 --- /dev/null +++ b/Principles_Of_Foundation_Engineering/Chapter09_1.ipynb @@ -0,0 +1,512 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:d9cb29be0932a6e1135cb07bf43a7e4c55a006ff68a1efd4e530482a24833ad9"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Chapter09:Sheet Pile Walls"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex9.1:Pg-419"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#example 9.1\n",
+ "\n",
+ "import math\n",
+ "from scipy.optimize import fsolve\n",
+ "sall=30;#sigma allowed\n",
+ "pi=math.pi;\n",
+ "zbar=12.1; # in ft\n",
+ "L1=10.0; # in ft\n",
+ "L2=20.0; #in ft\n",
+ "Gamma=0.12; # in lb/ft^3\n",
+ "Gamma1=0.1294-0.0624; # in lb/ft^3\n",
+ "phi=40*pi/180; # angle given\n",
+ "Ka=(math.tan(pi/4-phi/2))**2;\n",
+ "Kp=(math.tan(pi/4+phi/2))**2;\n",
+ "s1=Gamma*L1*Ka;#sigma1 in Kip/ft\n",
+ "s2=Gamma*L1*Ka+Gamma1*L2*Ka;#sigma2 in Kip/ft\n",
+ "L3=s2/(Gamma1*(Kp-Ka)); # in ft\n",
+ "print round(L3,2),\"is length in ft\"\n",
+ "P=1/2.0*s1*L1+s1*L2+1/2.0*(s2-s1)*L2+1/2.0*s2*L3;# in Kip/ft\n",
+ "print round(P,2),\" is force in kip/ft\"\n",
+ "s5=Gamma*L1*Kp+Gamma1*L2*Kp+Gamma*L3*(Kp-Ka);#sigma5 in Kip/ft\n",
+ "print round(s5,2),\" is pressure in kip/ft\"\n",
+ "A1=s5/(Gamma1*(Kp-Ka)); # in ft^2\n",
+ "A2=8.0*P/(Gamma1*(Kp-Ka)) # in ft^2\n",
+ "A3=6.0*P*(2.0*zbar*(Gamma1*(Kp-Ka))+s5)/(Gamma1*(Kp-Ka))**2.0 # in ft^2\n",
+ "A4=P*(6.0*zbar*s5+4.0*P)/(Gamma1*(Kp-Ka))**2.0 # in ft^2\n",
+ "print \"A1,A2,A3,A4 respectively is \",round(A1,1),round(A2,2),round(A3,2),round(A4,2)\n",
+ "print \"slight error due to rounding off error\"\n",
+ "#part(b)\n",
+ "def f(x):\n",
+ " return x**4+41.7*x**3-270.5*x**2-13363*x-106863\n",
+ "[x]=fsolve(f,20);\n",
+ "D=1.88+x;\n",
+ "print round(D,2),\" is value of D, in ft\"\n",
+ "TL=L1+L2+1.3*D;\n",
+ "print round(TL,2),\" is total length in ft\"\n",
+ "#partc\n",
+ "z=math.sqrt(2*P/(Gamma1*(Kp-Ka)));#zdash\n",
+ "Mmax=P*(z+zbar)-1/2.0*(Gamma1*(Kp-Ka))*z**2*z/3.0;\n",
+ "S=Mmax*12/sall;\n",
+ "print round(S,2),\"is section modulus in in^3/ft\"\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": [
+ "1.88 is length in ft\n",
+ "9.96 is force in kip/ft\n",
+ "12.67 is pressure in kip/ft\n",
+ "A1,A2,A3,A4 respectively is 43.2 271.33 13708.16 110880.89\n",
+ "slight error due to rounding off error\n",
+ "21.68 is value of D, in ft\n",
+ "58.19 is total length in ft\n",
+ "70.06 is section modulus in in^3/ft\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex9.2:Pg-426"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#example 9.2\n",
+ "import math\n",
+ "from scipy.optimize import fsolve\n",
+ "sall=172.5*1000;#sigma allowed in KN/m^2\n",
+ "pi=math.pi;\n",
+ "c=47.0; # in KN/m^2\n",
+ "zbar=1.78; # in m\n",
+ "L1=2.0; #in m\n",
+ "L2=3.0; # in m\n",
+ "Gamma=15.9; # in KN/m^3\n",
+ "Gamma1=19.33-9.81; # in KN/m^3\n",
+ "phi=32*pi/180;\n",
+ "Ka=(math.tan(pi/4-phi/2))**2;\n",
+ "Kp=(math.tan(pi/4+phi/2))**2;\n",
+ "s1=Gamma*L1*Ka;#sigma1 in KN/m^2\n",
+ "s2=Gamma*L1*Ka+Gamma1*L2*Ka;#sigma2 in KN/m^2\n",
+ "P=1/2.0*s1*L1+s1*L2+1/2.0*(s2-s1)*L2; # in kN/ft\n",
+ "print round(P,2),\" is force in kN/m\"\n",
+ "def f(x):\n",
+ " return 127.4*x**2-104.4*x-357.15\n",
+ "[x]=fsolve(f,2);\n",
+ "D=x;\n",
+ "print round(D,2),\" is value of D in m\"\n",
+ "print round(D*1.5,2),\"actual D in m\"\n",
+ "L4=D*(4*c-(Gamma*L1+Gamma1*L2)-P/D)/4/c;\n",
+ "print round(L4,2),\" is length in m\"\n",
+ "s6=4*c-(Gamma*L1+Gamma1*L2);#sigma6 in KN/m^2\n",
+ "s7=4*c+(Gamma*L1+Gamma1*L2);#sigma7 in KN/m^2\n",
+ "z=P/s6;#zdash\n",
+ "Mmax=P*(z+zbar)-1/2.0*s6*z**2; # in KN-m/m\n",
+ "S=Mmax*12.0/sall; # in m^3/m\n",
+ "print round(S,4),\" is section modulus in m**3/m\"\n",
+ "print \"is slight error due to rounding off error\"\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": [
+ "52.25 is force in kN/m\n",
+ "2.13 is value of D in m\n",
+ "3.2 actual D in m\n",
+ "1.17 is length in m\n",
+ "0.0072 is section modulus in m**3/m\n",
+ "is slight error due to rounding off error\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex9.3:Pg-433"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#example 9.3\n",
+ "import math\n",
+ "from scipy.optimize import fsolve\n",
+ "\n",
+ "pi=math.pi;\n",
+ "zbar=2.23; # in m\n",
+ "L1=2.0; # in m\n",
+ "L2=3.0; # in m\n",
+ "Gamma=15.9; # in KN/m^3\n",
+ "Gamma1=19.33-9.81; # in KN/m^3\n",
+ "phi=32*pi/180;\n",
+ "Ka=(math.tan(pi/4-phi/2))**2;\n",
+ "Kp=(math.tan(pi/4+phi/2))**2;\n",
+ "s1=Gamma*L1*Ka;#sigma1 in KN/m^2\n",
+ "s2=Gamma*L1*Ka+Gamma1*L2*Ka;#sigma2 in KN/m^2\n",
+ "L3=s2/(Gamma1*(Kp-Ka)); # in m\n",
+ "print round(L3,2),\"length in m\"\n",
+ "P=1/2.0*s1*L1+s1*L2+1/2.0*(s2-s1)*L2+1/2.0*s2*L3;\n",
+ "print round(P,2),\"force in kN/m\"\n",
+ "def f(x):\n",
+ " return x**3+6.99*x**2-14.55\n",
+ "[x]=fsolve(f,1.4);\n",
+ "D=L3+x;\n",
+ "print round(D,2),\"value of D in m\"\n",
+ "AL=1.4*D;\n",
+ "print round(AL,2),\"actual length in m\"\n",
+ "#partb\n",
+ "L4=1.4;\n",
+ "F=P-1/2.0*(Gamma1*(Kp-Ka)*L4**2);\n",
+ "print round(F,2),\"anchor force in kN/m\"\n",
+ "#partc\n",
+ "def f(x):\n",
+ " return x**2+6.682*x-14.44\n",
+ "[x]=fsolve(f,1.7);\n",
+ "z=x+2;\n",
+ "Mmax=-1/2.0*s1*L1*(x+2/3.0)+F*(x+1)-s1*x*x/2-1/2.0*Ka*Gamma1*x**3/3.0;\n",
+ "print round(Mmax,2),\" is maximum moment in kN-m/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": [
+ "0.66 length in m\n",
+ "58.38 force in kN/m\n",
+ "1.98 value of D in m\n",
+ "2.78 actual length in m\n",
+ "30.88 anchor force in kN/m\n",
+ "43.74 is maximum moment in kN-m/m\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex9.4:Pg-439"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#example 9.4\n",
+ "\n",
+ "Gamma=15.9; # in KN/m^3\n",
+ "Gamma1=19.33-9.81; # in KN/m^3\n",
+ "GD=0.23; # from fig. 9.16\n",
+ "CDL1=1.172; # from fig. 9.19\n",
+ "L1=2; # in m\n",
+ "L2=3; # in m\n",
+ "Dth=(L1+L2)*GD*CDL1;\n",
+ "print round(Dth,2),\"theoritical depth in m\"\n",
+ "Dac=1.4*Dth;\n",
+ "print round(Dac,2),\"actual depth in m\"\n",
+ "print \"approximate it as 2 m\"\n",
+ "#part(b)\n",
+ "CFL1=1.073;\n",
+ "GF=0.07;\n",
+ "Gammaa=(Gamma*L1**2+Gamma1*L2**2+2*Gamma*L1*L2)/(L1+L2)**2; # in KN/m^3\n",
+ "F=Gammaa*(L1+L2)**2*GF*CFL1; # in KN/m\n",
+ "print round(F,2),\"force in kN/m\"\n",
+ "#part(c)\n",
+ "GM=0.021; # from fig. 9.18\n",
+ "CML1=1.036; # from fig. 9.21\n",
+ "Mmax=Gammaa*(L1+L2)**3*GM*CML1; # in kN-m/m\n",
+ "print round(Mmax,2),\"maximum moment in kN-m/m\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "1.35 theoritical depth in m\n",
+ "1.89 actual depth in m\n",
+ "approximate it as 2 m\n",
+ "25.54 force in kN/m\n",
+ "36.99 maximum moment in kN-m/m\n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex9.5:Pg-442"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#example 9.5\n",
+ "import math\n",
+ "import matplotlib.pyplot as plt\n",
+ "import numpy\n",
+ "Mmax=43.72; # in kN-m/m\n",
+ "sp=[\"PSA-31\",\"PSA-23\"];#sheet pile\n",
+ "H=[7.9,7.9] # in m\n",
+ "I=[4.41e-6,5.63e-6]; # in m^4/m\n",
+ "p=[0.00466,0.00365];\n",
+ "S=[10.8e-5,12.8e-5]; # in m^3/m\n",
+ "Md=[18.63,22.08]; # kn-m/m\n",
+ "Logp=numpy.zeros(2)\n",
+ "k=numpy.zeros(2)\n",
+ "print \"SheetPile I(m**4/m) H(m) p\\t Logp S(m**3/m) Md(kN-m/m) Md/Mmax \\n\"\n",
+ "for i in range(0,2):\n",
+ " Logp[i]=math.log10(p[i]);\n",
+ " k[i]=Md[i]/Mmax;\n",
+ " print sp[i],\"\\t \",I[i],\" \",H[i],\" \",p[i],\" \",round(Logp[i],2),\" \",S[i],\" \",Md[i],\"\\t \",round(k[i],3)\n",
+ " \n",
+ "\n",
+ "plt.plot(Logp,k);\n",
+ "plt.title(\"Ex9.5\")\n",
+ "plt.xlabel(\"LogP\")\n",
+ "plt.ylabel(\"Md/Mmax\")\n",
+ "plt.show()\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "SheetPile I(m**4/m) H(m) p\t Logp S(m**3/m) Md(kN-m/m) Md/Mmax \n",
+ "\n",
+ "PSA-31 \t 4.41e-06 7.9 0.00466 -2.33 0.000108 18.63 \t 0.426\n",
+ "PSA-23 \t 5.63e-06 7.9 0.00365 -2.44 0.000128 22.08 \t 0.505\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex9.6:Pg-445"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#example 9.6\n",
+ "\n",
+ "import math\n",
+ "from scipy.optimize import fsolve\n",
+ "\n",
+ "pi=math.pi;\n",
+ "R=0.6;\n",
+ "L1=10.0; # in ft\n",
+ "L2=20.0; #in ft\n",
+ "Gammasat=122.4; # in lb/ft^3\n",
+ "l1=5; # in ft\n",
+ "Gamma=110.0; # in lb/ft^3\n",
+ "C=0.68;\n",
+ "L=L1+L2; # in ft\n",
+ "Gammaw=62.4; # in lb/ft^3\n",
+ "Gamma1=Gammasat-Gammaw;#gammadash in lb/ft^3\n",
+ "Gammaav=(Gamma*L1+Gamma1*L2)/(L1+L2); # in lb/ft^3\n",
+ "phi=35.0*pi/180;\n",
+ "Ka=(math.tan(pi/4-phi/2))**2;\n",
+ "sa=C*Ka*Gammaav*L;#sigmaa in lb/ft^2\n",
+ "sp=R*sa;#sigmap # in lb/ft^2\n",
+ "def f(x):\n",
+ " return x**2+50*x-1000\n",
+ "[x]=fsolve(f,15);\n",
+ "D=x;#in ft\n",
+ "print round(D,2),\" is depth in ft\"\n",
+ "R=L/D*(L-2*l1)/(2*L+D-2*l1);\n",
+ "print \"value of R=\",round(R,2),\" is OK\\n\"\n",
+ "#partb\n",
+ "F=sa*(L-R*D); # in lb/ft\n",
+ "print round(F,2),\" is Force in lb/ft\"\n",
+ "#partc\n",
+ "Mmax=0.5*sa*L**2*((1-R*D/L)**2-(2*l1/L)*(1-R*D/L)); # in lb-ft/ft\n",
+ "print round(Mmax,2),\"maximum moment lb-ft/ft\"\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": [
+ "15.31 is depth in ft\n",
+ "value of R= 0.6 is OK\n",
+ "\n",
+ "8821.24 is Force in lb/ft\n",
+ "47693.02 maximum moment lb-ft/ft\n"
+ ]
+ }
+ ],
+ "prompt_number": 31
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex9.7:Pg-451"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#example 9.7\n",
+ "import math\n",
+ "from scipy.optimize import fsolve\n",
+ "\n",
+ "pi=math.pi;\n",
+ "zbar=3.2; # in m\n",
+ "c=41; # in KN/m^2\n",
+ "L1=3; # in m\n",
+ "L2=6; # in m\n",
+ "Gamma=17;# in KN/m^3\n",
+ "Gamma1=20-9.81; # in KN/m^3\n",
+ "phi=35*pi/180;\n",
+ "Ka=(math.tan(pi/4-phi/2))**2;\n",
+ "Kp=(math.tan(pi/4+phi/2))**2;\n",
+ "s1=Gamma*L1*Ka;#sigma1 in kN/m**2\n",
+ "s2=Gamma*L1*Ka+Gamma1*L2*Ka;#sigma2 in kN/m**2\n",
+ "P=1/2.0*s1*L1+s1*L2+1/2.0*(s2-s1)*L2;\n",
+ "print round(P,2),\"Force in kN/m\"\n",
+ "s6=4*c-(Gamma*L1+Gamma1*L2);#sigma6 in kN/m**2\n",
+ "print round(s6,2),\"pressure in kN/m**2\"\n",
+ "def f(x):\n",
+ " return x**2+15*x-25.43\n",
+ "[x]=fsolve(f,1.6);\n",
+ "D=x; # in m\n",
+ "print round(D,1),\"depth in m\"\n",
+ "F=P-s6*D; # in kN/m\n",
+ "print round(F,2),\"force in kN/m\"\n",
+ "print \"slight error due to rounding off\"\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "153.36 Force in kN/m\n",
+ "51.86 pressure in kN/m**2\n",
+ "1.5 depth in m\n",
+ "73.61 force in kN/m\n",
+ "slight error due to rounding off\n"
+ ]
+ }
+ ],
+ "prompt_number": 35
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#example 9.8\n",
+ "import math\n",
+ "pi=math.pi;\n",
+ "Gamma=105.0; # in lb/ft^3\n",
+ "Cov=14.0;\n",
+ "B=15/12.0; # in inch\n",
+ "Ka=0.26;\n",
+ "phi=35.0*pi/180; # given angle in degree\n",
+ "H=37.5/12; # in inch\n",
+ "h=15/12.0; # in inch\n",
+ "t=6/12.0; # in inch\n",
+ "Gc=150.0;#gamma concrete in lb/ft^3\n",
+ "W=H*t*Gc; # in lb/ft\n",
+ "k=4.5;#kp*cos(delta)\n",
+ "Pu=1/2.0*Gamma*H**2*(k-Ka*math.cos(phi)); # in lb/ft\n",
+ "print round(Pu,2),\"force in lb/ft\"\n",
+ "Pus=((Cov+1)/(Cov+H/h))*Pu; # in lb/ft\n",
+ "print round(Pus,2),\"force in lb/ft\"\n",
+ "Be=0.227*(H+h)+B;\n",
+ "Pu=Pus*Be; # in lb/ft\n",
+ "print round(Pu,2),\" is resistance of anchor plate in lb/ft\"\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": [
+ "2197.94 force in lb/ft\n",
+ "1998.12 force in lb/ft\n",
+ "4482.04 is resistance of anchor plate in lb/ft\n"
+ ]
+ }
+ ],
+ "prompt_number": 37
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
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