diff options
Diffstat (limited to 'Principles_Of_Foundation_Engineering/Chapter08.ipynb')
| -rwxr-xr-x | Principles_Of_Foundation_Engineering/Chapter08.ipynb | 527 |
1 files changed, 527 insertions, 0 deletions
diff --git a/Principles_Of_Foundation_Engineering/Chapter08.ipynb b/Principles_Of_Foundation_Engineering/Chapter08.ipynb new file mode 100755 index 00000000..de2367cd --- /dev/null +++ b/Principles_Of_Foundation_Engineering/Chapter08.ipynb @@ -0,0 +1,527 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:ae926d3fc40f9f56d82ee333a9b5a7f719ff4a11c08f89381773660beb02ead3"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter08: Retaining walls"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex8.1:Pg-366"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#example 8.1\n",
+ "\n",
+ "import math\n",
+ "import numpy\n",
+ "H1=6*math.tan(10*math.pi/180.0); # in ft\n",
+ "H2=18.0; # in ft\n",
+ "H3=2.75; # in ft\n",
+ "Gamma1=117.0; # in lb/ft^3\n",
+ "Ka=0.294;#from table 7.1\n",
+ "H=H1+H2+H3; # in ft\n",
+ "Pa=1/2.0*Gamma1*H**2*Ka/1000; # in Kip/ft\n",
+ "Pr=Pa*math.sin(10*math.pi/180); # in Kip/ft\n",
+ "Ph=Pa*math.cos(10*math.pi/180); # in Kip/ft\n",
+ "Mo=Ph*H/3.0; # in Kip-ft/ft\n",
+ "Sum=0;#sigma Mr\n",
+ "S=[1, 2, 3, 4, 5];#section\n",
+ "W=[4.05, 1.35, 5.156, 13.01, 1.42];#weight\n",
+ "MA=[5.75, 4.67, 6.25, 9.5, 12.5, 12.5];#Moment Arm\n",
+ "M=numpy.zeros(5)\n",
+ "print \"Section Weight(kip/ft) Moment Arm(ft) Moment (kip-ft/ft)\\n\"\n",
+ "for i in range(0,5):\n",
+ " M[i]=W[i]*MA[i];\n",
+ " Sum=Sum+M[i];\n",
+ " print round(S[i],2),\"\\t \\t \",round(W[i],2),\"\\t \\t \\t\",round(MA[i],2),\"\\t \\t \\t \",round(M[i],2),\"\\n\"\n",
+ "\n",
+ "FSO=Sum/Mo;\n",
+ "if FSO>2 :\n",
+ " print \"safe in overturning with FS=\",round(FSO,2),\"\\n\"\n",
+ "\n",
+ "#for sliding\n",
+ "phi2=18*math.pi/180; # the given angle\n",
+ "V=24.986;\n",
+ "B=12.5;\n",
+ "c2=0.9; # in lb/ft^2\n",
+ "FSS=(V*math.tan(2/3.0*phi2)+B*2/3.0*c2)/Ph;\n",
+ "if FSS>2 :\n",
+ " print \"safe in sliding with FS=\",round(FSS,2),\"\\n\"\n",
+ "\n",
+ "#for bearing\n",
+ "e=B/2.0-(Sum-Mo)/V;\n",
+ "qtoe=V/B*(1+6*e/B); # in Kip/ft^2\n",
+ "Nc=13.1;\n",
+ "Nq=5.26;\n",
+ "Ny=4.07;\n",
+ "D=0.107;\n",
+ "Gamma2=4.0; # in lb/ft^3\n",
+ "B1=B-2*e;#Bdash\n",
+ "q=Gamma2*D # in lb/ft^2\n",
+ "Fcd=1+0.4*D/B1;\n",
+ "Fqd=1+2*math.tan(phi2)*(1-math.sin(phi2))**2*(D/B1);\n",
+ "Fyd=1;\n",
+ "zi=math.tan(Ph/V);\n",
+ "Fci=(1-zi/math.pi*2)**2;\n",
+ "Fqi=Fci;\n",
+ "Fyi=round((1-zi/phi2)**2);\n",
+ "qu=c2*Nc*Fcd*Fci+q*Nq*Fqd*Fqi+1/2.0*Gamma2*B1*Fyd*Fyi;\n",
+ "FSB=qu/qtoe;\n",
+ "if FSB>3 :\n",
+ " print \"bearing is safe with FS=\",round(FSB),\"\\n\\n\"\n",
+ " print \"slight changes due to round off error\"\n",
+ "\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Section Weight(kip/ft) Moment Arm(ft) Moment (kip-ft/ft)\n",
+ "\n",
+ "1.0 \t \t 4.05 \t \t \t5.75 \t \t \t 23.29 \n",
+ "\n",
+ "2.0 \t \t 1.35 \t \t \t4.67 \t \t \t 6.3 \n",
+ "\n",
+ "3.0 \t \t 5.16 \t \t \t6.25 \t \t \t 32.23 \n",
+ "\n",
+ "4.0 \t \t 13.01 \t \t \t9.5 \t \t \t 123.59 \n",
+ "\n",
+ "5.0 \t \t 1.42 \t \t \t12.5 \t \t \t 17.75 \n",
+ "\n",
+ "safe in overturning with FS= 3.47 \n",
+ "\n",
+ "bearing is safe with FS= 4.0 \n",
+ "\n",
+ "\n",
+ "slight changes due to round off error\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex8.2:Pg-369"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#example 8.2\n",
+ "\n",
+ "c=0.9; # # in lb/ft^2\n",
+ "B=12.5; # in ft\n",
+ "Gamma2=4; # in lb/ft^3\n",
+ "Fcd=1.138;\n",
+ "Fqd=1.107; \n",
+ "Nc=7.5;\n",
+ "Nq=4;\n",
+ "Ny=0;\n",
+ "q=0.428; # in lb/ft^2\n",
+ "qtoe=2.44; # in lb/ft^2\n",
+ "qu=c*Nc*Fcd+q*Nq*Fqd+1/2.0*Gamma2*B*Ny;\n",
+ "FSB=qu/qtoe; # factor of safety\n",
+ "if FSB>3.0 :\n",
+ " print \"safe in bearing with FS=\",round(FSB,2),\"\\n\\n\",\n",
+ "\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "safe in bearing with FS= 3.92 \n",
+ "\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex8.3:Pg-370"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#example 8.3\n",
+ "import math\n",
+ "import numpy\n",
+ "Msum=0;#sum of moment\n",
+ "Vsum=0;#sum of force\n",
+ "H=15+2.5;#Hdash in ft\n",
+ "phi=30*math.pi/180; # given angle in degree\n",
+ "Gamma=121.0; # in lb/ft^3\n",
+ "Ka=(math.tan(math.pi/4-phi/2))**2;\n",
+ "Pa=1/2.0*Gamma*H**2*Ka/1000; # in Kip/ft\n",
+ "Ph=Pa; # in Kip/ft\n",
+ "Mo=Ph*H/3.0; # in Kip-ft/ft\n",
+ "AN=[1.0,2.0,3.0,4.0,5.0,6.0];#area number\n",
+ "W=[0.9,3.375,5.906,3.863,4.764,2.723];#weight\n",
+ "MA=[1.783,2.8,5.3,5.15,7.05,9.55];#moment arm\n",
+ "\n",
+ "print \"AreaNo \\t Weight(kip/ft) \\t Moment Arm(ft) \\t Moment (kip-ft/ft)\\n\"\n",
+ "M= numpy.zeros(6)\n",
+ "for i in range(0,6):\n",
+ " M[i]=W[i]*MA[i];\n",
+ " Vsum=Vsum+W[i];\n",
+ " Msum=Msum+M[i];\n",
+ " print round(AN[i],2),\"\\t\\t \",round(W[i],2),\"\\t \\t \\t \",MA[i],\"\\t \\t \\t \",M[i],\"\\n\"\n",
+ "\n",
+ "FSO=(Msum)/Mo;\n",
+ "if FSO>2 :\n",
+ " print \"safe in overturning with FS=\",round(FSO,2)\n",
+ "\n",
+ "#for sliding\n",
+ "phi2=20*math.pi/180;\n",
+ "V=Vsum\n",
+ "B=10.3; # in ft\n",
+ "c2=1.0; # in lb/ft^2\n",
+ "FSS=(V*math.tan(2/3.0*phi2)+B*2/3.0*c2)/Ph;\n",
+ "print \"safe in sliding with FS=\",round(FSS,2),\"\\n\"\n",
+ "e=B/2.0-(Msum-Mo)/V;\n",
+ "qtoe=V/B*(1+6*e/B); # in kip/ft**2\n",
+ "print round(qtoe,2),\" is soil pressure at toe in kip/ft**2\"\n",
+ "qheel=V/B*(1-6*e/B); # in kip/ft**2\n",
+ "print round(qheel,2),\" is soil pressure at heel in kip/ft**2\"\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "AreaNo \t Weight(kip/ft) \t Moment Arm(ft) \t Moment (kip-ft/ft)\n",
+ "\n",
+ "1.0 \t\t 0.9 \t \t \t 1.783 \t \t \t 1.6047 \n",
+ "\n",
+ "2.0 \t\t 3.38 \t \t \t 2.8 \t \t \t 9.45 \n",
+ "\n",
+ "3.0 \t\t 5.91 \t \t \t 5.3 \t \t \t 31.3018 \n",
+ "\n",
+ "4.0 \t\t 3.86 \t \t \t 5.15 \t \t \t 19.89445 \n",
+ "\n",
+ "5.0 \t\t 4.76 \t \t \t 7.05 \t \t \t 33.5862 \n",
+ "\n",
+ "6.0 \t\t 2.72 \t \t \t 9.55 \t \t \t 26.00465 \n",
+ "\n",
+ "safe in overturning with FS= 3.38\n",
+ "safe in sliding with FS= 1.94 \n",
+ "\n",
+ "3.51 is soil pressure at toe in kip/ft**2\n",
+ "0.67 is soil pressure at heel in kip/ft**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 33
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex8.4:Pg-372"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#example 8.4\n",
+ "\n",
+ "import math\n",
+ "import numpy\n",
+ "Msum=0;#sum of moment\n",
+ "Vsum=0;#sum of force\n",
+ "H=5+1.5;#Hdash in m\n",
+ "phi=32*math.pi/180 # angle in degree\n",
+ "Gamma=18.5; # in KN/m^3\n",
+ "Ka=0.424;\n",
+ "Pa=1/2.0*Gamma*H**2*Ka; # in KN/m\n",
+ "Ph=Pa*math.cos(15*math.pi/180+2/3.0*phi); # in KN/m\n",
+ "Mo=Ph*H/3.0; # moment\n",
+ "AN=[1,2,3,4,5];#area number\n",
+ "A=[4.36, 3.42, 0.77, 2.8, 2.8];#area\n",
+ "W=[102.81, 80.64, 18.16, 66.02, 93.14];#weight\n",
+ "MA=[2.18, 1.37, 0.98, 1.75, 2.83];#moment arm\n",
+ "print \"AreaNo \\t Area(m**2) \\t Weight(kN/m) \\t Moment Arm(m) \\t Moment (kN-m/m)\\n\"\n",
+ "M= numpy.zeros(5)\n",
+ "for i in range(0,5):\n",
+ " M[i]=W[i]*MA[i];\n",
+ " Vsum=Vsum+W[i];\n",
+ " Msum=Msum+M[i];\n",
+ " print round(AN[i],2),\"\\t\\t \",round(A[i],2),\" \\t \\t\",round(W[i],2),\"\\t \\t \\t \",MA[i],\"\\t \\t \\t \",M[i],\"\\n\"\n",
+ "\n",
+ "FSO=Msum/Mo;\n",
+ "if FSO>2 :\n",
+ " print \"safe in overturning with FS=\",round(FSO,2),\"\\n\"\n",
+ "\n",
+ "#for sliding\n",
+ "phi2=24*math.pi/180;\n",
+ "V=Vsum\n",
+ "B=3.5; # in m\n",
+ "c2=30; # in KN/m^2\n",
+ "Pp=1/2.0*2.37*18*1.5**2+2*30*1.54*1.5;\n",
+ "FSS=(V*math.tan(2/3.0*phi2)+B*2/3.0*c2+Pp)/Ph;\n",
+ "print \"safe in sliding with FS=\",round(FSS,2),\"\\n\"\n",
+ "print \"if Pp is ignored then FS=1.37\"\n",
+ "e=B/2.0-(Msum-Mo)/V;\n",
+ "qtoe=V/B*(1+6*e/B); # in kN/m**2\n",
+ "print round(qtoe,2),\"soil pressure at toe in kN/m**2\"\n",
+ "qheel=V/B*(1-6*e/B); # in kN/m**2\n",
+ "print round(qheel,2),\"soil pressure at heel in kN/m**2\"\n",
+ "print \"there is difference in answer due to rounding off error\"\n",
+ "\n",
+ "# there is difference in answer due to rounding off error\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "AreaNo \t Area(m**2) \t Weight(kN/m) \t Moment Arm(m) \t Moment (kN-m/m)\n",
+ "\n",
+ "1.0 \t\t 4.36 \t \t102.81 \t \t \t 2.18 \t \t \t 224.1258 \n",
+ "\n",
+ "2.0 \t\t 3.42 \t \t80.64 \t \t \t 1.37 \t \t \t 110.4768 \n",
+ "\n",
+ "3.0 \t\t 0.77 \t \t18.16 \t \t \t 0.98 \t \t \t 17.7968 \n",
+ "\n",
+ "4.0 \t\t 2.8 \t \t66.02 \t \t \t 1.75 \t \t \t 115.535 \n",
+ "\n",
+ "5.0 \t\t 2.8 \t \t93.14 \t \t \t 2.83 \t \t \t 263.5862 \n",
+ "\n",
+ "safe in overturning with FS= 2.53 \n",
+ "\n",
+ "safe in sliding with FS= 2.7 \n",
+ "\n",
+ "if Pp is ignored then FS=1.37\n",
+ "195.67 soil pressure at toe in kN/m**2\n",
+ "10.48 soil pressure at heel in kN/m**2\n",
+ "there is difference in answer due to rounding off error\n"
+ ]
+ }
+ ],
+ "prompt_number": 49
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex8.6:Pg-393"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#example 8.6\n",
+ "import math\n",
+ "Sv=2; # in ft\n",
+ "Sh=3; # in ft\n",
+ "w=3/12.0; # in inch\n",
+ "fy=35000*144;\n",
+ "FSb=3;\n",
+ "pi=math.pi;\n",
+ "phi=36*pi/180;\n",
+ "Gamma1=105; # in lb/ft^3\n",
+ "H=30;\n",
+ "t=Gamma1*H*Sv*Sh*FSb/w/fy*(math.tan(pi/4-phi/2))**2;\n",
+ "t=t*12; #in inch\n",
+ "print round(t,2),\" is thickness in inches\"\n",
+ "t=t+0.001*50;\n",
+ "print \"so take thickness=0.2 inches\"\n",
+ "#for tie length\n",
+ "z=[5,10,15,20,25,30];\n",
+ "TL=[38.45, 35.89, 33.34, 30.79, 28.25, 25.7];#tie length\n",
+ "print \"z(ft)\\t Tie Length (ft)\\n\"\n",
+ "for i in range(0,6):\n",
+ " print z[i],\"\\t\",TL[i]\n",
+ "\n",
+ "print \"use tie length=40ft\"\n",
+ "#check for over turning\n",
+ "\n",
+ "z=30/3.0;\n",
+ "x1=20;\n",
+ "L=40;\n",
+ "Ka=0.26;\n",
+ "Pa=1/2.0*Gamma1*Ka*H**2; # in kip/ft**2\n",
+ "W1=Gamma1*H*L;\n",
+ "FSO=W1*x1/(Pa*z);\n",
+ "print round(FSO,2),\" is factor of safety is\" \n",
+ "print \"since FS>3 structure is safe\"\n",
+ "#check for sliding\n",
+ "k=2/3.0;\n",
+ "Pa=12285; # in kip/ft**2\n",
+ "FSS=W1*math.tan(k*phi)/Pa;\n",
+ "if FSS>3 :\n",
+ " print \"safe in sliding with FS=\",round(FSS,2)\n",
+ "\n",
+ "#check for bearing\n",
+ "Mr=126000*20; # in lb-ft/ft\n",
+ "Mo=12285*10; # in lb-ft/ft\n",
+ "V=126000;\n",
+ "e=L/2-Mr/V+Mo/V;\n",
+ "L1=L-2*e;#Ldash\n",
+ "c2=1000; # in lb/ft^2\n",
+ "Nc=25.8;\n",
+ "Gamma2=110; # in lb/ft^3\n",
+ "Ny=16.72;\n",
+ "qult=c2*Nc+1/2.0*Gamma2*L1*Ny\n",
+ "sigma0=Gamma1*H; # in lb/ft^2\n",
+ "FSB=qult/sigma0;\n",
+ "if FSB>5 :\n",
+ " print \"bearing is safe with FS=\",round(FSB,2)\n",
+ "\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "0.14 is thickness in inches\n",
+ "so take thickness=0.2 inches\n",
+ "z(ft)\t Tie Length (ft)\n",
+ "\n",
+ "5 \t38.45\n",
+ "10 \t35.89\n",
+ "15 \t33.34\n",
+ "20 \t30.79\n",
+ "25 \t28.25\n",
+ "30 \t25.7\n",
+ "use tie length=40ft\n",
+ "20.51 is factor of safety is\n",
+ "since FS>3 structure is safe\n",
+ "safe in sliding with FS= 4.57\n",
+ "safe in bearing with FS= 19.87\n"
+ ]
+ }
+ ],
+ "prompt_number": 56
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex8.7:Pg-397"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#example 8.7\n",
+ "import math\n",
+ "import numpy\n",
+ "pi=math.pi;\n",
+ "phi=36.0*pi/180;\n",
+ "Ka=(math.tan(pi/4-phi/2))**2;\n",
+ "z=[8.0, 12.0, 16.0]; # in ft\n",
+ "sigmaG=80*12.0; # in lb/ft^2\n",
+ "Gamma1=110.0; # in lb/ft^3\n",
+ "FS=1.5;\n",
+ "Sv=numpy.zeros(3)\n",
+ "for i in range(0,3):\n",
+ " Sv[i]=sigmaG/Gamma1/z[i]/Ka/FS*12.0;\n",
+ " print \"for z=\",z[i],\" ft Sv = \",round(Sv[i],2),\" inches\\n\"\n",
+ "\n",
+ "z=[16.0,56.0,76.0,96.0,112.0,144.0,176.0];\n",
+ "zf=numpy.zeros(7)\n",
+ "k2=numpy.zeros(7)\n",
+ "L=numpy.zeros(7)\n",
+ "for i in range(0,7):\n",
+ " zf[i]=z[i]/12.0;#z in ft\n",
+ "Sv=[1.67,1.67,1.67,1.67,1.33,1.33,1.33];\n",
+ "k=[7.48,5.78,4.93,4.08,3.4,2.04,0.68];#0.51(H-z)\n",
+ "print \"z(in) z(ft) Sv(ft) 0.51(H-z)(ft) 0.438Sv(ft) L(ft) \\n\"\n",
+ "for i in range(0,7):\n",
+ " k2[i]=0.438*Sv[i];#0.438Sv\n",
+ " L[i]=k[i]+k2[i];\n",
+ " print round(z[i],2),\"\\t \\t\",round(zf[i],2),\"\\t \",round(Sv[i],2),\"\\t \\t \",round(k[i],2),\"\\t \\t \\t\",round(k2[i],2),\"\\t \\t \\t \",round(L[i],2)\n",
+ "\n",
+ "Sv=20/12.0;\n",
+ "Ka=0.26;\n",
+ "FS=1.5;\n",
+ "l1=Sv*Ka*FS/4/math.tan(2/3.0*phi);\n",
+ "if l1<3:\n",
+ " l1=3;\n",
+ " print l1,\"length in ft\"\n",
+ "\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "for z= 8.0 ft Sv = 33.62 inches\n",
+ "\n",
+ "for z= 12.0 ft Sv = 22.41 inches\n",
+ "\n",
+ "for z= 16.0 ft Sv = 16.81 inches\n",
+ "\n",
+ "z(in) z(ft) Sv(ft) 0.51(H-z)(ft) 0.438Sv(ft) L(ft) \n",
+ "\n",
+ "16.0 \t \t1.33 \t 1.67 \t \t 7.48 \t \t \t0.73 \t \t \t 8.21\n",
+ "56.0 \t \t4.67 \t 1.67 \t \t 5.78 \t \t \t0.73 \t \t \t 6.51\n",
+ "76.0 \t \t6.33 \t 1.67 \t \t 4.93 \t \t \t0.73 \t \t \t 5.66\n",
+ "96.0 \t \t8.0 \t 1.67 \t \t 4.08 \t \t \t0.73 \t \t \t 4.81\n",
+ "112.0 \t \t9.33 \t 1.33 \t \t 3.4 \t \t \t0.58 \t \t \t 3.98\n",
+ "144.0 \t \t12.0 \t 1.33 \t \t 2.04 \t \t \t0.58 \t \t \t 2.62\n",
+ "176.0 \t \t14.67 \t 1.33 \t \t 0.68 \t \t \t0.58 \t \t \t 1.26\n",
+ "3 length in ft\n"
+ ]
+ }
+ ],
+ "prompt_number": 79
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |