{ "metadata": { "name": "", "signature": "sha256:6fa8fe978c728d97fa9f04464822ea9606521023bb2c2c301624274cfcebacb1" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 8 : GRAVITY DAMS" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.1 pg : 376" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "from scipy.integrate import quad \n", "\t\t\t\t\n", "#Given\n", "H = 100; \t\t\t\t#heigth of dam\n", "wb = 70; \t\t\t\t#width of base of dam\n", "wt = 7; \t\t\t\t#width of top of dam\n", "l = 1; \t\t\t\t#length of dam\n", "hw = 98; \t\t\t\t#heigth of water in dam\n", "hsu = 90; \t\t\t\t#heigth of slope on downstream side\n", "s = 1/0.7; \t\t\t\t#slope on downstream side\n", "gammad = 24; \t\t\t\t#unit weigth of dam\n", "gammaw = 9.81; \t\t\t\t#unit weigth of water\n", "E = 2.05e7; \t\t\t\t#modulus of elasticity\n", "\n", "\t\t\t\t#(a) inertial forces and moments\n", "alpha0 = 0.05; \t\t\t\t#from table 8.1\n", "alphah = 2*alpha0;\n", "\t\t\t\t#at 10m from top\n", "\n", "def f0(y): \n", "\t return 25.2-0.25*y\n", "\n", "F10 = quad(f0,0,10)[0]\n", "\n", "\n", "def f1(y): \n", "\t return 25.2*(1-0.01*y)*(10-y)\n", "\n", "M10 = quad(f1,0,10)[0]\n", "\n", "\t\t\t\t#at 100m below top\n", "\n", "def f2(y): \n", "\t return 0.15*(1-0.01*y)*16.8*y\n", "\n", "F100 = F10+ quad(f2,10,100)[0]\n", "\n", "\n", "def f3(y): \n", "\t return 0.15*(1-0.01*y)*16.8*y*(100-y)\n", "\n", "M100 = M10+90*F10+ quad(f3,10,100)[0]\n", "\n", "print \"Inertial forces:At 10m from top: F = %.2f kn;M = %ikn-mAt 100m from top: F = %.2f kn;M = %ikn-m.\"%(F10,M10,F100,M100);\n", "\n", "\t\t\t\t#(b) hydrodynamic pressure and moment\n", "\t\t\t\t#at 10m from top\n", "y = 8.;\n", "W10 = 1680.;\n", "alphah = F10/W10;\n", "Cm = 0.735;\n", "Cy = (Cm/2)*((y*(2-y/hw)/hw)+(y*(2-y/hw)/hw)**0.5);\n", "p = Cy*alphah*gammaw*hw;\n", "P10 = 0.726*p*y;\n", "Mp10 = 0.299*p*y**2;\n", "P10 = round(P10*100)/100;\n", "Mp10 = round(Mp10*100)/100;\n", "\t\t\t\t#at 100m from top\n", "y = 98;\n", "W100 = 84840;\n", "alphah = F100/W100;\n", "Cm = 0.735;\n", "Cy = (Cm/2)*(y*(2-y/hw)/hw+(y*(2-y/hw)/hw)**0.5);\n", "p = Cy*alphah*gammaw*hw;\n", "P100 = 0.726*p*y;\n", "Mp100 = 0.299*p*y**2;\n", "print \"Hydrodynamic forces:At 10m from top: F = %.2f kn;\\\n", "\\nM = %.2fkn-mAt 100m from top: F = %i kn;\\\n", "\\nM = %ikn-m.\"%(P10,Mp10,P100,Mp100);\n", "\n", "# rounding off error." ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Inertial forces:At 10m from top: F = 239.50 kn;M = 1218kn-mAt 100m from top: F = 4321.90 kn;M = 221790kn-m.\n", "Hydrodynamic forces:At 10m from top: F = 161.58 kn;\n", "M = 532.35kn-mAt 100m from top: F = 2561 kn;\n", "M = 103366kn-m.\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.2 pg : 378" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\t\t\t\t\n", "#Given\n", "H = 100; \t\t\t\t#heigth of dam\n", "wb = 70; \t\t\t\t#width of base of dam\n", "wt = 7; \t\t\t\t#width of top of dam\n", "l = 1; \t\t\t\t#length of dam\n", "hw = 98; \t\t\t\t#heigth of water in dam\n", "hsu = 90; \t\t\t\t#heigth of slope on downstream side\n", "s = 1/0.7; \t\t\t\t#slope on downstream side\n", "gammad = 24; \t\t\t\t#unit weigth of dam\n", "gammaw = 9.81; \t\t\t\t#unit weigth of water\n", "E = 2.05e7; \t\t\t\t#modulus of elasticity\n", "beta = 1;\n", "I = 2;\n", "Fo = 0.25; \t\t\t\t#from table 8.2\n", " \t\t\t\t#t = Sa/g;\n", "t = 0.19; \t\t\t\t#from fig. 8.4\n", "alphah = beta*I*Fo*t;\n", "T = 5.55*H**2/wb*(gammad/(gammaw*E))**0.5;\n", "\t\t\t\t#(a) Base shear\n", "W = l*gammad*(wt*H+((hsu/s)*hsu)/2);\n", "Fb = 0.6*W*alphah;\n", "print \"Base shear = %.2f KN.\"%(Fb);\n", "\n", "\t\t\t\t#(b) Base moment\n", "hbar = ((wt*H**2/2)+((hsu/s)*hsu**2/6))/((wt*H)+(hsu/s)*hsu/2);\n", "Mb = 0.9*W*hbar*alphah;\n", "print \"Base moment = %.2f KN-m.\"%(Mb);\n", "\n", "\t\t\t\t#(c) shear at 10m from top\n", "Cv = 0.08;\n", "F10 = Cv*Fb;\n", "F10 = round(F10);\n", "print \"shear at 10m from top = %.2f KN.\"%(F10);\n", "\n", "\t\t\t\t#(d) Moment at 10m from top\n", "Cm = 0.02;\n", "M10 = Cm*Mb;\n", "M10 = round(M10);\n", "print \"moment at 10m from top = %.2f KN.\"%(M10);\n", "\t\t\t\t#(e) Hydrodynamic pressure\n", "\t\t\t\t#at 10m from top\n", "y = 8;\n", "W10 = 1680;\n", "Cm = 0.735;\n", "Cy = (Cm/2)*((y*(2-y/hw)/hw)+(y*(2-y/hw)/hw)**0.5);\n", "p = Cy*alphah*gammaw*hw;\n", "P10 = 0.726*p*y;\n", "Mp10 = 0.299*p*y**2;\n", "P10 = round(P10*100)/100;\n", "Mp10 = round(Mp10*100)/100;\n", "\t\t\t\t#at 100m from top\n", "y = 98;\n", "W100 = 84840;\n", "Cm = 0.735;\n", "Cy = (Cm/2)*(y*(2-y/hw)/hw+(y*(2-y/hw)/hw)**0.5);\n", "p = Cy*alphah*gammaw*hw;\n", "P100 = 0.726*p*y;\n", "Mp100 = 0.299*p*y**2;\n", "print \"Hydrodynamic forces:At 10m from top: F = %.2f kn;\\\n", "\\nM = %.2fkn-mAt 100m from top: F = %i \\\n", "kn;M = %ikn-m.\"%(P10,Mp10,P100,Mp100);\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Base shear = 4835.88 KN.\n", "Base moment = 246342.60 KN-m.\n", "shear at 10m from top = 387.00 KN.\n", "moment at 10m from top = 4927.00 KN.\n", "Hydrodynamic forces:At 10m from top: F = 0.00 kn;\n", "M = 0.00kn-mAt 100m from top: F = 4776 kn;M = 192765kn-m.\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.3 pg : 379" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "from scipy.integrate import quad \n", "\n", "\n", "\t\t\t\t\n", "#Given\n", "H = 100; \t\t\t\t#heigth of dam\n", "wb = 70; \t\t\t\t#width of base of dam\n", "wt = 7; \t\t\t\t#width of top of dam\n", "l = 1; \t\t\t\t#length of dam\n", "hw = 98; \t\t\t\t#heigth of water in dam\n", "hsu = 90; \t\t\t\t#heigth of slope on downstream side\n", "s = 1/0.7; \t\t\t\t#slope on downstream side\n", "gammad = 24; \t\t\t\t#unit weigth of dam\n", "gammaw = 9.81; \t\t\t\t#unit weigth of water\n", "E = 2.05e7; \t\t\t\t#modulus of elasticity\n", "\t\t\t\t#(a) Seismic coefficient method\n", "alpha0 = 0.05; \t\t\t\t#from table 8.1\n", "alphah = 2*alpha0;\n", "alphav = 0.75*alphah;\n", "\t\t\t\t#at 10m from top\n", "\n", "def f4(y): \n", "\t return alphav*168*(1-0.01*y)\n", "\n", "F10 = quad(f4,0,10)[0]\n", "\n", "\t\t\t\t#at 100m below top\n", "\n", "def f5(y): \n", "\t return alphav*(1-0.01*y)*16.8*y\n", "\n", "F100 = F10+ quad(f5,10,100)[0]\n", "\n", "print \"Parta):At 10m from top: F = %.2f knAt 100m from top: F = %.2f kn.\"%(F10,F100);\n", "\n", "\t\t\t\t#(b)Response spectrum method\n", "beta = 1;\n", "I = 2;\n", "Fo = 0.25; \t\t\t\t#from table 8.2\n", " \t\t\t\t#t = Sa/g;\n", "t = 0.19; \t\t\t\t#from fig. 8.4\n", "alphah = beta*I*Fo*t;\n", "alphav = 0.75*alphah;\n", "\t\t\t\t#at 10m from top\n", "\n", "def f6(y): \n", "\t return alphav*168*(1-0.01*y)\n", "\n", "F10 = quad(f6,0,10)[0]\n", "\n", "\t\t\t\t#at 100m below top\n", "\n", "def f7(y): \n", "\t return alphav*(1-0.01*y)*16.8*y\n", "\n", "F100 = F10+ quad(f7,10,100)[0]\n", "\n", "F100 = round(F100*100)/100;\n", "print \"Partb):At 10m from top: F = %.2f knAt 100m from top: F = %.2f kn.\"%(F10,F100);\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Parta):At 10m from top: F = 119.70 knAt 100m from top: F = 2160.90 kn.\n", "Partb):At 10m from top: F = 113.72 knAt 100m from top: F = 2052.86 kn.\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.4 pg : 381\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "\n", "#Given\n", "H = 100.; \t\t\t\t#heigth of dam\n", "wb = 73.; \t\t\t\t#width of base of dam\n", "wt = 7; \t\t\t\t#width of top of dam\n", "l = 1.; \t\t\t\t#length of dam\n", "hw = 98.; \t\t\t\t#heigth of water in dam\n", "hsu = 90.; \t\t\t\t#heigth of slope on downstream side\n", "s = 1/0.7; \t\t\t\t#slope on downstream side\n", "gammad = 24.; \t\t\t\t#unit weigth of dam\n", "gammaw = 9.81; \t\t\t\t#unit weigth of water\n", "E = 2.05e7; \t\t\t\t#modulus of elasticity\n", "\n", "#at 10m from top\n", "y = 8;\n", "alphah = 0.1;\n", "Cm = 0.72;\n", "Cy = (Cm/2)*((y*(2-y/hw)/hw)+(y*(2-y/hw)/hw)**0.5);\n", "p10 = Cy*alphah*gammaw*hw;\n", "F10 = 0.726*p10*y;\n", "Mp10 = 0.299*p10*y**2;\n", "\n", "#at 40m from top\n", "y = 38;\n", "alphah = 0.1;\n", "Cm = 0.72;\n", "Cy = (Cm/2)*((y*(2-y/hw)/hw)+(y*(2-y/hw)/hw)**0.5);\n", "p40 = Cy*alphah*gammaw*hw;\n", "F40 = 0.726*p40*y;\n", "Mp40 = 0.299*p40*y**2;\n", "\n", "#at 100m from top\n", "y = 98;\n", "alphah = 0.1;\n", "Cm = 0.72;\n", "Cy = (Cm/2)*((y*(2-y/hw)/hw)+(y*(2-y/hw)/hw)**0.5);\n", "p100 = Cy*alphah*gammaw*hw;\n", "F100 = 0.726*p100*y;\n", "Mp100 = 0.299*p100*y**2;\n", "p10 = round(p10*1000)/1000;\n", "F10 = round(F10*1000)/1000;\n", "Mp10 = round(Mp10*10)/10;\n", "p40 = round(p40*1000)/1000;\n", "F40 = round(F40*1000)/1000;\n", "Mp40 = round(Mp40*10)/10;\n", "p100 = round(p100*100)/100;\n", "F100 = round(F100*1000)/1000;\n", "Mp100 = round(Mp100*10)/10;\n", "print \"Hydrodynamic Forces:At 10m from top: P = %.2f KN/square m;\\\n", "\\nF = %.2f KN;\\\n", "\\nM = %.2f KN-m.At 40m from top: P = %.2f KN/square m.;\\\n", "\\nF = %.2f KN;\\\n", "\\nM = %.2f KN-m.At 100m from top: P = %.2f KN/square m;\\\n", "\\nF = %.2f KN;\\\n", "\\nM = %.2f KN-m.\"%(p10,F10,Mp10,p40,F40,Mp40,p100,F100,Mp100);\n", "\n", "#vertical component of reservior water on horizontal section\n", "s1 = 3./60;\n", "Wh = (F100-F40)*s1;\n", "Wh = round(Wh*100)/100;\n", "print \"vertical component of reservior water on horizontal section = %.2f kN/m.\"%(Wh);\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Hydrodynamic Forces:At 10m from top: P = 19.12 KN/square m;\n", "F = 111.03 KN;\n", "M = 365.80 KN-m.At 40m from top: P = 49.00 KN/square m.;\n", "F = 1351.85 KN;\n", "M = 21156.60 KN-m.At 100m from top: P = 69.22 KN/square m;\n", "F = 4924.82 KN;\n", "M = 198770.00 KN-m.\n", "vertical component of reservior water on horizontal section = 178.65 kN/m.\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.8 pg : 413" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "\n", "#no tension is permissible\n", "#factor of safety against slidingis 1.5\n", "\n", "#Given\n", "\n", "wb = 3; \t\t\t\t#width of dam;\n", "miu = 0.5; \t\t\t\t#coefficient of friction\n", "Sg = 2.4; \t\t\t\t#specific gravity of masonary\n", "gamma_w = 9.81; \t\t\t\t#unit weigth of water\n", "c = 1;\n", "\n", "#when uplift is considered\n", "#when no tension is permissible then e = wb/6;\n", "\n", "p1 = wb*Sg*gamma_w;\n", "p2 = c*wb*gamma_w/2;\n", "p3 = p1-p2;\n", "p4 = p1*wb/2-p2*2;\n", "p5 = gamma_w/6;\n", "d1 = p4/p3; d2 = p5/p3;\n", "d3 = 1.5-d1;\n", "H = ((0.5-d3)/d2)**0.5;\n", "H = round(H*100)/100;\n", "print \"when uplift is considered:\"\n", "print \"Heigth of dam when no tension is permissible = %.2f m.\"%(H);\n", "H = p3*0.5/(1.5*p5*3);\n", "print \"Heigth of dam when factor of safety against sliding is 1.5 = %.2f m.\"%(H);\n", "\n", "#when uplift is not considered\n", "p1 = wb*Sg*gamma_w;\n", "p4 = p1*wb/2;\n", "p5 = gamma_w/6;\n", "d1 = p4/p1;\n", "d2 = p5/p1;\n", "H = (0.5/d2)**0.5;\n", "H = round(H*100)/100;\n", "print \"when uplift is not considered:\"\n", "print \"Heigth of dam when no tension is permissible = %.2f m.\"%(H);\n", "H = p1*0.5/(1.5*p5*3);\n", "print \"Heigth of dam when factor of safety against sliding is 1.5 = %.2f m.\"%(H);\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "when uplift is considered:\n", "Heigth of dam when no tension is permissible = 3.55 m.\n", "Heigth of dam when factor of safety against sliding is 1.5 = 3.80 m.\n", "when uplift is not considered:\n", "Heigth of dam when no tension is permissible = 4.65 m.\n", "Heigth of dam when factor of safety against sliding is 1.5 = 4.80 m.\n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.9 pg : 414" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "#Given\n", "c = 1;\n", "hw = 6; \t\t\t\t#heigth of water in reservior\n", "Bt = 1.5; \t\t\t\t#width of top of dam\n", "H = 6; \t\t\t\t#heigth of the dam\n", "wb = 4.5; \t\t\t\t#width of base of dam\n", "Sg = 2.4; \t\t\t\t#specific gravity of masonary\n", "gamma_w = 9.81; \t\t\t\t#weigth density of water\n", "\n", "W1 = Bt*gamma_w*Sg*H;\n", "W2 = gamma_w*Sg*H*(wb-Bt)/2;\n", "L1 = (wb-Bt)+(Bt/2);\n", "L2 = (2*(wb-Bt))/3\n", "M1 = W1*L1\n", "M2 = W2*L2\n", "\n", "#Reaervior empty\n", "SumW = W1+W2;\n", "SumM = M1+M2;\n", "x = SumM/SumW;\n", "e = wb/2-x;\n", "pnt = (SumW/wb)*(1+(6*e/wb));\n", "pnh = (SumW/wb)*(1-(6*e/wb));\n", "pnt = round(pnt*10)/10;\n", "pnh = round(pnh*10)/10;\n", "print \"Reservior empty:\";\n", "print \" Normal stress at toe = %.2f kN/square.m.\"%(pnt);\n", "print \"Normal stress at heel = %.2f kN/square.m.\"%(pnh);\n", "\n", "#Reservior full\n", "W3 = gamma_w*H**2/2;\n", "U = gamma_w*H*c*wb/2;\n", "SumV = SumW-U;\n", "L3 = hw/3;\n", "L4 = 2*wb/3; \t\t\t\t#lever arm\n", "M3 = W3*L3;\n", "M4 = U*L4; \t\t\t\t#moment about toe\n", "SumM1 = SumM-M4-M3;\n", "x = SumM1/SumV;\n", "e = wb/2-x;\n", "pnt = (SumV/wb)*(1+(6*e/wb));\n", "pnh = (SumV/wb)*(1-(6*e/wb));\n", "pnt = round(pnt*10)/10;\n", "pnh = round(pnh*10)/10;\n", "print \"Reservior full:\";\n", "print \" Normal stress at toe = %.2f kN/square.m.\"%(pnt);\n", "print \"Normal stress at heel = %.2f kN/square.m.\"%(pnh);\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Reservior empty:\n", " Normal stress at toe = 15.70 kN/square.m.\n", "Normal stress at heel = 172.70 kN/square.m.\n", "Reservior full:\n", " Normal stress at toe = 120.30 kN/square.m.\n", "Normal stress at heel = 9.20 kN/square.m.\n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.10 pg : 415" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "from numpy import roots\n", "\n", "\n", "#check the stability\n", "\n", "#Given\n", "c = 1;\n", "hw = 6; \t\t\t\t#heigth of water in reservior\n", "Bt = 1.5; \t\t\t\t#width of top of dam\n", "H = 6; \t\t\t\t#heigth of the dam\n", "gamma_m = 20; \t\t\t\t#unit weigth of masonary \n", "gamma_w = 9.81; \t\t\t\t#weigth density of water\n", "f = 1800; \t\t\t\t#compressive strength\n", "miu = 0.6; \t\t\t\t#coefficient of friction\n", "\n", "#to develop no tension e = b/6;x = b/3.\n", "#hence on solving the relations we get\n", "\n", "P = [1,2.944,-39.074]\n", "wb = roots(P)[1]; \t\t\t\t#sign of coefficient is 2.944 is not taken correctly in book\n", "#roots are 4.94 and -7.89\n", "#math.since negative value cannot be taken\n", "print \"Neglecting the negative value.Width of base is = 4.94 m.\";\n", "W1 = Bt*gamma_m*H;\n", "W2 = gamma_m*H*(wb-Bt)/2;\n", "L1 = (wb-Bt)+(Bt/2);\n", "L2 = (2*(wb-Bt))/3;\n", "M1 = W1*L1,\n", "M2 = W2*L2;\n", "U = gamma_w*H*c*wb/2;\n", "L4 = 2*wb/3;\n", "M4 = U*L4;\n", "W3 = gamma_w*H**2/2;\n", "L3 = hw/3;\n", "M3 = W3*L3;\n", "SumW = W1+W2-U;\n", "SumM = M1+M2-M4-M3;\n", "pn = 2*SumW/wb;\n", "pn = round(pn*10)/10;\n", "print \"Maximum stress = %.2f kN/square.m.\"%(pn);\n", "print \"Dam is safe against compression\";\n", "FOS = miu*SumW/W3;\n", "FOS = round(FOS*100)/100;\n", "print \"Factor of safety against sliding = %.2f. <1\"%(FOS);\n", "print \"Dam is unsafe against sliding.\";\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Neglecting the negative value.Width of base is = 4.94 m.\n", "Maximum stress = 97.50 kN/square.m.\n", "Dam is safe against compression\n", "Factor of safety against sliding = 0.82. <1\n", "Dam is unsafe against sliding.\n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.11 pg : 416" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "from numpy import roots\n", "\t\t\t\t#check the stability if uplift is neglected\n", "\t\t\t\t\n", "#Given\n", "c = 1;\n", "hw = 6; \t\t\t\t#heigth of water in reservior\n", "Bt = 1.5; \t\t\t\t#width of top of dam\n", "H = 6; \t\t\t\t#heigth of the dam\n", "gamma_m = 20; \t\t\t\t#unit weigth of masonary \n", "gamma_w = 9.81; \t\t\t\t#weigth density of water\n", "f = 1800; \t\t\t\t#compressive strength\n", "miu = 0.6; \t\t\t\t#coefficient of friction\n", "\n", "\t\t\t\t#to develop no tension e = b/6;x = b/3.\n", "\t\t\t\t#hence on solving the relations we get\n", "\n", "P = [1,1.5,-19.908]\n", "wb = roots(P)[1];\n", "\n", "#roots are 3.774 and -5.27\n", "#math.since negative value cannot be taken\n", "\n", "print \"Neglecting the negative value.Width of base is = %.2f m.\"%wb;\n", "\n", "W1 = Bt*gamma_m*H;\n", "W2 = gamma_m*H*(wb-Bt)/2;\n", "L1 = (wb-Bt)+(Bt/2);\n", "L2 = (2*(wb-Bt))/3;\n", "M1 = W1*L1,\n", "M2 = W2*L2;\n", "W3 = gamma_w*H**2/2;\n", "L3 = hw/3;\n", "M3 = W3*L3;\n", "SumW = W1+W2;\n", "SumM = M1+M2-M3;\n", "pn = 2*SumW/wb;\n", "pn = round(pn*10)/10;\n", "print \"Maximum stress = %.2f kN/square.m.\"%(pn);\n", "print \"Dam is safe against compression\";\n", "\n", "FOS = miu*SumW/W3;\n", "FOS = round(FOS*1000)/1000;\n", "print \"Factor of safety against sliding = %.2f. > 1\"%(FOS);\n", "print \"Dam is safe against sliding.\";\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Neglecting the negative value.Width of base is = 3.77 m.\n", "Maximum stress = 167.70 kN/square.m.\n", "Dam is safe against compression\n", "Factor of safety against sliding = 1.07. > 1\n", "Dam is safe against sliding.\n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.12 pg : 417" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# calculate maximum permissible heigth of shutter so that no tension develops\n", "\t\t\t\t\n", "#Given\n", "Bt = 3; \t\t\t\t#width of top of dam\n", "H = 12; \t\t\t\t#heigth of the dam\n", "wb = 9; \t\t\t\t#width of base of dam\n", "gamma_m = 21; \t\t\t\t#unit weigth of masonary\n", "gamma_w = 9.81; \t\t\t\t#weigth density of water\n", "\n", "W1 = Bt*gamma_m*H;\n", "W2 = gamma_m*H*(wb-Bt)/2;\n", "\n", "#taking moment about a point on base at 3m from toe\n", "L1 = 3+Bt/2;\n", "L2 = (2*(wb-Bt)/3)-3;\n", "M1 = W1*L1\n", "M2 = W2*L2;\n", "M = M1+M2;\n", "\n", "#net moment about this point should be zero for equilibrium\n", "s = (M*6/gamma_w)**(1./3)-12;\n", "s = round(s*100)/100;\n", "\n", "# Results\n", "print \"maximum permissible heigth of shutter = %.2f m.\"%(s);\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "maximum permissible heigth of shutter = 1.22 m.\n" ] } ], "prompt_number": 13 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.13 pg : 417" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "\n", "\t\t\t\t#moment at 50m below water surface\n", "\t\t\t\t\n", "#Given\n", "c = 1;\n", "H = 100; \t\t\t\t#heigth of dam\n", "hw = 100; \t\t\t\t#heigth of water in reservior\n", "FB = 1; \t\t\t\t#free board\n", "s = 0.15; \t\t\t\t#slope of upstream face\n", "gamma_w = 9.81; \t\t\t\t#unit weigth of water\n", "alphah = 0.1;\n", "\n", "theta = math.atan(s);\n", "y = 50;\n", "Cm = 0.735*(1-(theta*2/math.pi));\n", "Cy = (Cm/2)*((y*(2-y/hw)/hw)+(y*(2-y/hw)/hw)**0.5);\n", "pe = Cy*alphah*gamma_w*hw;\n", "F = 0.726*pe*y;\n", "M = 0.299*pe*y**2;\n", "pe = round(pe*1000)/1000;\n", "F = round(F*10)/10;\n", "M = round(M*10)/10;\n", "print \"hydrodynamic earthquake pressure = %.2f kN/square.mshear = %.2f kN/m.Moment = %.2f kN-m/m.\"%(pe,F,M);\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "hydrodynamic earthquake pressure = 65.27 kN/square.mshear = 2369.30 kN/m.Moment = 48788.60 kN-m/m.\n" ] } ], "prompt_number": 14 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.14 pg : 418" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "from sympy import sec\n", "\n", "#check stability\n", "\n", "\t\t\t\t\n", "#Given\n", "c = 1.;\n", "H = 10.; \t\t\t\t#heigth of dam\n", "hw = 10.; \t\t\t\t#heigth of water in reservior\n", "wb = 8.25; \t\t\t\t#bottom width\n", "Bt = 1.; \t\t\t\t#top width\n", "Hs1 = 0.1; \t\t\t\t#slope on upstream side\n", "gamma_w = 9.81; \t\t\t\t#unit weigth of water\n", "gamma_m = 22.4; \t\t\t\t#unit weigth of masonary\n", "f = 1400.; \t\t\t\t#permissible shear stress at joint\n", "miu = 0.75; \t\t\t\t#coefficient of friction\n", "fi = math.atan(0.625);\n", "theta = math.atan(0.1);\n", "\n", "W1 = Bt*H*gamma_m;\n", "W2 = H*H*Hs1*gamma_m/2;\n", "W3 = H*6.25*gamma_m/2;\n", "W4 = hw*gamma_w*H*Hs1/2;\n", "P = gamma_w*hw**2/2;\n", "U = wb*gamma_w*hw*c/2;\n", "SumV = W1+W2+W3+W4-U;\n", "L3 = 2*(wb-(Hs1*H)-Bt)/3;\n", "L1 = (wb-(Hs1*H)-Bt)+Bt/2;\n", "L2 = (wb-(Hs1*H)-Bt)+Bt+(Hs1*H/3);\n", "L4 = (wb-(Hs1*H)-Bt)+Bt+(2*Hs1*H/3);\n", "L5 = 2*wb/3;L6 = hw/3;\n", "M1 = W1*L1;\n", "M2 = W2*L2;\n", "M3 = W3*L3;\n", "M4 = W4*L4;\n", "M5 = U*L5;\n", "M6 = P*L6;\n", "SumM = M1+M2+M3+M4-M5-M6;\n", "Mplus = M1+M2+M3+M4;\n", "Mminus = M5+M6;\n", "FOS = miu*SumV/P;\n", "SFF = (miu*SumV+wb*1400)/P;\n", "FOO = Mplus/Mminus;\n", "FOS = round(FOS*100)/100;\n", "SFF = round(SFF*10)/10;\n", "FOO = round(FOO*100)/100;\n", "print \"Factor of safety against sliding = %.2f. >1 \"%(FOS);\n", "print \"Shear friction factor = %.2f.\"%(SFF);\n", "print \"Factor of safety against overturning = %.2f. <1.5\"%(FOO);\n", "print \"Dam is unsafe against overturning\";\n", "\n", "x = SumM/SumV;\n", "e = wb/2-x;\n", "p = hw*gamma_w;\n", "pnt = (SumV/wb)*(1+(6*e/wb)); \t\t\t\t#calculation is done wrong in book;value of b is not taken correctly\n", "pnh = (SumV/wb)*(1-(6*e/wb));\n", "sigmat = pnt*sec(fi)**2;\n", "sigmah = pnh*sec(theta)**2-p*math.tan(theta)**2;\n", "taut = pnt*math.tan(fi);\n", "tauh = -(pnh-p)*math.tan(theta);\n", "pnt = round(pnt*10)/10;\n", "pnh = round(pnh*10)/10;\n", "sigmat = round(sigmat*10)/10;\n", "sigmah = round(sigmah*10)/10;\n", "taut = round(taut*10)/10;\n", "tauh = round(tauh*10)/10;\n", "print \"Normal stress at toe = %.2f kN/square.m.\"%(pnt);\n", "print \"Normal stress at heel = %.2f kN/square.m.\"%(pnh);\n", "print \"Principal stress at toe = %.2f kN/square.m.\"%(sigmat);\n", "print \"Principal stress at heel = %.2f kN/square.m.\"%(sigmah);\n", "print \"Shear stress at toe = %.2f kN/square.m.\"%(taut);\n", "print \"Shear stress at heel = %.2f kN/square.m.\"%(tauh);\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Factor of safety against sliding = 1.04. >1 \n", "Shear friction factor = 24.60.\n", "Factor of safety against overturning = 1.47. <1.5\n", "Dam is unsafe against overturning\n", "Normal stress at toe = 170.70 kN/square.m.\n", "Normal stress at heel = -5.80 kN/square.m.\n", "Principal stress at toe = 237.40 kN/square.m.\n", "Principal stress at heel = -6.80 kN/square.m.\n", "Shear stress at toe = 106.70 kN/square.m.\n", "Shear stress at heel = 10.40 kN/square.m.\n" ] } ], "prompt_number": 15 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.15 pg : 420" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "\t\t\t\t#Check the stability and determine sliding factor and shear factor\n", "\t\t\t\t\n", "#Given\n", "c = 1;\n", "miu = 0.75; \t\t\t\t#coefficient of friction\n", "H = 90; \t\t\t\t#heigth of dam\n", "wb = 73.1; \t\t\t\t#width of base\n", "Bt = 7; \t\t\t\t#width of top of dam\n", "hw = 89; \t\t\t\t#heigth of water in reservior\n", "Hs1 = 28; \t\t\t\t#heigth of slope on upstream side\n", "Hs2 = 83; \t\t\t\t#heigth of slope on downstream side\n", "Cm = 0.735;\n", "alphah = 0.1;\n", "gamma_m = 23.5; \t\t\t\t#unit weigth of concrete\n", "gamma_w = 9.81; \t\t\t\t#unit weigth of water\n", "theta = math.atan(8./28);\n", "fi = math.atan(0.7);\n", "\t\t\t\t#self weigth of dam\n", "W1 = (Hs1*8*gamma_m)/2\n", "W2 = (Bt*H*gamma_m)\n", "W3 = (Hs2**2*0.7*gamma_m)/2\n", "\t\t\t\t#weigth of superimposed water\n", "W4 = (Hs1*8*gamma_w)/2\n", "W5 = (hw-Hs1)*8*gamma_w\n", "U = hw*wb*2*gamma_w/6; \t\t\t\t#uplift force\n", "wp = hw**2*gamma_w/2; \t\t\t\t#water pressure\n", "hp = 0.726*Cm*alphah*gamma_w*hw**2; \t\t\t\t#hydrodynamic pressure\n", "Mhp = 0.299*Cm*alphah*gamma_w*hw**3; \t\t\t\t#moment due to hydrodynamic pressure\n", "\t\t\t\t#inertial load due to horizontal acceleration\n", "I1 = W2/10;\n", "I2 = W3/10;\n", "I3 = W1/10;\n", "SumV = W1+W2+W3+W4+W5-U;\n", "SumH = wp+hp+I1+I2+I3;\n", "L1 = (wb-8)+8/3\n", "L2 = (0.7*Hs2)+(Bt/2)\n", "L3 = (2*Hs2*0.7)/3.\n", "L4 = (wb-8)+(2*8)/3.\n", "L5 = (wb-8)+(8./2)\n", "L6 = hw/3;\n", "L7 = 2*wb/3;\n", "M1 = W1*L1\n", "M2 = W2*L2\n", "M3 = W3*L3\n", "M4 = W4*L4;\n", "M5 = W5*L5;\n", "M6 = wp*L6;\n", "M7 = U*L7;\n", "M8 = I1*45;\n", "M9 = I2*83/3;\n", "M10 = I3*28/3;\n", "Mplus = M1+M2+M3+M4+M5;\n", "Mminus = M6+M7+M8+M9+M10+Mhp;\n", "SumM = Mplus-Mminus;\n", "x = SumM/SumV;\n", "e = wb/2-x;\n", "pnt = (SumV/wb)*(1+(6*e/wb));\n", "pnh = (SumV/wb)*(1-(6*e/wb));\n", "sigmat = pnt*sec(fi)**2;\n", "p = hw*gamma_w;\n", "pe = Cm*alphah*gamma_w*hw;\n", "sigmah = pnh*sec(theta)**2-(p+pe)*math.tan(theta)**2;\n", "taut = pnt*math.tan(fi);\n", "tauh = -(-pnh-(p+pe))*math.tan(theta);\n", "print \"Normal stress at toe = %i kN/square.m.\"%(pnt);\n", "print \"Normal stress at heel = %i kN/square.m.\"%(pnh);\n", "print \"Principal stress at toe = %i kN/square.m.\"%(sigmat);\n", "print \"Principal stress at heel = %i kN/square.m.\"%(sigmah);\n", "print \"Shear stress at toe = %i kN/square.m.\"%(taut);\n", "print \"Shear stress at heel = %i kN/square.m.\"%(tauh);\n", "\n", "FOS = miu*SumV/SumH;\n", "SFF = (miu*SumV+wb*1400)/SumH;\n", "FOO = Mplus/Mminus;\n", "Ffi = 1.2;Fc = 2.4;\n", "F = (miu*SumV/Ffi+1400*wb/Fc)/SumH;\n", "FOS = round(FOS*100)/100;\n", "F = round(F*100)/100;\n", "SFF = round(SFF*100)/100;\n", "FOO = round(FOO*100)/100;\n", "print \"Factor of safety against sliding as per IS:6512-1972 = %.2f. <1.5\"%(FOS);\n", "print \"Factor of safety against sliding as per IS:6512-1984 = %.2f. >1\"%(F);\n", "print \"Shear friction factor = %.2f. <6\"%(SFF);\n", "print \"Factor of safety against overturning = %.2f. <1.5\"%(FOO);\n", "print \"Dam is unsafe for given loading conditions\";\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Normal stress at toe = 1929 kN/square.m.\n", "Normal stress at heel = -323 kN/square.m.\n", "Principal stress at toe = 2874 kN/square.m.\n", "Principal stress at heel = -426 kN/square.m.\n", "Shear stress at toe = 1350 kN/square.m.\n", "Shear stress at heel = 175 kN/square.m.\n", "Factor of safety against sliding as per IS:6512-1972 = 0.87. <1.5\n", "Factor of safety against sliding as per IS:6512-1984 = 1.57. >1\n", "Shear friction factor = 2.90. <6\n", "Factor of safety against overturning = 1.45. <1.5\n", "Dam is unsafe for given loading conditions\n" ] } ], "prompt_number": 16 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.16 pg : 423" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "\t\t\t\t#Check the stability and determine principal and shear stress at toe and heel\n", "\t\t\t\t\n", "#Given\n", "c = 1;\n", "miu = 0.7; \t\t\t\t#coefficient of friction\n", "H = 70; \t\t\t\t#heigth of dam\n", "ht = 0; \t\t\t\t#heigth of tail water\n", "Lf = 6.5; \t\t\t\t#location of foundation gallery from heel\n", "wb = 52.5; \t\t\t\t#width of base\n", "Bt = 7; \t\t\t\t#width of top of dam\n", "hw = 70; \t\t\t\t#heigth of water in reservior\n", "Hs1 = 35; \t\t\t\t#heigth of slope on upstream side\n", "Hs2 = 60; \t\t\t\t#heigth of slope on downstream side\n", "gamma_m = 24; \t\t\t\t#unit weigth of concrete\n", "gamma_w = 9.81; \t\t\t\t#unit weigth of water\n", "theta = math.atan(0.1);\n", "fi = math.atan(0.7);\n", "\t\t\t\t#self weigth of dam\n", "W1 = (Hs1*3.5*gamma_m)/2\n", "W2 = (Bt*H*gamma_m)\n", "W3 = (Hs2**2*0.7*gamma_m)/2\n", "\t\t\t\t#weigth of superimposed water\n", "W4 = (Hs1*3.5*gamma_w)/2\n", "W5 = (hw-Hs1)*3.5*gamma_w\n", "wp = hw**2*gamma_w/2; \t\t\t\t#water pressure\n", "Pt = gamma_w*ht\n", "Ph = gamma_w*hw\n", "Pg = (ht+(hw-ht)/3)*gamma_w\n", "U = (Pt*(wb-Lf))+(Pg*Lf)+((Ph-Pg)*Lf/2)+((Pg-Pt)*(wb-Lf)/2)*c\n", "l1 = (wb-Lf)/2\n", "l2 = (2*(wb-Lf))/3\n", "l3 = (wb-Lf)+(Lf/2)\n", "l4 = (wb-Lf)+((2*Lf)/3)\n", "L7 = (((Pt*(wb-Lf))*l1)+((Pg-Pt)*(wb-Lf)*l2/2)+((Pg*Lf)*l3)+((Ph-Pg)*Lf*l4/2))/U\n", "L1 = (wb-3.5)+3.5/3\n", "L2 = (0.7*Hs2)+(Bt/2)\n", "L3 = (2*Hs2*0.7)/3\n", "L4 = (wb-3.5)+(2*3.5)/3\n", "L5 = (wb-3.5)+(3.5/2)\n", "L6 = hw/3;\n", "M1 = W1*L1\n", "M2 = W2*L2\n", "M3 = W3*L3\n", "M4 = W4*L4;\n", "M5 = W5*L5;\n", "M6 = wp*L6;\n", "M7 = U*L7;\n", "SumV1 = W1+W2+W3;\n", "SumM1 = M1+M2+M3;\n", "SumV2 = SumV1+W4+W5;\n", "SumM2 = SumM1+M4+M5-M6;\n", "SumV3 = SumV2-U;\n", "SumM3 = SumM2-M7;\n", "Mplus = 1547377;\n", "Mminus = 870421;\n", "SumH = wp;\n", "\n", "\t\t\t\t#case 1. Reservior empty\n", "x = SumM1/SumV1;\n", "e = wb/2-x;\n", "pnt = (SumV1/wb)*(1+(6*e/wb));\n", "pnh = (SumV1/wb)*(1-(6*e/wb));\n", "sigmat = pnt*sec(fi)**2;\n", "sigmah = pnh*sec(theta)**2;\n", "taut = pnt*math.tan(fi);\n", "tauh = pnh*math.tan(theta);\n", "pnt = round(pnt*10)/10;\n", "pnh = round(pnh*10)/10;\n", "sigmat = round(sigmat*10)/10;\n", "sigmah = round(sigmah*10)/10;\n", "taut = round(taut*10)/10;\n", "tauh = round(tauh*10)/10;\n", "print \"case 1. Reservior empty:\";\n", "print \"Normal stress at toe = %.2f kN/square.m.\"%(pnt);\n", "print \"Normal stress at heel = %.2f kN/square.m.\"%(pnh);\n", "print \"Principal stress at toe = %.2f kN/square.m.\"%(sigmat);\n", "print \"Principal stress at heel = %.2f kN/square.m.\"%(sigmah);\n", "print \"Shear stress at toe = %.2f kN/square.m.\"%(taut);\n", "print \"Shear stress at heel = %.2f kN/square.m.\"%(tauh);\n", "\n", "\t\t\t\t#case2. reservior full without uplift\n", "x = SumM2/SumV2;\n", "e = wb/2-x;\n", "p = hw*gamma_w;\n", "pnt = (SumV2/wb)*(1+(6*e/wb));\n", "pnh = (SumV2/wb)*(1-(6*e/wb));\n", "sigmat = pnt*sec(fi)**2;\n", "sigmah = pnh*sec(theta)**2-p*math.tan(theta)**2;\n", "taut = pnt*math.tan(fi);\n", "tauh = -(pnh-p)*math.tan(theta);\n", "pnt = round(pnt*10)/10;\n", "pnh = round(pnh*10)/10;\n", "sigmat = round(sigmat*10)/10;\n", "sigmah = round(sigmah*10)/10;\n", "taut = round(taut*10)/10;\n", "tauh = round(tauh*10)/10;\n", "print \"case 2. reservior full without uplift:\";\n", "print \"Normal stress at toe = %.2f kN/square.m.\"%(pnt);\n", "print \"Normal stress at heel = %.2f kN/square.m.\"%(pnh);\n", "print \"Principal stress at toe = %.2f kN/square.m.\"%(sigmat);\n", "print \"Principal stress at heel = %.2f kN/square.m.\"%(sigmah);\n", "print \"Shear stress at toe = %.2f kN/square.m.\"%(taut);\n", "print \"Shear stress at heel = %.2f kN/square.m.\"%(tauh);\n", "\n", "\t\t\t\t#case3. reservior full with uplift\n", "x = SumM3/SumV3;\n", "e = wb/2-x;\n", "p = hw*gamma_w;\n", "pnt = (SumV3/wb)*(1+(6*e/wb));\n", "pnh = (SumV3/wb)*(1-(6*e/wb));\n", "sigmat = pnt*sec(fi)**2;\n", "sigmah = pnh*sec(theta)**2-p*math.tan(theta)**2;\n", "taut = pnt*math.tan(fi);\n", "tauh = -(pnh-p)*math.tan(theta);\n", "pnt = round(pnt);\n", "pnh = round(pnh);\n", "sigmat = round(sigmat);\n", "sigmah = round(sigmah);\n", "taut = round(taut);\n", "tauh = round(tauh);\n", "print \"case 3. reservior full with uplift:\";\n", "print \"Normal stress at toe = %.2f kN/square.m.\"%(pnt);\n", "print \"Normal stress at heel = %.2f kN/square.m.\"%(pnh);\n", "print \"Principal stress at toe = %.2f kN/square.m.\"%(sigmat);\n", "print \"Principal stress at heel = %.2f kN/square.m.\"%(sigmah);\n", "print \"Shear stress at toe = %.2f kN/square.m.\"%(taut);\n", "print \"Shear stress at heel = %.2f kN/square.m.\"%(tauh);\n", "\n", "FOS = miu*SumV3/SumH;\n", "SFF = (miu*SumV3+wb*1400)/SumH;\n", "FOO = Mplus/Mminus;\n", "Ffi = 1.5;Fc = 3.6;\n", "F = (miu*SumV3/Ffi+1400*wb/Fc)/SumH;\n", "FOS = round(FOS*1000)/1000;\n", "SFF = round(SFF*100)/100;\n", "FOO = round(FOO*100)/100;\n", "F = round(F*1000)/1000;\n", "print \"Factor of safety against sliding = %.2f.\"%(FOS);\n", "print \"Shear friction factor = %.2f.\"%(SFF);\n", "print \"Factor of safety against overturning = %.2f.\"%(FOO);\n", "print \"Factor of safety for load combination B = %.2f. > 1\"%(F);\n", "print \"Dam is safe \";\n", "\n", "\t\t\t\t#Case4.considering seismic forces\n", "Cm = 0.712;\n", "alphah = 0.1;\n", "alphav = 0.08;\n", "hp = 0.726*Cm*alphah*gamma_w*hw**2; \t\t\t\t#hydrodynamic pressure\n", "Mhp = 0.299*Cm*alphah*gamma_w*hw**3; \t\t\t\t#moment due to hydrodynamic pressure\n", "\t\t\t\t#inertial load due to horizontal acceleration\n", "I1 = W2/10;\n", "I2 = W3/10;\n", "I3 = W1/10;\n", "v = SumV1*alphav;\n", "Mv = 116444;\n", "SumV4 = SumV3-v;\n", "SumH1 = SumH+I1+I2+I3+hp;\n", "M8 = I1*35;\n", "M9 = I2*20;\n", "M10 = I3*35/3;\n", "Mminus1 = 1161849;\n", "SumM4 = SumM3-M8-M9-M10-Mhp-Mv;\n", "\n", "x = SumM4/SumV4;\n", "e = wb/2-x;\n", "p = hw*gamma_w;\n", "pe = Cm*alphah*gamma_w*hw;\n", "pnt = (SumV4/wb)*(1+(6*e/wb));\n", "pnh = (SumV4/wb)*(1-(6*e/wb));\n", "sigmat = pnt*sec(fi)**2;\n", "sigmah = pnh*sec(theta)**2-(p+pe)*math.tan(theta)**2;\n", "taut = pnt*math.tan(fi);\n", "tauh = (-pnh+(p+pe))*math.tan(theta);\n", "pnt = round(pnt);\n", "pnh = round(pnh);\n", "sigmat = round(sigmat);\n", "sigmah = round(sigmah);\n", "taut = round(taut);\n", "tauh = round(tauh);\n", "print \"case 4.considering seismic forces\";\n", "print \"Normal stress at toe = %.2f kN/square.m.\"%(pnt);\n", "print \"Normal stress at heel = %.2f kN/square.m.\"%(pnh);\n", "print \"Principal stress at toe = %.2f kN/square.m.\"%(sigmat);\n", "print \"Principal stress at heel = %.2f kN/square.m.\"%(sigmah);\n", "print \"Shear stress at toe = %.2f kN/square.m.\"%(taut);\n", "print \"Shear stress at heel = %.2f kN/square.m.\"%(tauh); \t\t\t\t#answer is wrong in book\n", "\n", "FOS = miu*SumV4/SumH1;\n", "SFF = (miu*SumV4+wb*1400)/SumH1;\n", "FOO = Mplus/Mminus1;\n", "Ffi = 1.2;Fc = 2.7;\n", "F = (miu*SumV4/Ffi+1400*wb/Fc)/SumH1;\n", "FOS = round(FOS*1000)/1000;\n", "SFF = round(SFF*100)/100;\n", "FOO = round(FOO*100)/100;\n", "F = round(F*100)/100;\n", "print \"Factor of safety against sliding = %.2f.\"%(FOS);\n", "print \"Shear friction factor = %.2f.\"%(SFF);\n", "print \"Factor of safety against overturning = %.2f.\"%(FOO);\n", "print \"Factor of safety for load combination E = %.2f. > 1\"%(F);\n", "print \"Dam is safe \";\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "case 1. Reservior empty:\n", "Normal stress at toe = 156.30 kN/square.m.\n", "Normal stress at heel = 1499.70 kN/square.m.\n", "Principal stress at toe = 232.80 kN/square.m.\n", "Principal stress at heel = 1514.70 kN/square.m.\n", "Shear stress at toe = 109.40 kN/square.m.\n", "Shear stress at heel = 150.00 kN/square.m.\n", "case 2. reservior full without uplift:\n", "Normal stress at toe = 1297.10 kN/square.m.\n", "Normal stress at heel = 427.60 kN/square.m.\n", "Principal stress at toe = 1932.60 kN/square.m.\n", "Principal stress at heel = 425.00 kN/square.m.\n", "Shear stress at toe = 907.90 kN/square.m.\n", "Shear stress at heel = 25.90 kN/square.m.\n", "case 3. reservior full with uplift:\n", "Normal stress at toe = 1344.00 kN/square.m.\n", "Normal stress at heel = 70.00 kN/square.m.\n", "Principal stress at toe = 2002.00 kN/square.m.\n", "Principal stress at heel = 64.00 kN/square.m.\n", "Shear stress at toe = 941.00 kN/square.m.\n", "Shear stress at heel = 62.00 kN/square.m.\n", "Factor of safety against sliding = 1.08.\n", "Shear friction factor = 4.14.\n", "Factor of safety against overturning = 1.00.\n", "Factor of safety for load combination B = 1.57. > 1\n", "Dam is safe \n", "case 4.considering seismic forces\n", "Normal stress at toe = 1713.00 kN/square.m.\n", "Normal stress at heel = -432.00 kN/square.m.\n", "Principal stress at toe = 2552.00 kN/square.m.\n", "Principal stress at heel = -443.00 kN/square.m.\n", "Shear stress at toe = 1199.00 kN/square.m.\n", "Shear stress at heel = 117.00 kN/square.m.\n", "Factor of safety against sliding = 0.76.\n", "Shear friction factor = 3.14.\n", "Factor of safety against overturning = 1.00.\n", "Factor of safety for load combination E = 1.52. > 1\n", "Dam is safe \n" ] } ], "prompt_number": 17 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.17 pg : 429" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "#design practical profile of gravity dam\n", "\t\t\t\t\n", "#Given\n", "c = 1;\n", "rlb = 1450; \t\t\t\t#R.L of base of dam\n", "rlw = 1480.5; \t\t\t\t#R.L of water level\n", "Sg = 2.4; \t\t\t\t#specific gravity of masonary\n", "gamma_w = 9.81; \t\t\t\t#unit weigth of water\n", "w = 1; \t\t\t\t#heigth of waves\n", "f = 1200; \t\t\t\t#safe compressive stress for masonary\n", "FB = 1.5*w;\n", "rlt = FB+rlw; \t\t\t\t#R.L of top of dam\n", "H = rlt-rlb; \t\t\t\t#heigth of dam\n", "LH = f/(gamma_w*(Sg+1))\n", "LH = round(LH*100)/100;\n", "print \"Heigth of dam = %.2f m.\"%(H);\n", "print \"limiting heigth of dam = %.2f m.\"%(LH);\n", "print \"Dam is low gravity dam\";\n", "hw = rlw-rlb;\n", "\t\t\t\t#keep top width,a = 4.5.\n", "a = 4.5;\n", "P = hw/(Sg**0.5);\n", "P = round(P*10)/10;\n", "print \"Base width of elementary profile = %.2f m.\"%(P);\n", "uo = a/16;\n", "wb = uo+P;\n", "wb = round(wb);\n", "print \"Base width = %.2f m.\"%(wb);\n", "D = 2*a*(Sg**0.5);\n", "D = round(D);\n", "print \"Dismath.tance upto which u/s slope is vertical from water level = %.2f m.\"%(D);\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Heigth of dam = 32.00 m.\n", "limiting heigth of dam = 35.98 m.\n", "Dam is low gravity dam\n", "Base width of elementary profile = 19.70 m.\n", "Base width = 20.00 m.\n", "Dismath.tance upto which u/s slope is vertical from water level = 14.00 m.\n" ] } ], "prompt_number": 18 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.18 pg : 430" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "#determine if dam is safe against sliding\n", "\t\t\t\t\n", "#Given\n", "hw = 97.; \t\t\t\t#heigth of water in reservior\n", "Bt = 7.; \t\t\t\t#width of top of dam\n", "H = 100.; \t\t\t\t#heigth of the dam\n", "Hs2 = 90.; \t\t\t\t#heigth of slope on downstream side\n", "wb = 75.; \t\t\t\t#width of base of dam\n", "miu = 0.75; \t\t\t\t#coefficient of friction\n", "gamma_d = 2.4; \t\t\t\t#weigth density of concrete\n", "gamma_w = 1000.; \t\t\t\t#weigth density of water\n", "\n", "# Calculations\n", "P = gamma_w*hw**2/(2*1000);\n", "W1 = Bt*gamma_d*H;\n", "W2 = (wb-Bt)*Hs2*gamma_d/2;\n", "W = W1+W2;\n", "FOS = miu*W/P;\n", "FOS = round(FOS*1000)/1000;\n", "\n", "# Results\n", "print \"Factor of safety against sliding = %.2f.\"%(FOS);\n", "print \"Dam is safe against sliding\";\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Factor of safety against sliding = 1.44.\n", "Dam is safe against sliding\n" ] } ], "prompt_number": 24 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.19 pg : 430" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "#Factor of safety against overturning\n", "#Factor of safety against sliding\n", "#Shear friction factor\n", "\n", "#Given\n", "c = 1.;\n", "H = 10.; \t\t\t\t#heigth of dam\n", "hw = 10.; \t\t\t\t#heigth of water in reservior\n", "wb = 8.25; \t\t\t\t#bottom width\n", "Bt = 1.; \t\t\t\t#top width\n", "Hs1 = 0.1; \t\t\t\t#slope on upstream side\n", "gamma_w = 9.81; \t\t\t\t#unit weigth of water\n", "gamma_m = 22.4; \t\t\t\t#unit weigth of masonary\n", "f = 1400.; \t\t\t\t#permissible shear stress at joint\n", "miu = 0.75; \t\t\t\t#coefficient of friction\n", "fi = math.atan(0.625);\n", "theta = math.atan(0.1);\n", "\n", "# Calculations\n", "W1 = Bt*H*gamma_m;\n", "W2 = H*H*Hs1*gamma_m/2;\n", "W3 = H*6.25*gamma_m/2;\n", "W4 = hw*gamma_w*H*Hs1/2;\n", "P = gamma_w*hw**2/2;\n", "U = wb*gamma_w*hw*c/2;\n", "SumV = W1+W2+W3+W4-U;\n", "L3 = 2*(wb-(Hs1*H)-Bt)/3;\n", "L1 = (wb-(Hs1*H)-Bt)+Bt/2;\n", "L2 = (wb-(Hs1*H)-Bt)+Bt+(Hs1*H/3);\n", "L4 = (wb-(Hs1*H)-Bt)+Bt+(2*Hs1*H/3);\n", "L5 = 2*wb/3;L6 = hw/3;\n", "M1 = W1*L1;M2 = W2*L2;M3 = W3*L3;M4 = W4*L4;\n", "M5 = U*L5;M6 = P*L6;\n", "SumM = M1+M2+M3+M4-M5-M6;\n", "Mplus = M1+M2+M3+M4;\n", "Mminus = M5+M6;\n", "FOS = miu*SumV/P;\n", "SFF = (miu*SumV+wb*1400)/P;\n", "FOO = Mplus/Mminus;\n", "FOS = round(FOS*100)/100;\n", "SFF = round(SFF*10)/10;\n", "FOO = round(FOO*100)/100;\n", "\n", "# Results\n", "print \"Factor of safety against sliding = %.2f.\"%(FOS);\n", "print \"Shear friction factor = %.2f.\"%(SFF);\n", "print \"Factor of safety against overturning = %.2f.\"%(FOO);\n", "print \"Dam is unsafe against overturning\";\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Factor of safety against sliding = 1.04.\n", "Shear friction factor = 24.60.\n", "Factor of safety against overturning = 1.47.\n", "Dam is unsafe against overturning\n" ] } ], "prompt_number": 23 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.20 pg : 431" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "\t\t\t\t\n", "#Given\n", "c = 1.;\n", "hw = 80.; \t\t\t\t#heigth of water in reservior\n", "Bt = 6.; \t\t\t\t#width of top of dam\n", "H = 84.; \t\t\t\t#heigth of the dam\n", "Hs2 = 75.; \t\t\t\t#heigth of slope on downstream side\n", "wb = 56.; \t\t\t\t#width of base of dam\n", "Lf = 8.; \t\t\t\t#dismath.tance of foundation gallery from heel\n", "gamma_d = 23.5; \t\t\t\t#weigth density of concrete\n", "gamma_w = 9.81; \t\t\t\t#weigth density of water\n", "ht = 6.; \t\t\t\t#heigth of tail water\n", "\n", "# Calculations\n", "W1 = Bt*gamma_d*H;\n", "W2 = gamma_d*Hs2*(wb-Bt)/2;\n", "W3 = gamma_w*ht*4/2;\n", "W4 = gamma_w*hw**2/2;\n", "W5 = gamma_w*ht**2/2;\n", "Pt = gamma_w*ht\n", "Ph = gamma_w*hw\n", "Pg = (ht+(hw-ht)/3)*gamma_w\n", "U = (Pt*(wb-Lf))+(Pg*Lf)+((Ph-Pg)*Lf/2)+((Pg-Pt)*(wb-Lf)/2)*c\n", "l1 = (wb-Lf)/2\n", "l2 = (2*(wb-Lf))/3\n", "l3 = (wb-Lf)+(Lf/2)\n", "l4 = (wb-Lf)+((2*Lf)/3)\n", "L6 = (((Pt*(wb-Lf))*l1)+((Pg-Pt)*(wb-Lf)*l2/2)+((Pg*Lf)*l3)+((Ph-Pg)*Lf*l4/2))/U\n", "L1 = (wb-Bt)+(Bt/2)\n", "L2 = (2*(wb-Bt))/3\n", "L3 = 4./3;\n", "L4 = hw/3;\n", "L5 = ht/3;\n", "M1 = W1*L1\n", "M2 = W2*L2\n", "M3 = W3*L3\n", "M4 = W4*L4\n", "M5 = W5*L5\n", "M6 = U*L6;\n", "SumV = W1+W2+W3-U;\n", "SumH = W4-W5;\n", "SumM = M1+M2+M3-M4+M5-M6;\n", "x = SumM/SumV;\n", "e = wb/2-x;\n", "pnt = (SumV/wb)*(1+(6*e/wb));\n", "pnh = (SumV/wb)*(1-(6*e/wb));\n", "pnt = round(pnt*10)/10;\n", "pnh = round(pnh*10)/10;\n", "\n", "# Results\n", "print \"Maximum Normal stress at toe = %.2f kN/square.m.\"%(pnt);\n", "print \"Maximum Normal stress at heel = %.2f kN/square.m.\"%(pnh);\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Maximum Normal stress at toe = 1586.70 kN/square.m.\n", "Maximum Normal stress at heel = -49.30 kN/square.m.\n" ] } ], "prompt_number": 22 } ], "metadata": {} } ] }