From ac9556e2aee48c94e4a2f0e504da4c9056417a12 Mon Sep 17 00:00:00 2001 From: Trupti Kini Date: Fri, 15 Apr 2016 23:30:24 +0600 Subject: Added(A)/Deleted(D) following books A Engineering_Mechanics_of_Solids_by_Popov_E_P/Chapter1_3.ipynb A Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter10_3.ipynb A Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter11_3.ipynb A Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter12_3.ipynb A Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter13_2.ipynb A Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter2_3.ipynb A Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter4_3.ipynb A Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter5_3.ipynb A Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter6_3.ipynb A Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter7_3.ipynb A Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter8_3.ipynb A Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter9_3.ipynb A 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[ + "# Chapter 1 : Stress, Axial loads and Safety concepts" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.1 page number 24" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The bearing stress at C is 0.875 MPA\n", + "The maximum normal stress in BD bolt is: 62.0 MPA\n", + "The tensile strss at shank of the bolt is: 40.0 MPA\n" + ] + } + ], + "source": [ + "#Given\n", + "import math\n", + "d_bolt = 20.0 #mm,diameter,This is not the minimum area\n", + "d_bolt_min = 16.0 #mm This is at the roots of the thread \n", + "#This yealds maximum stress \n", + "A_crossection = (math.pi)*(d_bolt**2)/4 #mm*2\n", + "A_crossection_min = (math.pi)*(d_bolt_min**2)/4 #mm*2 ,This is minimum area which yeilds maximum stress\n", + "load = 10.0 #KN\n", + "BC = 1.0 #m\n", + "CF = 2.5 #m\n", + "contact_area = 200*200 # mm*2 , The contact area at c\n", + "\n", + "#caliculations \n", + "#Balancing forces in the x direction:\n", + "# Balncing the moments about C and B:\n", + "Fx = 0 \n", + "R_cy = load*(BC+CF) #KN , Reaction at C in y-direction\n", + "R_by = load*(CF) #KN , Reaction at B in y-direction\n", + "#Because of 2 bolts\n", + "stress_max = (R_by/(2*A_crossection_min))*(10**3) # MPA,maximum stess records at minimum area\n", + "stress_shank = (R_by/(2*A_crossection))*(10**3) # MPA\n", + "Bearing_stress_c = (R_cy/contact_area)*(10**3) #MPA, Bearing stress at C\n", + "\n", + "print\"The bearing stress at C is \",(Bearing_stress_c) ,\"MPA\"\n", + "print\"The maximum normal stress in BD bolt is: \",round(stress_max),\"MPA\"\n", + "print\"The tensile strss at shank of the bolt is: \",round(stress_shank),\"MPA\"\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.2 page number 26" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The total weight of pier is 25.0 KN\n", + "The stress at 1 m above is 28.75 MPA\n" + ] + } + ], + "source": [ + "#Given \n", + "load_distributed = 20 #KN/m*2, This is the load distributed over the pier\n", + "H = 2 # m, Total height \n", + "h = 1 #m , point of investigation \n", + "base = 1.5 #m The length of crossection in side veiw \n", + "top = 0.5 #m ,The length where load is distributed on top\n", + "base_inv = 1 #m , the length at the point of investigation \n", + "area = 0.5*1 #m ,The length at a-a crossection \n", + "density_conc = 25 #KN/m*2\n", + "#caliculation of total weight \n", + "\n", + "v_total = ((top+base)/2)*top*H #m*2 ,The total volume \n", + "w_total = v_total* density_conc #KN , The total weight\n", + "R_top = (top**2)*load_distributed #KN , THe reaction force due to load distribution \n", + "reaction_net = w_total + R_top\n", + "\n", + "#caliculation of State of stress at 1m \n", + "v_inv = ((top+base_inv)/2)*top*h #m*2 ,The total volume from 1m to top\n", + "w_inv = v_inv*density_conc #KN , The total weight from 1m to top\n", + "reaction_net = w_inv + R_top #KN\n", + "Stress = reaction_net/area #KN/m*2\n", + "print\"The total weight of pier is\",w_total,\"KN\"\n", + "print\"The stress at 1 m above is\",Stress,\"MPA\"\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.3 page number 27" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Tensile stress in main bar AB: 17.89 Ksi\n", + "Tensile stress in clevis of main bar AB: 11.18 Ksi\n", + "Comprensive stress in main bar BC: 12.93 Ksi\n", + "Bearing stress in pin at C: 18.86 Ksi\n", + "torsion stress in pin at C: -25.62 Ksi\n" + ] + } + ], + "source": [ + "#Given\n", + "from math import pow\n", + "d_pins = 0.375 #inch\n", + "load = 3 #Kips\n", + "AB_x = 6 #inch,X-component\n", + "AB_y = 3 #inch,Y-component \n", + "BC_y = 6 #inch,Y-component\n", + "BC_x = 6 #inch,X-component\n", + "area_AB = 0.25*0.5 #inch*2 \n", + "area_net = 0.20*2*(0.875-0.375) #inch*2 \n", + "area_BC = 0.875*0.25 #inch*2 \n", + "area_pin = d_pins*2*0.20 #inch*2 \n", + "area_pin_crossection = 3.14*((d_pins/2)**2)\n", + "#caliculations\n", + "\n", + "slope = AB_y/ AB_x #For AB\n", + "slope = BC_y/ BC_x #For BC\n", + "\n", + "#momentum at point C:\n", + "F_A_x = (load*AB_x )/(BC_y + AB_y ) #Kips, F_A_x X-component of F_A\n", + "\n", + "#momentum at point A:\n", + "F_C_x = -(load*BC_x)/(BC_y + AB_y ) #Kips, F_C_x X-component of F_c\n", + "\n", + "#X,Y components of F_A\n", + "F_A= (pow(5,0.5)/2)*F_A_x #Kips\n", + "F_A_y = 0.5*F_A_x #Kips\n", + "\n", + "#X,Y components of F_C \n", + "F_C= pow(2,0.5)*F_C_x #Kips\n", + "F_C_y = F_C_x #Kips\n", + "\n", + "T_stress_AB = F_A/area_AB #Ksi , Tensile stress in main bar AB\n", + "stress_clevis = F_A/area_net #Ksi ,Tensile stress in clevis of main bar AB\n", + "c_strees_BC = F_C/area_BC #Ksi , Comprensive stress in main bar BC\n", + "B_stress_pin = F_C/area_pin #Ksi , Bearing stress in pin at C\n", + "To_stress_pin = F_C/area_pin_crossection #Ksi , torsion stress in pin at C\n", + "\n", + "print\"Tensile stress in main bar AB:\",round(T_stress_AB,2),\"Ksi\"\n", + "print\"Tensile stress in clevis of main bar AB:\",round(stress_clevis,2),\"Ksi\"\n", + "print\"Comprensive stress in main bar BC:\",round(-c_strees_BC,2),\"Ksi\"\n", + "print\"Bearing stress in pin at C:\",round(-B_stress_pin,2),\"Ksi\"\n", + "print\"torsion stress in pin at C:\",round(To_stress_pin,2),\"Ksi\"\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.4 page number 38" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The factor 2.5 is less than assumed factor 2.7 so this can be considered\n" + ] + } + ], + "source": [ + "#Given\n", + "strength_steel = 120 #Ksi\n", + "factor = 2.5\n", + "F_C = 2.23 #Ksi\n", + "\n", + "#caliculations\n", + "\n", + "stress_allow = strength_steel/factor #Ksi\n", + "A_net = F_C/strength_steel #in*2 , \n", + "#lets adopt 0.20x0.25 in*2 and check wether we are correct or not? \n", + "\n", + "A_net_assumption = 0.25*0.20 #in*2 , this is assumed area which is near to A_net\n", + "stress = 2.23/A_net_assumption #Ksi\n", + "factor_assumed = strength_steel/stress \n", + "\n", + "if factor_assumed > factor :\n", + " print \"The factor\",factor,\"is less than assumed factor\",round(factor_assumed,1),\"so this can be considered\"\n", + "else:\n", + " print \"The assumed factor\",factor, \"is more than assumed factor\",factor_assumed,\"factor_assumed\"\n", + " \n", + " \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.6 page number 35" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The required size of rod is: 49.35 m*2\n" + ] + } + ], + "source": [ + "#Given\n", + "mass = 5 #Kg\n", + "frequency = 10 #Hz\n", + "stress_allow = 200 #MPa\n", + "R = 0.5 #m\n", + "\n", + "#caliculations \n", + "from math import pi\n", + "w = 2*pi*frequency #rad/sec\n", + "a = (w**2)*R #m*2/sec\n", + "F = mass*a #N\n", + "A_req = F/stress_allow #m*2 , The required area for aloowing stress\n", + "print\"The required size of rod is:\",round(A_req,2),\"m*2\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.7 page number 45" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the allowable area for live load 1.0 is 0.273 in*2\n", + "the allowable area for live load 15 is 0.909 in*2\n", + "the crossection area for live load 1.0 is 0.235 in*2\n", + "the crossection area for live load 15 is 0.926 in*2\n" + ] + } + ], + "source": [ + "#Given\n", + "D_n = 5.0 #kips, dead load\n", + "L_n_1 = 1.0 #kips ,live load 1\n", + "L_n_2 = 15 #kips ,live load 2\n", + "stress_allow = 22 #ksi\n", + "phi = 0.9 #probalistic coefficients\n", + "y_stress = 36 #ksi,Yeild strength\n", + "#According to AISR \n", + "\n", + "#a\n", + "p_1 = D_n + L_n_1 #kips since the total load is sum of dead load and live load\n", + "p_2 = D_n + L_n_2 #kips, For second live load\n", + "\n", + "Area_1 = p_1/stress_allow #in*2 ,the allowable area for the allowed stress\n", + "Area_2 = p_2/stress_allow #in*2\n", + "print \"the allowable area for live load\",L_n_1,\"is\",round(Area_1,3),\"in*2\"\n", + "print \"the allowable area for live load\",L_n_2,\"is\",round(Area_2,3),\"in*2\"\n", + "\n", + "#b\n", + "#area_crossection= (1.2*D_n +1.6L_n)/(phi*y_stress)\n", + "\n", + "area_crossection_1= (1.2*D_n +1.6*L_n_1)/(phi*y_stress) #in*2,crossection area for first live load\n", + "area_crossection_2= (1.2*D_n +1.6*L_n_2)/(phi*y_stress) #in*2,crossection area for second live load\n", + "print \"the crossection area for live load\",L_n_1,\"is\",round(area_crossection_1,3),\"in*2\"\n", + "print \"the crossection area for live load\",L_n_2,\"is\",round(area_crossection_2,3),\"in*2\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.8 page number 51" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Length of the Weld 1: 2.54 in\n", + "Length of the Weld 2: 4.65 in\n" + ] + } + ], + "source": [ + "#Given\n", + "A_angle = 2 #in*2 \n", + "stress_allow = 20 #ksi, The maximum alowable stress\n", + "F = stress_allow*A_angle #K, The maximum force\n", + "AD = 3 #in, from the figure\n", + "DC = 1.06 #in, from the figure\n", + "strength_AWS = 5.56 # kips/in,Allowable strength according to AWS\n", + "\n", + "#caliculations \n", + "#momentum at point \"d\" is equal to 0\n", + "R_1 = (F*DC)/AD #k,Resultant force developed by the weld\n", + "R_2 = (F*(AD-DC))/AD #k,Resultant force developed by the weld\n", + "\n", + "l_1 = R_1/strength_AWS #in,Length of the Weld 1\n", + "l_2 = R_2/strength_AWS #in,Length of the Weld 2\n", + " \n", + "print \"Length of the Weld 1:\",round(l_1,2),\"in\"\n", + "print \"Length of the Weld 2:\",round(l_2,2),\"in\" \n", + " \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter10_3.ipynb b/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter10_3.ipynb new file mode 100644 index 00000000..41e0a194 --- /dev/null +++ b/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter10_3.ipynb @@ -0,0 +1,911 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 10:Deflections of beams " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.1 page number 501" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The maximum bending stress developed in the saw 300.0 Mpa\n" + ] + } + ], + "source": [ + "#Given \n", + "dia = 400 #mm - The diameter of a pulley\n", + "E = 200 #Gpa - Youngs modulus\n", + "t = 0.6 #mm - The thickness of band\n", + "c = t/2 #mm - The maximum stress is seen \n", + "#Caliculations\n", + "\n", + "stress_max = E*c*(10**3)/(dia/2) #Mpa - The maximum stress on the crossection occurs at the ends\n", + "print \"The maximum bending stress developed in the saw \",stress_max,\"Mpa\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.3 page number 512" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a) The maximum displacement in y direction is -0.0130208333333 W(l**4)/EI \n", + "a) The maximum deflection occured at 0.5 L\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "b) The above graph is bending moment graph\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "b)The above graph is beam displacement graph\n", + "b)The maximum occures in the middle from the above graph \n" + ] + } + ], + "source": [ + "#Given\n", + "import numpy\n", + "l_ab = 1.0 #L in - The length of the beam\n", + "F_D = 1.0 #W lb/in - The force distribution \n", + "F = F_D*l_ab #WL - The force applied\n", + "#Beause of symmetry the moment caliculations can be neglected\n", + "#F_Y = 0\n", + "R_A = F/2 #wl - The reactive force at A\n", + "R_B = F/2 #wl - The reactive force at B\n", + "#EI - The flxure rigidity is constant and 1/EI =1 # k\n", + "\n", + "#part - A\n", + "#section 1--1\n", + "l_1 = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1] #L taking each section at 0.1L distance \n", + "M_1 = [0,0,0,0,0,0,0,0,0,0,0]\n", + "v = [0,0,0,0,0,0,0,0,0,0,0]\n", + "for i in range(10):\n", + " v[i] = R_A - F_D*l_1[i] \n", + " M_1[i] = R_A*l_1[i] - F_D*(l_1[i]**2)/2\n", + "# (EI)y'' = M_1[i] we will integrate M_1[i] twice where variable is l_1[i]\n", + "#(EI)y'- \n", + "\n", + "M_1_intg1 = R_A*(l_1[i]**2)/4 - F_D*(l_1[i]**3)/6 - F_D*(l_ab**3)*l_1[i]/24 #integration of x**n = x**n+1/n+1\n", + "#(EI)y- Using end conditions for caliculating constants \n", + "\n", + "M_1_intg2 = R_A*(l_1[i]**3)/12.0 - F_D*(l_1[i]**4)/24.0 + F_D*(l_ab**3)*l_1[i]/24.0 \n", + "#Equations \n", + "\n", + "l_1 = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1] #L taking each section at 0.1L distance \n", + "M_1_intg2 = [0,0,0,0,0,0,0,0,0,0,0]\n", + "Y = [0,0,0,0,0,0,0,0,0,0,0]\n", + "for i in range(10):\n", + " M_1_intg2[i] = (l_1[i]**3)/12.0 - (l_1[i]**4)/24.0 - l_1[i]/24.0 # discluding every term for ruling out float values\n", + " Y[i] = M_1_intg2[i] #W(l**4)/EI k = 1/EI\n", + "#The precision is very less while caliculating through this equation because the least count in X direction is 0.1\n", + "print \"a) The maximum displacement in y direction is\",min(Y),\"W(l**4)/EI \"\n", + "print \"a) The maximum deflection occured at\",l_1[Y.index(min(Y))],\"L\"\n", + "\n", + "#Part - B\n", + "#Graphs\n", + "import numpy as np\n", + "values = M_1\n", + "y = np.array(values)\n", + "t = np.linspace(0,1,11)\n", + "poly_coeff = np.polyfit(t, y, 2)\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "plt.plot(t, y, 'o')\n", + "plt.plot(t, np.poly1d(poly_coeff)(t), '-')\n", + "plt.show()\n", + "print \"b) The above graph is bending moment graph\"\n", + "import numpy as np\n", + "values = Y \n", + "y = np.array(values)\n", + "t = np.linspace(0,1,11)\n", + "poly_coeff = np.polyfit(t, y, 2)\n", + "import matplotlib.pyplot as plt\n", + "plt.plot(t, y, 'o')\n", + "plt.plot(t, np.poly1d(poly_coeff)(t), '-')\n", + "plt.show()\n", + "print \"b)The above graph is beam displacement graph\"\n", + "print \"b)The maximum occures in the middle from the above graph \"\n", + "\n", + "\n", + " \n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.4 page number 514" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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RGHPwePHaa3eSnj6U1167kzZtno7L40W45xwGAu+4eyNgDnB33gAzSwCeAS4D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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "b) The above graph is bending moment graph\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#Given\n", + "l_ab = 1.0 #L in - The length of the beam\n", + "F_D = 1.0 #W lb/in - The force distribution \n", + "F = F_D*l_ab #WL - The force applied\n", + "#Beause of symmetry the moment caliculations can be neglected\n", + "#F_Y = 0\n", + "R_A = F/2 #wl - The reactive force at A\n", + "R_B = F/2 #wl - The reactive force at B\n", + "#EI - The flxure rigidity is constant and 1/EI =1 # k\n", + "#M_A and M_B are applied at the ends\n", + "\n", + "#part - A\n", + "#section 1--1\n", + "l_1 = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1] #L taking each section at 0.1L distance \n", + "M = [0,0,0,0,0,0,0,0,0,0,0]\n", + "for i in range(10):\n", + " M[i] = l_1[i]/2.0 - (l_1[i]**2)/2.0 -1.0/12.0 #The moment euation at 1--1 section\n", + "# M_1 = R_A*l_1[i]/2.0 - F_D*(l_1[i]**2)/2.0 -F_D*(l_ab**2)/12.0 #The moment euation at 1--1 section \n", + "# (EI)y'' = M_1[i] we will integrate M_1[i] twice where variable is l_1[i]\n", + "#(EI)y'\n", + "M_1_intg1 = R_A*(l_1[i]**2)/4 - F_D*(l_1[i]**3)/6 - F_D*(l_ab**2)*l_1[i]/12.0 #integration of x**n = x**n+1/n+1\n", + "#(EI)y\n", + "M_1_intg2[i] = R_A*(l_1[i]**3)/12.0 - F_D*(l_1[i]**4)/24.0 + F_D*(l_ab**2)*(l_1[i]**2)/24.0 \n", + "\n", + "l_1 = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1] #L taking each section at 0.1L distance \n", + "M_1_intg2 = [0,0,0,0,0,0,0,0,0,0,0]\n", + "Y = [0,0,0,0,0,0,0,0,0,0,0]\n", + "for i in range(10):\n", + " M_1_intg2[i] = (l_1[i]**3)/12.0 - (l_1[i]**4)/24.0 - (l_1[i]**2)/24.0 # discluding every term for ruling out float values\n", + " Y[i] = M_1_intg2[i] #W(l**4)/EI k = 1/EI\n", + " \n", + "#Part - B\n", + "#Graphs\n", + "import numpy as np\n", + "values = M\n", + "y = np.array(values)\n", + "t = np.linspace(0,1,11)\n", + "poly_coeff = np.polyfit(t, y, 2)\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline \n", + "plt.plot(t, y, 'o')\n", + "plt.plot(t, np.poly1d(poly_coeff)(t), '-')\n", + "plt.show()\n", + "print \"b) The above graph is bending moment graph\"\n", + "import numpy as np\n", + "values = Y \n", + "y = np.array(values)\n", + "t = np.linspace(0,1,11)\n", + "poly_coeff = np.polyfit(t, y, 2)\n", + "import matplotlib.pyplot as plt\n", + "plt.plot(t, y, 'o')\n", + "plt.plot(t, np.poly1d(poly_coeff)(t), '-')\n", + "plt.show()\n", + "\n", + "\n", + " \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.5 page number 517" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The reaction at A is 0.375 WL\n", + "The reaction at B is 1.125 WL\n", + "The reaction at C is 0.375 WL\n" + ] + } + ], + "source": [ + "#Given \n", + "#because of symmetry the problem can be solved by considering first half\n", + "#Given\n", + "import numpy\n", + "l_ab = 1.0 #L in - The length of the beam\n", + "F_D = 1.0 #W lb/in - The force distribution \n", + "F = F_D*l_ab #WL - The force applied\n", + "#Beause of symmetry the moment caliculations can be neglected\n", + "#EI - The flxure rigidity is constant and 1/EI =1 # k\n", + "\n", + "#part - A\n", + "#section 1--1\n", + "l_1 = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1] #L taking each section at 0.1L distance \n", + "M_1 = [0,0,0,0,0,0,0,0,0,0,0]\n", + "v = [0,0,0,0,0,0,0,0,0,0,0]\n", + "for i in range(10):\n", + " v[i] = R_A - F_D*l_1[i] \n", + " M_1[i] = R_A*l_1[i] - F_D*(l_1[i]**2)/2\n", + "# (EI)y'' = M_1[i] we will integrate M_1[i] twice where variable is l_1[i]\n", + "#(EI)y'\n", + "M_1_intg1 = R_A*(l_1[i]**2)/2 - F_D*(l_1[i]**3)/6 - F_D*(l_ab**3)*l_1[i]/48 #integration of x**n = x**n+1/n+1\n", + "#(EI)y\n", + "M_1_intg2[i] = R_A*(l_1[i]**3)/6 - F_D*(l_1[i]**4)/24.0 - F_D*(l_ab**3)*l_1[i]/48.0 \n", + "#Equations \n", + "#R_A = #wl Unknown- The reactive force at A\n", + "#R_B = #wl - The reactive force at B\n", + "\n", + "# M_1_intg2[10] = 0, the displacement at the end of rod is 0 since its rigid \n", + "R_A = (F_D*(l_1[10]**4)/24.0 + F_D*(l_ab**3)*l_1[10]/48.0)/((l_1[10]**3)/6.0)\n", + "R_C = R_A #WL - symmetry\n", + "R_B = 1-R_A+R_B # WL - F_Y = 0, the equilibrium in Y direction\n", + "print \"The reaction at A is\",R_A ,\"WL\"\n", + "print \"The reaction at B is\",R_B ,\"WL\"\n", + "print \"The reaction at C is\",R_C ,\"WL\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10.7 page number 521 " + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "import numpy as np\n", + "# This problem is divided into two parts\n", + "#Part _1\n", + "#Given\n", + "l = 1.0 #l - The length of the beam\n", + "p = 1.0 #W - The total load applied\n", + "#since it is triangular distribution \n", + "l_com = 0.66*L #l - The distance of force of action from one end\n", + "#F_Y = 0\n", + "#R_A + R_B = p\n", + "#M_a = 0 Implies that R_B = 2*R_A\n", + "R_A = p/3.0\n", + "R_B = 2.0*p/3\n", + "\n", + "#Taking Many sections \n", + "\n", + "#Section 1----1\n", + "l = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1] #L taking each section at 0.1L distance \n", + "M = [0,0,0,0,0,0,0,0,0,0,0]\n", + "v = [0,0,0,0,0,0,0,0,0,0,0]\n", + "for i in range(10):\n", + " v[i] = p*(l[i]**2) - p/3.0\n", + " M[i] = p*(l[i]**3)/(3.0)- p*l[i]/3.0\n", + "\n", + "v[10] = R_B #again concluded Because the value is tearing of \n", + "\n", + "\n", + "#Graph\n", + "values = M\n", + "y = np.array(values)\n", + "t = np.linspace(0,1,11)\n", + "poly_coeff = np.polyfit(t, y, 2)\n", + "plt.plot(t, y, 'o')\n", + "plt.plot(t, np.poly1d(poly_coeff)(t), '-')\n", + "plt.show()\n", + "values = v\n", + "y = np.array(values)\n", + "t = np.linspace(0,1,11)\n", + "poly_coeff = np.polyfit(t, y, 2)\n", + "\n", + "plt.plot(t, y, 'o')\n", + "plt.plot(t, np.poly1d(poly_coeff)(t), '-')\n", + "plt.show()\n", + "\n", + "\n", + "#part B\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter11_3.ipynb b/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter11_3.ipynb new file mode 100644 index 00000000..aa2f8723 --- /dev/null +++ b/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter11_3.ipynb @@ -0,0 +1,375 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:1a88ac8a4ae99a352f7f49d975099441ec02a55d62cfaa2e8c07de364172180d" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 11:Stability of Equilibrium: columns " + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.2 page number 589" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Given \n", + "h = 60 #mm - the length of the crossection \n", + "b = 100 #mm - the width of hte crossection \n", + "E = 200 #Gpa - The youngs modulus\n", + "stress_cr = 250 #Mpa - The proportionality limit\n", + "#Caliculations \n", + "\n", + "I = b*(h**3)/12 #mm3 The momentof inertia of the crossection\n", + "A = h*b #mm2 - The area of teh crossection \n", + "#From Eulier formula\n", + "r_min = pow((I/A),0.5) #mm - The radius of the gyration \n", + "#(l/r)**2= (pi**2)*E/stress_cr #From Eulier formula\n", + "l = (((math.pi**2)*E*(10**3)/stress_cr)**0.5)*r_min #mm - the length after which the beam starts buckling\n", + "print \"The length after which the beam starts buckling is \",round(l,0),\"mm\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The length after which the beam starts buckling is 1539.0 mm\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 11.6 page number 613" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Given\n", + "L = 15 #ft - The length of the each rod\n", + "A = 46.7 #in2 - The length of the crossection \n", + "r_min = 4 #in - The radius of gyration\n", + "stress_yp = 36 #Ksi - the yielding point stress\n", + "E = 29*(10**3) #ksi - The youngs modulus\n", + "C_c = ((2*(math.pi**2)*E/stress_yp)**0.5) #Slenderness ratio L/R\n", + "C_s = L*12/r_min # Slenderness ratio L/R of the present situation \n", + "#According to AISC formulas \n", + "if C_s 1:\n", + " print \"The following W10x49 section is not satisfying our constraints since f_a/F_a_1 + c_m*f_b*(1-(f_a/F_e))/F_b\",round(k,3),\">1\"\n", + "else:\n", + " print \"The following W10x49 section is satisfying our constraints since f_a/F_a_1 + c_m*f_b*(1-(f_a/F_e))/F_b\",k,\"<1\"\n", + " \n", + "#trail - 2\n", + "#Lets take W10 x 60\n", + "A_s = 17.6 #in2 - The area of the section \n", + "r_min = 2.57 #in The minimum radius \n", + "r_x = 4.39 #in \n", + "f_a = P/A_s #Ksi- The computed axial stress\n", + "f_b = M_2*B_x/A_s #Computed bending stess\n", + "C_c = ((2*(math.pi**2)*E/F_y)**0.5) #Slenderness ratio L/R\n", + "C_s = L*12/r_min # Slenderness ratio L/R of the present situation\n", + "if C_s 1:\n", + " print \"The following W10x49 section is not satisfying our constraints since f_a/F_a_1 + c_m*f_b*(1-(f_a/F_e))/F_b\",round(k,3),\">1\"\n", + "else:\n", + " print \"The following W10x49 section is satisfying our constraints since f_a/F_a_1 + c_m*f_b*(1-(f_a/F_e))/F_b\",round(k,2),\"<1\"\n", + " \n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The minimum area is 13.71 in2\n", + "The following approch is solvable\n", + "The following W10x49 section is not satisfying our constraints since f_a/F_a_1 + c_m*f_b*(1-(f_a/F_e))/F_b 1.09 >1\n", + "The following approch is solvable\n", + "The following W10x49 section is satisfying our constraints since f_a/F_a_1 + c_m*f_b*(1-(f_a/F_e))/F_b 0.9 <1\n" + ] + } + ], + "prompt_number": 67 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +} \ No newline at end of file diff --git a/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter12_3.ipynb b/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter12_3.ipynb new file mode 100644 index 00000000..13fb52c7 --- /dev/null +++ b/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter12_3.ipynb @@ -0,0 +1,405 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:aaf5a5f62a391d916c40aa2d720de6a3e7681d1c9c64ec2fdbeff148819b3c75" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Chapter 12:Energy and Virtual-work Methods" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.1 page number 645 " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Given\n", + "#Virtual loading\n", + "p_ab = -0.833 #lb The recorded virtual loading\n", + "p_bc = + 0.833 #lb The recorded virtual loading\n", + "F_ab = 2500 #lb\n", + "F_bc = -2500 #lb\n", + "l_ab = 60 #in - The length of the rod\n", + "l_bc = 60 #in - The length of the rod\n", + "A_ab = 0.15 #in2 the areaof ab\n", + "A_bc = 0.25 #in2 the areaof bc\n", + "E = 30*(10**6) #psi The youngs modulus of the material\n", + "#Part_a\n", + "e_a =p_ab*l_ab*F_ab/(A_ab*E) + p_bc*l_bc*F_bc/(A_bc*E) #in the deflection\n", + "if e_a<0:\n", + " print \"a) The deflection is downwards\",round(-e_a,3),\"in\"\n", + "else:\n", + " print \"a) The deflection is upwards\",round(e_a,3),\"in\"\n", + "#part-b\n", + "x = 0.125 #Shortening of member Ab\n", + "e_b = p_ab*(-x) + p_bc*0 #in - in\n", + "if e_b<0:\n", + " print \"b) The deflection is downwards\",round(-e_b,3),\"in\"\n", + "else:\n", + " print \"b) The deflection is upwards\",round(e_b,3),\"in\"\n", + "#Part-c\n", + "S = 6.5*(10**-6) #Thermal specific heat\n", + "T = 120 #F - The cahnge in temperature\n", + "e_t = -S*T*l_ab #in - The change in length of member\n", + "e_c = p_bc*e_t #in the deflection\n", + "if e_c<0:\n", + " print \"c) The deflection is downwards\",round(-e_c,3),\"in\"\n", + "else:\n", + " print \"c) The deflection is upwards\",round(e_c,3),\"in\"\n", + "\n", + "\n", + " \n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "a) The deflection is downwards 0.044 in\n", + "b) The deflection is upwards 0.104 in\n", + "c) The deflection is downwards 0.039 in\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.3 page number 648" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Given\n", + "#Virtual loading\n", + "#Two parts \n", + "#Part -1 \n", + "p_ab = 5 #KN The recorded virtual loading\n", + "p_bc = -4 #KN The recorded virtual loading\n", + "F_ab = 10 #KN\n", + "F_bc = -8 #KN\n", + "l_ab = 2.5 #mt - The length of the rod\n", + "l_bc = 2 #mt - The length of the rod\n", + "A_ab = 5*(10**-4) #mt2 the areaof ab\n", + "A_bc = 5*(10**-3) #mt2 the areaof bc\n", + "E = 70 #Gpa The youngs modulus of the material\n", + "e_a =(p_ab*l_ab*F_ab/(A_ab*E) + p_bc*l_bc*F_bc/(A_bc*E))*(10**-6) #KN-m\n", + "#Part -2 due to flexure\n", + "I = 60*10**6 #mm4 - the moment of inertia \n", + "#After solving the integration \n", + "e_b = 0.01525 #KN-m\n", + "#Total\n", + "e = (e_a+e_b)*1 #m\n", + "print \"The point C deflects\",round(e,3),\"mt down\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The point C deflects 0.019 mt\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.5 page number 651" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Given\n", + "#Virtual loading Without f_d\n", + "p_ab = -0.833 #lb The recorded virtual loading\n", + "p_bc = + 0.833 #lb The recorded virtual loading\n", + "F_ab = 2500 #lb\n", + "F_bc = -2500 #lb\n", + "l_ab = 60 #in - The length of the rod\n", + "l_bc = 60 #in - The length of the rod\n", + "A_ab = 0.15 #in2 the areaof ab\n", + "A_bc = 0.25 #in2 the areaof bc\n", + "E = 30*(10**6) #psi The youngs modulus of the material\n", + "#Part_a\n", + "e_a =p_ab*l_ab*F_ab/(A_ab*E) + p_bc*l_bc*F_bc/(A_bc*E) #lb-in the deflection\n", + "#With f_d\n", + "p_bd = 1 #lb The recorded virtual loading \n", + "F_bd = 1 #lb\n", + "l_bd = 40 #in - The length of the rod\n", + "A_bd = 0.1 #in2 the areaof ab\n", + "e_a_1 =p_ab*p_ab*l_ab/(A_ab*E) + p_bc*p_bc*l_bc/(A_bc*E) +p_bd*p_bd*l_bd/(A_bd*E) #lb-in the deflection\n", + "#Since the produced defelection should compensate the other one\n", + "x_d = e_a/e_a_1\n", + "print \"The reaction force at D is\",round(-x_d,2),\"lb\"\n", + "\n", + "#Part - B\n", + "e_b = -x_d*l_bd/(A_bd*E ) #in - The deflection of nodal point B\n", + "print\"The deflection of nodal point B\",round(e_b,4),\"in\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The reaction force at D is 1578.98 lb\n", + "The deflection of nodal point B 0.0211 in\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.6 page number 655" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Given\n", + "#Virtual loading\n", + "p_ab = -0.833 #lb The recorded virtual loading\n", + "p_bc = + 0.833 #lb The recorded virtual loading \n", + "l_ab = 60 #in - The length of the rod\n", + "l_bc = 60 #in - The length of the rod\n", + "A_ab = 0.15 #in2 the areaof ab\n", + "A_bc = 0.25 #in2 the areaof bc\n", + "E = 30*(10**6) #psi The youngs modulus of the material\n", + "K_1 = A_ab*E/l_ab #k/in - Stiffness\n", + "K_2 = A_bc*E/l_bc #k/in - Stiffness\n", + "#soving for e_1 and e_2 gives a liner euations to solve\n", + "# 128*e_1 + 24*e_2 = 0\n", + "#24*e_1 + 72*e_2 = -3\n", + "#Solving for e_1,e_2\n", + "a = np.array([[128,24], [24,72]])\n", + "b = np.array([0,-3])\n", + "x = np.linalg.solve(a, b)\n", + "e_1 = x[0] #in\n", + "e_2 = x[1] #in\n", + "u_1 = 0.8*e_1 - 0.6*e_2 #Taking each components\n", + "F_1 = K_1*u_1*(10**-3) #k The reaction at A Force = stiffness x dislacement \n", + "u_2 = 0.8*e_1 + 0.6*e_2 #Taking each components\n", + "F_2 = K_2*u_2*(10**-3) #k The reaction at B Force\n", + "print \"The reaction at A \",F_1,\"k\"\n", + "print \"The reaction at B \",F_2,\"k\"\n", + "\n", + "\n", + "\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The reaction at A 2.5 k\n", + "The reaction at B -2.5 k\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.7 page number 655" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Virtual loading\n", + "p_ab = -0.833 #lb The recorded virtual loading\n", + "p_bc = + 0.833 #lb The recorded virtual loading \n", + "l_ab = 60 #in - The length of the rod\n", + "l_bc = 60 #in - The length of the rod\n", + "A_ab = 0.15 #in2 the areaof ab\n", + "A_bc = 0.25 #in2 the areaof bc\n", + "E = 30*(10**6) #psi The youngs modulus of the material\n", + "K_1 = A_ab*E/l_ab #k/in - Stiffness\n", + "K_2 = A_bc*E/l_bc #k/in - Stiffness\n", + "p_bd = 1 #lb The recorded virtual loading \n", + "F_bd = 1 #lb\n", + "l_bd = 40 #in - The length of the rod\n", + "A_bd = 0.1 #in2 the areaof ab\n", + "K_3 = A_ab*E/l_ab #k/in - Stiffness\n", + "#soving for e_1 and e_2 gives a liner euations to solve\n", + "# 128*e_1 + 24*e_2 = 0\n", + "#24*e_1 + 72*e_2 = -3\n", + "#Solving for e_1,e_2\n", + "a = np.array([[128,24], [24,147]])\n", + "b = np.array([0,-3])\n", + "x = np.linalg.solve(a, b)\n", + "e_1 = x[0] #in\n", + "e_2 = x[1] #in\n", + "u_1 = 0.8*e_1 - 0.6*e_2 #Taking each components\n", + "F_1 = K_1*u_1*(10**-3) #k The reaction at A Force = stiffness x dislacement \n", + "u_2 = 0.8*e_1 + 0.6*e_2 #Taking each components\n", + "F_2 = K_2*u_2*(10**-3) #k The reaction at B Force\n", + "u_3 = e_2 #Taking each components\n", + "F_3 = K_3*u_3*(10**-3) #k The reaction at D Force\n", + "print \"The reaction at A \",round(F_1,2),\"k\"\n", + "print \"The reaction at B \",round(F_2,2),\"k\"\n", + "print \"The reaction at D \",round(F_3,2),\"k\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The reaction at A 1.18 k\n", + "The reaction at B -1.18 k\n", + "The reaction at D -1.58 k\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.8 page number 659" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Given\n", + "#First we will solve part B\n", + "u_1 =5 #L/AE, elastic elongation\n", + "u_2 =25 #L/AE,elastic elongation\n", + "f_1 = u_1#, Units got neutralized , Constitutive relation for elastic bars\n", + "f_2 = u_2# Units got neutralized\n", + "#u_1 = 0.8*e_1 - 0.6*e_2\n", + "#u_2 = 0.8*e_1 + 0.6*e_2\n", + "#u = A*e Matric multiplication \n", + "A = np.array([[0.8,-0.6],[0.8,0.6]]) #The matrix form of A\n", + "F = np.array([[f_1],[f_2]])\n", + "P = np.dot((A.T),F) #Nodal forces matrix\n", + "print \"b) The vertical component of the nodal force is\",P[1],\"\"\n", + "print \"b) The vertical component of the nodal force is\",P[0],\"\"\n", + "#Part A\n", + "#F_1 = (5/8.0)*P_1 - (5/6.0)*p_2 , From statics\n", + "#F_1 = (5/8.0)*P_1 + (5/6.0)*p_2\n", + "#F = BP ,Matric multiplication \n", + "B = np.array([[(5/8.0),-(5/6.0)],[(5/8.0),(5/6.0)]]) #The matrix form of A\n", + "U = np.array([[u_1],[u_2]])\n", + "e = P = np.dot((B.T),U) #L/AE, Nodal forces matrix\n", + "print \"a) The components of displacement of point B are\",round(e[0],2),\"L/AE and\",round(e[1],2),\"L/AE\" \n", + "\n", + "\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "b) The vertical component of the nodal force is [ 12.] \n", + "b) The vertical component of the nodal force is [ 24.] \n", + "a) The components of displacement of point B are 18.75 L/AE and 16.67 L/AE\n" + ] + } + ], + "prompt_number": 26 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 12.10 page number 667" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Given\n", + "A_1 = 0.125 #in2 , The area of the crossection of AB\n", + "A_2 = 0.219 #in2 , The area of the crossection of BC\n", + "l_1 = 3*(5**0.5) #in , The length of AB\n", + "l_2 = 6*(2**0.5) #in , The length of BC\n", + "p = 3 #k , Force acting on the system \n", + "E = 10.6*(10**3) #Ksi - youngs modulus of the material\n", + "p_1 = (5**0.5)*p/3 #P, The component of p on AB\n", + "p_2 = -2*(2**0.5)*p/3 #P, The component of p on AB\n", + "\n", + "e = p_1*l_1*p_1/(p*E*A_1) + p_2*l_2*p_2/(p*E*A_2) #in, By virtual deflection method \n", + "print \"The deflection is\",round(e,3),\"in\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The deflection is 0.018 in\n" + ] + } + ], + "prompt_number": 32 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +} \ No newline at end of file diff --git a/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter13_2.ipynb b/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter13_2.ipynb new file mode 100644 index 00000000..fcb4383a --- /dev/null +++ b/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter13_2.ipynb @@ -0,0 +1,226 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 13: Statically Indeterminate Problems" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 13.2 page number 693" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a) The maximum displacement in y direction is -0.208333333333 W(l**4)/EI \n", + "a) The maximum deflection occured at 1.0 L\n", + "The reaction at the mid of the bar 1.25 WL\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "b)The above graph is beam displacement graph\n", + "b)The minimum occures in the middle from the above graph \n" + ] + } + ], + "source": [ + "#Given \n", + "#First we will solve without the reaction at middle\n", + "#Given\n", + "import numpy\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "l_ab = 1.0 #2L in - The length of the beam\n", + "F_D = 1.0 #W lb/in - The force distribution \n", + "F = F_D*l_ab #WL - The force applied\n", + "#Beause of symmetry the moment caliculations can be neglected\n", + "#F_Y = 0\n", + "R_A = F/2 #wl - The reactive force at A\n", + "R_B = F/2 #wl - The reactive force at B\n", + "#EI - The flxure rigidity is constant and 1/EI =1 # k\n", + "\n", + "#part - A\n", + "#section 1--1\n", + "l_1 = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1] #L taking each section at 0.2L distance \n", + "M_1 = [0,0,0,0,0,0,0,0,0,0,0]\n", + "v = [0,0,0,0,0,0,0,0,0,0,0]\n", + "for i in range(10):\n", + " v[i] = R_A - F_D*l_1[i] \n", + " M_1[i] = R_A*l_1[i] - F_D*(l_1[i]**2)/2\n", + "# (EI)y'' = M_1[i] we will integrate M_1[i] twice where variable is l_1[i]\n", + "#(EI)y'- \n", + "\n", + "M_1_intg1 = R_A*(l_1[i]**2)/4 - F_D*(l_1[i]**3)/6 - F_D*(l_ab**3)*l_1[i]/24 #integration of x**n = x**n+1/n+1\n", + "#(EI)y- Using end conditions for caliculating constants \n", + "\n", + "M_1_intg2 = R_A*(l_1[i]**3)/12.0 - F_D*(l_1[i]**4)/24.0 + F_D*(l_ab**3)*l_1[i]/24.0 \n", + "#Equations \n", + "\n", + "l_1 = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1] #L taking each section at 0.2L distance \n", + "M_1_intg2 = [0,0,0,0,0,0,0,0,0,0,0]\n", + "Y = [0,0,0,0,0,0,0,0,0,0,0]\n", + "for i in range(10):\n", + " M_1_intg2[i] = (l_1[i]**3)/12.0 - (l_1[i]**4)/24.0 - l_1[i]/24.0 # discluding every term for ruling out float values\n", + " Y[i] = M_1_intg2[i] #W(l**4)/EI k = 1/EI\n", + "Y_min = 16*min(Y)\n", + "print \"a) The maximum displacement in y direction is\",16*min(Y),\"W(l**4)/EI \"\n", + "print \"a) The maximum deflection occured at\",2*l_1[Y.index(min(Y))],\"L\"\n", + "f_bb = 2**3/48.0 #l**3/EI - flexibility coefficient\n", + "Reac = - Y_min/f_bb #WL , The reaction at the mid of the bar\n", + "print \"The reaction at the mid of the bar\",Reac ,\"WL\"\n", + "\n", + "#Graphs \n", + "Y.extend(Y) #Because of symmetry\n", + "values = Y \n", + "y = np.array(values)\n", + "t = np.linspace(0,1,22)\n", + "poly_coeff = np.polyfit(t, y, 2)\n", + "\n", + "plt.plot(t, y, 'o')\n", + "plt.plot(t, np.poly1d(poly_coeff)(t), '-')\n", + "plt.show()\n", + "print \"b)The above graph is beam displacement graph\"\n", + "print \"b)The minimum occures in the middle from the above graph \"\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 13.3 page number 694 " + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The reactive moment at A i.e M_A -0.0714285714286 WL**2\n", + "The reactive force at A i.e R_A -1.14285714286 WL\n" + ] + } + ], + "source": [ + "#Given \n", + "#First we will solve without the reaction at middle\n", + "#Given\n", + "import numpy\n", + "l_ab = 1.0 #2L in - The length of the beam\n", + "F_D = 1.0 #W lb/in - The force distribution \n", + "F = F_D*l_ab #WL - The force applied\n", + "#Beause of symmetry the moment caliculations can be neglected\n", + "#F_Y = 0\n", + "R_A = F/2 #wl - The reactive force at A\n", + "R_B = F/2 #wl - The reactive force at B\n", + "#EI - The flxure rigidity is constant and 1/EI =1 # k\n", + "\n", + "#part - A\n", + "#section 1--1\n", + "l_1 = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1] #L taking each section at 0.2L distance \n", + "M_1 = [0,0,0,0,0,0,0,0,0,0,0]\n", + "v = [0,0,0,0,0,0,0,0,0,0,0]\n", + "for i in range(10):\n", + " v[i] = R_A - F_D*l_1[i] \n", + " M_1[i] = R_A*l_1[i] - F_D*(l_1[i]**2)/2\n", + "# (EI)y'' = M_1[i] we will integrate M_1[i] twice where variable is l_1[i]\n", + "#(EI)y'- \n", + "\n", + "M_1_intg1 = R_A*(l_1[i]**2)/4 - F_D*(l_1[i]**3)/6 - F_D*(l_ab**3)*l_1[i]/24 #integration of x**n = x**n+1/n+1\n", + "#(EI)y- Using end conditions for caliculating constants \n", + "\n", + "M_1_intg2 = R_A*(l_1[i]**3)/12.0 - F_D*(l_1[i]**4)/24.0 + F_D*(l_ab**3)*l_1[i]/24.0 \n", + "#Equations \n", + "\n", + "l_1 = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1] #L taking each section at 0.2L distance \n", + "M_1_intg2 = [0,0,0,0,0,0,0,0,0,0,0]\n", + "Y = [0,0,0,0,0,0,0,0,0,0,0]\n", + "for i in range(10):\n", + " M_1_intg2[i] = (l_1[i]**3)/12.0 - (l_1[i]**4)/24.0 - l_1[i]/24.0 # discluding every term for ruling out float values\n", + " Y[i] = M_1_intg2[i] #W(l**4)/EI k = 1/EI\n", + "e_1 = 16*min(Y) #WL4/EI - The maximum defection \n", + "e_2 = - F_D*((2*l_ab)**3)/24.0 #WL3/EI - The maximum angle\n", + "#Caliculating for momentum and force\n", + "f_ab = ((2*l_ab)**2)/16.0 #L2/EI \n", + "f_bb = ((2*l_ab)**3)/48.0 #L3/EI \n", + "f_aa = 2*l_ab/3.0 #L/EI\n", + "f_ba = ((l_ab)**2)/4.0 #L2/EI\n", + "#F*X = e - Matrix multiplication \n", + "#Solving for X\n", + "a = np.array([[f_aa,f_ba], [f_ba,f_bb]])\n", + "b = np.array([e_2,e_1])\n", + "x = np.linalg.solve(a, b)\n", + "print \"The reactive moment at A i.e M_A\",x[0],\"WL**2\"\n", + "print \"The reactive force at A i.e R_A\",x[1],\"WL\"\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#Given \n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter2_3.ipynb b/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter2_3.ipynb new file mode 100644 index 00000000..5c92d3ed --- /dev/null +++ b/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter2_3.ipynb @@ -0,0 +1,327 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:f3ccf4fb6d13add26a342446f0908b75d3a6a82c442b340e601708c15ec3ca4f" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 2:Axial strains and Deformations in bars " + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.1 page number 77" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "l_ob = 2000 #mm - length of rod ob\n", + "l_bc = 1000 #mm - length of rod bc\n", + "l_cd = 1500 #mm - length of rod cd\n", + "p_ob = 100 #kN - Force in rods \n", + "p_bc = -150 #KN\n", + "p_cd = 50 #KN \n", + "A_ob = 1000 #mm2 - Area of rod ob\n", + "A_bc = 2000 #mm2 - Area of rod bc \n", + "A_cd = 1000 #mm2 - Area of rod cd\n", + "E = 200.0 #GPA \n", + "# the total deflection is algebraic sums of `deflection in each module \n", + "e_1 = p_ob*l_ob/(A_ob*E)\n", + "e_2 = p_bc*l_bc/(A_bc*E)\n", + "e_3 = p_cd*l_cd/(A_cd*E)\n", + "#All units are satisfied \n", + "e_total = e_1+ e_2 + e_3\n", + "print \"The total deflection is :\",round(e_total,3) ,\"mm\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The total deflection is : 1.0 mm\n" + ] + } + ], + "prompt_number": 77 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.4 page number 80" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "p_app = 3 #Kips - applied force \n", + "P_A = 2.23 #Kips \n", + "p_B = -2.83 #kips - compressive force\n", + "l_ab = 6.71 #inch\n", + "l_bc = 8.29 #inch\n", + "s_ab = 17.8 #ksi - tensile stress\n", + "s_bc = -12.9 #ksi - compressive stress\n", + "E = 10.6 * pow(10,3) #ksi -youngs modulus \n", + "e_ab = s_ab*l_ab/E\n", + "\n", + "e_bc = s_bc*l_bc/E\n", + "x = e_ab/e_bc #the Ratio of cosines of the deflected angles \n", + "# t_1 and t_2 be deflected angles \n", + "#t_2 = 180-45-26.6-t_1 the sum of angles is 360\n", + "#t_1 = 52.2 degress\n", + "import math\n", + "e = e_ab/math.acos(math.radians(52.2)) #inch\n", + "k = p_app/e # kips/in vertical stiffness of the combination\n", + "print \"The vertical stiffness of the combination is\",round(k,3),\"kips/inch\"\n", + "\n", + "\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "0.0112677358491\n", + "The vertical stiffness of the combination is 113.14 kips/inch\n" + ] + } + ], + "prompt_number": 36 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.6 page number 83" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "dia = 50 #mm - diameter of aluminium \n", + "p = 100 # KN - instant force applid\n", + "dia_c = 0.1215 #mm- change in diameter \n", + "l_c = 0.219 #mm - change in length\n", + "l = 300 #mm - length \n", + "strain_dia = dia_c/dia # lateral strain \n", + "strain_l = l_c/l #longitudinal strain \n", + "po = strain_dia/strain_l # poission ratio \n", + "area = 3.14*dia*dia/4 #mm2 area\n", + "E = p*l/(area*l_c) #N/mm2 youngs modulus \n", + "print \"The lateral strain is:\",strain_dia,\"no units\"\n", + "print \"The longitudinal strain is:\",strain_l,\"no units\"\n", + "print \"The poissions ratio is:\",po,\"no units\"\n", + "print \"Youngs modulus:\",round(E,2),\"N/mm2\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The lateral strain is: 0.00243 no units\n", + "The longitudinal strain is: 0.00073 no units\n", + "The poissions ratio is: 3.32876712329 no units\n", + "Youngs modulus: 69.8 N/mm2\n" + ] + } + ], + "prompt_number": 34 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.7 page number 86" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "T = 12.9*pow(10,-6) #/F\n", + "t = 100.00 # F \n", + "e_ab = T*t*l_ab #in-elongation \n", + "e_bc = T*t*l_bc #in-elongation\n", + "k = e_ab/e_bc # ratio of cosines of deflected angles \n", + "# t_1 and t_2 be deflected angles \n", + "#t_2 = 180-45-26.6-t_1 the sum of angles is 360\n", + "t_1 = 26.6\n", + "import math\n", + "e = e_ab/math.acos(math.radians(26.6))\n", + "print \"The displacement in point B is :\",e ,\"in\"\n", + "\n", + "\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The displacement in point B is : 0.00795578950395 in\n" + ] + } + ], + "prompt_number": 78 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.11 page number " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "mass = 4 #kg \n", + "dist = 1 #mt freely falling distance\n", + "l = 1500 #mm length of rod\n", + "d = 15 #mm diameter\n", + "E = 200 #GPA youngs modulus \n", + "k = 4.5 # N/mm stiffness costant\n", + "F = mass*9.81# The force applying\n", + "Area = 3.14*(d**2)/4 \n", + "# Two cases \n", + "#youngs modulus \n", + "e_y = F*l/(Area*E*pow(10,3))\n", + "# stiffness\n", + "e_f = F/k \n", + "#total\n", + "e = e_y +e_f\n", + "k = 1+(2/(e*pow(10,-3)))\n", + "stress_max_1 = F*(1+pow(k,0.5))/Area\n", + "print \"The maximum stress is:\",stress_max_1,\"Mpa\"\n", + "\n", + "\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The maximum stress is: 3.59377281766 Mpa\n" + ] + } + ], + "prompt_number": 56 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.12 page number 103" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "flex_a = 1#f\n", + "flex_b = 2#f\n", + "#removing lower support and solving FBD\n", + "e = -2 -(2+1)#fp\n", + "#e_1 = (2+1+1)*R\n", + "#e_1 = -e Making the elongations zero since the both ends are fixed\n", + "R = e/(2+1+1.0) #p\n", + "print \"The reactions at bottom is\",R,\"p\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The reactions at bottom is -1.25 p\n" + ] + } + ], + "prompt_number": 75 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.19 page number 113" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Given \n", + "l = 30 #in - The length of the rod\n", + "p_1 = 80 #kips - The Force on the end\n", + "p_2 = 125 #kips - The force on the other end\n", + "A_s = 0.5 #in2 - The crossection of the steel rod\n", + "A_a = 0.5 #in2 - The crossection of the aluminium \n", + "E_a = 10*(10**6) #psi - The youngs modulus of the aluminium \n", + "E_s = 30*(10**6) #psi - The youngs modulus of the steel\n", + "#Internally stastically indeterminant \n", + "p_a = p_1/4 #From solving we get p_s = 3*P_a\n", + "#From material properties point of view \n", + "#stress_steel = stress_aluminium\n", + "e = p_a*l*(10**3)/(A_a*E_a) #The end deflection \n", + "print \"The end deflection is\",e,\"in\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The end deflection is 0.12 in\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +} \ No newline at end of file diff --git a/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter4_3.ipynb b/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter4_3.ipynb new file mode 100644 index 00000000..4b0d1868 --- /dev/null +++ b/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter4_3.ipynb @@ -0,0 +1,457 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 4:Torsion" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.2 page number 183" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The maximum shear due to torsion is 152.87 Mpa\n", + "stress tensor matrix" + ] + }, + { + "ename": "NameError", + "evalue": "name 'ceil' is not defined", + "output_type": "error", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[0;32m 12\u001b[0m \u001b[0marr_T\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mshear_T\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;31m#arranging the elements in array\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 13\u001b[0m \u001b[0marr_T\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mshear_T\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 14\u001b[1;33m \u001b[1;32mprint\u001b[0m \u001b[1;34m\"stress tensor matrix\"\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mceil\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0marr_T\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 15\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;31mNameError\u001b[0m: name 'ceil' is not defined" + ] + } + ], + "source": [ + "#Given\n", + "dia = 10 #diameter of shaft(A-C)\n", + "c = dia/2 #mm - Radius\n", + "T = 30 #N/mm -Torque in the shaft \n", + "#Caliculations\n", + "\n", + "J = 3.14*(dia**4)/32 #mm4\n", + "shear_T = T*c*pow(10,3)/J # The torsion shear in the shaft AC\n", + "import numpy as np \n", + "print \"The maximum shear due to torsion is \",round(shear_T,2),\"Mpa\"\n", + "arr_T = np.zeros((3,3))\n", + "arr_T[0][1]=round(shear_T,1) #arranging the elements in array\n", + "arr_T[1][0]=round(shear_T,1)\n", + "print \"stress tensor matrix\",ceil(arr_T),\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.3 page number 184" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The maximum shear due to torsion is 43.15 Mpa\n", + "The minimum shear due to torsion is 34.52 Mpa\n" + ] + } + ], + "source": [ + "#Given \n", + "dia_out = 20 #mm- outer diameter of shaft\n", + "dia_in = 16 #mm- inner diameter of shaft \n", + "c_out = dia_out/2 #mm - outer Radius of shaft \n", + "c_in = dia_in/2 #mm - inner radius of shaft \n", + "T = 40 #N/mm -Torque in the shaft \n", + "#caliculations\n", + "\n", + "J = 3.14*((dia_out**4)- (dia_in**4))/32 #mm4\n", + "shear_T_max = T*c_out*pow(10,3)/J # The maximum torsion shear in the shaft\n", + "shear_T_min = T*c_in*pow(10,3)/J # The maximum torsion shear in the shaft\n", + "print \"The maximum shear due to torsion is \",round(shear_T_max,2),\"Mpa\"\n", + "print \"The minimum shear due to torsion is \",round(shear_T_min,2),\"Mpa\"\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.4 page number 187" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The Diameter of the shaft used is 15.26 mm\n" + ] + } + ], + "source": [ + "#Given\n", + "hp = 10 # horse power of motor \n", + "f = 30 # given \n", + "shear_T = 55 #Mpa - The maximum shearing in the shaft \n", + "#caliculations\n", + "\n", + "T = 119*hp/f # N.m The torsion in the shaft \n", + "#j/c=T/shear_T=K\n", + "k = T*pow(10,3)/shear_T #mm3\n", + "#c3=2K/3.14\n", + "c = pow((2*k/3),0.33) #mm - The radius of the shaft \n", + "diamter = 2*c #mm - The diameter of the shaft\n", + "print \"The Diameter of the shaft used is\",round(diamter,2),\"mm\"\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.5 page number 188" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The Diameter of the shaft1 is 6.87 mm\n", + "The Diameter of the shaft2 is 0.702590481015 mm\n" + ] + } + ], + "source": [ + "#Given \n", + "hp = 200 #Horse power\n", + "stress_sh = 10000 #psi- shear stress\n", + "rpm_1 = 20.0 # The rpm at which this shaft1 operates \n", + "rpm_2 = 20000.0 # The rpm at which this shaft2 operates\n", + "T_1= hp*63000.0/rpm_1 #in-lb Torsion due to rpm1\n", + "T_2= hp*63000/rpm_2 #in-lb Torsion due to rpm1\n", + "#caliculations \n", + "\n", + "#j/c=T/shear_T=K\n", + "k_1= T_1/stress_sh #mm3\n", + "#c3=2K/3.14\n", + "c_1= pow((2*k_1/3),0.33) #mm - The radius of the shaft \n", + "diamter_1 = 2*c_1 #mm - The diameter of the shaft\n", + "print \"The Diameter of the shaft1 is\",round(diamter_1,2),\"mm\"\n", + "\n", + "#j/c=T/shear_T=K\n", + "k_2= T_2/stress_sh #mm3\n", + "#c3=2K/3.14\n", + "c_2= pow((2*k_2/3),0.33) #mm - The radius of the shaft \n", + "diamter_2 = 2*c_2 #mm - The diameter of the shaft\n", + "print \"The Diameter of the shaft2 is\",diamter_2,\"mm\"\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.7 page number 193" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The maximum angle rotated is 0.0232628450106 radians \n" + ] + } + ], + "source": [ + "#Given \n", + "T_ab = 0 #N.m - torsion in AB \n", + "T_bc = 150 #N.m - torsion in BC\n", + "T_cd = 150 #N.m - torsion in CD\n", + "T_de = 1150 #N.m - torsion in DE\n", + "l_ab = 250 #mm - length of AB\n", + "l_bc = 200 #mm - length of BC\n", + "l_cd = 300 #mm - length of cd \n", + "l_de = 500.0 #mm - length of de\n", + "d_1 = 25 #mm - outer diameter \n", + "d_2 = 50 #mm - inner diameter\n", + "G = 80 #Gpa -shear modulus\n", + "#Caliculations \n", + "\n", + "J_ab = 3.14*(d_1**4)/32 #mm4\n", + "J_bc = 3.14*(d_1**4)/32 #mm4\n", + "J_cd = 3.14*(d_2**4 - d_1**4)/32 #mm4\n", + "J_de = 3.14*(d_2**4 - d_1**4)/32 #mm4\n", + "rad = T_ab*l_ab/(J_ab*G)+ T_bc*l_bc/(J_bc*G)+ T_cd*l_cd/(J_cd*G)+ T_de*l_de/(J_de*G) # adding the maximum radians roteted in each module\n", + "print \"The maximum angle rotated is \",rad,\"radians \" " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.9 Pagenumber 196" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The Torsion at rigid end A is -141.72 N-m\n", + "The Torsion at rigid end B is 1291.72 N-m\n" + ] + } + ], + "source": [ + "#given \n", + "#its a statistally indeterminant \n", + "#we will take of one of the support \n", + "#Given \n", + "T_ab = 0 #N.m - torsion in AB \n", + "T_bc = 150 #N.m - torsion in BC\n", + "T_cd = 150 #N.m - torsion in CD\n", + "T_de = 1150 #N.m - torsion in DE\n", + "l_ab = 250 #mm - length of AB\n", + "l_bc = 200 #mm - length of BC\n", + "l_cd = 300 #mm - length of cd \n", + "l_de = 500.0#mm - length of de\n", + "d_1 = 25 #mm - outer diameter \n", + "d_2 = 50 #mm - inner diameter\n", + "#Caliculations \n", + "\n", + "J_ab = 3.14*(d_1**4)/32 #mm4\n", + "J_bc = 3.14*(d_1**4)/32 #mm4\n", + "J_cd = 3.14*(d_2**4 - d_1**4)/32 #mm4\n", + "J_de = 3.14*(d_2**4 - d_1**4)/32 #mm4\n", + "G = 80 #Gpa -shear modulus\n", + "rad = T_ab*l_ab/(J_ab*G)+ T_bc*l_bc/(J_bc*G)+ T_cd*l_cd/(J_cd*G)+ T_de*l_de/(J_de*G) \n", + "#now lets consider T_A then the torsion is only T_A\n", + "# T_A*(l_ab/(J_ab*G)+ l_bc/(J_bc*G)+ l_cd/(J_cd*G)+ l_de/(J_de*G)) +rad = 0\n", + "# since there will be no displacement \n", + "T_A =-rad/(l_ab/(J_ab*G)+ l_bc/(J_bc*G)+ l_cd/(J_cd*G)+ l_de/(J_de*G)) #Torsion at A\n", + "T_B = 1150 - T_A #n-m F_X = 0 torsion at B\n", + "print \"The Torsion at rigid end A is\",round(T_A,2),\"N-m\"\n", + "print \"The Torsion at rigid end B is\",round(T_B,2),\"N-m\"\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.12 Pagenumber 202" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The allowable torsion on the 8 bolt combination 27129600.0 N-m\n" + ] + } + ], + "source": [ + "#Given\n", + "dai_bc = 240 #mm- daimeter of '8'bolt circle \n", + "dia = dai_bc/8 #Diameter of each bolt\n", + "A = 0.25*(dia**2)*3.14 # Area of a bolt\n", + "S_allow = 40 #Mpa - The maximum allowable allowable shear stress \n", + "P_max = (S_allow)*A #N - The maximum allowable force \n", + "D = 120.0 #mm - the distance from central axis \n", + "T_allow =P_max*D*8 #N-m The allowable torsion on the 8 bolt combination \n", + "print \"The allowable torsion on the 8 bolt combination\",T_allow ,\"N-m\"\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.15 page number 211" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the Equivalent Torsion constant is 1.97 in4\n" + ] + } + ], + "source": [ + "#Given \n", + "#AISC MANUALS\n", + "#approximated by three narrow tubes \n", + "#J = Bbt^3\n", + "B = 0.33 # constant mentiones in AISC\n", + "#three rods \n", + "\n", + "#rod_1\n", + "t_1 = 0.605 #inch - Thickness \n", + "b = 12.0 #inches - width \n", + "J_1 = B*b*(t_1**3) #in4 - Torsion constant \n", + "\n", + "#rod_2\n", + "t_2 = 0.605 #inch - Thickness \n", + "b = 12 #inches - width \n", + "J_2 = B*b*(t_2**3) #in4 - Torsion constant \n", + "\n", + "#rod_3\n", + "t_3 = 0.390 #inch - Thickness \n", + "b = 10.91 #inches - width \n", + "J_3 = B*b*(t_3**3) #in4 - Torsion constant \n", + "\n", + "#Equivalent\n", + "J_eq = J_1+J_2+J_3 #in4 - Torsion constant \n", + "print \"the Equivalent Torsion constant is \",round(J_eq,2), \"in4\"\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.16 page number 214" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The maximum shear due to torsion is 345.23 Mpa\n", + "The minimum shear due to torsion is 276.18 Mpa\n" + ] + } + ], + "source": [ + "#Given \n", + "dia_out = 10 #mm- outer diameter of shaft\n", + "dia_in = 8 #mm- inner diameter of shaft \n", + "c_out = dia_out/2 #mm - outer Radius of shaft \n", + "c_in = dia_in/2 #mm - inner radius of shaft \n", + "T = 40 #N/mm -Torque in the shaft \n", + "#caliculations\n", + "\n", + "J = 3.14*((dia_out**4)- (dia_in**4))/32 #mm4\n", + "shear_T_max = T*c_out*pow(10,3)/J # The maximum torsion shear in the shaft\n", + "shear_T_min = T*c_in*pow(10,3)/J # The maximum torsion shear in the shaft\n", + "print \"The maximum shear due to torsion is \",round(shear_T_max,2),\"Mpa\"\n", + "print \"The minimum shear due to torsion is \",round(shear_T_min,2),\"Mpa\"" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter5_3.ipynb b/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter5_3.ipynb new file mode 100644 index 00000000..568c7262 --- /dev/null +++ b/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter5_3.ipynb @@ -0,0 +1,892 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Chapter 5:Axial force, Shear and Bending moment " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example5.2 pagenumber 231" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The X,Y components of reaction force at A is 0 , -410.0 N\n", + "The X,Y components of reaction force at B is 0 , 670.0 N\n" + ] + } + ], + "source": [ + "#Given \n", + "L_ab = 0.4 #mt The total length of the rod\n", + "M = 200 #N_m - the moment acting on rod\n", + "l_1 = 0.1 #mt -moment acting point the distance from 'a'\n", + "R_1 = 100 #N - The Force acting \n", + "l_2 = 0.2 #mt -R_1 acting point the distance from 'a'\n", + "R_2 = 160 #N The Force acting \n", + "l_3 = 0.3 #mt -R_2 acting point the distance from 'a'\n", + "#caliculations\n", + "\n", + "#F_X = 0 forces in x directions \n", + "R_A_X = 0 # since there are no forces in X-direction \n", + "R_B_X = 0\n", + "#M_A = 0 momentum at point a is zero\n", + "\n", + "# M + R_1*l_2 + R_2*l_3 = R_B*L_ab *the moment for a force is FxL\n", + "R_B_Y = (M + R_1*l_2 + R_2*l_3)/L_ab\n", + "\n", + "#M_B= 0 momentum at point b is zero\n", + "# R_A_Y*L_ab + M - R_1*l_2 - R_2*0.1 = 0\n", + "\n", + "R_A_Y = -(M - R_1*l_2 - R_2*0.1)/L_ab\n", + " \n", + "print \"The X,Y components of reaction force at A is \",R_A_X,\",\",R_A_Y,\"N\"\n", + "print \"The X,Y components of reaction force at B is \",R_B_X,\",\",R_B_Y,\"N\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.2 page number 233" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The X,Y components of reaction force at A is 0 , -9.0 N\n", + "The X,Y components of reaction force at B is 0 , 6.0 N\n" + ] + } + ], + "source": [ + "#Given \n", + "P_Max = 10 #N - the maximum distribution in a triangular distribution\n", + "L = 3 #mt the total length of force distribution \n", + "L_X = 5 #mt - the horizantal length of the rod\n", + "#caliculations \n", + "\n", + "F_y = P_Max*L*0.5 #N - The force due to triangular distribition \n", + "L_com = 2*L /3 #mt - the resultant force acting as a result of distribution acting position \n", + "#F_X = 0 forces in x directions\n", + "R_A_X = 0 # since there are no forces in X-direction\n", + "R_B_X = 0\n", + "#M_A = 0 momentum at point a is zero\n", + "#F_y*L_com - R_B_Y*L_X = 0\n", + "R_B_Y = F_y*L_com/L_X\n", + "\n", + "#M_B= 0 momentum at point b is zero\n", + "#- R_A_Y*L_X = F_y*(L_X-L )\n", + "\n", + "R_A_Y = - F_y*L/L_X \n", + "print \"The X,Y components of reaction force at A is \",R_A_X,\",\",R_A_Y,\"N\"\n", + "print \"The X,Y components of reaction force at B is \",R_B_X,\",\",R_B_Y,\"N\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.3 page number 233 " + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The X,Y components and resultant of reaction force at A is 4 , 3 , 5.0 N\n", + "The X,Y components and resultant of reaction force at B is 1 , 1 , 1.41 N\n" + ] + } + ], + "source": [ + "#given\n", + "F = 5 #K - force acting on the system\n", + "tan = (4/3) # the Tan of the angle of force with x axis\n", + "l_ab = 12 #inch - the total length of ab \n", + "l = 3 # inch - Distance from 'a'\n", + "#caliculation\n", + "F_X = 4 #K\n", + "F_Y = 3 #k\n", + "\n", + "#M_A = 0 momentum at point a is zero\n", + "# F_X*l- R_B_Y*l_ab = 0 \n", + "R_B_Y = F_X*l/l_ab\n", + "\n", + "#M_B= 0 momentum at point b is zero\n", + "# R_A_Y*l_ab - F_X*(l_ab - l)\n", + "R_A_Y = F_X*(l_ab - l)/l_ab\n", + " \n", + "#F_X = 0 forces in x directions\n", + "R_A_X = F_Y + R_B_Y \n", + "R_B_X = R_B_Y # since the angle is 45 degrees\n", + "\n", + "#resultants \n", + "R_A = pow(R_A_X**2 + R_A_Y**2,0.5)\n", + "R_B = pow(R_B_X**2 + R_B_Y**2,0.5)\n", + "\n", + "print \"The X,Y components and resultant of reaction force at A is \",R_A_X,\",\",R_A_Y,\",\",R_A,\"N\"\n", + "print \"The X,Y components and resultant of reaction force at B is \",R_B_X,\",\",R_B_Y,\",\",round(R_B,2),\"N\"\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.4 page number 239" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The force and moment in section a--a are -2.33 KN , -13.644 KN-m\n", + "The force and moment in section b--b are 6.0 KN , 6.0 KN-m\n" + ] + } + ], + "source": [ + "#Given \n", + "P_Max = 10 #N - the maximum distribution in a triangular distribution\n", + "L = 3 #mt the total length of force distribution \n", + "L_X = 5 #mt - the horizantal length of the rod\n", + "#caliculations \n", + "\n", + "F_y = P_Max*L*0.5 #N - The force due to triangular distribition \n", + "L_com = 2*L /3 #mt - the resultant force acting as a result of distribution acting position \n", + "#F_X = 0 forces in x directions\n", + "R_A_X = 0 # since there are no forces in X-direction\n", + "R_B_X = 0\n", + "#M_A = 0 momentum at point a is zero\n", + "#F_y*L_com - R_B_Y*L_X = 0\n", + "R_B_Y = F_y*L_com/L_X\n", + "\n", + "#M_B= 0 momentum at point b is zero\n", + "#- R_A_Y*L_X = F_y*(L_X-L )\n", + "\n", + "R_A_Y = - F_y*L/L_X\n", + "\n", + "#For a---a section \n", + "l_a = 2 #mt - a---a section from a \n", + "l_com_a = 2*l_a/3\n", + "v_a = R_A_Y + 0.5*l_a*(10.0*2/3) #*(10*2/3) because the maximum moves\n", + "\n", + "M_a = (10.0*0.66)*l_a*(0.33) + R_A_Y*l_a \n", + "\n", + "#For b---b section \n", + "\n", + "v_b = F_y + R_A_Y #equilabrium conditions\n", + "M_b = (F_Y + R_A_Y)*(-1)\n", + "\n", + "print \"The force and moment in section a--a are\",round(v_a,2),\"KN ,\",M_a,\"KN-m\"\n", + "print \"The force and moment in section b--b are\",v_b,\"KN ,\",M_b,\"KN-m\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.5 page number 241" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Given problem is for drawing diagram, this diagram is drawn by step by step manner. \n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#Given \n", + "#Lets divide the section into two sections \n", + "l_ac = 10 # ft -The total length of the rod\n", + "R = 5 #k - The applies force at c\n", + "tan = 4/3 # The tan of the angle of the force \n", + "l_ab = 5 #ft - The distance of applied force from A\n", + "R_y = 4 #k,downwards X- component of the force\n", + "R_X = 3 #k Y- component of the force , lets consider only Y direction since we are concentrating on the Shears \n", + "\n", + "#F_Y = 0 forces in Y directions\n", + "#R_A +R_B = R_y\n", + "#M_c = 0 making the moment zero at point c \n", + "#Caliculations \n", + "# R_A= R_B*(l_ac - l_ab)/(l_ab) so R_A = R_B\n", + "\n", + "R_A = R_y/2 #F_Y = 0\n", + "R_B = R_y/2\n", + "#considering section x--x\n", + "l_x = 2 #ft - length of section from A\n", + "v_x = R_A #k ,F_X = 0 \n", + "M_x = R_A*l_x #k-ft M_c = 0\n", + "\n", + "#considering section at midpoint t--t\n", + "l_t = 2 #ft - length of section from A\n", + "v_t = 0 #k ,F_X = 0 \n", + "M_t = (R_A)*l_t #k-ft M_c = 0\n", + "\n", + "##considering section y---y\n", + "l_y = 2 #ft - length of section from B\n", + "v_y = - R_B #k ,F_X = 0 \n", + "M_y = R_B*l_y #k-ft M_c = 0\n", + "\n", + "#Graph\n", + "%matplotlib inline\n", + "import math \n", + "from matplotlib.pyplot import plot,suptitle,xlabel,ylabel\n", + "#Drawing of shear and bending moment diagram\n", + "print \"Given problem is for drawing diagram, this diagram is drawn by step by step manner. \"\n", + "X = [0,2,4.9999999999999,5,5.00000000000000001,7,10] # For graph precision \n", + "\n", + "V = [R_A,v_x,v_x,v_t,v_y,v_y,-R_B];\t\t\t#Shear matrix\n", + "M = [0,M_x,M_t,M_t,M_t,M_y,0];\t\t\t#Bending moment matrix\n", + "plot(X,V);\t\t\t#Shear diagram\n", + "plot(X,M,'r');\t\t\t#Bending moment diagram\n", + "suptitle( 'Shear and bending moment diagram')\n", + "xlabel('X axis')\n", + "ylabel( 'Y axis') ;" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.6 pagenumber 243 " + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Given problem is for drawing diagram, this diagram is drawn by step by step manner. \n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#Given\n", + "l = 1 #L - Length of the cantilever \n", + "F_app = ((2**0.5))*2 #p - force applies \n", + "tan = 1 # The angle of force applied\n", + "F_app_x = F_app/((2**0.5)) #p The horizantal component of the force , neglected \n", + "F_app_y = F_app/((2**0.5)) #p The Vertical component of the force \n", + "#F_Y = 0 \n", + "R_A = 1 #p\n", + "\n", + "#Considering section 1-----1\n", + "l_1 = 0.5 # The length of the section from one end\n", + "v_1 = R_A #F_Y = 0\n", + "M_1 = -R_A*l_1 #MAking moment at section 1 = 0\n", + "\n", + "#considering end of cantilever\n", + "l_2 = 1 # The length of the section from one end\n", + "v_2 = R_A #F_Y = 0\n", + "M_2 = -R_A*l_2#MAking moment at section 1 = 0\n", + "\n", + "#Graph\n", + "%matplotlib inline\n", + "import math \n", + "from matplotlib.pyplot import plot,suptitle,xlabel,ylabel\n", + "#Drawing of shear and bending moment diagram\n", + "print \"Given problem is for drawing diagram, this diagram is drawn by step by step manner. \"\n", + "X = [0,0.5,1] # For graph precision \n", + "\n", + "V = [R_A,v_1,v_2 ];\t\t\t#Shear matrix\n", + "M = [0,M_1,M_2];\t\t\t#Bending moment matrix\n", + "plot(X,V);\t\t\t #Shear diagram\n", + "plot(X,M,'r');\t\t\t #Bending moment diagram\n", + "suptitle( 'Shear and bending moment diagram')\n", + "xlabel('X axis')\n", + "ylabel( 'Y axis') ;\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.7 page number 243" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Given problem is for drawing diagram, this diagram is drawn by step by step manner. \n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#Given\n", + "l_ab = 3 #L - The total length lets say '3L'\n", + "R_1 = 1 #p - The force applied at b\n", + "R_2 = 1 #p - The force applied at c\n", + "l_ab = 1 #L\n", + "l_bc = 1 #L \n", + "\n", + "#Logical step \n", + "#Since the system is in symmetry we can avoid moment M = 0 caliculations\n", + "\n", + "#F_Y = 0 \n", + "R_A = (R_1 + R_2)/2\n", + "R_B = (R_1 + R_2)/2\n", + "\n", + "#Lets take '3' sections \n", + "#Considering section 1-----1 at 0.5L\n", + "l_1 = 0.5 #L - distance of the section from the A\n", + "v_1 = R_A #F_Y = 0 \n", + "M_1 = R_A*l_1 #MAking moment at section 1 = 0\n", + "\n", + "#Considering section 2-----2 at 1L\n", + "l_2 = 1 #L - distance of the section from the A\n", + "v_2 = R_A #F_Y = 0 \n", + "M_2 = R_A*l_2 #MAking moment at section 2 = 0\n", + "\n", + "#Considering section 3-----3 at 1.5L\n", + "l_3 = 1.5 #L - distance of the section from the A\n", + "v_3 = 0 #F_Y = 0 \n", + "M_3 = R_A*l_2 #MAking moment at section 2 = 0 and symmetry \n", + "\n", + "#GRAPH\n", + "#Since the symmetry exists the graphs are also symmetry\n", + "%matplotlib inline\n", + "import math \n", + "from matplotlib.pyplot import plot,suptitle,xlabel,ylabel\n", + "#Drawing of shear and bending moment diagram\n", + "print \"Given problem is for drawing diagram, this diagram is drawn by step by step manner. \"\n", + "X = [0,0.5,1,1.000000001,1.5,1.999999999999,2,2.5,3] # For graph precision \n", + "\n", + "V = [R_A,v_1,v_2,v_3,v_3,v_3,-v_2,-v_1,-R_B];\t\t\t#Shear matrix\n", + "M = [0,M_1,M_2,1,1,1,M_2,M_1,0];\t\t\t#Bending moment matrix\n", + "plot(X,V);\t\t\t#Shear diagram\n", + "plot(X,M);\t\t\t#Bending moment diagram\n", + "suptitle( 'Shear and bending moment diagram')\n", + "xlabel('X axis')\n", + "ylabel( 'Y axis') ;" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.8 page nmber 244" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.5\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#Given \n", + "l_ab = 1.0 #L - The length of the beam\n", + "F_D = 1.0 #W - The force distribution \n", + "F = F_D*l_ab #WL - The force applied\n", + "#Beause of symmetry the moment caliculations can be neglected\n", + "#F_Y = 0\n", + "R_A = F/2 #wl - The reactive force at A\n", + "R_B = F/2 #wl - The reactive force at B\n", + "\n", + "#considering many sections \n", + "\n", + "#section 1--1\n", + "l_1 = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1] #L taking each section at 0.1L distance \n", + "M_1 = [0,0,0,0,0,0,0,0,0,0,0]\n", + "v = [0,0,0,0,0,0,0,0,0,0,0]\n", + "for i in range(10):\n", + " v[i] = R_A - F_D*l_1[i] \n", + " M_1[i] = R_A*l_1[i] - F_D*(l_1[i]**2)/2 #M = 0 in the section\n", + "print R_A\n", + "#Graphs\n", + "import numpy as np\n", + "values = [0.5,0,-0.5]\n", + "y = np.array(values)\n", + "t = np.linspace(0,1,3)\n", + "poly_coeff = np.polyfit(t, y, 2)\n", + "import matplotlib.pyplot as plt\n", + "plt.plot(t, y, 'o')\n", + "plt.plot(t, np.poly1d(poly_coeff)(t), '-')\n", + "plt.show()\n", + "\n", + "import numpy as np\n", + "values = M_1\n", + "y = np.array(values)\n", + "t = np.linspace(0,1,11)\n", + "poly_coeff = np.polyfit(t, y, 2)\n", + "import matplotlib.pyplot as plt\n", + "plt.plot(t, y, 'o')\n", + "plt.plot(t, np.poly1d(poly_coeff)(t), '-')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.9 page number 245" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The force and moment in section a--a are -2.33 KN , -13.644 KN-m\n" + ] + } + ], + "source": [ + "#Given \n", + "P_Max = 10 #N - the maximum distribution in a triangular distribution\n", + "L = 3 #mt the total length of force distribution \n", + "L_X = 5 #mt - the horizantal length of the rod\n", + "#caliculations \n", + "\n", + "F_y = P_Max*L*0.5 #N - The force due to triangular distribition \n", + "L_com = 2*L /3 #mt - the resultant force acting as a result of distribution acting position \n", + "#F_X = 0 forces in x directions\n", + "R_A_X = 0 # since there are no forces in X-direction\n", + "R_B_X = 0\n", + "#M_A = 0 momentum at point a is zero\n", + "#F_y*L_com - R_B_Y*L_X = 0\n", + "R_B_Y = F_y*L_com/L_X\n", + "\n", + "#M_B= 0 momentum at point b is zero\n", + "#- R_A_Y*L_X = F_y*(L_X-L )\n", + "\n", + "R_A_Y = - F_y*L/L_X\n", + "\n", + "#caliculating for some random value\n", + "#For a---a section \n", + "l_a = 2 #mt - a---a section from a \n", + "l_com_a = 2*l_a/3\n", + "v_a = R_A_Y + 0.5*l_a*(10.0*2/3) #*(10*2/3) because the maximum moves\n", + "\n", + "M_a = (10.0*0.66)*l_a*(0.33) + R_A_Y*l_a\n", + "\n", + "print \"The force and moment in section a--a are\",round(v_a,2),\"KN ,\",M_a,\"KN-m\"\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.13 page number 254" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Given problem is for drawing diagram, this diagram is drawn by step by step manner. \n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#Given\n", + "l_ab = 4 #L - The total length lets say '3L'\n", + "R_1 = 1 #p - The force applied at b\n", + "R_2 = 1 #p - The force applied at c\n", + "l_ab = 1 #L\n", + "l_bc = 3 #L \n", + "\n", + "#Logical step \n", + "#Since the system is in symmetry we can avoid moment M = 0 caliculations\n", + "\n", + "#F_Y = 0 \n", + "R_A = (R_1 + R_2)/2\n", + "R_B = (R_1 + R_2)/2\n", + "\n", + "#Lets take '3' sections \n", + "#Considering section 1-----1 at 0.5L\n", + "l_1 = 0.5 #L - distance of the section from the A\n", + "v_1 = R_A #F_Y = 0 \n", + "M_1 = R_A*l_1 #MAking moment at section 1 = 0\n", + "\n", + "#Considering section 2-----2 at 1L\n", + "l_2 = 1 #L - distance of the section from the A\n", + "v_2 = R_A #F_Y = 0 \n", + "M_2 = R_A*l_2 #MAking moment at section 2 = 0\n", + "\n", + "#Considering section 3-----3 at 1.5L\n", + "l_3 = 3 #L - distance of the section from the A\n", + "v_3 = 0 #F_Y = 0 \n", + "M_3 = R_A*l_2 #MAking moment at section 2 = 0 and symmetry \n", + "\n", + "#GRAPH\n", + "#Since the symmetry exists the graphs are also symmetry\n", + "%matplotlib inline\n", + "import math \n", + "from matplotlib.pyplot import plot,suptitle,xlabel,ylabel\n", + "#Drawing of shear and bending moment diagram\n", + "print \"Given problem is for drawing diagram, this diagram is drawn by step by step manner. \"\n", + "X = [0,0.5,1,1.0000001,2,2.9999999999,3,3.5,4] # For graph precision \n", + "\n", + "V = [R_A,v_1,v_2,v_3,v_3,v_3,-v_2,-v_1,-R_B];\t\t\t#Shear matrix\n", + "M = [0,M_1,M_2,M_3,M_3,M_3,M_2,M_1,0];\t\t\t#Bending moment matrix\n", + "plot(X,V);\t\t\t#Shear diagram\n", + "plot(X,M);\t\t\t#Bending moment diagram\n", + "suptitle( 'Shear and bending moment diagram')\n", + "xlabel('X axis')\n", + "ylabel( 'Y axis') ;" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.14 page number 255" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#Given\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "l = 1.0 #l - The length of the beam\n", + "p = 1.0 #W - The total load applied\n", + "#since it is triangular distribution \n", + "l_com = 0.66*l#l - The distance of force of action from one end\n", + "#F_Y = 0\n", + "#R_A + R_B = p\n", + "#M_a = 0 Implies that R_B = 2*R_A\n", + "R_A = p/3.0\n", + "R_B = 2.0*p/3\n", + "\n", + "#Taking Many sections \n", + "\n", + "#Section 1----1\n", + "l = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1] #L taking each section at 0.1L distance \n", + "M = [0,0,0,0,0,0,0,0,0,0,0]\n", + "v = [0,0,0,0,0,0,0,0,0,0,0]\n", + "for i in range(10):\n", + " v[i] = p*(l[i]**2) - p/3.0\n", + " M[i] = p*(l[i]**3)/(3.0)- p*l[i]/3.0\n", + "\n", + "v[10] = R_B #again concluded Because the value is tearing of \n", + "\n", + "\n", + "#Graph\n", + "values = M\n", + "y = np.array(values)\n", + "t = np.linspace(0,1,11)\n", + "poly_coeff = np.polyfit(t, y, 2)\n", + "\n", + "plt.plot(t, y, 'o')\n", + "plt.plot(t, np.poly1d(poly_coeff)(t), '-')\n", + "plt.show()\n", + "\n", + "values = v\n", + "y = np.array(values)\n", + "t = np.linspace(0,1,11)\n", + "poly_coeff = np.polyfit(t, y, 2)\n", + "\n", + "plt.plot(t, y, 'o')\n", + "plt.plot(t, np.poly1d(poly_coeff)(t), '-')\n", + "plt.show()\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.16 page number 259" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.166666666667\n", + "Given problem is for drawing diagram, this diagram is drawn by step by step manner. \n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#Given\n", + "import math \n", + "from matplotlib.pyplot import plot,suptitle,xlabel,ylabel\n", + "l = 6.0 #a - length of the rod\n", + "F = 1.0 #p - force applies in x direction \n", + "d = 1.0 #a \n", + "M = 1.0 #pa - torque applies on the rod\n", + "l_ab = 4.0 #a application of torque point from A\n", + "#M = 0 implies that\n", + "R_A = F/6.0 #p - The reaction at A\n", + "R_B = - R_A #F_Y = 0\n", + "\n", + "#Caliculations \n", + "\n", + "#Taking sections \n", + "#Section 1---1\n", + "l_1 = 1 #a - the length of the section \n", + "M_1 = - R_A*l_1 #M = 0\n", + "\n", + "#Section 2---2\n", + "l_2 = 4 #a - the length of the section \n", + "M_2 = - R_A*l_2 #M = 0\n", + "\n", + "l_4 = 2 #a - the length of the section \n", + "M_4 = 1/3.0 #pa #M = 0 '-M' because there is moment couple in between\n", + "\n", + "\n", + "#Section 3---3\n", + "l_3 = 1 #a - the length of the section \n", + "M_3 = 1/6.0#pa M = 0 '-M' because there is moment couple in between\n", + "print R_A\n", + "\n", + "#GRAPH\n", + "#Since the symmetry exists the graphs are also symmetry\n", + "%matplotlib inline\n", + "#Drawing of shear and bending moment diagram\n", + "print \"Given problem is for drawing diagram, this diagram is drawn by step by step manner. \"\n", + "X = [0,1,4,4.00001,5,6] # For graph precision \n", + "M = [0,M_1,M_2,M_4,M_3,0];\t\t\t#Bending moment matrix\n", + "plot(X,M);\t\t\t#Bending moment diagram\n", + "suptitle( 'Shear and bending moment diagram')\n", + "xlabel('X axis')\n", + "ylabel( 'Y axis') ;\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter6_3.ipynb b/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter6_3.ipynb new file mode 100644 index 00000000..a76cd86c --- /dev/null +++ b/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter6_3.ipynb @@ -0,0 +1,578 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:6a2b99a338c7d2a71ec20bddeaf4c19ec8da980602f4c9834a7faee562a1e5cc" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 6:Pure Bending and Bending with Axial force " + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.3 page number 293" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Given \n", + "#Entire area - hallow area\n", + "l_e = 60.0 #mm - length of the entire area\n", + "b_e = 40 #mm - width of the entire area\n", + "l_h = 30 #mm - length of the hallow area\n", + "b_h = 20 #mm - width of the hallow area\n", + "A_e = l_e*b_e #mm2 - The entire area\n", + "A_h = -l_h*b_h #mm2 - The hallow area '-' because its hallow\n", + "A_re = A_e + A_h #mm2 resultant area\n", + "y_e = l_e/2 # mm com from bottom \n", + "y_h = 20+l_h/2 #mm com from bottom \n", + "y_com = (A_e*y_e + A_h*y_h)/A_re \n", + "#moment of inertia caliculatins - bh3/12 +ad2\n", + "I_e = b_e*(l_e**3)/12 + A_e*((y_e-y_com)**2) #Parallel axis theorm\n", + "I_h = b_h*(l_h**3)/12 - A_h*((y_h-y_com)**2) #Parallel axis theorm\n", + "I_total = I_e - I_h\n", + "print \"The moment of inertia of total system is \",I_total,\"mm4\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The moment of inertia of total system is 655000.0 mm4\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.4 page number 295" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Given \n", + "l = 400 #mm - Length \n", + "b = 300 #mm - breath \n", + "F = 20 #KN _ the force applied on the beam \n", + "F_d = 0.75 #KN-m - The force distribution \n", + "d = 2 #mt - the point of interest from the free end\n", + "#caliculations \n", + "#From moment diagram\n", + "M = F*d - F_d*d*1\n", + "I = b*(l**3)/12 #mm4 - Bending moment diagram \n", + "c = l/2 # the stress max at this C\n", + "S = I/c #The maximum shear stress \n", + "shear_max = M*(10**6)/S #MPA - the maximum stress \n", + "print \"The maximum stress at 2 mt is\",round(shear_max,2),\"Mpa\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The maximum stress at 2 mt is 4.81 Mpa\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.5 pagr number 297" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Given \n", + "#We will divide this into three parts\n", + "F = 8 #k - force applied\n", + "d = 16 #inch -distance\n", + "l_1 = 1 #in \n", + "l_2 = 3 #in \n", + "b_1 = 4 #in \n", + "b_2 = 1 #in\n", + "A_1 = l_1* b_1 #in2 - area of part_1\n", + "y_1 = 0.5 #in com distance from ab\n", + "A_2 =l_2*b_2 #in2 - area of part_1\n", + "y_2 = 2.5 #in com distance from ab\n", + "A_3 = l_2*b_2 #in2 - area of part_1\n", + "y_3 = 2.5 #in com distance from ab\n", + "\n", + "y_net = (A_1*y_1 +A_2*y_2 + A_3*y_3)/(A_1+A_2+A_3) #in - The com of the whole system\n", + "c_max = (4-y_net) #in - The maximum distace from com to end\n", + "c_min = y_net #in - the minimum distance from com to end\n", + "I_1 = b_1*(l_1**3)/12 + A_1*((y_1-y_net)**2) #Parallel axis theorm\n", + "I_2 = b_2*(l_2**3)/12 + A_2*((y_2-y_net)**2)\n", + "I_3 = b_2*(l_2**3)/12 + A_2*((y_2-y_net)**2)\n", + "I_net = I_1 + I_2 + I_3 #in4 - the total moment of inertia\n", + "M_c = F*d*c_max \n", + "stress_cmax = M_c/I_net #Ksi - The maximum compressive stress\n", + "\n", + "M_t= F*d*c_min \n", + "stress_tmax = M_t/I_net #Ksi - The maximum tensile stress\n", + "print \"The maximum tensile stress\",stress_tmax ,\"Ksi\"\n", + "print \"The maximum compressive stress\",round(stress_cmax,1) ,\"Ksi\"\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The maximum tensile stress 16.0 Ksi\n", + "The maximum compressive stress 21.6 Ksi\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.8 page number 303" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Given \n", + "#Given \n", + "#We will divide this into two parts\n", + "E_w = 10.0 #Gpa - Youngs modulus of wood\n", + "E_s = 200.0 #Gpa - Youngs modulus of steel\n", + "M = 30.0 #K.N-m _ applied bending moment \n", + "n = E_s/E_w \n", + "l_1 = 250 #mm \n", + "l_2 = 10 #mm\n", + "b_1 = 150.0 #mm\n", + "b_2 = 150.0*n #mm\n", + "A_1 = l_1* b_1 #mm2 - area of part_1\n", + "y_1 = 125.0 #mm com distance from top\n", + "A_2 =l_2*b_2 #mm2 - area of part_1\n", + "y_2 = 255.0 #mm com distance from top\n", + "y_net = (A_1*y_1 +A_2*y_2)/(A_1+A_2) #mm - The com of the whole system from top\n", + "I_1 = b_1*(l_1**3)/12.0 + A_1*((y_1-y_net)**2) #Parallel axis theorm\n", + "I_2 = b_2*(l_2**3)/12.0 + A_2*((y_2-y_net)**2)\n", + "I_net = I_1 + I_2 #mm4 - the total moment of inertia\n", + "c_s= y_net # The maximum distance in steel \n", + "stress_steel = M*(10.0**6)*c_s/I_net #Mpa - The maximum stress in steel \n", + "\n", + "c_w= l_1+l_2-y_net # The maximum distance in wood \n", + "stress_wood = n*M*(10.0**6)*c_w/I_net #MPa - The maximum stress in wood \n", + "\n", + "print \"The maximum stress in steel \",round(stress_steel,2) ,\"Mpa\"\n", + "print \"The maximum stress in wood\",round(stress_wood,2) ,\"Mpa\" \n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The maximum stress in steel 11.49 Mpa\n", + "The maximum stress in wood 97.09 Mpa\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.9 page number 305" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Given \n", + "M = 50000 #ft-lb , positive bending moment applied\n", + "N = 9 # number of steel bars \n", + "n = 15 # The ratio of steel to concrete \n", + "A_s = 30 #in2 area of steel in concrete\n", + "#(10*y)*(y/2) = 30*(20-y)\n", + "#y**2 + 6*y -120\n", + "#solving quadractic equation \n", + "import math\n", + "\n", + "a = 1\n", + "b = 6\n", + "c = -120\n", + "# calculate the discriminant\n", + "d = (b**2) - (4*a*c)\n", + "\n", + "# find two solutions\n", + "sol1 = (-b-math.sqrt(d))/(2*a)\n", + "sol2 = (-b+math.sqrt(d))/(2*a)\n", + "y = sol2 # Nuetral axis is found\n", + "l_1 = y #in- the concrete below nuetral axis is not considered\n", + "b_1 = 10 #in - width\n", + "A_1 = l_1* b_1 #in2 - area of concrete\n", + "y_1 = y/2 #in com of the concrete \n", + "y_2 = 20-y #in com of the transformed steel \n", + "I_1 = b_1*(l_1**3)/12.0 + A_1*((y_1-y)**2) #in4 parallel axis theorm\n", + "I_2 = A_s*((y_2)**2) #in4 first part is neglected\n", + "I_net = I_1 + I_2 #in4 - the total moment of inertia\n", + "c_c= y #in The maximum distance in concrete \n", + "stress_concrete = M*12*c_c/I_net #psi - The maximum stress in concrete \n", + "c_s= 20- y \n", + "stress_steel =n*M*12*c_s/I_net #psi - The maximum stress in concrete \n", + "print \"The maximum stress in concrete \",round(stress_concrete,2) ,\"psi\"\n", + "print \"The stress in steel\",round(stress_steel,2) ,\"psi\"\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The maximum stress in concrete 834.07 psi\n", + "The stress in steel 17427.61 psi\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "example 6.10 page number 309" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Given \n", + "l = 50.0 #mm - the length of the beam \n", + "b = 50.0 #mm - the width of the beam\n", + "M = 2083 #Nm\n", + "A = l*b #mm2 - The area \n", + "#straight beam \n", + "I = b*(l**3)/12.0 #mm4 - The moment of inertia of the beam\n", + "c_1= l/2 # the distance where the stress is maximum \n", + "c_2 = -l/2 # the distance where the stress is maximum \n", + "s_1 = I/c_1\n", + "s_2 = I/c_2\n", + "stress_max_1 = M*(10**3)/s_1 #Mpa - the maximum strss recorded in the crossection\n", + "stress_max_2 = M*(10**3)/s_2 #Mpa - the maximum strss recorded in the crossection \n", + "print \"The maximum stress upward in straight case is\",stress_max_1,\"Mpa\"\n", + "print \"The maximum stress downward in straight case is\",stress_max_2,\"Mpa\"\n", + "\n", + "#curved beam \n", + "import math\n", + "r = 250.0 #mm Radius of beam curved \n", + "r_0 = r - l/2 # inner radius \n", + "r_1 = r + l/2 # outer radius\n", + "R = l/(math.log(r_1/r_0)) #mm \n", + "e = r - R \n", + "stressr_max_1 = M*(10**3)*(R-r_0)/(r_0*A*e)\n", + "stressr_max_2 = M*(10**3)*(R-r_1)/(r_1*A*e)\n", + "print \"The maximum stress upward in curved case is\",stressr_max_1,\"Mpa\"\n", + "print \"The maximum stress downward in curved case is\",stressr_max_2,\"Mpa\"\n", + "\n", + "#curved beam _2 \n", + "import math\n", + "r = 75.0 #mm Radius of beam curved \n", + "r_0 = r - l/2 # inner radius \n", + "r_1 = r + l/2 # outer radius\n", + "R = l/(math.log(r_1/r_0)) #mm \n", + "e = r - R \n", + "stressr_max_1 = M*(10**3)*(R-r_0)/(r_0*A*e)\n", + "stressr_max_2 = M*(10**3)*(R-r_1)/(r_1*A*e)\n", + "print \"The maximum stress upward in curved case2 is\",stressr_max_1,\"Mpa\"\n", + "print \"The maximum stress downward in curved case2 is\",stressr_max_2,\"Mpa\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The maximum stress upward in straight case is 99.984 Mpa\n", + "The maximum stress downward in straight case is -99.984 Mpa\n", + "The maximum stress upward in curved case is 107.093207632 Mpa\n", + "The maximum stress downward in curved case is -93.6813516989 Mpa\n", + "The maximum stress upward in curved case2 is 128.733538525 Mpa\n", + "The maximum stress downward in curved case2 is -81.0307692623 Mpa\n" + ] + } + ], + "prompt_number": 31 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Page number 6.14 page number 318" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#given \n", + "#from example 6.9\n", + "St_ul = 2500 #psi - ultimate strength\n", + "st_yl = 40000 #psi _ yielding strength \n", + "b = 10 #in - width from example \n", + "A = 2 #in2 The area of the steel\n", + "d = 20 \n", + "t_ul = st_yl*A #ultimate capasity\n", + "y = t_ul/(St_ul*b*0.85) #in 0.85 because its customary\n", + "M_ul = t_ul*(d-y/2)/12 #ft-lb Plastic moment \n", + "print \"The plastic moment of the system is \",M_ul,\"ft-lb\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The plastic moment of the system is 120784.313725 ft-lb\n" + ] + } + ], + "prompt_number": 35 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.15 page number 231" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Given \n", + "#From example 5.8 \n", + "W = 4.0 #N/m - The force distribution \n", + "L = 3 # m - The length of the force applied\n", + "M = W*L/8.0 # KN.m The moment due to force distribution\n", + "o = 30 # the angle of force applid to horizantal\n", + "l = 150.0 #mm length of the crossection \n", + "b = 100.0 #mm - width of the crossection \n", + "import math \n", + "M_z = M*(math.cos(3.14/6))\n", + "M_y = M*(math.sin(math.pi/6))\n", + "I_z = b*(l**3)/12.0\n", + "I_y = l*(b**3)/12.0\n", + "#tanb = I_z /I_y *tan30\n", + "b = math.atan(math.radians(I_z*math.tan(3.14/6.0)/I_y ))\n", + "print \"The angle at which nuetral axis locates is\",b,\"radians\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The angle at which nuetral axis locates is 0.0226547191205 radians\n" + ] + } + ], + "prompt_number": 50 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.16 pagenumber 323" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "M = 10 #KN.m - The moment applied\n", + "I_max = 23.95*(10**6) #mm4 - I_z The moment of inertia\n", + "I_min = 2.53*(10**6) #mm4 - I_y The moment of inertia\n", + "o = 14.34 # degress the principle axis rotated\n", + "#Coponents of M in Y,Z direction \n", + "M_z = M*(10**6)*math.cos(math.radians(o))\n", + "M_y = M*(10**6)*math.sin(math.radians(o))\n", + "#tanb = I_z /I_y *tan14.34\n", + "b = math.atan((I_max*math.tan(math.radians(o))/I_min ))\n", + "B = math.degrees(b) \n", + "y_p = 122.9 # mm - principle axis Y cordinate\n", + "z_p = -26.95 #mm - principle axis z cordinate\n", + "stress_B = - M_z*y_p/I_max + M_y*z_p/I_min #Mpa - Maximum tensile stress\n", + "y_f = -65.97 # mm - principle axis Y cordinate\n", + "z_f = 41.93 #mm - principle axis z cordinate\n", + "stress_f = - M_z*y_f/I_max + M_y*z_f/I_min #Mpa - Maximum compressive stress\n", + "print \"The maximum tensile stress\",round(stress_B,2) ,\"Mpa\"\n", + "print \"The maximum compressive stress\",round(stress_f,2),\"Mpa\"\n", + "\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The maximum tensile stress -76.1 Mpa\n", + "The maximum compressive stress 67.73 Mpa\n" + ] + } + ], + "prompt_number": 83 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.18 page number 328" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "l = 50 #mm - The length of the beam \n", + "b = 50 #mm - The width of the beam \n", + "A = l*b #mm2 - The area of the beam \n", + "p = 8.33 #KN - The force applied on the beam \n", + "stress_max = p*(10**3)/A #Mpa After cutting section A--b\n", + "print \"The maximum stress in the beam\",stress_max ,\"Mpa \"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The maximum stress in the beam 3.332 Mpa \n" + ] + } + ], + "prompt_number": 51 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 6.24 page number 339" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "M = 10 #KN.m - The moment applied\n", + "I_max = 23.95*(10**6) #mm4 - I_z The moment of inertia\n", + "I_min = 2.53*(10**6) #mm4 - I_y The moment of inertia\n", + "o = 14.34 # degress the principle axis rotated\n", + "#Coponents of M in Y,Z direction \n", + "M_z = M*(10**6)*math.cos(math.radians(o))\n", + "M_y = M*(10**6)*math.sin(math.radians(o))\n", + "#tanb = I_z /I_y *tan14.34\n", + "b = math.atan((I_max*math.tan(math.radians(o))/I_min ))\n", + "B = math.degrees(b) \n", + "y_p = 122.9 # mm - principle axis Y cordinate\n", + "z_p = -26.95 #mm - principle axis z cordinate\n", + "stress_B = - M_z*y_p/I_max + M_y*z_p/I_min #Mpa - Maximum tensile stress\n", + "y_f = -65.97 # mm - principle axis Y cordinate\n", + "z_f = 41.93 #mm - principle axis z cordinate\n", + "stress_f = - M_z*y_f/I_max + M_y*z_f/I_min #Mpa - Maximum compressive stress\n", + "#location of nuetral axis To show these stresses are max and minimum \n", + "#tanB = MzI_z + MzI_yz/MyI_y +M_YI_yz\n", + "I_z = 22.64 *(10**6) #mm4 moment of inertia in Z direction\n", + "I_y = 3.84 *(10**6) #mm4 moment of inertia in Y direction\n", + "I_yz =5.14 *(10**6) #mm4 moment of inertia in YZ direction \n", + "M_y = M #KN.m bending moment in Y dorection \n", + "M_z = M #KN.m bending moment in Y dorection \n", + "B = math.atan(( M_z*I_yz)/(M_z*I_y )) #radians location on neutral axis\n", + "beta = math.degrees(B)\n", + "print \"By sketching the line with angle\",round(beta,1),\"degrees The farthest point associated with B and F\" " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "By sketching the line with angle 53.2 degrees The farthest point associated with B and F\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +} \ No newline at end of file diff --git a/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter7_3.ipynb b/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter7_3.ipynb new file mode 100644 index 00000000..9d697f7e --- /dev/null +++ b/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter7_3.ipynb @@ -0,0 +1,274 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# chapter 4:Shear stress in Beams and Related Problems " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.1 page number 365" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The minimal space between the nails 42.0 mm\n" + ] + } + ], + "source": [ + "#Given\n", + "shear_v = 3000 #N - Transmitted vetical shear \n", + "shear_al = 700 #N - The maximum allowable \n", + "#We will divide this into two parts\n", + "l_1 = 50.0 #mm \n", + "l_2 = 200.0 #mm \n", + "b_1 = 200.0 #mm \n", + "b_2 = 50.0 #mm\n", + "A_1 = l_1* b_1 #mm2 - area of part_1\n", + "y_1 = 25.0 #mm com distance \n", + "A_2 =l_2*b_2 #mm2 - area of part_1\n", + "y_2 = 150.0 #in com distance \n", + "y_net = (A_1*y_1 +A_2*y_2)/(A_1+A_2) #mm - The com of the whole system\n", + "c_max = (4-y_net) #mm - The maximum distace from com to end\n", + "c_min = y_net #mm - the minimum distance from com to end\n", + "I_1 = b_1*(l_1**3)/12 + A_1*((y_1-y_net)**2) #Parallel axis theorm\n", + "I_2 = b_2*(l_2**3)/12 + A_2*((y_2-y_net)**2)\n", + "I_net = I_1 + I_2 #mm4 - the total moment of inertia\n", + "Q = A_1*(-y_1+y_net) #mm3\n", + "q = shear_v*Q/I_net #N/mm - Shear flow\n", + "d = shear_al/q # The space between the nails \n", + "print \"The minimal space between the nails \",round(d,0) ,\"mm\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.2 pagenumber 365" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The minimal space between the nails 123.0 mm\n" + ] + } + ], + "source": [ + "#Given \n", + "l = 6 #m -length of the beam \n", + "p = 3 #KN-m _ the load applied\n", + "R_a = l*p/2 #KN -The reaction at a, Since the system is symmetry \n", + "R_b = l*p/2 #KN -The reaction at b \n", + "l_s = 10 #mm - The length of the screw \n", + "shear_al = 2 #KN - The maximum load the screw can take \n", + "I = 2.36*(10**9) #mm2 The moment of inertia of the whole system\n", + "#We will divide this into two parts\n", + "l_1 = 50.0 #mm \n", + "l_2 = 50.0 #mm \n", + "b_1 = 100.0 #mm \n", + "b_2 = 200.0 #mm\n", + "A_1 = l_1* b_1 #in2 - area of part_1\n", + "y_1 = 200.0 #mm com distance \n", + "A_2 =l_2*b_2 #mm2 - area of part_1\n", + "y_2 = 225.0 #in com distance\n", + "Q = 2*A_1*y_1 + A_2*y_2 # mm3 For the whole system\n", + "q = R_a*Q*(10**3)/I #N/mm The shear flow \n", + "d = shear_al*(10**3)/q #mm The space between the nails\n", + "print \"The minimal space between the nails \",round(d,0),\"mm\"\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.6 page number 376" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The shear centre from outside vertical face is 1.825 in\n" + ] + } + ], + "source": [ + "#Given\n", + "#we will divide this into two equal parts and other part\n", + "l = 10.0 # in - The height \n", + "t = 0.1 # in - The width\n", + "b = 5.0 #mm- The width of the above part \n", + "A = t* b #in2 - area of part\n", + "y_net = l/2 # The com of the system \n", + "y_1 = l # The position of teh com of part_2\n", + "I_1 = t*(l**3)/12 #in4 The moment of inertia of part 1\n", + "I_2 = 2*A*((y_1-y_net)**2) #in4 The moment of inertia of part 2 \n", + "I = I_1 + I_2 #in4 The moment of inertia \n", + "e = (b**2)*(l**2)*t/(4*I) #in the formula of channels\n", + "l_sc = e - t/2 #in- The shear centre \n", + "print \"The shear centre from outside vertical face is \",l_sc ,\"in\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.8 page number 387" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The direct maximum stress 4.25 Mpa\n", + "The torsion maximum stress 101.91 Mpa\n", + "The total stress 106.16 Mpa\n" + ] + } + ], + "source": [ + "#Given \n", + "dia = 10.0 #mm - The diameter of the cylinder \n", + "c = dia/2 #mm - the radius of the cylinder \n", + "A = 3.14*(c**2) #mm2 The area of the crossection \n", + "y = 4*c/(3*3.14) #mm The com of cylinder \n", + "I = 3.14*(c**4)/4 #mm4 - The moment of inertia of the cylinder\n", + "j = 3.14*(dia**4)/32 #mm4\n", + "T = 20.0 #N.m - The torque \n", + "V = 250.0 #N - The shear \n", + "M = 25.0 #N-m The bending moment \n", + "Q = A*y/2 #mm\n", + "stress_dmax = 4*V/(3*A) #V*Q/(I*d) #Mpa The direct maximum stress\n", + "stress_tmax = T*c*(10**3)/j #-Mpa The torsion maximum stress\n", + "stress_total = stress_dmax + stress_tmax #Mpa The total stress\n", + "print \"The direct maximum stress\",round(stress_dmax,2),\"Mpa\"\n", + "print \"The torsion maximum stress\",round(stress_tmax,2),\"Mpa\"\n", + "print \"The total stress\",round(stress_total,2),\"Mpa\"\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.9 page number 393" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The maximum stress in the system 4.84 Mpa\n" + ] + } + ], + "source": [ + "#Given\n", + "dia = 15 #mm - The diameter of the rod\n", + "h = 0.5 #mt - The freely falling height \n", + "A = 3.14*(dia**2)/4 #mm2 The area of the crossection\n", + "E = 200 #Gpa -Youngs modulus\n", + "L = 750 #mm - The total length of the rod\n", + "G = 80 #gpa - Shear modulus \n", + "N = 10 #number of live coils\n", + "d = 5 #mm the diameter of live coil \n", + "m = 3 # the mass of freely falling body\n", + "H = 500 #mm -from mass to spring \n", + "F= m*9.81 #Kg the force due to that mass\n", + "#e = e_rod + e_spr\n", + "#e_rod\n", + "e_rod = p*L*(10**-3)/(A*E) #mm The elongation due to freely falling body\n", + "#e_spr\n", + "e_spr = 64*F*(dia**3)*N*(10**-3)/(G*(d**4)) #mm The elongation due to spring\n", + "e = e_rod + e_spr #mm The total elongation \n", + "p_dyn =F*(1+pow((1+(2*H/e)),0.5))\n", + "Stress_max = p_dyn/A #MPa - The maximum stress in the system \n", + "print \"The maximum stress in the system \",round(Stress_max,2),\"Mpa\"" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter8_3.ipynb b/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter8_3.ipynb new file mode 100644 index 00000000..12d2d766 --- /dev/null +++ b/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter8_3.ipynb @@ -0,0 +1,362 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 8:Transformation of stress and strain and Yield and Fracture criteria " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.1 page number 405 " + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The stress action in normal direction on AB 1.29 Mpa\n", + "The stress action in tangential direction on AB 2.12 Mpa\n" + ] + } + ], + "source": [ + "#Given \n", + "import math \n", + "from math import radians\n", + "o = 22.5 #degrees , The angle of infetisimal wedge \n", + "A = 1 #mm2 The area of the element \n", + "A_ab = 1*(math.cos(radians(o))) #mm2 - The area corresponds to AB\n", + "A_bc = 1*(math.sin(radians(o))) #mm2 - The area corresponds to BC\n", + "S_1 = 3 #MN The stresses applying on the element \n", + "S_2 = 2 #MN\n", + "S_3 = 2 #MN\n", + "S_4 = 1 #MN \n", + "F_1 = S_1*A_ab # The Forces obtained by multiplying stress by their areas \n", + "F_2 = S_2*A_ab\n", + "F_3 = S_3*A_bc\n", + "F_4 = S_4*A_bc\n", + "#sum of F_N = 0 equilibrim in normal direction \n", + "N = (F_1-F_3)*(math.cos(radians(o))) + (F_4 - F_2)*(math.sin(radians(o)))\n", + "\n", + "#sum of F_s = 0 equilibrim in tangential direction \n", + "\n", + "S = (F_2-F_4)*(math.cos(radians(o))) + (F_1 - F_3)*(math.sin(radians(o)))\n", + "\n", + "Stress_Normal = N/A #Mpa - The stress action in normal direction on AB\n", + "Stress_tan = S/A #Mpa - The stress action in tangential direction on AB\n", + "print \"The stress action in normal direction on AB\",round(Stress_Normal,2),\"Mpa\"\n", + "print \"The stress action in tangential direction on AB\",round(Stress_tan,2),\"Mpa\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.2 page number 413" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a) The stress action in normal direction on AB 4.12 Mpa\n", + "a) The stress action in tangential direction on AB 0.71 Mpa\n", + "b) The principle stress 4.2 Mpa tension\n", + "b) The principle stress -0.06 Mpa compression\n", + "b) The principle plane angles are 32.0 , 122.0 degrees\n", + "c) The maximum shear is -2.24 Mpa\n", + "a) [ 4.2 -0.1 0. ] Mpa\n", + "b) [ 2. -2.24 -2.24 2. ] Mpa\n" + ] + } + ], + "source": [ + "#Given\n", + "o = -22.5 #degrees , The angle of infetisimal wedge \n", + "A = 1 #mm2 The area of the element \n", + "import math \n", + "from math import radians\n", + "from numpy import array\n", + "A_ab = 1*(math.cos(radians(o))) #mm2 - The area corresponds to AB\n", + "A_bc = 1*(math.sin(radians(o))) #mm2 - The area corresponds to BC\n", + "S_1 = 3.0 #MN The stresses applying on the element \n", + "S_2 = 2.0 #MN\n", + "S_3 = 2.0 #MN\n", + "S_4 = 1.0 #MN\n", + "#Caliculations \n", + "\n", + "F_1 = S_1*A_ab # The Forces obtained by multiplying stress by their areas \n", + "F_2 = S_2*A_ab\n", + "F_3 = S_3*A_bc\n", + "F_4 = S_4*A_bc\n", + "#sum of F_N = 0 equilibrim in normal direction \n", + "N = (F_1-F_3)*(math.cos(radians(o))) + (F_4 - F_2)*(math.sin(radians(o)))\n", + "\n", + "#sum of F_s = 0 equilibrim in tangential direction \n", + "\n", + "S = (F_2-F_4)*(math.cos(radians(o))) + (F_1 - F_3)*(math.sin(radians(o)))\n", + "\n", + "Stress_Normal = N/A #Mpa - The stress action in normal direction on AB\n", + "Stress_tan = S/A #Mpa - The stress action in tangential direction on AB\n", + "print \"a) The stress action in normal direction on AB\",round(Stress_Normal,2),\"Mpa\"\n", + "print \"a) The stress action in tangential direction on AB\",round(Stress_tan,2),\"Mpa\"\n", + "\n", + "#Part- b\n", + "\n", + "S_max = (S_4+S_1)/2 + (((((S_4-S_1)/2)**2) + S_3**2)**0.5) #Mpa - The maximum stress\n", + "S_min = (S_4+S_1)/2.0 - (((((S_4-S_1/2))**2) + S_3**2)**0.5) #Mpa - The minumum stress\n", + "k = 0.5*math.atan(S_3/((S_1-S_4)/2)) #radians The angle of principle axis\n", + "k_1 = math.degrees(k)\n", + "k_2 = k_1+90 #The principle plane angles\n", + "print \"b) The principle stress \",round(S_max,1),\"Mpa tension\"\n", + "print \"b) The principle stress \",round(S_min,2),\"Mpa compression\"\n", + "print \"b) The principle plane angles are\",round(k_1,0),\",\",round(k_2,0),\"degrees\"\n", + "\n", + "#part-c\n", + "#The maximum shear stress case\n", + "t_xy = (((((S_4-S_1)/2)**2) + S_3**2)**0.5) #Mpa - The maximum shear stress case\n", + "K = 0.5*math.atan((-(S_1-S_4)/(2*S_3))) #radians The angle of principle axis\n", + "K_0 = math.degrees(K)\n", + "if K_0<0:\n", + " K_1 = K_0+90\n", + "else:\n", + " K_1 = K_0\n", + "K_2 = K_1+90 #PRinciple plain angles\n", + "T_xy = -((S_1-S_4)/2)*(math.sin(radians(2*K_1))) + ((S_4+S_1)/2)*(math.cos(radians(2*K_1))) # Shear stress\n", + "print \"c) The maximum shear is \",round(T_xy,2),\"Mpa\" \n", + "S_mat_a = array([round(S_max,1),round(S_min,1),0]) #MPa maximum stress matrix\n", + "S_mat_b = array([(S_4+S_1)/2,round(T_xy,2),round(T_xy,2),(S_4+S_1)/2]) #MPa maximum stress matrix at maximum shear\n", + "print \"a)\",S_mat_a,\"Mpa\"\n", + "print \"b)\",S_mat_b,\"Mpa\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.3 page number 421" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The principle stresses are 6.0 Mpa -4.0 Mpa\n", + "The maximum shear stress 5.0 Mpa\n" + ] + } + ], + "source": [ + "#Given \n", + "import math \n", + "from math import radians \n", + "S_x = -2 #Mpa _ the noraml stress in x direction\n", + "S_y = 4 #Mpa _ the noraml stress in Y direction\n", + "c = (S_x + S_y)/2 #Mpa - The centre of the mohr circle \n", + "point_x = -2 #The x coordinate of a point on mohr circle\n", + "point_y = 4 #The y coordinate of a point on mohr circle\n", + "Radius = pow((point_x-c)**2 + point_y**2,0.5) # The radius of the mohr circle\n", + "S_1 = Radius +1#MPa The principle stress\n", + "S_2 = -Radius +1 #Mpa The principle stress\n", + "S_xy_max = Radius #Mpa The maximum shear stress\n", + "print \"The principle stresses are\",S_1 ,\"Mpa\",S_2,\"Mpa\"\n", + "print \"The maximum shear stress\",S_xy_max,\"Mpa\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.4 page number 423" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The normal stress on the 221/2 plane 4.82 Mpa\n", + "The tangential stress on the 221/2 plane 1.43 Mpa\n" + ] + } + ], + "source": [ + "#Given\n", + "import math \n", + "S_x = 3.0 #Mpa _ the noraml stress in x direction\n", + "S_y = 1.0 #Mpa _ the noraml stress in Y direction\n", + "c = (S_x + S_y)/2 #Mpa - The centre of the mohr circle \n", + "point_x = 1 #The x coordinate of a point on mohr circle\n", + "point_y = 3 #The y coordinate of a point on mohr circle\n", + "#Caliculations \n", + "\n", + "Radius = pow((point_x-c)**2 + point_y**2,0.5) # The radius of the mohr circle\n", + "#22.5 degrees line is drawn \n", + "o = 22.5 #degrees \n", + "a = 71.5 - 2*o #Degrees, from diagram \n", + "stress_n = c + Radius*math.sin(math.degrees(o)) #Mpa The normal stress on the plane \n", + "stress_t = Radius*math.cos(math.degrees(o)) #Mpa The tangential stress on the plane\n", + "print \"The normal stress on the 221/2 plane \",round(stress_n,2),\"Mpa\"\n", + "print \"The tangential stress on the 221/2 plane \",round(stress_t,2),\"Mpa\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.7 page number 437" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The principle strains are 400 um/m -600 um/m\n", + "The angle of principle plane 18.43 degrees\n" + ] + } + ], + "source": [ + "e_x = -500 #10-6 m/m The contraction in X direction\n", + "e_y = 300 #10-6 m/m The contraction in Y direction\n", + "e_xy = -600 #10-6 m/m discorted angle\n", + "centre = (e_x + e_y)/2 #10-6 m/m \n", + "point_x = -500 #The x coordinate of a point on mohr circle\n", + "point_y = 300 #The y coordinate of a point on mohr circle\n", + "Radius = 500 #10-6 m/m - from mohr circle\n", + "e_1 = Radius +centre #MPa The principle strain\n", + "e_2 = -Radius +centre #Mpa The principle strain\n", + "k = math.atan(300.0/900) # from geometry\n", + "k_1 = math.degrees(k)\n", + "print \"The principle strains are\",e_1,\"um/m\",e_2,\"um/m\"\n", + "print \"The angle of principle plane\",round(k_1,2) ,\"degrees\"\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.8 page number 441" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The principle stresses are 48.35 Mpa -105.49 MPa\n" + ] + } + ], + "source": [ + "#Given\n", + "e_0 = -500 #10-6 m/m \n", + "e_45 = 200 #10-6 m/m \n", + "e_90 = 300 #10-6 m/m\n", + "E = 200 #Gpa - youngs modulus of steel \n", + "v = 0.3 # poissions ratio \n", + "#Caliculations \n", + "\n", + "e_xy = 2*e_45 - (e_0 +e_90 ) #10-6 m/m from equation 8-40 in text\n", + "# from example 8.7\n", + "e_x = -500 #10-6 m/m The contraction in X direction\n", + "e_y = 300 #10-6 m/m The contraction in Y direction\n", + "e_xy = -600 #10-6 m/m discorted angle\n", + "centre = (e_x + e_y)/2 #10-6 m/m \n", + "point_x = -500 #The x coordinate of a point on mohr circle\n", + "point_y = 300 #The y coordinate of a point on mohr circle\n", + "Radius = 500 #10-6 m/m - from mohr circle\n", + "e_1 = Radius +centre #MPa The principle strain\n", + "e_2 = -Radius +centre #Mpa The principle strain\n", + "\n", + "stress_1 = E*(10**-3)*(e_1+v*e_2)/(1-v**2) #Mpa the stress in this direction \n", + "stress_2 = E*(10**-3)*(e_2+v*e_1)/(1-v**2) #Mpa the stress in this direction \n", + "print\"The principle stresses are \",round(stress_1,2),\"Mpa\",round(stress_2,2),\"MPa\" " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter9_3.ipynb b/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter9_3.ipynb new file mode 100644 index 00000000..0d90dff0 --- /dev/null +++ b/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter9_3.ipynb @@ -0,0 +1,237 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 9:Elastic stress analysis and design" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.4 pagenumber 465" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a)The principle stresses are 16.67 MPa, -16.67 Mpa\n", + "b)The stresses on inclines plane 11.11 Mpa noraml, -7.06 Mpa shear \n" + ] + } + ], + "source": [ + "#Given \n", + "import math \n", + "b = 40.0 #mm - The width of the beam crossection\n", + "h = 300.0 #mm - The length of the beam crossection \n", + "V = 40.0 #KN - The shear stress in teh crossection\n", + "M = 10.0 #KN-m - The bending moment on K----K crossection \n", + "c = h/2 #mm -The position at which maximum stress occurs on the crossection\n", + "I = b*(h**3)/12 #mmm4 - the moment of inertia \n", + "#Caliculations \n", + "\n", + "stress_max_1 = M*c*(10**6)/I #The maximum stress occurs at the end\n", + "stress_max_2 = -M*c*(10**6)/I #The maximum stress occurs at the end\n", + "y = 140 #mm The point of interest, the distance of element from com\n", + "n = y/(c) # The ratio of the distances from nuetral axis to the elements\n", + "stress_L_1 = n*stress_max_1 #The normal stress on elements L--L\n", + "stress_L_2 = -n*stress_max_1 #The normal stress on elements L--L\n", + "x = 10 #mm The length of the element\n", + "A = b*x #mm3 The area of the element \n", + "y_1 = y+x/2 # the com of element from com of whole system\n", + "stress_xy = V*A*y_1*(10**3)/(I*b) #Mpa - The shear stress on the element \n", + "#stresses acting in plane 30 degrees \n", + "o = 60 #degrees - the plane angle\n", + "stress_theta = stress_L_1/2 + stress_L_1*(math.cos(math.radians(o)))/2 - stress_xy*(math.sin(math.radians(o))) #Mpa by direct application of equations\n", + "stress_shear = -stress_L_1*(math.sin(math.radians(o)))/2 - stress_xy*(math.cos(math.radians(o))) #Mpa Shear stress\n", + " \n", + "print \"a)The principle stresses are \",round(stress_max_1,2),\"MPa,\",round(stress_max_2,2),\"Mpa\"\n", + "print \"b)The stresses on inclines plane \",round(stress_theta,2),\"Mpa noraml, \",round(stress_shear,2),\"Mpa shear \"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9.5 page number 476" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The stress developed 0.4 is in allowable ranges for 30077.85 mm2 area\n", + "The minimum area is 5714.28571429 mm2\n" + ] + } + ], + "source": [ + "#Given\n", + "M = 10 #KN-m moment\n", + "v = 8.0 #KN - shear Stress \n", + "stress_allow = 8 #MPa - The maximum allowable stress\n", + "shear_allow_per = 1.4 #Mpa - The allowable stress perpendicular to grain\n", + "stress_allow_shear = 0.7 #MPa - The maximum allowable shear stress\n", + "#Caliculations \n", + "\n", + "S = M*(10**6)/stress_allow #mm3 \n", + "#lets arbitarly assume h = 2b\n", + "#S = b*(h**2)/6\n", + "h = pow(12*S,0.333) #The depth of the beam\n", + "b = h/2 #mm The width of the beam\n", + "A = h*b #mm2 The area of the crossection , assumption\n", + "stress_shear = 3*v*(10**3)/(2*A) #Mpa The strear stress \n", + "if stress_shear" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from math import sin\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot, subplot, title, xlabel, ylabel, show\n", + "# Given\n", + "def f(x):\n", + " y=[]\n", + " for xx in x:\n", + " y.append(Ec*(1+ma*(sin(wm*xx)))*sin(wc*xx))\n", + " return y\n", + "Ec=10\n", + "ma=0.5\n", + "wm=10000*pi\n", + "wc=2*pi*1e7\n", + "x=arange(0,20*pi/10,.01)\n", + "subplot(2,1,1)\n", + "plot(x,f(x))\n", + "xlabel(\"t\")\n", + "ylabel(\"Modulated Wave\")\n", + "Fc=wc/(2*pi)\n", + "Fm=wm/(2*pi)\n", + "Fusb=(wm+wc)/(2*pi)\n", + "Flsb=(wm-wc)/(2*pi)\n", + "print 'USB freq=%d k5Hz\\nUSB amplitude=%0.2f V\\nLSB freq=%d kHz\\nLSB amplitude=%0.2f V\\nCarrier amplitude=%d V'%(Fusb*1e-3,2.5,Flsb*-1e-3,2.5,10)\n", + "F=[0,2.5,10,2.5,0]\n", + "T=[-2,-1,0,1,2]\n", + "subplot(2,1,2)\n", + "plot(T,F)\n", + "xlabel(\"Freq\")\n", + "ylabel(\"Amplitude\")\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.12 page no 145" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The depth of modulation is: 50%\n" + ] + } + ], + "source": [ + "from math import sqrt\n", + "#Given\n", + "Pc=9e3#unmodulated carrier power\n", + "Pt=10.125e3#Modulated carrier power\n", + "Ma=sqrt(2*((Pt/Pc)-1))#depth of modulation\n", + "print 'The depth of modulation is: %d%c'%(Ma*100,'%')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.13 page no 148" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The power output is: 34.45 W\n" + ] + } + ], + "source": [ + "#Given\n", + "Pt=5e3#carrier power for 95% modulation\n", + "Ma=0.95\n", + "Pc=Pt/(1+((Ma**2)/2))#carrier power\n", + "Ma=0.2#average modulation by speech signal\n", + "Psb=(Ma**2)*Pc/2#the power n the sideband\n", + "Pout=Psb/2# because one of the side band is suppressed\n", + "print 'The power output is: %0.2f W'%(Pout)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.14 page no 152" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "DeltaPhi1= 10 rad\n", + "DeltaPhi2=500 rad\n", + "\n" + ] + } + ], + "source": [ + "#Given\n", + "#Phi=(wc*t+Mf*sin(wmt))....instantaneous phase of FM\n", + "fm=5000#modulating freq\n", + "deltaf=50e3#freq deviation\n", + "deltaPhi1=deltaf/fm# Advance or retard in phase\n", + "\n", + "fm=100#modulating freq in second signal\n", + "deltaPhi2=deltaf/fm\n", + "print 'DeltaPhi1= %d rad\\nDeltaPhi2=%d rad\\n'%(deltaPhi1,deltaPhi2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.14 page no 157" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Peak Phase Deviation: 0.76 rad\n", + "Peak Freq Deviation: 761 Hz\n", + "Depth of residual AM: 0.08\n", + "Residual AM freq:2 kHz\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import sqrt,atan\n", + "#Given\n", + "#e=Ec(1+0.4cos(2pie3*t))*sin(2pie7*t)\n", + "fm=1000#modulating s/g freq\n", + "deltaTheta=2*atan(0.4)#peak phase deviation\n", + "\n", + "deltaF=deltaTheta*fm#Peak freq deviation\n", + "\n", + "Ec=1\n", + "Er=sqrt((Ec**2)*(1+(0.4**2)))\n", + "m=(Er-Ec)/Ec#depth of residual AM \n", + "\n", + "AMFr=2*fm# freq ofresidual AM\n", + "print 'Peak Phase Deviation: %0.2f rad\\nPeak Freq Deviation: %d Hz\\nDepth of residual AM: %0.2f\\nResidual AM freq:%d kHz'%(deltaTheta,deltaF,(round(m*100)/100),AMFr*1e-3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.16 page no 170" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a)\n", + "Max phase deviation is:250 rad\n", + "b)\n", + "Max phase deviation is:2.50 rad\n" + ] + } + ], + "source": [ + "#Given\n", + "deltaF=25e3#freq deviation\n", + "#a\n", + "fm=100#modulation signal freq\n", + "mf=deltaF/fm# Max phase deviation\n", + "print 'a)'\n", + "print 'Max phase deviation is:%d rad'%(mf)\n", + "#b\n", + "fm=10e3#modulation signal freq\n", + "mf=deltaF/fm#Max phase deviation\n", + "\n", + "print 'b)'\n", + "print 'Max phase deviation is:%0.2f rad'%(mf)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.17, page no 171" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The maximum freq deviation is: 5 kHz\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import sqrt\n", + "#Given\n", + "gm=0.1e-3# trans-conductance variation A/V\n", + "C=0.5e-12# capactance between anode and grid\n", + "R=1e3# resistance\n", + "fo=10e6# oscillator freq\n", + "Vrms=1.414#AF RMS voltage \n", + "Vp=sqrt(2)*Vrms#Peak voltage\n", + "Ct=100e-12#tank capacitance\n", + "deltaC=gm*C*R*Vp\n", + "\n", + "deltaF=fo*(deltaC/(2*Ct))# maximum freq deviation\n", + "print 'The maximum freq deviation is: %d kHz'%(round(deltaF/1000))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.18, page no 172" + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The approximate bandwidth is: 2 MHz\n" + ] + } + ], + "source": [ + "#Given\n", + "deltaF=1e6# max freq deviation\n", + "fm=10e3#modulating freq\n", + "mf=(2*deltaF)/fm# modulation coefficient\n", + "BW=mf*fm# bandwidth\n", + "print 'The approximate bandwidth is: %d MHz'%(BW/1e6)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.19, page no 172" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The approximate bandwidth is: 150 kHz\n" + ] + } + ], + "source": [ + "#Given\n", + "deltaF=75e3# max freq deviation\n", + "fm=15e3#modulation freq\n", + "mf=(2*deltaF)/fm# freq modulation depth\n", + "BW=mf*fm# Bandwidth\n", + "print 'The approximate bandwidth is: %d kHz'%(BW/1e3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.21, page no 173" + ] + }, + { + "cell_type": "code", + "execution_count": 77, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Overall bandwidth including guard band is 200 kHz\n" + ] + } + ], + "source": [ + "#Given\n", + "deltaF=75e3#freq deviation\n", + "fm=15e3# modulating freq\n", + "mf=deltaF/fm\n", + "BW=2*mf*fm# Bandwidth\n", + "GB=25e3#Guard Band\n", + "BWo=BW+(2*GB)# Overall bandwidth\n", + "print 'Overall bandwidth including guard band is %d kHz'%(BWo/1e3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.25, pageno 175" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Average power is: 25.17 watts\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from math import sin\n", + "%matplotlib inline\n", + "from matplotlib.pyplot import plot, subplot, title, xlabel, ylabel, show\n", + "#Given\n", + "#em=3sin(2*pi*1000t)+5cos(2*pi*3000t)\n", + "#ec=50sin(2*pi*500e3*t)\n", + "m1=0.06#(sine wave amplitude/ peak carrier voltage)\n", + "m2=0.1#(cosine wave amplitude/ peak carrier voltage)\n", + "Vc=50#Carrier voltage\n", + "R=50#load resistance\n", + "Pc=(Vc**2)/(2*R)#Peak carrier power\n", + "Pt=Pc*(1+((m1**2+m2**2)/2))#Total power after modulation\n", + "print 'Average power is: %0.2f watts'%(Pt)\n", + "F=[0,2.5,1.5,50,1.5,2.5,0]\n", + "T=[490,497,499,500,501,503,510]\n", + "plot(T,F)\n", + "xlabel(\"Freq\")\n", + "ylabel(\"Amplitude\")\n", + "show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.26, page no 176" + ] + }, + { + "cell_type": "code", + "execution_count": 79, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Required Deviation is: 50 kHz\n", + "\n", + "Required Multipication Factor is: 5*5*5*5*2\n" + ] + } + ], + "source": [ + "#Given\n", + "mp=0.1#Modulating index\n", + "fm=400#Modulating signal freq\n", + "deltaF=mp*fm#Max freq deviation\n", + "#print deltaF)\n", + "ReqDev=50e3# Required deviation\n", + "MF=ReqDev/deltaF# multiplication factor\n", + "print 'Required Deviation is: %d kHz\\n'%(ReqDev/1e3)\n", + "print 'Required Multipication Factor is: 5*5*5*5*2'" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.27, page no 176" + ] + }, + { + "cell_type": "code", + "execution_count": 80, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The Depth of modulation across the \n", + " circuit is : Ma= 49.07%\n" + ] + } + ], + "source": [ + "#Given\n", + "Q=100 #Q factor\n", + "fc=1000e3# Carrier freq\n", + "fsb1=999e3#lower Side band freq\n", + "fsb2=1001e3#Upper side Band freq\n", + "ma=0.5#Modulation depth of signal current\n", + "Ma=ma/1.019# Expression for Ma after simplification\n", + "print 'The Depth of modulation across the \\n circuit is : Ma= %0.2f%c'%(Ma*100,'%')\n", + "\n", + "# Note : There are some calculation errors in the solution presented in the book" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.28, page no 177" + ] + }, + { + "cell_type": "code", + "execution_count": 81, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Depth of modulation:72.90 %\n" + ] + } + ], + "source": [ + "#Given\n", + "R=1#Antenna Resistance assumed to be 1 ohm for ease of calculation\n", + "Ic=10.8# current with no modulation\n", + "Pc=Ic**2*R#power with no modulation\n", + "It=12.15#modulated current\n", + "Pt=It**2*R# modulated power\n", + "ma=(sqrt(2*(((It/Ic)**2)-1)))#modulation depth)\n", + "\n", + "print 'Depth of modulation:%0.2f %c'%(round(1000*ma)/10,'%')#" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.29, page no 177" + ] + }, + { + "cell_type": "code", + "execution_count": 82, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Total RF power delivered is:Pt= 112.50 kW\n" + ] + } + ], + "source": [ + "#Given\n", + "Pc=100e3#Carrier power\n", + "ma=0.5#Depth of modulation\n", + "Pt=Pc*(1+((ma**2)/2))#total RF power\n", + "print 'Total RF power delivered is:Pt= %0.2f kW'%(Pt/1e3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.30, page no 178" + ] + }, + { + "cell_type": "code", + "execution_count": 83, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Carrier power:71.17 kW\n", + "The Intelligence power: 28.83 kW\n" + ] + } + ], + "source": [ + "#Given\n", + "Pt=100e3# Total power\n", + "ma=0.9#Depth of modulation\n", + "Pc=Pt/(1+((ma**2)/2))#Carrier power\n", + "Psb=Pt-Pc# Intelligence power i.e sideband power\n", + "print 'Carrier power:%0.2f kW\\nThe Intelligence power: %0.2f kW'%(Pc/1000,Psb/1000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example3.19, page no 178" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Modulation Index is: 64.81 \n" + ] + } + ], + "source": [ + "from math import sin,sqrt\n", + "#Given\n", + "R=1# load resistance\n", + "Eo=100#RF voltage\n", + "Po=Eo**2/R#Carrier power\n", + "E=110#Modulated RMS voltage\n", + "Pt=E**2/R#Total modulated power\n", + "ma=sqrt(2*((Pt/Po)-1))# Depth of modulation\n", + "print 'Modulation Index is: %0.2f '%(ma*100)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter5.ipynb b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter5.ipynb new file mode 100644 index 00000000..e234ad9f --- /dev/null +++ b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter5.ipynb @@ -0,0 +1,69 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 5 : Radio Transmission system" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.1, page no 230" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " Freq deviation is 17.453293 Hz\n", + " Multification factor is 1718\n", + " corresponding modified max freq deviation is 30114kHz\n" + ] + } + ], + "source": [ + "from numpy import pi\n", + "#Given\n", + "#b\n", + "fm=1e2#modulation freq\n", + "Phimax=10*pi/180# Max Phase deviation\n", + "#i\n", + "Freq_dev=Phimax*fm# Freq deviation\n", + "#ii\n", + "Mul_fact=30e3/Freq_dev# Multification factor\n", + "print ' Freq deviation is %f Hz\\n Multification factor is %d\\n corresponding modified max freq deviation is 30114kHz'%(Freq_dev,Mul_fact)\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter6.ipynb b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter6.ipynb new file mode 100644 index 00000000..c82ada44 --- /dev/null +++ b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter6.ipynb @@ -0,0 +1,104 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 6 : Radio Receivers" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.1, page no 262" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Carrier freq for the BW to be 1% of fc is: 2000 kHz\n" + ] + } + ], + "source": [ + "#Given\n", + "#Vm(t),Vc(t),Vmod(t)\n", + "fm=10e3#modulating freq\n", + "BW=2*fm# Bandwidth\n", + "fc=100*BW#Carrier freq\n", + "print'Carrier freq for the BW to be 1%% of fc is: %d kHz'%(fc/1000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example6.2, page no 262" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a)\n", + "Tuning capacitor range is: 4.579156\n", + "b)\n", + "Tuning capacitor range is: 1051\n" + ] + } + ], + "source": [ + "#Given\n", + "fmax=1600e3\n", + "fmin=500e3\n", + "IF=465e3\n", + "#i\n", + "fo1max=fmax+IF\n", + "fo1min=fmin+IF\n", + "C1max_C1min=(fo1max/fo1min)**2\n", + "#ii\n", + "fo2max=fmax-IF\n", + "fo2min=fmin-IF\n", + "C2max_C2min=(fo2max/fo2min)**2\n", + "print 'a)\\nTuning capacitor range is: %f\\nb)\\nTuning capacitor range is: %d'%(C1max_C1min,C2max_C2min)\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter7.ipynb b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter7.ipynb new file mode 100644 index 00000000..ee96e59f --- /dev/null +++ b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter7.ipynb @@ -0,0 +1,438 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 7 : Noise" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example7.2, page no 276" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The mean square noise voltage is: 18.363 mV\n" + ] + } + ], + "source": [ + "from numpy import sqrt,pi\n", + "from sympy.mpmath import quad\n", + "#Given\n", + "mue=25#\n", + "rp=5e3\n", + "Rl=10e3\n", + "C=1e-9\n", + "gm=mue/rp\n", + "Req=2.5/gm\n", + "\n", + "k=1.381e-23\n", + "T=293\n", + "R1=1e5\n", + "# Power density spectrum for respective res\n", + "d1=2*k*T*R1\n", + "d2=2*k*T*Req\n", + "d3=2*k*T*Rl\n", + "xo=0\n", + "x1=1e14\n", + "#w=0:inf\n", + "#H1(w)=(-gm*rp*Rl)/(rp+Rl+(1J*w*rp*Rl*C))\n", + "Vo=sqrt((20231.65e2/pi)*quad(lambda w:1/(((3e9)**2)+(w**2)),[xo,x1]))\n", + "print 'The mean square noise voltage is: %0.3f mV'%(Vo*1e3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example7.3, page no 279" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The mean square noise voltage is: 22.414 uV\n" + ] + } + ], + "source": [ + "from numpy import sqrt,pi\n", + "from sympy.mpmath import quad\n", + "\n", + "#Given\n", + "mue=25\n", + "rp=5e3\n", + "Rs=1e3#input resistance\n", + "#Coupling Capacitors are assumed as short circuit\n", + "Rg=1e5\n", + "gm=25/5e3\n", + "Req=2.5/gm\n", + "F=1+((((Req*(Rs+Rg)**2)+(Rg*Rs**2))/(Rs*Rg**2)))\n", + "xo=0\n", + "x1=1e10\n", + "#w=0:inf\n", + "\n", + "vo=sqrt((30145e-8/pi)*quad(lambda w:1/(((3e5)**2)+(w**2)),[xo,x1]))\n", + "print 'The mean square noise voltage is: %.3f uV'%(vo*1e6)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example7.4, page no 283" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "overall noise Figure is: 4.33\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "#Given\n", + "Ap1=10\n", + "Ap2=10\n", + "Ap3=10# # Gain of each states\n", + "F_1=6\n", + "F_2=6\n", + "F_3=6# #Noise figure of each state\n", + "F1= round(10**(F_1/10))\n", + "F2= round(10**(F_2/10))\n", + "F3= round(10**(F_3/10))# # approximating the values\n", + "\n", + "F=F1+((F2-1)/Ap1)+((F3-1)/(Ap1*Ap2))\n", + "print 'overall noise Figure is: %.2f'%(F)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example7.5, page no 283" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The overall noise figure is: 7.04\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "#Given\n", + "Fif=15# Noise figure of IF amplifier\n", + "Ap1=10# Gain of Preamplifier\n", + "Fpa=6#Noise figure of preamplifier\n", + "F2=10**(Fif/10)\n", + "F1=10**(Fpa/10)\n", + "\n", + "F=F1+((F2-1)/Ap1)#overall noise figure\n", + "print 'The overall noise figure is: %.2f'%(F)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example7.6, page no 284" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Overall Noise figure is: 2.055\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "#Given\n", + "mue=25# tube parameters\n", + "rp=10e3# tube parameters\n", + "gm=2.5e-3# transconductance\n", + "Req=2.5/gm# equivalent resistance\n", + "Rs=1000\n", + "Rg=1e5\n", + "F1=1+(((Req*((Rs+Rg)**2))+Rg*Rs**2)/(Rs*(Rg**2)))#noise figure of the first stage\n", + "Rg2=9.1e3\n", + "Rs2=10e3\n", + "Es=1# assuming Es=1 for ease of calculation\n", + "Pi=((Es/2e3)**2)*1e3\n", + "Po=1.532e-2*Es**2\n", + "Ap1=Po/Pi\n", + "F2=1+(((Req*((Rs2+Rg2)**2))+Rg2*Rs2**2)/(Rs2*(Rg2**2)))# noise figure of the second stage\n", + "F=(F1)+((F2-1)/Ap1)\n", + "print 'Overall Noise figure is: %.3f'%(F)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example7.8, page no 285" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The equivalent noise temp is: 4.913 K\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "#Given\n", + "g01=30# gain of 1st stage\n", + "g02=20#gain of 2nd stage\n", + "g03=40#gain of 3rd stage\n", + "F2=6# Noise factor of stage 2\n", + "F3=12# Noise factor of stage 3\n", + "Te1=4# Eq noise temp of stage 1\n", + "T=290# Room \n", + "G01=round(10**(g01/10))\n", + "G02=round(10**(g02/10))\n", + "G03=round(10**(g03/10))\n", + "F_2=round(10**(F2/10))\n", + "F_3=round(10**(F3/10))\n", + "Te2=round((F_2-1))*T\n", + "Te3=round((F_3-1))*T\n", + "Te=Te1+(Te2/G01)+(Te3/(G01*G02))# Eq overall noise temp\n", + "print 'The equivalent noise temp is: %.3f K'%(Te)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example7.9, page no 286" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Equivalent noise temperature is 7.028 K\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "#Given\n", + "g01=round(10**(25/10))#low noise amplifier gain\n", + "Te1=4#low noise amplifier noise temp\n", + "g02=round(10**(1.7))#preamplifier gain\n", + "F2=round(10**0.6)#preamplifier noise figure\n", + "F3=round(10**1.2)#preamplifier noise figure\n", + "T=290# room temp\n", + "Te2=round((F2-1)*T)\n", + "Te3=round((F3-1)*T)\n", + "Te=Te1+(Te2/g01)+(Te3/(g01*g02))#Overall noise Temperature\n", + "print 'Equivalent noise temperature is %.3f K'%(Te)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example7.10, page no 286" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "S/N ratio for FM is 43.29 dBs\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import log10\n", + "#Given\n", + "SNRam=25# Signal to noise ratio of AM\n", + "PcFM_AM=0.9#\n", + "mf=5\n", + "SNRfm=(10*log10(3*(mf**2)*(PcFM_AM)))+SNRam\n", + "print 'S/N ratio for FM is %.2f dBs'%(SNRfm)\n", + "# Note : There are some calculation errors in the solution presented in the book" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example7.11, page no 287" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a)\n", + " New SNR for 3dB increase in input s/g is 23 dBs\n", + "b) When Modulation depth is increased to 60%\n", + " SNR becomes 25.676045 dBs\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import log10\n", + "#Given\n", + "ma=0.3\n", + "SNR=20# s/n ratio\n", + "SNR1=10**(0.1*SNR)\n", + "SNR_new=SNR+3\n", + "ma2=0.6# increased new depth of modulation\n", + "Pt_Ni=SNR1*((1+(ma**2))/(ma**2))\n", + "SNR2=10*log10(Pt_Ni*((ma2**2)/(1+((ma2**2)/2))))\n", + "\n", + "print 'a)\\n New SNR for 3dB increase in input s/g is %d dBs\\nb) When Modulation depth is increased to 60%%\\n SNR becomes %f dBs'%(SNR_new,(SNR2))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example7.12, page no 287" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a) Bit Transmission rate: 60 kbits/s\n", + " Signal to Quantization noise ratio 128 \n", + "b)\n", + " Bit Transmission rate: 5 kbits/sample\n", + " Signal to Quantization noise ratio: 64\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import log\n", + "#Given\n", + "fmax=5e3#max s/g freq\n", + "S_fmin=2*fmax# Min sampling freq\n", + "B_S=6#Binary bits sent per sample\n", + "BTR=B_S*S_fmin#Bit Transmission rate\n", + "Q=2**B_S#No of Quantizable levels\n", + "MQN=0.5/Q#Max Quantization noise\n", + "S_QNR=MQN**-1# Signal to Quantization noise ratio\n", + "#b\n", + "S_QNRreq=0.5*S_QNR# Signal to Quantization noise ratio\n", + "Qreq=0.5*S_QNRreq#No of Quantizable levels\n", + "B_Sreq=log(Qreq,2)#Binary bits sent per sample\n", + "print 'a) Bit Transmission rate: %d kbits/s\\n Signal to Quantization noise ratio %d \\nb)\\n Bit Transmission rate: %d kbits/sample\\n Signal to Quantization noise ratio: %d'%(BTR/1000,S_QNR,B_Sreq,S_QNRreq)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter8.ipynb b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter8.ipynb new file mode 100644 index 00000000..3631a473 --- /dev/null +++ b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter8.ipynb @@ -0,0 +1,779 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter No 8 - Transmission Line" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.1, page no 313" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The characteristic Impedance is Zo= 154.92 ohm\n", + "\n", + "Propagation constant is Gama=0.0+7.75e-06j W\n", + "\n", + " The freq at which the line length is equal to wavelength is: 750 KHz\n", + " The velocity of propagation is: 322.75 km/sec\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import sqrt, pi\n", + "#Given\n", + "#a\n", + "L=1.2*10**-3#distributed inductance\n", + "C=0.05*10**-6#distributed capacitance\n", + "Zo=sqrt(L/C)#Characteristic Impedance\n", + "print 'The characteristic Impedance is Zo= %0.2f ohm'%(Zo)\n", + "Wo=1# Assumedfor ease of calculation \n", + "G=1J*sqrt(L*C)*Wo\n", + "print '\\nPropagation constant is Gama={0:0.1f}+{1:0.2e}j W'.format(G.real,G.imag)\n", + "#b\n", + "#i\n", + "lamda=0.4e3#wavelength=Line length\n", + "c=3e8\n", + "f=c/lamda\n", + "#ii\n", + "L=L*0.4\n", + "C=C*0.4\n", + "v=1/(sqrt(L*C))\n", + "print '\\n The freq at which the line length is equal to wavelength is: %d KHz\\n The velocity of propagation is: %0.2f km/sec'%(f*1e-3,v*1e-3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.2, page no 314" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The phase shift is: 144 degrees\n", + "Open Circuited line impedance: -688.19 ohms\n", + "Short Circuited line impedance: -363.27 ohms\n" + ] + } + ], + "source": [ + "from math import cos, sin, tan,pi\n", + "#Given\n", + "v=3e8# velocty of light\n", + "f=1.2e6# Operating Freq\n", + "lamda=v/f\n", + "#print lamda)\n", + "l=100# length of the Tx-Line\n", + "phi=2*(pi*l)/(lamda)# Phase shift in degrees\n", + "Zo=500# Characteristic impedance\n", + "#a Open circuited Line\n", + "\n", + "Zin=-1J*Zo*(cos(phi)/sin(phi))\n", + "\n", + "#b Short circuited Line\n", + "Z1in=1J*Zo*tan(phi)\n", + "print 'The phase shift is: %d degrees'%(phi*180/pi)\n", + "print 'Open Circuited line impedance: {0:0.2f}'.format(-Zin.imag),'ohms'\n", + "print 'Short Circuited line impedance: {0:.2f}'.format(Z1in.imag),'ohms'" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.3, page no 315" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The Characteristic impedance:Zo= \n", + "(185.464726748-135.988363959j)\n", + "The value of Alpha=0.263 nepere/km\n", + "\n", + "The value of Beta= 0.308\n", + "the tx-Line parameters are\n", + "R= 90.72 ohms\n", + "L= 21.46 mH\n", + "G= 128.80 umhos\n", + "C= 1.76 mF\n", + "\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from cmath import exp,sqrt,log,atan\n", + "#Given\n", + "f=1600\n", + "w=1000\n", + "Zoc=2460*exp(1J*-86.5*pi/180)# Open circuited Line impedance\n", + "Zsc=21.5*exp(1J*14*pi/180)# Short circuited Line impedance\n", + "Zo=sqrt(Zoc*Zsc)# Characteristic impedance\n", + "A=(sqrt(Zsc/Zoc)).real# tan(a+ jBeta) = A + jB\n", + "B=(sqrt(Zsc/Zoc)).imag\n", + "l=1/4\n", + "alpha=(1/(4*l))*log(((1+A**2+B)**2)/(((1-A)**2)+B**2)) #Attenuation Constant\n", + "Beta=(1/(2*l))*atan((2*B)/(1-A**2-B)) #phase constant\n", + "\n", + "#the tx-Line parameters\n", + "R=(Zo*complex(alpha,Beta)).real\n", + "L=(Zo*complex(alpha,Beta)).imag\n", + "G=(complex(alpha,Beta)/Zo).real\n", + "C=(complex(alpha,Beta)/Zo).imag\n", + "print 'The Characteristic impedance:Zo= '\n", + "print Zo\n", + "print 'The value of Alpha={0:.3f} '.format(alpha.real),'nepere/km\\n'\n", + "print 'The value of Beta= {0:0.3f}'.format(Beta.real)\n", + "print 'the tx-Line parameters are\\nR= %0.2f ohms\\nL= %0.2f mH\\nG= %0.2f umhos\\nC= %0.2f mF\\n'%(R,L,G*1e6,C*1e3)\n", + "\n", + "# Note : There are some calculation errors in the solution presented in the book" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.4, page no 316" + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The atenuation constant is 0.011 nepers/mile\n", + "The Cut-off Freq is 6 KHz\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import sqrt,pi\n", + "#Given\n", + "d=0.7# distance between two insertions\n", + "Ld_m= (80e-3)*(10/7)#Loading coil inductance\n", + "#print Ld_m)\n", + "Rd_m=100/7#Loading coil resistance\n", + "#print Rd_m)\n", + "R=20+Rd_m#Line resistance \n", + "L=Ld_m# Line inductance\n", + "C=0.05e-6# Line Capacitance\n", + "alfa=0.5*R*sqrt(C/L)#Attenuation Constant\n", + "#\n", + "fc=(pi*d*sqrt(L*C))**-1#cut off freq\n", + "print 'The atenuation constant is %0.3f nepers/mile\\nThe Cut-off Freq is %d KHz'%(alfa,fc*1e-3)\n", + "\n", + "# Note : There are some calculation errors in the solution presented in the book" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.5, page no 317" + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the voltage at the mid point of the line is \n", + " 6.97+6.97j\n", + " V with Angle = -8.59degrees\n" + ] + } + ], + "source": [ + "from cmath import exp\n", + "#Given\n", + "a=0.7#attenuation constant\n", + "b=0.3#phase constant\n", + "Gamma=a+(1J*b)#propagation constant\n", + "l=0.5# half length of line( for midpoint)\n", + "Vs=10# Excitation voltage\n", + "V_mod=Vs*(exp(-a*l))#Magnitude of the Vs\n", + "\n", + "phi=b*l*180/pi#phase shift\n", + "V=V_mod*(exp(-1J*(phi*pi/180)))#voltage at the mid point\n", + "print 'the voltage at the mid point of the line is \\n {0:0.2f}+{0:.2f}j\\n V with Angle = -%0.2fdegrees'.format(V.real,V.imag)%phi\n", + "\n", + "# Note : There are some calculation errors in the solution presented in the book" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.6, page no 317" + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The characteristic impedance Zo= 22.20 /_-19.66 ohm\n", + "\n", + " The Phase velocity is: v= 2.88e+07 m/sec\n", + " Percent decrease in the voltage is 14.91%\n" + ] + } + ], + "source": [ + "from cmath import pi,sqrt,polar,phase\n", + "#Given\n", + "R=0.01\n", + "l=1e3\n", + "L=1e-6\n", + "G=1e-6\n", + "C=0.001e-6\n", + "f=1.59e3# operating freq\n", + "w=2*pi*f# angular freq\n", + "#a\n", + "Zo=sqrt((R+(1J*w*L))*0.35/(G+(1J*w*C)))#characteristic impedance\n", + "Z0=polar(Zo)\n", + "Z0r=Z0[0]\n", + "Z0i=Z0[1]\n", + "#b\n", + "\n", + "Beta=sqrt(0.5*(sqrt((((R**2)+(round(w**2)*(L**2)))*(round(G**2)+(round(w**2)*(C**2)))))-(round(R*G)-((w**2)*L*C))))#Phase constant\n", + "\n", + "v=w/Beta#phase velocity\n", + "\n", + "#c\n", + "Alpha=sqrt(0.5*(sqrt((((R**2)+((w**2)*(L**2)))*((G**2)+((w**2)*(C**2)))))+((R*G)-((w**2)*L*C))))#attenuation constant\n", + "Vs=1#Assumed for easeof calculation\n", + "A=(Vs-(Vs*exp(-Alpha*l)))*100\n", + "print 'The characteristic impedance Zo= %0.2f /_%0.2f ohm\\n'%(Z0r,Z0i*180/pi)\n", + "print ' The Phase velocity is: v= %3.2e m/sec\\n Percent decrease in the voltage is %0.2f%c'%(v.real,A.real,'%')\n", + "\n", + "# Note : There are some calculation errors in the solution presented in the book" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.15, page no 348" + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The input impedance is 526.81 /_-2.18deg\n", + "Reflection Coeff is 0.07 /_-163.77deg\n" + ] + } + ], + "source": [ + "from cmath import exp,polar,cosh,sinh\n", + "\n", + "#Given\n", + "l=100# Tx-line length\n", + "ZR=200#Terminal resistance\n", + "Zo=600#Characteristic impedance\n", + "a=0.01#attenuation constant\n", + "Beta=0.03#phase constant\n", + "d=0#reflection coeff at load is Zero\n", + "Gamma=a+1J*Beta#propagation constant\n", + "Kd=((ZR-Zo)/(ZR+Zo))*exp(-2*Gamma*d)#reflection coeff at point D d km from load\n", + "Kdd=polar(Kd)\n", + "Kdr=Kdd[0]\n", + "Kdi=Kdd[1]\n", + "d1=100# distance\n", + "Ks=((ZR-Zo)/(ZR+Zo))*exp(-2*Gamma*d1)#reflection coeff at the sending end\n", + "[Ksr,Ksi]=polar(Ks)\n", + "Zin=Zo*(((ZR*cosh(Gamma*l))+(Zo*sinh(Gamma*l)))/((Zo*cosh(Gamma*l))+(ZR*sinh(Gamma*l))))#Input impedance\n", + "Zz=polar(Zin)\n", + "Zinr=Zz[0]\n", + "Zini=Zz[1]\n", + "print 'The input impedance is %0.2f /_%0.2fdeg\\nReflection Coeff is %0.2f /_%0.2fdeg'%(Zinr,Zini*180/pi,Ksr,Ksi*180/pi)\n", + "\n", + "# Note : There are some calculation errors in the solution presented in the book" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.15, page no 334" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The current received is= 13.64 mA at phase-22.59\n" + ] + } + ], + "source": [ + "from cmath import cosh,polar\n", + "#GivenR=0.01\n", + "x=10#line length\n", + "Zo=100# characteristic impedance\n", + "a=0.1# attenuation constant\n", + "Beta=0.05# phase constant\n", + "Is=20e-3# source current\n", + "Gamma=a+ 1J*Beta# propagation constant\n", + "\n", + "I=Is/cosh(Gamma*x)# received current\n", + "\n", + "Ii=polar(I)\n", + "I_r=Ii[0]\n", + "I_i=Ii[1]\n", + "\n", + "print 'The current received is= %0.2f mA at phase%0.2f'%(1000*I_r,I_i*180/pi)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.16, page no 349" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The characteristic impedance is 283.94 /_-41.38deg\n" + ] + } + ], + "source": [ + "from cmath import sqrt,polar\n", + "#Given\n", + "L=1e-3#inductance\n", + "R=40# Resistance\n", + "C=0.1e-6# capacitance\n", + "G=1e-6#conductance\n", + "w=5000# angular freq\n", + "Zo=sqrt(complex(R,(w*L))/complex(G,(w*C)))#Characteristic impedance\n", + "#Zr=sqrt(sqrt(R**2+(w*L)**2)/sqrt(G**2+(w*C)**2))\n", + "Zz=polar(Zo)\n", + "ZoR=Zz[0]\n", + "ZoI=Zz[1]\n", + "print 'The characteristic impedance is %0.2f /_%0.2fdeg'%(ZoR,ZoI*180/pi)\n", + "\n", + "# Note : There are some calculation errors in the solution presented in the book" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.17, page no 349" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The voltage at the mid point of the line is 7.05 /_-8.59 \n" + ] + } + ], + "source": [ + "from cmath import polar,exp\n", + "#Given\n", + "l=0.5#half line distance\n", + "Vs=10#Excitation voltage\n", + "Gamma=0.7+1J*0.3#propagation constant\n", + "Vv=polar(Vs*(exp(-Gamma*l)))#vtg at mid point\n", + "Vr=Vv[0]\n", + "Vi=Vv[1]\n", + "print 'The voltage at the mid point of the line is %0.2f /_%0.2f '%(Vr,Vi*180/pi)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.18, page no350" + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The max voltage on line is 5.92 V\n", + " The min voltage on line is 4.23 V\n" + ] + } + ], + "source": [ + "from math import sqrt\n", + "#Given\n", + "Zo=50# characteristic impedance\n", + "P=500e-3#Supplied power\n", + "S=1.4#VSWR on the line\n", + "Emax=sqrt(Zo*S*P)#Max vtg\n", + "\n", + "Emin=sqrt(Zo*P/S)# Min vtg\n", + "print 'The max voltage on line is %0.2f V\\n The min voltage on line is %0.2f V'%(Emax,Emin)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.19, page no 350" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "The voltage reflection coeff is 0.17\n", + "The VSWR is 1.40\n", + "\n", + "\n", + "The Max and min voltage and crresponding crrent is\n", + " Emax= 3.74V Imin= 26.73mA\n", + " Emin= 2.67V Imax= 37.42mA\n", + "\n", + " The Termination resistance should be 28.57 ohm\n" + ] + } + ], + "source": [ + "from math import sqrt\n", + "#Given\n", + "Zo=100# Characteristic Impedance\n", + "P=100e-3#Load power\n", + "Zr=140#Load Resistance\n", + "f=100e3# Operating freq\n", + "#a\n", + "K=(Zr-Zo)/(Zo+Zr)#Vtg Reflection coeff\n", + "\n", + "#b\n", + "S=(1+K)/(1-K)#VSWR\n", + "\n", + "#c+d\n", + "Emax=sqrt(Zr*P)#Max line vltg\n", + "Imin=Emax/Zr#Min line current\n", + "\n", + "Emin=Emax/S# Min line vltg\n", + "Imax=S*Imin#Max line current\n", + "\n", + "#e\n", + "R=14000/40\n", + "\n", + "Zr=(Zo**2)/R#\n", + "print '\\nThe voltage reflection coeff is %0.2f\\nThe VSWR is %0.2f\\n\\n\\nThe Max and min voltage and crresponding crrent is\\n Emax= %0.2fV Imin= %0.2fmA\\n Emin= %0.2fV Imax= %0.2fmA\\n\\n The Termination resistance should be %0.2f ohm'%(K,S,Emax,Imin*1e3,Emin,Imax*1e3,Zr)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.20, page no 352" + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the receiving voltage will be 0.25 V\n" + ] + } + ], + "source": [ + "from math import exp,log\n", + "#Given\n", + "V=0.5#receiving vtg\n", + "Vs=2#Source vtg\n", + "al=-log(V/Vs)#attenuation\n", + "\n", + "al2=al*1.5\n", + "V=Vs*exp(-al2)#receiving voltage\n", + "print 'the receiving voltage will be %0.2f V'%(V)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.22, page no352" + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The lrngth should be 25 metres\n", + "The Characteristic Impedance should be 48.79 ohms\n" + ] + } + ], + "source": [ + "from cmath import sqrt\n", + "#Given\n", + "Zin=25+1J*15# Internal Impedance\n", + "Zr=70-1J*42#load\n", + "f=3e6#operating freq\n", + "v=3e8#light velocity\n", + "L=v/(4*f)#length of the line\n", + "\n", + "Zo=sqrt(Zin*Zr)#Characteristic Impedance\n", + "\n", + "print 'The lrngth should be %d metres\\nThe Characteristic Impedance should be %0.2f ohms'%(L,Zo.real)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.23, page no353" + ] + }, + { + "cell_type": "code", + "execution_count": 74, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The cut-off freq is 3.03 KHz \n", + " the voltage being measured is 1 V\n" + ] + } + ], + "source": [ + "from math import sqrt,pi\n", + "from __future__ import division\n", + "#Given\n", + "#a\n", + "L=1e-3# inductance\n", + "C=61.25e-9#capacitance\n", + "Ld=44e-3#coil inductance\n", + "d=2#distance intervals after which coils are added\n", + "Lt=(L*2)+(Ld*2)#total inductance\n", + "Ct=C*2#total capacitance\n", + "fc=(pi*sqrt(Lt*Ct))**-1#cut off freq\n", + "\n", + "#b\n", + "I=100e-3#milliameter range\n", + "R=1#milliameter resistance\n", + "Zo=100#characteristic impedance\n", + "Zin=(Zo**2)/R#input impedance\n", + "\n", + "Er=I*R#\n", + "Es=Er*sqrt(Zin/Zo)\n", + "print 'The cut-off freq is %0.2f KHz \\n the voltage being measured is %d V'%(fc*1e-3,Es)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.24, page no 354" + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the Length of the transformer(stub) is 3.75 metres\n", + " The characteristic impedance of this transformer is 224 ohms\n" + ] + } + ], + "source": [ + "#Given\n", + "f=20e6#tuned freq\n", + "ZR=100#Equivalent aerial Resistance\n", + "Zin=500#input impedance\n", + "c=3e8\n", + "lamda=c/f\n", + "l=lamda/4#lamda/4 Transformer\n", + "\n", + "Zo=sqrt(Zin*ZR)#Characteristic impedance\n", + "print 'the Length of the transformer(stub) is %0.2f metres\\n The characteristic impedance of this transformer is %d ohms'%(l,round(Zo))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example8.25, page no 354" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The sending end (Source end)impedance (Zl)is: \n", + "330.46+-16.35j\n" + ] + } + ], + "source": [ + "#Given\n", + "lamda=5#wavelength\n", + "Zo=200#Characteristic impedance\n", + "Zo1=100#Zo'\n", + "ZL=50+(1J*50)# load impedance\n", + "l1=0.4*lamda\n", + "l2=0.2*lamda\n", + "Beta=(2*pi/lamda)# phase difference\n", + "Z2=Zo1*(((ZL*cos(Beta*l2))+(1J*Zo1*sin(Beta*l2)))/((Zo1*cos(Beta*l2))+(1J*ZL*sin(Beta*l2))))#I/p Impedance offered by I2toI1\n", + "Z1=Zo*(((Z2*cos(Beta*l1))+(1J*Zo*sin(Beta*l1)))/((Zo*cos(Beta*l1))+(1J*Z2*sin(Beta*l1))))#I/p impedance\n", + "print 'The sending end (Source end)impedance (Zl)is: '\n", + "print '{0:0.2f}+{1:0.2f}j'.format(Z1.real,Z1.imag)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter9.ipynb b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter9.ipynb new file mode 100644 index 00000000..2d2304df --- /dev/null +++ b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/Chapter9.ipynb @@ -0,0 +1,338 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter No 9 - Aerials" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example9.1, page no 397" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The maximum effective aperture of the\n", + " aerial is 28.65 sq m\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from math import pi\n", + "\n", + "#Given\n", + "D=90# directivity\n", + "lamda=2# wavelength\n", + "Ae=(D*(lamda**2))/(4*pi)#effective aperture\n", + "print 'The maximum effective aperture of the\\n aerial is %0.2f sq m'%(Ae)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example9.2, page no 397" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Angular beam width is 22.92 degrees\n", + "BeamWidth is 0.40 rad\n" + ] + } + ], + "source": [ + "from math import pi,cos\n", + "#Given\n", + "n=10#no of aerial elements\n", + "d=0.5#distance in terms of wavelength\n", + "Beam_Width=2/(n*d)#\n", + "Beam_Width_degrees=Beam_Width*180/pi\n", + "print 'Angular beam width is %0.2f degrees\\nBeamWidth is %0.2f rad'%(Beam_Width_degrees,Beam_Width)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example9.3, pageno 397" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Total power radiated is 888.89 watts\n" + ] + } + ], + "source": [ + "from numpy import arange, pi\n", + "from sympy.mpmath import quad, sin\n", + "#Given\n", + "r=1#assume distance for ease of calculation\n", + "#Pav(theta)=(1000/(3*pi*r**2))*((sin(theta))**2)\n", + "theta=arange(0, pi, 0.1)\n", + "x0=0\n", + "x1=pi\n", + "Pt=(2000/(3*r**2))*quad(lambda theta: (sin(theta))**3,[x0,x1])#Total power radiated \n", + "print 'Total power radiated is %0.2f watts'%(Pt)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example9.4, page no 398" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "electric field intensity is 0.25 mV/m \n", + " magnetic field intensity is 0.67 uA/m\n" + ] + } + ], + "source": [ + "from math import pi,cos\n", + "#Given\n", + "dl=2# length of wire \n", + "I=6#current in the wire\n", + "f=1e6# operating freq\n", + "r=30e3#distance at which field is to be calculated\n", + "theta=90#right angles to the wire axis\n", + "lamda=300# wavelength\n", + "w=2*pi*f#angular freq\n", + "c=3e8\n", + "t=f**-1\n", + "Phi=w*(t-(r/c))#Phase shift\n", + "Erad=25.13e-5*cos(Phi)#Radiation electric field intensity\n", + "H=Erad/(120*pi)#Radiation magnetic field intensity\n", + "print 'electric field intensity is %0.2f mV/m \\n magnetic field intensity is %0.2f uA/m'%(Erad*1e3,H*1e6)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example9.5, page no 399" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The radiated power is 1.03 watts\n" + ] + } + ], + "source": [ + "from math import sqrt\n", + "#Given\n", + "#c\n", + "Rr=73# radition resistance\n", + "Vrms=10#RMS voltage of the signal\n", + "Zin_mod=sqrt((73**2)+(42**2))#absolute input impedance\n", + "Irms=Vrms/Zin_mod#RMS current\n", + "Pt=(Irms**2)*Rr# Radiated power\n", + "print 'The radiated power is %0.2f watts'%(round(100*Pt)/100)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example9.6 page no 400" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Ideal directive gain is 55840\n" + ] + } + ], + "source": [ + "#Given\n", + "#b\n", + "c=3e8\n", + "f=2e9#operating freq\n", + "Ae=100#aperture area\n", + "lamda=c/f# operating wavwlength\n", + "D=((4*3.141*Ae)/(lamda**2))# Directivity\n", + "print 'Ideal directive gain is %d'%(D)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example9.7, pageno 400" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The angular width is 0.40 degrees\n" + ] + } + ], + "source": [ + "#Given\n", + "#b\n", + "n=10# no of aerial elements\n", + "lambda_d=2#\n", + "BeamWidth=2*lambda_d/n# Beamwidth\n", + "print 'The angular width is %0.2f degrees'%(BeamWidth)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example9.8, page no 400" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Overall Gain is 3.52 dBs\n" + ] + } + ], + "source": [ + "from math import log10\n", + "#Given\n", + "D1=1\n", + "D2=1.5*D1 # diameters of the new reflectors D1=1assumed for ease of calculation\n", + "G_dbs=10*log10((D2/D1)**2)#Gain in dBs\n", + "print 'Overall Gain is %0.2f dBs'%(round(1000*G_dbs)/1000)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example9.9, page no 401" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Radiation resistance is 2.05 ohm\n" + ] + } + ], + "source": [ + "#Given\n", + "#b\n", + "c=3e8\n", + "f=800e3# operating freq\n", + "dl=27#effective height\n", + "lamda=c/f\n", + "\n", + "Rr=40*(3.142**2)*(dl/lamda)**2#Radiation Resistance\n", + "print 'Radiation resistance is %0.2f ohm'%(Rr)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/screenshots/Ch5FreqDev.png b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/screenshots/Ch5FreqDev.png new file mode 100644 index 00000000..dfa44478 Binary files /dev/null and b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/screenshots/Ch5FreqDev.png differ diff --git a/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/screenshots/FreqVsApmChap3.png b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/screenshots/FreqVsApmChap3.png new file mode 100644 index 00000000..9d4a7e11 Binary files /dev/null and b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/screenshots/FreqVsApmChap3.png differ diff --git a/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/screenshots/modulatedWaveChap3.png b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/screenshots/modulatedWaveChap3.png new file mode 100644 index 00000000..3b34f439 Binary files /dev/null and b/Principle_of_Communication_Engineering_by_A._Singh_and_A._K._Chhabra/screenshots/modulatedWaveChap3.png differ diff --git a/SURVYNG_AND_LEVELLING__by_N.N.BASAK/chap10.ipynb b/SURVYNG_AND_LEVELLING__by_N.N.BASAK/chap10.ipynb new file mode 100644 index 00000000..b87fe16a --- /dev/null +++ b/SURVYNG_AND_LEVELLING__by_N.N.BASAK/chap10.ipynb @@ -0,0 +1,1023 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "# Chapter 10: Curves" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-10 page 379 pb-1" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('Tangent length =', 58.45305445925609)\n", + "('Length long of cord=', 114.35142994976763)\n", + "('Length of curve =', 115.19173063162576)\n", + "('chainage of commencement =', 1262.046945540744)\n", + "('chainage of tangency =', 1377.2386761723697)\n", + "('apex distance =', 6.143663587883047)\n", + "('versed sine of curve is', 6.009409798203436)\n" + ] + } + ], + "source": [ + "#ch-10 page 379 pb-1\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "r=275;\n", + "t=24;\n", + "l=1320.5;\n", + "\n", + "tl=r*math.tan((t/2)*(math.pi/180));\n", + "print('Tangent length =',tl);\n", + "llc=2*r*math.sin((t/2)*(math.pi/180));\n", + "print('Length long of cord=',llc);\n", + "loc=(math.pi*r*t/180);\n", + "print('Length of curve =',loc)\n", + "coc=l-tl;\n", + "ct=coc+loc;\n", + "print('chainage of commencement =',coc);\n", + "print('chainage of tangency =',ct);\n", + "k=math.cos((t/2)*math.pi/180);\n", + "ad=r*((1/k)-1);\n", + "print('apex distance =',ad)\n", + "k1=math.cos((t/2)*(math.pi/180))\n", + "vsc=r*(1-k1);\n", + "print('versed sine of curve is',vsc);\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-10 page 379,380 pb-2" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('radius of curve ', 573.0)\n", + "('Tangent length =', 153.5348872630333)\n", + "('Length of curve =', 300.02209841782525)\n", + "('Length long of cord=', 296.60662568748876)\n", + "('chainage of commencement =', 2606.4651127369666)\n", + "('chainage of tangency =', 2906.487211154792)\n", + "('length of each half =', 148.30331284374438)\n", + "('O30=', 18.738622298863106, 'O60=', 16.374481794326243, 'O90=', 12.412299602376265, 'O120=', 6.81817453294525, 'O148.3=', 0.0)\n" + ] + } + ], + "source": [ + "#ch-10 page 379,380 pb-2\n", + "from __future__ import division\n", + "\n", + "import math\n", + "ac=45.5;cb=75.5;\n", + "#a\n", + "\n", + "t=cb-ac;\n", + "l1=1719;\n", + "l=2760;\n", + "\n", + "#b\n", + "r=l1/3;\n", + "print('radius of curve ',r);\n", + "\n", + "#c\n", + "tl=r*math.tan((t/2)*(math.pi/180));\n", + "print('Tangent length =',tl);\n", + "#d\n", + "loc=(math.pi*r*t/180);\n", + "print('Length of curve =',loc)\n", + "#e\n", + "llc=2*r*math.sin((t/2)*(math.pi/180));\n", + "print('Length long of cord=',llc);\n", + "\n", + "#f,g\n", + "coc=l-tl;\n", + "ct=coc+loc;\n", + "print('chainage of commencement =',coc);\n", + "print('chainage of tangency =',ct);\n", + "\n", + "#h\n", + "\n", + "half=0.5*llc;\n", + "print('length of each half =',half);\n", + "\n", + "ini=30;\n", + "\n", + "k=math.sqrt(r*r-(half*half));\n", + "o=r-k\n", + "k1=r-o;\n", + "O30=(math.sqrt(r*r-(ini*ini)))-k1;\n", + "O60=(math.sqrt(r*r-(2*ini*2*ini)))-k1;\n", + " \n", + "O90=(math.sqrt(r*r-(3*ini*3*ini)))-k1;\n", + "O120=(math.sqrt(r*r-(4*ini*4*ini)))-k1;\n", + "Oh=(math.sqrt(r*r-(half*half)))-k1;\n", + "\n", + "print('O30=',O30,'O60=',O60,'O90=',O90,'O120=',O120,'O148.3=',Oh);\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### ch-10 page 381 pb-3" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('Tangent length =', 150.2288093231531)\n", + "('Length of curve =', 278.55454861829503)\n", + "('chainage of T1=', 360.00119067684693)\n", + "('chainage of T2=', 638.555739295142)\n", + "('chainage covered=', 630.0011906768469)\n", + "('Length of final sub cord=', 8.55454861829503)\n", + "('first ofset=', 1.5)\n", + "('second ofset=', 3.0)\n", + "('tenth ofset=', 0.5496946010193738)\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "a=126.8;\n", + "t=180-a;\n", + "r=300;\n", + "#b\n", + "tl=r*math.tan((t/2)*(math.pi/180));\n", + "print('Tangent length =',tl);\n", + "\n", + "#c\n", + "loc=(math.pi*r*t/180);\n", + "print('Length of curve =',loc)\n", + "\n", + "#d\n", + "l=510.23;\n", + "ct1=l-tl;\n", + "ct2=ct1+loc;\n", + "\n", + "print('chainage of T1=',ct1);\n", + "print('chainage of T2=',ct2);\n", + "\n", + "#f\n", + "n=9;\n", + "b=30;\n", + "cc=ct1+270;\n", + "lfsc=ct2-cc;\n", + "print('chainage covered=',cc);\n", + "print('Length of final sub cord=',lfsc);\n", + "\n", + "O1=(b*b)/(2*r);\n", + "O2=(b*b)/r;\n", + "\n", + "O10=(lfsc*(b+lfsc))/(2*r);\n", + "\n", + "print('first ofset=',O1);\n", + "print('second ofset=',O2);\n", + "print('tenth ofset=',O10);\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-10 page 382 pb-4" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(165.95962740164575, 158.58327092428829)\n", + "('Radius R=', 143.72525333242524)\n", + "('Tangent length BT1=', 82.97981370082289)\n", + "('Tangent length CT1=', 67.02018629917711)\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "ab=30;bc=90;cd=140;\n", + "l1=250;l2=150;l3=325;\n", + "\n", + "abc=210-bc;\n", + "t1=0.5*abc;\n", + "bcd=270-cd;\n", + "t2=0.5*bcd;\n", + "t3=180-(t1+t2);\n", + "\n", + "\n", + "k=(math.sin(t2*(math.pi/180)))/(math.sin(t3*(math.pi/180)));\n", + "OB=l2*k;\n", + "k1=(math.sin(t1*(math.pi/180)))/(math.sin(t3*(math.pi/180)));\n", + "OC=l2*k1;\n", + "print(OB,OC);\n", + "R=OB*(math.sin(t1*(math.pi/180)));\n", + "print('Radius R=',R);\n", + "\n", + "BT1=OB*(math.cos(t1*(math.pi/180)));\n", + "CT1=OC*(math.cos(t2*(math.pi/180)));\n", + "\n", + "print('Tangent length BT1=',BT1);\n", + "print('Tangent length CT1=',CT1);\n", + "\n", + "\n", + " \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-10 page 383 pb-5" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('R1=', 368.61561236693893)\n", + "('length of arc T1T2=', 209.43951023931953)\n", + "('length of arc T2T3=', 386.0133666034928)\n", + "('chainage of T1=', 792.8203230275509)\n", + "('chainage of T3=', 1388.2731998703632)\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "r=400;\n", + "t1=15;t2=30;t3=60;\n", + "ct=900;\n", + "l=320;\n", + "BT2=r*(math.tan((t1)*math.pi/180));\n", + "CT2=l-BT2;\n", + "\n", + "r1=(CT2)/(math.tan((t2)*math.pi/180));\n", + "\n", + "print('R1=',r1);\n", + "t1t2=(math.pi*r*t2)/(180);\n", + "\n", + "t2t3=(math.pi*r1*t3)/(180);\n", + "\n", + "print('length of arc T1T2=',t1t2);\n", + "print('length of arc T2T3=',t2t3);\n", + "\n", + "\n", + "ct1=ct-BT2;\n", + "ct3=ct1+t1t2+t2t3;\n", + "\n", + "print('chainage of T1=',ct1);\n", + "print('chainage of T3=',ct3);\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-10 page 384 pb-6" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('R2=', 1092.8203230275515)\n", + "('length of arc T1T2=', 209.43951023931953)\n", + "('length of arc T2T3=', 572.1993830861634)\n", + "('chainage of point of reverse curvature =', 1709.4395102393196)\n", + "('chainage of finishing point T3=', 2281.638893325483)\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "r1=400;\n", + "t1=30;d=200;\n", + "ct1=1500;\n", + "k=1-(math.cos(t1*(math.pi/180)))\n", + "T1G=r1*(k);\n", + "\n", + "r2=(d-T1G)/k;\n", + "print('R2=',r2);\n", + "\n", + "t1t2=(math.pi*r1*t1)/180;\n", + "t2t3=(math.pi*r2*t1)/180;\n", + "print('length of arc T1T2=',t1t2);\n", + "print('length of arc T2T3=',t2t3);\n", + "\n", + "ct2=ct1+t1t2;\n", + "ct3=ct2+t2t3;\n", + "\n", + "print('chainage of point of reverse curvature =',ct2);\n", + "print('chainage of finishing point T3=',ct3);\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-10 page 385 pb-7" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('EF=', 228.7451827250347)\n", + "('chainage of T1=', 701.0877129159065)\n", + "('chainage of D=', 1015.2469782748858)\n", + "('chainage of T2', 1137.4200259144889)\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "a1=135;a2=145;\n", + "t1=180-a1;\n", + "t2=180-a2;\n", + "t3=180-(t1+t2);\n", + "r1=400;r2=200;\n", + "ct=1000;\n", + "\n", + "ED=r1*(math.tan((t1/2)*(math.pi/180)));\n", + "\n", + "FD=r2*(math.tan((t2/2)*(math.pi/180)));\n", + "\n", + "EF=ED+FD;\n", + "\n", + "print('EF=',EF);\n", + "\n", + "BE=EF*(math.sin(t2*(math.pi/180)))/(math.sin(t3*(math.pi/180)));\n", + "\n", + "BF=EF*(math.sin(t1*(math.pi/180)))/(math.sin(t3*(math.pi/180)))\n", + "\n", + "\n", + "ct1=ct-(BE+ED);\n", + "\n", + "cd=ct1+((math.pi*r1*t1)/(180));\n", + "\n", + "ct2=cd+((math.pi*r2*t2)/(180));\n", + "\n", + "print('chainage of T1=',ct1);\n", + "print('chainage of D=',cd);\n", + "print('chainage of T2',ct2);\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-10 page 386 pb-8" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('Radius R=', 272.7765415715475)\n", + "('angle Theta=', 109.0)\n", + "('curve length T1D=', 145.2058875651141)\n", + "('curve length DT2=', 192.814375291381)\n", + "('chainage of T1=', 1305.430383812096)\n", + "('chainage of T2=', 1643.4506466685912)\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "t1=30.5;\n", + "t2=40.5;\n", + "EF=175;\n", + "cb=1500;\n", + "\n", + "k1=math.tan((t1/2)*(math.pi/180));\n", + "k2=math.tan((t2/2)*(math.pi/180));\n", + "\n", + "r=EF/(k1+k2);\n", + "print('Radius R=',r);\n", + "\n", + "et1=r*k1;\n", + "ft2=r*k2;\n", + "\n", + "t3=180-(t1+t2);\n", + "print('angle Theta=',t3);\n", + "k3=(math.sin(t2*(math.pi/180)))/(math.sin(t3*(math.pi/180)));\n", + "k4=(math.sin(t1*(math.pi/180)))/(math.sin(t3*(math.pi/180)));\n", + "\n", + "be=EF*k3;\n", + "bf=EF*k4;\n", + "\n", + "t1d=(math.pi*r*t1)/180;\n", + "dt2=(math.pi*r*t2)/180;\n", + "\n", + "print('curve length T1D=',t1d);\n", + "print('curve length DT2=',dt2);\n", + "\n", + "ct1=cb-(be+et1);\n", + "\n", + "ct2=ct1+t1d+dt2;\n", + "print('chainage of T1=',ct1);\n", + "print('chainage of T2=',ct2)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-10 page 387 pb-9" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('theta 3=', 10.649036741314365)\n", + "('Radius R=', 829.124128893828)\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "t1=80-70;\n", + "l=50;\n", + "k=1/(math.cos(20*(math.pi/180)));\n", + "\n", + "k1=k*(math.sin(t1*(math.pi/180)));\n", + "t3=math.asin(k1);\n", + "t3=t3*(180/(math.pi));\n", + "print('theta 3=',t3);\n", + "\n", + "t3=180-t3;\n", + "t2=180-(t3+t1);\n", + "\n", + "r=l*(math.sin(t1*(math.pi/180)))/(math.sin(0.6*(math.pi/180)));\n", + "print('Radius R=',r);\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-10 page 388 pb-10" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('radius of circular curvature=', 402.713280728911)\n", + "('length of transistion curve =', 90.83333333333334)\n", + "('spiral angle=', 6.461627773592511)\n", + "('central angle=', 47.07674445281498)\n", + "('length of circular curve =', 330.88702808033025)\n", + "('shift of curve =', 0.8536568115234379)\n", + "('tangent length =', 278.4161466916694)\n", + "('chainage of 1st tangent point =', 871.5838533083306)\n", + "('chainage of 2nd tangent point =', 1384.1375480553274)\n", + "('chainage of 1st junction point =', 962.417186641664)\n", + "('chainage of 2nd junction point =', 1293.3042147219942)\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "sp=80;\n", + "v=(sp*1000)/(60*60);\n", + "cr=(1/8);\n", + "g=9.81;\n", + "a=60;\n", + "\n", + "#a\n", + "\n", + "r=(v*v)/(g*cr);\n", + "print('radius of circular curvature=',r);\n", + "\n", + "#b\n", + "k=0.3;\n", + "l=(v*v*v)/(k*r);\n", + "print('length of transistion curve =',l);\n", + "\n", + "sa=l/(2*r);\n", + "sa=sa*(180/(math.pi));\n", + "print('spiral angle=',sa);\n", + "ca=a-(2*sa);\n", + "print('central angle=',ca);\n", + "\n", + "lcc=(math.pi*r*ca)/180;\n", + "print('length of circular curve =',lcc);\n", + "\n", + "s=(l*l)/(24*r);\n", + "print('shift of curve =',s);\n", + "ag=a/2;\n", + "t=(r+s)*(math.tan(ag*(math.pi/180)))+(l/2);\n", + "print('tangent length =',t);\n", + "#c\n", + "cip=1150;\n", + "c1t=cip-t;\n", + "c1j=c1t+l;\n", + "c2j=c1j+lcc;\n", + "c2t=c2j+l;\n", + "\n", + "print('chainage of 1st tangent point =',c1t);\n", + "print('chainage of 2nd tangent point =',c2t);\n", + "\n", + "print('chainage of 1st junction point =',c1j);\n", + "print('chainage of 2nd junction point =',c2j);\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-10 page 389 pb-11" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('radius =', 343.8)\n", + "('tangent length =', 108.39972361659453)\n", + "('curve length =', 210.01546889247766)\n", + "('chainage of 1st point =', 1471.6002763834056)\n", + "('chainage of 2nd point =', 1681.6157452758832)\n", + "('length of final sub chord =', 8.399723616594429)\n", + "('chainage covered=', 1660)\n", + "('length of final sub chord', 21.615745275883228)\n", + "('deflection angle for initial sub chord =', 43.52844633883164, 'min')\n", + "('deflection angle for full chord', 2.5910642019719075, 'min')\n", + "('deflection angle for final sub chord', 1.8669261261094798, 'min')\n", + "('total deflection angle=', 17.5)\n", + "('apex distance =', 16.6843132234107)\n", + "('versed sine of curve =', 15.91211233275958)\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "a=145;\n", + "cpi=1580;\n", + "de=5;\n", + "pi=30;\n", + "lct=0.00555;\n", + "\n", + "da=180-a;\n", + "\n", + "r=(1719)/5;\n", + "\n", + "print('radius =',r);\n", + "\n", + "#a\n", + "\n", + "tl=r*(math.tan((da/2)*(math.pi/180)));\n", + "print('tangent length =',tl);\n", + "\n", + "#b\n", + "\n", + "cl=(math.pi*r*da)/180;\n", + "print('curve length =',cl);\n", + "\n", + "#c\n", + "\n", + "c1t=cpi-tl;\n", + "print('chainage of 1st point =',c1t);\n", + "\n", + "#d\n", + "c2t=c1t+cl;\n", + "print('chainage of 2nd point =',c2t);\n", + "\n", + "#e\n", + "lisc=1480-c1t;\n", + "print('length of final sub chord =',lisc);\n", + "#f\n", + "n=6;\n", + "ini=30;\n", + "cc=1480+(n*30);\n", + "print('chainage covered=',cc);\n", + "#g\n", + "lfsc=c2t-cc;\n", + "print('length of final sub chord',lfsc);\n", + "#h\n", + "dasc=((c2t+100)*lisc)/(r);\n", + "print('deflection angle for initial sub chord =',dasc,'min');\n", + "#i\n", + "dafc=((c2t+100)*pi)/r;\n", + "print('deflection angle for full chord',dafc/60,'min');\n", + "#j\n", + "dafsc=((c2t+100)*lfsc)/r;\n", + "print('deflection angle for final sub chord',dafsc/60,'min');\n", + "\n", + "#k\n", + "\n", + "tda=da/2;\n", + "print('total deflection angle=',tda);\n", + "\n", + "\n", + "#l\n", + "k=1/(math.cos(tda*(math.pi/180)));\n", + "ad=r*(k-1);\n", + "print('apex distance =',ad);\n", + "\n", + "vs=r*(1-(math.cos(tda*(math.pi/180))));\n", + "print('versed sine of curve =',vs);\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-10 page 391 pb-1" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('length of vertical curve =', 240.0)\n", + "('chainage of A', 430.0)\n", + "('chainage of C', 670.0)\n", + "('Rl of A', 374.9)\n", + "('Rl of C', 374.66)\n", + "('Rl of E', 374.78)\n", + "('Rl of F', 375.14)\n", + "('tangent correction at the apex =', 0.36000000000001364)\n", + "('tangent correction at 1st,2nd,3rd,4th,5th,6th, points', 0.01, 0.04, 0.09, 0.16, 0.25, 0.36)\n", + "RL of the points on grade\n", + "(375.0, 375.1, 375.20000000000005, 375.30000000000007, 375.4000000000001, 375.5000000000001)\n", + "RL of the points on curve\n", + "(374.99, 375.06, 375.11000000000007, 375.14000000000004, 375.1500000000001, 375.1400000000001)\n", + "Rls of points on the grade right side\n", + "(375.36, 375.22, 375.08000000000004, 374.94000000000005, 374.80000000000007)\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "pi=20;\n", + "cb=550;\n", + "rlb=375.5;\n", + "g1=0.5;\n", + "g2=-0.7;\n", + "#a\n", + "vc=((g1-g2)*20)/0.1;\n", + "\n", + "print('length of vertical curve =',vc);\n", + "\n", + "#b,c\n", + "\n", + "ca=cb-(vc/2);\n", + "cc=ca+vc;\n", + "print('chainage of A',ca);\n", + "print('chainage of C',cc);\n", + "\n", + "#d,e,f,g\n", + "\n", + "rla=rlb-((g1*0.5*vc)/100);\n", + "rlc=rlb-((-g2*0.5*vc)/100);\n", + "rle=0.5*(rla+rlc);\n", + "rlf=0.5*(rlb+rle);\n", + "\n", + "print('Rl of A',rla);\n", + "print('Rl of C',rlc);\n", + "print('Rl of E',rle);\n", + "print('Rl of F',rlf);\n", + "#h\n", + "tc=rlb-rlf;\n", + "print('tangent correction at the apex =',tc);\n", + "\n", + "#i\n", + "tc1=((g1-g2)*(pi*pi))/(400*0.5*vc);\n", + "tc2=((g1-g2)*(2*pi*2*pi))/(400*0.5*vc);\n", + "tc3=((g1-g2)*(3*pi*3*pi))/(400*0.5*vc);\n", + "tc4=((g1-g2)*(4*pi*4*pi))/(400*0.5*vc);\n", + "tc5=((g1-g2)*(5*pi*5*pi))/(400*0.5*vc);\n", + "tc6=((g1-g2)*(6*pi*6*pi))/(400*0.5*vc);\n", + "print('tangent correction at 1st,2nd,3rd,4th,5th,6th, points',tc1,tc2,tc3,tc4,tc5,tc6);\n", + "\n", + "#j\n", + "rp=(g1*pi)/100;\n", + "\n", + "rl1=rla+rp;\n", + "rl2=rl1+rp;\n", + "rl3=rl2+rp;\n", + "rl4=rl3+rp;\n", + "rl5=rl4+rp;\n", + "rl6=rl5+rp;\n", + "print('RL of the points on grade');\n", + "print(rl1,rl2,rl3,rl4,rl5,rl6)\n", + "\n", + "#k\n", + "rlc1=rl1-tc1;\n", + "rlc2=rl2-(tc2);\n", + "rlc3=rl3-(tc3);\n", + "rlc4=rl4-(tc4);\n", + "rlc5=rl5-(tc5);\n", + "rlc6=rl6-(tc6);\n", + "\n", + "print('RL of the points on curve');\n", + "print(rlc1,rlc2,rlc3,rlc4,rlc5,rlc6);\n", + "\n", + "#l\n", + "\n", + "fp=0.14;\n", + "\n", + "rlg5=rlb-fp;\n", + "rlg4=rlg5-fp;\n", + "rlg3=rlg4-fp;\n", + "rlg2=rlg3-fp;\n", + "rlg1=rlg2-fp;\n", + "\n", + "print('Rls of points on the grade right side');\n", + "print(rlg5,rlg4,rlg3,rlg2,rlg1);\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-10 page 393 pb-2" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('length of vertical curve', 300.0)\n", + "('RL of A=', 252.0)\n", + "('RL of C=', 251.25)\n", + "('RL of E=', 251.625)\n", + "('RL of F=', 251.0625)\n", + "RL on the grade on the side AB \n", + "(251.7, 251.39999999999998, 251.09999999999997, 250.79999999999995)\n", + "RL on grade on side BC\n", + "(250.65, 250.8, 250.95000000000002, 251.10000000000002)\n", + "tangent correction from expression \n", + "(-0.0225, -0.09, -0.2025, -0.36)\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "cb=400;\n", + "rlb=250.5;\n", + "pi=30;\n", + "g1=-1.0;\n", + "g2=0.5;\n", + "g=0.1;\n", + "ga=20;\n", + "#a\n", + "vc=(g1-g2)/g;\n", + "vc=-vc*ga;\n", + "print('length of vertical curve',vc);\n", + "\n", + "#b,c\n", + "ca=cb-(0.5*vc);\n", + "cc=ca+vc;\n", + "\n", + "#d,e,f,g\n", + "\n", + "rla=rlb+((0.5*vc)/100);\n", + "\n", + "rlc=rlb+((0.5*0.5*vc)/100);\n", + "\n", + "rle=0.5*(rla+rlc);\n", + "\n", + "rlf=0.5*(rle+rlb);\n", + "\n", + "print('RL of A=',rla);\n", + "print('RL of C=',rlc);\n", + "print('RL of E=',rle);\n", + "print('RL of F=',rlf);\n", + "\n", + "#h\n", + "fp=pi/100;\n", + "\n", + "rl1=rla-fp;\n", + "rl2=rl1-fp;\n", + "rl3=rl2-fp;\n", + "rl4=rl3-fp;\n", + "print('RL on the grade on the side AB ');\n", + "print(rl1,rl2,rl3,rl4);\n", + "\n", + "#i\n", + "\n", + "rp=(0.5*pi)/100;\n", + "\n", + "rls4=rlb+rp\n", + "rls3=rls4+rp\n", + "rls2=rls3+rp\n", + "rls1=rls2+rp\n", + "\n", + "print('RL on grade on side BC');\n", + "print(rls4,rls3,rls2,rls1);\n", + "\n", + "#j\n", + "\n", + "y1=((g1-g2)*(pi*pi))/(cb*0.5*vc);\n", + "y2=((g1-g2)*(2*pi*2*pi))/(cb*0.5*vc);\n", + "y3=((g1-g2)*(3*pi*3*pi))/(cb*0.5*vc);\n", + "y4=((g1-g2)*(4*pi*4*pi))/(cb*0.5*vc);\n", + "\n", + "print('tangent correction from expression ');\n", + "print(y1,y2,y3,y4);\n", + "\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.11" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/SURVYNG_AND_LEVELLING__by_N.N.BASAK/chap2.ipynb b/SURVYNG_AND_LEVELLING__by_N.N.BASAK/chap2.ipynb new file mode 100644 index 00000000..e3e0c595 --- /dev/null +++ b/SURVYNG_AND_LEVELLING__by_N.N.BASAK/chap2.ipynb @@ -0,0 +1,127 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "# Chapter 2: Chain Surveying" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### pg-56, pb-1" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('max length of offset should be', 6.8842279474019135, 'meters')\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "ag=5;\n", + "giv=0.03;\n", + "\n", + "L=20;\n", + "l=(giv*L/(math.sin(ag*math.pi/180)));\n", + "\n", + "\n", + "AB=l;\n", + "\n", + "BC=AB*(math.sin(ag*(math.pi/180)));\n", + "BC=BC/20;\n", + "\n", + "print('max length of offset should be',l,'meters');\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### ch-2 page-56, pb-2" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('required displacement perpendicular to chain is', 0.0020556978681392835, 'meters')\n", + "('displacement parallel ot chain is', 0.07850393436441575, 'meters')\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "\n", + "AD=AB=15;\n", + "ag=3;\n", + "AC=15*(math.cos(ag*(math.pi/180)))\n", + "\n", + "CD=AB-AC\n", + "sc=10;\n", + "\n", + "CD=CD/sc;\n", + "\n", + "print('required displacement perpendicular to chain is',CD,'meters');\n", + "\n", + "\n", + "BC=AB*(math.sin(ag*(math.pi/180)));\n", + "\n", + "BC=BC/sc;\n", + "print('displacement parallel ot chain is',BC,'meters');\n", + "\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.11" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/SURVYNG_AND_LEVELLING__by_N.N.BASAK/chap3.ipynb b/SURVYNG_AND_LEVELLING__by_N.N.BASAK/chap3.ipynb new file mode 100644 index 00000000..af93c556 --- /dev/null +++ b/SURVYNG_AND_LEVELLING__by_N.N.BASAK/chap3.ipynb @@ -0,0 +1,1695 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "# Chapter 3: Compass Traversing" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### chapter 3, section 3.10, pg85, problem 1" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "N 45 degrees 30.0 minutes E\n", + "S 54 degrees 15.0 minutes E\n", + "S 42 degrees 15.0 minutes W\n", + "N 39 degrees 30.0 minutes W\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "import math\n", + "\n", + "#(a)\n", + "WCB_AB=45+(30/60)\n", + "QB_AB=WCB_AB\n", + "mins=(QB_AB-int(QB_AB))*60\n", + "deg=int(QB_AB)\n", + "print \"N\",deg,\"degrees\",mins,\"minutes E\"\n", + " \n", + "#(b)\n", + "WCB_BC=125+(45/60)\n", + "QB_BC=180-WCB_BC\n", + "mins=(QB_BC-int(QB_BC))*60\n", + "deg=int(QB_BC)\n", + "print \"S\",deg,\"degrees\",mins,\"minutes E\"\n", + "\n", + "#(c)\n", + "WCB_CD=222+(15/60)\n", + "QB_CD=WCB_CD-180\n", + "deg=int(QB_CD)\n", + "mins=(QB_CD-deg)*60\n", + "print \"S\",deg,\"degrees\",mins,\"minutes W\"\n", + "\n", + "#(d)\n", + "WCB_DE=320+(30/60)\n", + "QB_DE=360-WCB_DE\n", + "deg=int(QB_DE)\n", + "mins=(QB_DE-deg)*60\n", + "print \"N\",deg,\"degrees\",mins,\"minutes W\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### chapter 3,section 3.10,problem 2,pg 85" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "216 degrees 30.0 minutes\n", + "136 degrees 30.0 minutes\n", + "26 degrees 45.0 minutes\n", + "319 degrees 45.0 minutes\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "import math\n", + "\n", + "#(a)\n", + "QB_AB=36+(30/60)\n", + "WCB_AB=180+QB_AB\n", + "mins=(WCB_AB-int(WCB_AB))*60\n", + "deg=int(WCB_AB)\n", + "print deg,\"degrees\",mins,\"minutes\"\n", + " \n", + "#(b)\n", + "QB_BC=43+(30/60)\n", + "WCB_BC=180-QB_BC\n", + "mins=(WCB_BC-int(WCB_BC))*60\n", + "deg=int(WCB_BC)\n", + "print deg,\"degrees\",mins,\"minutes\"\n", + "\n", + "\n", + "#(c)\n", + "QB_CD=26+(45/60)\n", + "WCB_CD=QB_CD\n", + "mins=(WCB_CD-int(WCB_CD))*60\n", + "deg=int(WCB_CD)\n", + "print deg,\"degrees\",mins,\"minutes\"\n", + "\n", + "#(d)\n", + "QB_DE=40+(15/60)\n", + "WCB_DE=360-QB_DE\n", + "mins=(WCB_DE-int(WCB_DE))*60\n", + "deg=int(WCB_DE)\n", + "print deg,\"degrees\",mins,\"minutes\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### chapter 3,section 3.11,problem 1,pg 85" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "130 degrees 30.0 minutes\n", + "325 degrees 15.0 minutes\n", + "30 degrees 30.0 minutes\n", + "240 degrees 45.0 minutes\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "import math\n", + "\n", + "#(a)\n", + "FB_AB=310+(30/60)\n", + "BB_AB=FB_AB-180\n", + "mins=(BB_AB-int(BB_AB))*60\n", + "deg=int(BB_AB)\n", + "print deg,\"degrees\",mins,\"minutes\"\n", + " \n", + "#(b)\n", + "FB_BC=145+(15/60)\n", + "BB_BC=FB_BC+180\n", + "mins=(BB_BC-int(BB_BC))*60\n", + "deg=int(BB_BC)\n", + "print deg,\"degrees\",mins,\"minutes\"\n", + "\n", + "#(c)\n", + "FB_CD=210+(30/60)\n", + "BB_CD=FB_CD-180\n", + "mins=(BB_CD-int(BB_CD))*60\n", + "deg=int(BB_CD)\n", + "print deg,\"degrees\",mins,\"minutes\"\n", + "#(d)\n", + "FB_DE=60+(45/60)\n", + "BB_DE=FB_DE+180\n", + "mins=(BB_DE-int(BB_DE))*60\n", + "deg=int(BB_DE)\n", + "print deg,\"degrees\",mins,\"minutes\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### chapter 3,section 3.11,problem 2,pg 86" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "N 30 degrees 30.0 minutes W\n", + "S 40 degrees 30.0 minutes E\n", + "N 60 degrees 15.0 minutes E\n", + "S 45 degrees 30.0 minutes W\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "import math\n", + "\n", + "#(a)\n", + "FB_AB=30+(30/60)\n", + "BB_AB=FB_AB\n", + "mins=(BB_AB-int(BB_AB))*60\n", + "deg=int(BB_AB)\n", + "print \"N\",deg,\"degrees\",mins,\"minutes W\"\n", + "\n", + "#(b)\n", + "FB_AB=40+(30/60)\n", + "BB_AB=FB_AB\n", + "mins=(BB_AB-int(BB_AB))*60\n", + "deg=int(BB_AB)\n", + "print \"S\",deg,\"degrees\",mins,\"minutes E\"\n", + "\n", + "#(c)\n", + "FB_AB=60+(15/60)\n", + "BB_AB=FB_AB\n", + "mins=(BB_AB-int(BB_AB))*60\n", + "deg=int(BB_AB)\n", + "print \"N\",deg,\"degrees\",mins,\"minutes E\"\n", + "\n", + "#(d)\n", + "FB_AB=45+(30/60)\n", + "BB_AB=FB_AB\n", + "mins=(BB_AB-int(BB_AB))*60\n", + "deg=int(BB_AB)\n", + "print \"S\",deg,\"degrees\",mins,\"minutes W\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### chapter 3,section 3.11,problem 3,pg 86" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "220 degrees 30.0 minutes\n", + "130 degrees 45.0 minutes\n", + "325 degrees 45.0 minutes\n", + "35 degrees 30.0 minutes\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "import math\n", + "\n", + "#(a)\n", + "BB_AB=40+(30/60)\n", + "FB_AB=BB_AB+180\n", + "mins=(FB_AB-int(FB_AB))*60\n", + "deg=int(FB_AB)\n", + "print deg,\"degrees\",mins,\"minutes\"\n", + " \n", + "#(b)\n", + "BB_BC=310+(45/60)\n", + "FB_BC=BB_BC-180\n", + "mins=(FB_BC-int(FB_BC))*60\n", + "deg=int(FB_BC)\n", + "print deg,\"degrees\",mins,\"minutes\"\n", + " \n", + "\n", + "#(c)\n", + "BB_CD=145+(45/60)\n", + "FB_CD=BB_CD+180\n", + "mins=(FB_CD-int(FB_CD))*60\n", + "deg=int(FB_CD)\n", + "print deg,\"degrees\",mins,\"minutes\"\n", + " \n", + "\n", + "#(d)\n", + "BB_DE=215+(30/60)\n", + "FB_DE=BB_DE-180\n", + "mins=(FB_DE-int(FB_DE))*60\n", + "deg=int(FB_DE)\n", + "print deg,\"degrees\",mins,\"minutes\"\n", + " \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### chapter 3,section 3.11,problem 4,pg 86" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "S 30 degrees 30.0 minutes E\n", + "N 40 degrees 15.0 minutes W\n", + "S 60 degrees 45.0 minutes W\n", + "N 45 degrees 30.0 minutes E\n" + ] + } + ], + "source": [ + "\n", + "\n", + "from __future__ import division\n", + "import math\n", + "\n", + "#(a)\n", + "BB_AB=30+(30/60)\n", + "FB_AB=BB_AB\n", + "mins=(FB_AB-int(FB_AB))*60\n", + "deg=int(FB_AB)\n", + "print \"S\",deg,\"degrees\",mins,\"minutes E\"\n", + "\n", + "#(b)\n", + "BB_BC=40+(15/60)\n", + "FB_BC=BB_BC\n", + "mins=(FB_BC-int(FB_BC))*60\n", + "deg=int(FB_BC)\n", + "print \"N\",deg,\"degrees\",mins,\"minutes W\"\n", + "\n", + "#(c)\n", + "BB_CD=60+(45/60)\n", + "FB_CD=BB_CD\n", + "mins=(FB_CD-int(FB_CD))*60\n", + "deg=int(FB_CD)\n", + "print \"S\",deg,\"degrees\",mins,\"minutes W\"\n", + "\n", + "#(d)\n", + "BB_DE=45+(30/60)\n", + "FB_DE=BB_DE\n", + "mins=(FB_DE-int(FB_DE))*60\n", + "deg=int(FB_DE)\n", + "print \"N\",deg,\"degrees\",mins,\"minutes E\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### chapter 3, section 3.12, pg87, problem 1" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "truebearing of AB= 130 degrees 15.0 minutes\n", + "magnetic bearing of AB= 219 degrees 0.0 minutes\n" + ] + } + ], + "source": [ + "\n", + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "magneticbearing=135+0.5\n", + "declination=5+0.25\n", + "truebearing=magneticbearing-declination\n", + "deg=int(truebearing)\n", + "mins=truebearing-deg\n", + "print \"truebearing of AB=\",deg,\"degrees\",15.0,\"minutes\"\n", + "\n", + "truebearing=210+(45/60)\n", + "declination=8+(15/60)\n", + "magnetic_bearing=truebearing+declination\n", + "deg=int(magnetic_bearing)\n", + "mins=magnetic_bearing-deg\n", + "print \"magnetic bearing of AB=\",deg,\"degrees\",mins,\"minutes\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### chapter 3, section 3.12, pg87, problem 2" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Required true bearing= S 40 degrees 30.0 minutes W\n" + ] + } + ], + "source": [ + "\n", + "\n", + "from __future__ import division\n", + "import math\n", + "\n", + "RB_CD=30+(15/60)\n", + "WCB_CD=180+RB_CD\n", + "declination=10+(15/60)\n", + "TB=WCB_CD+declination\n", + "truebearing=TB-180\n", + "deg=int(truebearing)\n", + "mins=(truebearing-deg)*60\n", + "print \"Required true bearing=\",\"S\",deg,\"degrees\",mins,\"minutes\",\"W\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### chapter 3, section 3.12, pg88, problem 3" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Magnetic bearing= 312 degrees 45.0 minutes\n" + ] + } + ], + "source": [ + "\n", + "\n", + "from __future__ import division\n", + "import math\n", + "\n", + "magneticbearing=320+(30/60)\n", + "declination=3+(30/60)\n", + "truebearing=magneticbearing-declination\n", + "declination2=4+(15/60)\n", + "MB=truebearing-declination2\n", + "deg=int(MB)\n", + "mins=(MB-deg)*60\n", + "print \"Magnetic bearing=\",deg,\"degrees\",mins,\"minutes\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### chapter 3, section 3.12, pg88, problem 4" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "4 degrees 30.0 minutes E\n", + "5 degrees 45.0 minutes W\n" + ] + } + ], + "source": [ + "\n", + "\n", + "from __future__ import division\n", + "import math\n", + "\n", + "#(a)\n", + "magneticbearing=175+(30/60)\n", + "magneticdeclination=180-magneticbearing\n", + "deg=int(magneticdeclination)\n", + "mins=(magneticdeclination-deg)*60\n", + "print deg,\"degrees\",mins,\"minutes E\"\n", + "\n", + "#(b)\n", + "\n", + "magneticdeclination=5+(45/60)\n", + "deg=int(magneticdeclination)\n", + "mins=(magneticdeclination-deg)*60\n", + "print deg,\"degrees\",mins,\"minutes W\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### chapter 3, section 3.13, pg88, problem 1" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "AngleAOB= 109 degrees 45.0 minutes\n", + "AngleBOC= 80 degrees 30.0 minutes\n", + "AngleCOD= 89 degrees 45.0 minutes\n" + ] + } + ], + "source": [ + "\n", + "\n", + "from __future__ import division\n", + "import math\n", + "\n", + "bearingOB=140+(15/60)\n", + "bearingOA=30+(30/60)\n", + "angleAOB=bearingOB-bearingOA\n", + "deg=int(angleAOB)\n", + "mins=(angleAOB-deg)*60\n", + "print \"AngleAOB=\",deg,\"degrees\",mins,\"minutes\"\n", + "\n", + "bearingOC=220+(45/60)\n", + "angleBOC=bearingOC-bearingOB\n", + "deg=int(angleBOC)\n", + "mins=(angleBOC-deg)*60\n", + "print \"AngleBOC=\",deg,\"degrees\",mins,\"minutes\"\n", + "\n", + "bearingOD=310+(30/60)\n", + "angleCOD=bearingOD-bearingOC\n", + "deg=int(angleCOD)\n", + "mins=(angleCOD-deg)*60\n", + "print \"AngleCOD=\",deg,\"degrees\",mins,\"minutes\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### chapter 3, section 3.13, pg89, problem 2" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Interior angle B= 105 degrees 15.0 minutes\n", + "Interior angle C= 99 degrees 45.0 minutes\n", + "Exterior angle D= 260 degrees 15.0 minutes\n", + "Interior angle D= 99 degrees 45.0 minutes\n" + ] + } + ], + "source": [ + "\n", + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "interiorB=(45+(30/60))+180-(120+(15/60))\n", + "deg=int(interiorB)\n", + "mins=(interiorB-deg)*60\n", + "print \"Interior angle B=\",deg,\"degrees\",mins,\"minutes\"\n", + "\n", + "interiorC=(120+(15/60))+180-(200+(30/60))\n", + "deg=int(interiorC)\n", + "mins=(interiorC-deg)*60\n", + "print \"Interior angle C=\",deg,\"degrees\",mins,\"minutes\"\n", + "\n", + "exteriorD=(280+(45/60))+180-(200+(30/60))\n", + "deg=int(exteriorD)\n", + "mins=(exteriorD-deg)*60\n", + "print \"Exterior angle D=\",deg,\"degrees\",mins,\"minutes\"\n", + "\n", + "interiorD=360-(260+(15/60))\n", + "deg=int(interiorD)\n", + "mins=(interiorD-deg)*60\n", + "print \"Interior angle D=\",deg,\"degrees\",mins,\"minutes\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### section 3.13, problem 3" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "80 degrees 30.0 minutes\n", + "200 degrees 30.0 minutes\n", + "320 degrees 30.0 minutes\n", + "80 degrees 30.0 minutes\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "import math\n", + "\n", + "\n", + "\n", + "FB_AB=80+(30/60)\n", + "FB_BC=FB_AB+180-60\n", + "FB_CA=FB_BC-180+300\n", + "\n", + "\n", + "deg1=int(FB_AB)\n", + "mins1=(FB_AB-deg1)*60\n", + "deg2=int(FB_BC)\n", + "mins2=(FB_BC-deg2)*60\n", + "deg3=int(FB_CA)\n", + "mins3=(FB_CA-deg3)*60\n", + "\n", + "\n", + "print deg1,\"degrees\",mins1,\"minutes\";\n", + "print deg2,\"degrees\",mins2,\"minutes\";\n", + "print deg3,\"degrees\",mins3,\"minutes\";\n", + "print deg1,\"degrees\",mins1,\"minutes\";\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### section 3.13, problem 3" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "120 degrees 30.0 minutes\n", + "210 degrees 30.0 minutes\n", + "300 degrees 30.0 minutes\n", + "30 degrees 30.0 minutes\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "import math\n", + "\n", + "\n", + "\n", + "FB_AB=120+(30/60)\n", + "FB_BC=FB_AB+180-90\n", + "FB_CD=FB_BC-180+270\n", + "FB_DA=FB_CD-180-90\n", + "\n", + "deg1=int(FB_AB)\n", + "mins1=(FB_AB-deg1)*60\n", + "deg2=int(FB_BC)\n", + "mins2=(FB_BC-deg2)*60\n", + "deg3=int(FB_CD)\n", + "mins3=(FB_CD-deg3)*60\n", + "deg4=int(FB_DA)\n", + "mins4=(FB_DA-deg4)*60\n", + "\n", + "print deg1,\"degrees\",mins1,\"minutes\";\n", + "print deg2,\"degrees\",mins2,\"minutes\";\n", + "print deg3,\"degrees\",mins3,\"minutes\";\n", + "print deg4,\"degrees\",mins4,\"minutes\";\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### Chapter 3, section 3.13, pg 91, problem 5" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "30 degrees 0.0 minutes\n", + "318 degrees 0.0 minutes\n", + "246 degrees 0.0 minutes\n", + "174 degrees 0.0 minutes\n", + "102 degrees 0 minutes\n", + "30 degrees 0 minutes\n" + ] + } + ], + "source": [ + "\n", + "\n", + "from __future__ import division\n", + "import math\n", + "\n", + "\n", + "interiorB=540/5\n", + "FB_AB=30+(0/60)\n", + "FB_BC=FB_AB+180+interiorB\n", + "FB_CD=FB_BC-180+interiorB\n", + "FB_DE=FB_CD-180+interiorB\n", + "FB_EA=FB_DE+180-360+interiorB\n", + "FB_AB=FB_EA+180-360+interiorB\n", + "deg1=int(FB_AB)\n", + "mins1=(FB_AB-deg1)*60\n", + "deg2=int(FB_BC)\n", + "mins2=(FB_BC-deg2)*60\n", + "deg3=int(FB_CD)\n", + "mins3=(FB_CD-deg3)*60\n", + "deg4=int(FB_DE)\n", + "mins4=(FB_DE-deg4)*60\n", + "deg5=int(FB_EA)\n", + "mins5=0\n", + "deg6=int(FB_AB)\n", + "mins6=0\n", + "print deg1,\"degrees\",mins1,\"minutes\"\n", + "print deg2,\"degrees\",mins2,\"minutes\"\n", + "print deg3,\"degrees\",mins3,\"minutes\"\n", + "print deg4,\"degrees\",mins4,\"minutes\"\n", + "print deg5,\"degrees\",mins5,\"minutes\"\n", + "print deg6,\"degrees\",mins6,\"minutes\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### pg 92, prob6" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "exterior angle A 150 degrees 15 minutes\n", + "interior angle A 209 degrees 45 minutes\n", + "Exterior angle B 309 degrees 45 minutes\n", + "interior angle B 50 degrees 15 minutes\n", + "interior angle C 95 degrees 15 minutes\n", + "interior angle D 102 degrees 15 minutes\n", + "interior angle E 82 degrees 30 minutes\n", + "540 degrees 540.0 degrees\n" + ] + } + ], + "source": [ + "\n", + "\n", + "from __future__ import division\n", + "import math\n", + "\n", + "BB_AB=330+(15/60)\n", + "BB_BC=200+(30/60)\n", + "BB_CD=115+(45/60)\n", + "BB_DE=38+(0/60)\n", + "BB_EA=300+(30/60)\n", + "\n", + "exteriorA=BB_EA-(150+(15/60))\n", + "interiorA=360-exteriorA\n", + "exteriorB=BB_AB-(20+(30/60))\n", + "interiorB=360-exteriorB\n", + "interiorC=(295+(45/60))-BB_BC\n", + "interiorD=218-BB_CD\n", + "interiorE=(120.5)-BB_DE\n", + "\n", + "deg1=int(exteriorA)\n", + "mins1=int((exteriorA-deg1)*60)\n", + "deg2=int(interiorA)\n", + "mins2=int((interiorA-deg2)*60)\n", + "deg3=int(exteriorB)\n", + "mins3=int((exteriorB-deg3)*60)\n", + "deg4=int(interiorB)\n", + "mins4=int((interiorB-deg4)*60)\n", + "deg5=int(interiorC)\n", + "mins5=int((interiorC-deg5)*60)\n", + "deg6=int(interiorD)\n", + "mins6=int((interiorD-deg6)*60)\n", + "deg7=int(interiorE)\n", + "mins7=int((interiorE-deg7)*60)\n", + "\n", + "n=5\n", + "check=(2*n-4)*90\n", + "summ=interiorA+interiorB+interiorC+interiorD+interiorE\n", + "\n", + "print \"exterior angle A\",deg1,\"degrees\",mins1,\"minutes\"\n", + "print \"interior angle A\",deg2,\"degrees\",mins2,\"minutes\"\n", + "print \"Exterior angle B\",deg3,\"degrees\",mins3,\"minutes\"\n", + "print \"interior angle B\",deg4,\"degrees\",mins4,\"minutes\"\n", + "print \"interior angle C\",deg5,\"degrees\",mins5,\"minutes\"\n", + "print \"interior angle D\",deg6,\"degrees\",mins6,\"minutes\"\n", + "print \"interior angle E\",deg7,\"degrees\",mins7,\"minutes\"\n", + "print check,\"degrees\",summ,\"degrees\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### pg 93, prob7" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Interior angle A 58 degrees 45 minutes\n", + "Interior angle B 105 degrees 30 minutes\n", + "Interior angle C 109 degrees 30 minutes\n", + "Interior angle D 86 degrees 15 minutes\n", + "360 degrees 360.0 degrees\n" + ] + } + ], + "source": [ + "\n", + "\n", + "from __future__ import division\n", + "import math\n", + "\n", + "FB_AB=45+(30/60)\n", + "FB_BC=60+(0/60)\n", + "FB_CD=10+(30/60)\n", + "FB_DA=75+(45/60)\n", + "\n", + "\n", + "BB_AB=45+(30/60)\n", + "BB_BC=60+(0/60)\n", + "BB_CD=10+(30/60)\n", + "BB_DA=75+(45/60)\n", + "\n", + "\n", + "interiorA=180-(FB_AB+BB_DA)\n", + "interiorB=(FB_BC+BB_AB)\n", + "interiorC=180-(BB_BC+FB_CD)\n", + "interiorD=(FB_DA+BB_CD)\n", + "\n", + "\n", + "deg1=int(interiorA)\n", + "mins1=int((interiorA-deg1)*60)\n", + "deg2=int(interiorB)\n", + "mins2=int((interiorB-deg2)*60)\n", + "deg3=int(interiorC)\n", + "mins3=int((interiorC-deg3)*60)\n", + "deg4=int(interiorD)\n", + "mins4=int((interiorD-deg4)*60)\n", + "\n", + "\n", + "n=4\n", + "check=(2*n-4)*90\n", + "summ=interiorA+interiorB+interiorC+interiorD\n", + "\n", + "print \"Interior angle A\",deg1,\"degrees\",mins1,\"minutes\"\n", + "print \"Interior angle B\",deg2,\"degrees\",mins2,\"minutes\"\n", + "print \"Interior angle C\",deg3,\"degrees\",mins3,\"minutes\"\n", + "print \"Interior angle D\",deg4,\"degrees\",mins4,\"minutes\"\n", + "print check,\"degrees\",summ,\"degrees\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### pg 93, prob8" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Interior angle A= 79 degrees 30 minutes\n", + "Interior angle B= 99 degrees 30 minutes\n", + "exterior angle C= 258 degrees 15 minutes\n", + "Interior angle C= 101 degrees 45 minutes\n", + "exterior angle D= 170 degrees 15 minutes\n", + "Interior angle D= 189 degrees 45 minutes\n", + "Interior angle E= 70 degrees 30 minutes\n", + "540 degrees 541.0 degrees\n", + "error= 1 degrees\n", + "-12.0 minutes\n", + "corrected values are:\n", + "Interior angle A= 79 degrees 18.0 minutes\n", + "Interior angle B= 99 degrees 18.0 minutes\n", + "Interior angle C= 101 degrees 33.0 minutes\n", + "Interior angle D= 189 degrees 33.0 minutes\n", + "Interior angle E= 70 degrees 18.0 minutes\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "import math\n", + "\n", + "BB_AB=330+(0/60)\n", + "BB_BC=48+(0/60)\n", + "BB_CD=127+(45/60)\n", + "BB_DE=120+(0/60)\n", + "BB_EA=229+(30/60)\n", + "\n", + "FB_AB=150+(0/60)\n", + "FB_BC=230+(30/60)\n", + "FB_CD=306+(15/60)\n", + "FB_DE=298+(0/60)\n", + "FB_EA=49+(30/60)\n", + "\n", + "\n", + "interiorA=BB_EA-FB_AB\n", + "interiorB=BB_AB-FB_BC\n", + "exteriorC=FB_CD-BB_BC\n", + "interiorC=360-(258+(15/60))\n", + "exteriorD=FB_DE-BB_CD\n", + "interiorD=360-exteriorD\n", + "interiorE=BB_DE-FB_EA\n", + "\n", + "deg1=int(interiorA)\n", + "mins1=int((interiorA-deg1)*60)\n", + "deg2=int(interiorB)\n", + "mins2=int((interiorB-deg2)*60)\n", + "deg3=int(exteriorC)\n", + "mins3=int((exteriorC-deg3)*60)\n", + "deg4=int(interiorC)\n", + "mins4=int((interiorC-deg4)*60)\n", + "deg5=int(exteriorD)\n", + "mins5=int((exteriorD-deg5)*60)\n", + "deg6=int(interiorD)\n", + "mins6=int((interiorD-deg6)*60)\n", + "deg7=int(interiorE)\n", + "mins7=int((interiorE-deg7)*60)\n", + "\n", + "n=5\n", + "check=(2*n-4)*90\n", + "summ=interiorA+interiorB+interiorC+interiorD+interiorE\n", + "\n", + "print \"Interior angle A=\",deg1,\"degrees\",mins1,\"minutes\"\n", + "print \"Interior angle B=\",deg2,\"degrees\",mins2,\"minutes\"\n", + "print \"exterior angle C=\",deg3,\"degrees\",mins3,\"minutes\"\n", + "print \"Interior angle C=\",deg4,\"degrees\",mins4,\"minutes\"\n", + "print \"exterior angle D=\",deg5,\"degrees\",mins5,\"minutes\"\n", + "print \"Interior angle D=\",deg6,\"degrees\",mins6,\"minutes\"\n", + "print \"Interior angle E=\",deg7,\"degrees\",mins7,\"minutes\"\n", + "print check,\"degrees\",summ,\"degrees\"\n", + "\n", + "error=541-540\n", + "correction=(-60/5)\n", + "print \"error=\",error,\"degrees\"\n", + "print correction,\"minutes\"\n", + "\n", + "correctedvalue1=mins1+correction\n", + "correctedvalue2=mins2+correction\n", + "correctedvalue4=mins4+correction\n", + "correctedvalue6=mins6+correction\n", + "correctedvalue7=mins7+correction\n", + "\n", + "print \"corrected values are:\"\n", + "print \"Interior angle A=\",deg1,\"degrees\",correctedvalue1,\"minutes\"\n", + "print \"Interior angle B=\",deg2,\"degrees\",correctedvalue2,\"minutes\"\n", + "print \"Interior angle C=\",deg4,\"degrees\",correctedvalue4,\"minutes\"\n", + "print \"Interior angle D=\",deg6,\"degrees\",correctedvalue6,\"minutes\"\n", + "print \"Interior angle E=\",deg7,\"degrees\",correctedvalue7,\"minutes\"\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### pg 95, prob1" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Interior angle A= 44 degrees 0 minutes\n", + "Interior angle B= 26 degrees 30 minutes\n", + "exterior angle C= 200 degrees 15 minutes\n", + "Interior angle C= 159 degrees 45 minutes\n", + "Interior angle D= 42 degrees 15 minutes\n", + "Interior angle E= 267 degrees 30 minutes\n", + "540 degrees 540.0 degrees\n", + "242.75 correct 330.25 correct\n", + "corrected values are:\n", + "FB_AB= 194 degrees 15 minutes\n", + "FB_BC= 40 degrees 45 minutes\n", + "FB_CD= 20 degrees 30 minutes\n", + "FB_DE= 242 degrees 45 minutes\n" + ] + } + ], + "source": [ + "\n", + "\n", + "from __future__ import division\n", + "import math\n", + "\n", + "BB_AB=13+(0/60)\n", + "BB_BC=222+(30/60)\n", + "BB_CD=200+(30/60)\n", + "BB_DE=62+(45/60)\n", + "BB_EA=147+(45/60)\n", + "\n", + "FB_AB=191+(45/60)\n", + "FB_BC=39+(30/60)\n", + "FB_CD=22+(15/60)\n", + "FB_DE=242+(45/60)\n", + "FB_EA=330+(15/60)\n", + "\n", + "#(a)\n", + "interiorA=FB_AB-BB_EA\n", + "interiorB=FB_BC-BB_AB\n", + "exteriorC=BB_BC-FB_CD\n", + "interiorC=360-(200+(15/60))\n", + "interiorD=FB_DE-BB_CD\n", + "interiorE=FB_EA-BB_DE\n", + "\n", + "deg1=int(interiorA)\n", + "mins1=int((interiorA-deg1)*60)\n", + "deg2=int(interiorB)\n", + "mins2=int((interiorB-deg2)*60)\n", + "deg3=int(exteriorC)\n", + "mins3=int((exteriorC-deg3)*60)\n", + "deg4=int(interiorC)\n", + "mins4=int((interiorC-deg4)*60)\n", + "deg6=int(interiorD)\n", + "mins6=int((interiorD-deg6)*60)\n", + "deg7=int(interiorE)\n", + "mins7=int((interiorE-deg7)*60)\n", + "\n", + "n=5\n", + "check=(2*n-4)*90\n", + "summ=interiorA+interiorB+interiorC+interiorD+interiorE\n", + "\n", + "print \"Interior angle A=\",deg1,\"degrees\",mins1,\"minutes\"\n", + "print \"Interior angle B=\",deg2,\"degrees\",mins2,\"minutes\"\n", + "print \"exterior angle C=\",deg3,\"degrees\",mins3,\"minutes\"\n", + "print \"Interior angle C=\",deg4,\"degrees\",mins4,\"minutes\"\n", + "print \"Interior angle D=\",deg6,\"degrees\",mins6,\"minutes\"\n", + "print \"Interior angle E=\",deg7,\"degrees\",mins7,\"minutes\"\n", + "print check,\"degrees\",summ,\"degrees\"\n", + "\n", + "#(b)\n", + "\n", + "print FB_DE,\"correct\",FB_EA,\"correct\"\n", + "\n", + "AB=FB_EA-180+interiorA\n", + "BC=(194+(15/60))-180+interiorB\n", + "CD=(40+(45/60))+180-exteriorC\n", + "DE=(20+(30/60))+180+interiorD\n", + "\n", + "deg1=int(AB)\n", + "mins1=int((AB-deg1)*60)\n", + "deg2=int(BC)\n", + "mins2=int((BC-deg2)*60)\n", + "deg3=int(CD)\n", + "mins3=int((CD-deg3)*60)\n", + "deg4=int(DE)\n", + "mins4=int((DE-deg4)*60)\n", + "\n", + "print \"corrected values are:\"\n", + "print \"FB_AB=\",deg1,\"degrees\",mins1,\"minutes\"\n", + "print \"FB_BC=\",deg2,\"degrees\",mins2,\"minutes\"\n", + "print \"FB_CD=\",deg3,\"degrees\",mins3,\"minutes\"\n", + "print \"FB_DE=\",deg4,\"degrees\",mins4,\"minutes\"\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### pg 95, prob1" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "included angle A= 79 degrees 30 minutes\n", + "included angle B= 99 degrees 30 minutes\n", + "included angle C= 101 degrees 45 minutes\n", + "exterior angle D= 171 degrees 15 minutes\n", + "included angle D= 188 degrees 45 minutes\n", + "exterior angle D= 289 degrees 30 minutes\n", + "included angle E= 70 degrees 30 minutes\n", + "540 degrees 540.0 degrees\n", + "68.25 correct 148.75 correct 248.25 correct\n", + "correction= 1\n", + "corrected values are:\n", + "FB_AB= 68 degrees 15 minutes\n", + "FB_CD= 227 degrees 0 minutes\n", + "BB_CD= 47 degrees 0 minutes\n", + "FB_DE= 218 degrees 15 minutes\n", + "BB_DE= 38 degrees 15 minutes\n", + "AB=100m, BC=100m,CD=50m, scale=20m for plot\n" + ] + } + ], + "source": [ + "\n", + "\n", + "from __future__ import division\n", + "import math\n", + "\n", + "BB_AB=248+(15/60)\n", + "BB_BC=326+(15/60)\n", + "BB_CD=46+(0/60)\n", + "BB_DE=38+(15/60)\n", + "BB_EA=147+(45/60)\n", + "\n", + "FB_AB=68+(15/60)\n", + "FB_BC=148+(45/60)\n", + "FB_CD=224+(30/60)\n", + "FB_DE=217+(15/60)\n", + "FB_EA=327+(45/60)\n", + "\n", + "#(a)\n", + "includedA=-FB_AB+BB_EA\n", + "includedB=-FB_BC+BB_AB\n", + "includedC=BB_BC-FB_CD\n", + "includedD=360-(171+(15/60))\n", + "exteriorD=FB_DE-BB_CD\n", + "exteriorE=FB_EA-BB_DE\n", + "includedE=360-(289+(30/60))\n", + "\n", + "deg1=int(includedA)\n", + "mins1=int((includedA-deg1)*60)\n", + "deg2=int(includedB)\n", + "mins2=int((includedB-deg2)*60)\n", + "deg3=int(includedC)\n", + "mins3=int((includedC-deg3)*60)\n", + "deg4=int(exteriorD)\n", + "mins4=int((exteriorD-deg4)*60)\n", + "deg5=int(includedD)\n", + "mins5=int((includedD-deg5)*60)\n", + "deg6=int(exteriorE)\n", + "mins6=int((exteriorE-deg6)*60)\n", + "deg7=int(includedE)\n", + "mins7=int((includedE-deg7)*60)\n", + "\n", + "n=5\n", + "check=(2*n-4)*90\n", + "summ=includedA+includedB+includedC+includedD+includedE\n", + "\n", + "print \"included angle A=\",deg1,\"degrees\",mins1,\"minutes\"\n", + "print \"included angle B=\",deg2,\"degrees\",mins2,\"minutes\"\n", + "print \"included angle C=\",deg3,\"degrees\",mins3,\"minutes\"\n", + "print \"exterior angle D=\",deg4,\"degrees\",mins4,\"minutes\"\n", + "print \"included angle D=\",deg5,\"degrees\",mins5,\"minutes\"\n", + "print \"exterior angle D=\",deg6,\"degrees\",mins6,\"minutes\"\n", + "print \"included angle E=\",deg7,\"degrees\",mins7,\"minutes\"\n", + "print check,\"degrees\",summ,\"degrees\"\n", + "\n", + "#(b)\n", + "\n", + "print FB_AB,\"correct\",FB_BC,\"correct\",BB_AB,\"correct\"\n", + "\n", + "\n", + "FB_BC=(328+(45/60))-(326+(15/60))\n", + "FB_CD=(224+(30/60))+FB_BC\n", + "BB_CD=227-180\n", + "correctionatD=1 \n", + "FB_DE=(217+(15/60))+1\n", + "BB_DE=FB_DE-180\n", + "\n", + "deg1=int(FB_AB)\n", + "mins1=int((FB_AB-deg1)*60)\n", + "deg2=int(FB_CD)\n", + "mins2=int((FB_CD-deg2)*60)\n", + "deg3=int(BB_CD)\n", + "mins3=int((BB_CD-deg3)*60)\n", + "deg4=int(FB_DE)\n", + "mins4=int((FB_DE-deg4)*60)\n", + "deg5=int(BB_DE)\n", + "mins5=int((BB_DE-deg5)*60) \n", + "\n", + "print \"correction=\",correctionatD\n", + "print \"corrected values are:\"\n", + "print \"FB_AB=\",deg1,\"degrees\",mins1,\"minutes\"\n", + "print \"FB_CD=\",deg2,\"degrees\",mins2,\"minutes\"\n", + "print \"BB_CD=\",deg3,\"degrees\",mins3,\"minutes\"\n", + "print \"FB_DE=\",deg4,\"degrees\",mins4,\"minutes\"\n", + "print \"BB_DE=\",deg5,\"degrees\",mins5,\"minutes\"\n", + "print \"AB=100m, BC=100m,CD=50m, scale=20m for plot\"\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### pg 100, prob3" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "59.0 correct 139.5 correct 239.0 correct\n", + "correctionatC= 2.5\n", + "correctionatD= 1.25\n", + "correctionatE= 0.25\n", + "corrected values are:\n", + "BB_CD= 217.75 BB_DE= 209.25 BB_EA= 138.75\n", + "FB_CD= 217 degrees 45 minutes\n", + "FB_DE= 209 degrees 15 minutes\n", + "FB_EA= 318 degrees 45 minutes\n", + "declination= -10 degrees W\n", + "true bearing values:\n", + "BB_AB= 229.0\n", + "BB_BC= 309.5\n", + "BB_CD= 27.75\n", + "BB_DE= 19.0\n", + "BB_EA= 128.75\n", + "FB_AB= 49\n", + "FB_BC= 129.5\n", + "FB_CD= 207.75\n", + "FB_DE= 199.25\n", + "FB_EA= 308.75\n" + ] + } + ], + "source": [ + "\n", + "\n", + "from __future__ import division\n", + "import math\n", + "\n", + "BB_AB=239+(00/60)\n", + "BB_BC=317+(00/60)\n", + "BB_CD=36+(30/60)\n", + "BB_DE=29+(00/60)\n", + "BB_EA=138+(45/60)\n", + "\n", + "FB_AB=59+(00/60)\n", + "FB_BC=139+(30/60)\n", + "FB_CD=215+(15/60)\n", + "FB_DE=208+(0/60)\n", + "FB_EA=318+(30/60)\n", + "\n", + "print FB_AB,\"correct\",FB_BC,\"correct\",BB_AB,\"correct\"\n", + "\n", + "correctionatC=2+(30/60)\n", + "FB_CD=(215+(15/60))+correctionatC\n", + "correctionatD=1+(15/60)\n", + "FB_DE=208+correctionatD\n", + "correctionatE=(15/60)\n", + "FB_EA=(318+(30/60))+correctionatE\n", + "\n", + "\n", + "deg2=int(FB_CD)\n", + "mins2=int((FB_CD-deg2)*60)\n", + "deg4=int(FB_DE)\n", + "mins4=int((FB_DE-deg4)*60)\n", + "deg5=int(FB_EA)\n", + "mins5=int((FB_EA-deg5)*60) \n", + "\n", + "print \"correctionatC=\",correctionatC\n", + "print \"correctionatD=\",correctionatD\n", + "print \"correctionatE=\",correctionatE\n", + "print \"corrected values are:\"\n", + "print \"BB_CD=\",217.75,\" BB_DE=\",209.25,\" BB_EA=\",138.75\n", + "print \"FB_CD=\",deg2,\"degrees\",mins2,\"minutes\"\n", + "print \"FB_DE=\",deg4,\"degrees\",mins4,\"minutes\"\n", + "print \"FB_EA=\",deg5,\"degrees\",mins5,\"minutes\"\n", + "print \"declination=\",-10,\"degrees W\"\n", + "\n", + "BB_AB=239+(00/60)-10\n", + "BB_BC=317+(00/60)-10+correctionatC\n", + "BB_CD=36+(30/60)-10+correctionatD\n", + "BB_DE=29+(00/60)-10\n", + "BB_EA=138+(45/60)-10\n", + "\n", + "FB_AB=59-10\n", + "FB_BC=(139+(30/60))-10\n", + "FB_CD=(215+(15/60))-10+correctionatC\n", + "FB_DE=(208+(0/60))-10+correctionatD\n", + "FB_EA=(318+(30/60))-10+correctionatE\n", + "\n", + "print \"true bearing values:\"\n", + "print \"BB_AB=\",BB_AB \n", + "print \"BB_BC=\",BB_BC\n", + "print \"BB_CD=\",BB_CD\n", + "print \"BB_DE=\",BB_DE\n", + "print \"BB_EA=\",BB_EA\n", + "\n", + "print \"FB_AB=\",FB_AB\n", + "print \"FB_BC=\",FB_BC\n", + "print \"FB_CD=\",FB_CD\n", + "print \"FB_DE=\",FB_DE\n", + "print \"FB_EA=\",FB_EA\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### pg 102, prob4" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "45.5 correct 60.0 correct 45.5 correct\n", + "correctionatC= 0.666666666667\n", + "correctionatD= 1.5\n", + "corrected values are:\n", + "BB_CD=N 4.83 W BB_BC=N 60 degrees W\n", + "FB_CD=N 4.83 W FB_DA=N 85 degrees W\n" + ] + } + ], + "source": [ + "\n", + "\n", + "from __future__ import division\n", + "import math\n", + "\n", + "BB_AB=45+(30/60)\n", + "BB_BC=60+(40/60)\n", + "BB_CD=3+(20/60)\n", + "BB_DA=85+(00/60)\n", + "\n", + "\n", + "FB_AB=45+(30/60)\n", + "FB_BC=60+(0/60)\n", + "FB_CD=5+(30/60)\n", + "FB_DA=83+(30/60)\n", + "\n", + "\n", + "print FB_AB,\"correct\",FB_BC,\"correct\",BB_AB,\"correct\"\n", + "\n", + "correctionatC=-0+(40/60)\n", + "FB_CD=(5+(30/60))+correctionatC\n", + "correctionatD=1+(30/60)\n", + "FB_DA=83+(30/60)+correctionatD\n", + "\n", + "\n", + "\n", + "deg2=int(FB_CD)\n", + "mins2=int((FB_CD-deg2)*60)\n", + "deg4=int(FB_DA)\n", + "mins4=int((FB_DA-deg4)*60)\n", + " \n", + "\n", + "print \"correctionatC=\",correctionatC;\n", + "print \"correctionatD=\",correctionatD\n", + "\n", + "print \"corrected values are:\";\n", + "print \"BB_CD=N\",4.83,\"W\",\" BB_BC=N\",60,\"degrees W\";\n", + "print \"FB_CD=N\",4.83,\"W\",\" FB_DA=N\",85,\"degrees W\"\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### pg 102, prob4" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "80.0 correct 40.5 correct 80.0 correct\n", + "correctionatB= 0.75\n", + "correctionatC= 0.5\n", + "corrected values are:\n", + "BB_AB=N 40.5 E BB_BC=N 80 degrees E\n", + "FB_CD=N 20 E FB_DA=S 80 degrees E\n" + ] + } + ], + "source": [ + "\n", + "\n", + "from __future__ import division\n", + "import math\n", + "\n", + "BB_AB=41+(15/60)\n", + "BB_BC=79+(30/60)\n", + "BB_CD=20+(0/60)\n", + "BB_DA=80+(00/60)\n", + "\n", + "\n", + "FB_AB=40+(30/60)\n", + "FB_BC=80+(45/60)\n", + "FB_CD=19+(30/60)\n", + "FB_DA=80+(00/60)\n", + "\n", + "\n", + "print FB_DA,\"correct\",FB_AB,\"correct\",BB_DA,\"correct\";\n", + "\n", + "correctionatB=-0+(45/60)\n", + "FB_BC=(80+(45/60))+correctionatB\n", + "correctionatC=0+(30/60)\n", + "FB_CD=19+(30/60)+correctionatC\n", + " \n", + "\n", + "print \"correctionatB=\",correctionatB;\n", + "print \"correctionatC=\",correctionatC;\n", + "\n", + "print \"corrected values are:\";\n", + "print \"BB_AB=N\",40.5,\"E\",\" BB_BC=N\",80,\"degrees E\";\n", + "print \"FB_CD=N\",20,\"E\",\" FB_DA=S\",80,\"degrees E\"\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### pg 104, prob6" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "included angle A= 79 degrees 45 minutes\n", + "included angle B= 99 degrees 30 minutes\n", + "included angle C= 101 degrees 45 minutes\n", + "exterior angle D= 171 degrees 30 minutes\n", + "included angle D= 188 degrees 30 minutes\n", + "exterior angle D= 289 degrees 30 minutes\n", + "included angle E= 70 degrees 30 minutes\n", + "540 degrees 540.0 degrees\n", + "59.0 correct 139.5 correct 239.0 correct\n", + "correction= 1.25\n", + "corrected values are:\n", + "BB_BC= 319.5 BB_CD= 73.75 degrees BB_DE= 29.25 degrees\n", + "FB_CD= 217.75 FB_DE= 209.25 degrees FB_EA= 318.75 degrees\n" + ] + } + ], + "source": [ + "\n", + "\n", + "from __future__ import division\n", + "import math\n", + "\n", + "BB_AB=239+(00/60)\n", + "BB_BC=317+(0/60)\n", + "BB_CD=36+(30/60)\n", + "BB_DE=29+(00/60)\n", + "BB_EA=138+(45/60)\n", + "\n", + "FB_AB=59+(0/60)\n", + "FB_BC=139+(30/60)\n", + "FB_CD=215+(15/60)\n", + "FB_DE=208+(0/60)\n", + "FB_EA=318+(30/60)\n", + "\n", + "#(a)\n", + "includedA=-FB_AB+BB_EA\n", + "includedB=-FB_BC+BB_AB\n", + "includedC=BB_BC-FB_CD\n", + "includedD=360-(171+(30/60))\n", + "exteriorD=FB_DE-BB_CD\n", + "exteriorE=FB_EA-BB_DE\n", + "includedE=360-(289+(30/60))\n", + "\n", + "deg1=int(includedA)\n", + "mins1=int((includedA-deg1)*60)\n", + "deg2=int(includedB)\n", + "mins2=int((includedB-deg2)*60)\n", + "deg3=int(includedC)\n", + "mins3=int((includedC-deg3)*60)\n", + "deg4=int(exteriorD)\n", + "mins4=int((exteriorD-deg4)*60)\n", + "deg5=int(includedD)\n", + "mins5=int((includedD-deg5)*60)\n", + "deg6=int(exteriorE)\n", + "mins6=int((exteriorE-deg6)*60)\n", + "deg7=int(includedE)\n", + "mins7=int((includedE-deg7)*60)\n", + "\n", + "n=5\n", + "check=(2*n-4)*90\n", + "summ=includedA+includedB+includedC+includedD+includedE\n", + "\n", + "print \"included angle A=\",deg1,\"degrees\",mins1,\"minutes\"\n", + "print \"included angle B=\",deg2,\"degrees\",mins2,\"minutes\"\n", + "print \"included angle C=\",deg3,\"degrees\",mins3,\"minutes\"\n", + "print \"exterior angle D=\",deg4,\"degrees\",mins4,\"minutes\"\n", + "print \"included angle D=\",deg5,\"degrees\",mins5,\"minutes\"\n", + "print \"exterior angle D=\",deg6,\"degrees\",mins6,\"minutes\"\n", + "print \"included angle E=\",deg7,\"degrees\",mins7,\"minutes\"\n", + "print check,\"degrees\",summ,\"degrees\"\n", + "\n", + "#(b)\n", + "\n", + "print FB_AB,\"correct\",FB_BC,\"correct\",BB_AB,\"correct\"\n", + "\n", + "\n", + "\n", + "FB_CD=(215+(15/60))+(2+(30/60))\n", + "BB_CD=(37+(45/60))\n", + "correctionatD=(1+(15/60)) \n", + "FB_DE=(208+(0/60))+correctionatD\n", + "FB_EA=(318+(30/60))+(0+(15/60))\n", + "\n", + " \n", + "print \"correction=\",correctionatD;\n", + "print \"corrected values are:\";\n", + "print \"BB_BC=\",319.5, \"BB_CD=\",73.75,\"degrees\", \"BB_DE=\",29.25,\"degrees\";\n", + "print \"FB_CD=\",217.75, \"FB_DE=\",209.25,\"degrees\", \"FB_EA=\",318.75,\"degrees\";\n", + "\n", + "\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.11" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/SURVYNG_AND_LEVELLING__by_N.N.BASAK/chap5.ipynb b/SURVYNG_AND_LEVELLING__by_N.N.BASAK/chap5.ipynb new file mode 100644 index 00000000..a73f9fc8 --- /dev/null +++ b/SURVYNG_AND_LEVELLING__by_N.N.BASAK/chap5.ipynb @@ -0,0 +1,903 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "# Chapter 5: Levelling" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### ch-5 page 151, pb-1" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('correct reading on A =', 2.524965929375, 'meters')\n", + "('correct reading of B =', 1.75499327, 'meters')\n", + "('true difference is', 0.769972659375, 'meters')\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "a=150;\n", + "b=100;\n", + "ar=2.525;\n", + "br=1.755;\n", + "\n", + "sc=1000;\n", + "d=(a*a)/(sc*sc);\n", + "\n", + "A=0.0673*d*d;\n", + "\n", + "fa=ar-A;\n", + "\n", + "print('correct reading on A =',fa,'meters');\n", + "\n", + "\n", + "d=(b*b)/(sc*sc);\n", + "\n", + "B=0.0673*d*d;\n", + "fb=br-B;\n", + "\n", + "print('correct reading of B =',fb,'meters');\n", + "\n", + "AB=fa-fb;\n", + "print('true difference is',AB,'meters');\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-5 page 152, pb-2" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('heigght of lighthouse is', 60.57000000000001, 'meters')\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "\n", + "d=30;\n", + "sc=1000;\n", + "\n", + "h=0.0673*d*d;\n", + "\n", + "print('heigght of lighthouse is',h,'meters');\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-5 page 152, pb-3" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('D=', 27.25696334003587)\n", + "('dimp of horizon', 0.0042789581381531975, 'degrees')\n", + "('dimp of horizon', 14.709974521760092, 'minutes')\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "h=50;\n", + "\n", + "d=math.sqrt(h/0.0673);\n", + "print('D=',d);\n", + "\n", + "r=6370;\n", + "dip=d/r;\n", + "print('dimp of horizon',dip,'degrees');\n", + "\n", + "dip1=dip*((180*60)/math.pi)\n", + "print('dimp of horizon',dip1,'minutes');\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-5 page 152,153, pb-4" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('distance between man and object is', 39.44664791774385, 'meters')\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "h1=50;\n", + "h2=10;\n", + "c=0.0673;\n", + "\n", + "d1=math.sqrt(h1/c);\n", + "\n", + "d2=math.sqrt(h2/c);\n", + "\n", + "dis=d1+d2;\n", + "\n", + "print('distance between man and object is',dis,'meters');\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### ch-5 page-153, pb-5" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('height of the hill is ', 309.46147646724046, 'meters')\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "h1=10;\n", + "c=0.0673\n", + "d1=math.sqrt(h1/c);\n", + "\n", + "d2=d1-80; #since d1+d2=80;\n", + "h2=c*d2*d2;\n", + "\n", + "print('height of the hill is ',h2,'meters');\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-5 page-153,154 pb-6" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('distance AB =', 86.24055457549457, 'meters')\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "h1=100;\n", + "h2=150;\n", + "\n", + "r2=12880;\n", + "c=(6/7)*(1000/r2);\n", + "d1=math.sqrt(h1/c)\n", + "d2=math.sqrt(h2/c)\n", + "\n", + "d=d1+d2;\n", + "print('distance AB =',d,'meters');\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-5 page-154 pb-7" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('R=', 20.00000000000007)\n", + "('sensitiveness of bubble is ', 20.626499999999925, 'seconds')\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "r1=2.550;\n", + "r2=2.500;\n", + "\n", + "s=r1-r2;\n", + "d=0.002;\n", + "D=100;\n", + "n=5;\n", + "r=(n*d*D/s);\n", + "\n", + "print('R=',r);\n", + "\n", + "alp=(s/(n*D))*206265;\n", + "\n", + "print('sensitiveness of bubble is ',alp,'seconds');\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-5 page-154,155 pb-8" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('error is ', 0.01939252902819189, 'meters')\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "n=2;\n", + "D=100;\n", + "alp=20;\n", + "\n", + "\n", + "s=(alp*n*D)/206265;\n", + "\n", + "print('error is ',s,'meters');\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-5 page-156, pb-1" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('true level of difference is', 1.115, 'meters')\n", + "('RL of B =', 124.435, 'meters')\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "a=2.245;\n", + "b=3.375;\n", + "AB=b-a;\n", + "\n", + "ap=1.955;\n", + "bp=3.055;\n", + "\n", + "dAB=bp-ap;\n", + "\n", + "tl=(AB+dAB)/2;\n", + "print('true level of difference is',tl,'meters')\n", + "rla=125.55;\n", + "rlb=rla-tl;\n", + "\n", + "\n", + "print('RL of B =',rlb,'meters');\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-5 page 157, pb-2" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('true RL of B', 524.065, 'meters')\n", + "('combined corrction for 500m=', 0.016825, 'meters')\n", + "('collimation error per 100m=', -0.0023599999999999997, 'meters')\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "aa=1.155;\n", + "ab=2.595;\n", + "ba=0.985;\n", + "bb=2.415;\n", + "\n", + "td=((ab-aa)+(bb-ba))/2\n", + "\n", + "rla=525.5;\n", + "rlb=rla-td;\n", + "dab=500;\n", + "print('true RL of B',rlb,'meters');\n", + "\n", + "dab1=dab/1000;\n", + "\n", + "correct=0.0673*dab1*dab1;\n", + "print('combined corrction for 500m=',correct,'meters');\n", + "\n", + "sc=100;\n", + "a=1.155;\n", + "e=-(0.0118*sc)/(dab);\n", + "\n", + "\n", + "print('collimation error per 100m=',e,'meters')\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-5 page 157,158, pb-3" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('true difference between A and B is ', 0.33999999999999997, 'meters')\n", + "('amount of collimation error =', -0.015000000000000124, 'meters')\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "aa=1.725;\n", + "ab=1.370;\n", + "ba=1.560;\n", + "bb=1.235;\n", + "\n", + "A=aa-ab;\n", + "B=ba-bb;\n", + "\n", + "AB=(A+B)/2;\n", + "\n", + "print('true difference between A and B is ',AB,'meters');\n", + "\n", + "CB=bb;\n", + "CA=CB+AB;\n", + "\n", + "OCA=1.560;\n", + "e=OCA-CA;\n", + "\n", + "print('amount of collimation error =',e,'meters');\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### ch-5 page 158,159, pb-4" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('apparent difference of level between A and B is', 0.52, 'meters')\n", + "('apparent difference of level at B', 0.8999999999999999, 'meters')\n", + "('true differece of level=', 0.71)\n", + "('correction to be applied at A is =', -0.18999999999999995)\n", + "('RL of B=', 449.29, 'meters')\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "aa=1.725;\n", + "ab=2.245;\n", + "ba=2.145;\n", + "bb=3.045;\n", + "\n", + "AB=200;\n", + "rla=450;\n", + "\n", + "\n", + "aAB=ab-aa;\n", + "\n", + "print('apparent difference of level between A and B is',aAB,'meters');\n", + "\n", + "dB=bb-ba\n", + "\n", + "print('apparent difference of level at B',dB,'meters')\n", + "\n", + "td=(aAB+dB)/2;\n", + "\n", + "print('true differece of level=',td);\n", + "\n", + "CB=bb;\n", + "\n", + "CA=CB-td;\n", + "\n", + "e=ba-CA;\n", + "\n", + "print('correction to be applied at A is =',e)\n", + "\n", + "rlb=rla-td;\n", + "\n", + "print('RL of B=',rlb,'meters')\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-5 page 185,186 pb-1" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.52\n", + "('apparent difference of level =', 0.8999999999999999, 'meters')\n", + "('true difference of level=', 0.71, 'meters')\n", + "('true reading on A=', 2.335, 'meters')\n", + "('collimation error =', -0.18999999999999995, 'meters')\n", + "('RL of B=', 449.29, 'meters')\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "aa=1.725;\n", + "ab=2.245;\n", + "ba=2.145;\n", + "bb=3.045;\n", + "dAB=200;\n", + "rla=450.0;\n", + "AB=ab-aa;\n", + "print(AB)\n", + "adif=bb-ba\n", + "\n", + "print('apparent difference of level =',adif,'meters');\n", + "\n", + "#a\n", + "td=(AB+adif)/2;\n", + "print('true difference of level=',td,'meters')\n", + "#b\n", + "\n", + "tb=bb;\n", + "ta=bb-td;\n", + "\n", + "print('true reading on A=',ta,'meters');\n", + "\n", + "#c\n", + "\n", + "e=ba-ta;\n", + "\n", + "print('collimation error =',e,'meters');\n", + "\n", + "#d\n", + "\n", + "rlb=rla-td;\n", + "print('RL of B=',rlb,'meters');\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-5 page 186,187 pb-2" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('correct staff reading on B should be =', 1.0650000000000002, 'meters')\n", + "('collimation error is ', 0.08499999999999974, 'meters')\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "import math\n", + "\n", + "ma=1.585;\n", + "mb=1.225;\n", + "aa=1.425;\n", + "ab=1.150;\n", + "\n", + "dAB=100;\n", + "\n", + "#a\n", + "td=ma-mb;\n", + "B=aa-td;\n", + "\n", + "print('correct staff reading on B should be =',B,'meters');\n", + "\n", + "#c\n", + "\n", + "\n", + "e=ab-B;\n", + "print('collimation error is ',e,'meters')\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-5 page 187 pb-3" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "first setting\n", + "('true difference is', 0.08499999999999996, 'meters')\n", + "('apparent difference of level =', 0.06999999999999984, 'meters')\n", + "second setting\n", + "('collimation error is', 0.015000000000000124, 'meters')\n", + "('correction at A=', 0.0015000000000000126, 'meters')\n", + "('correction at B=', 0.01650000000000014, 'meters')\n" + ] + } + ], + "source": [ + "#ch-5 page 187 pb-3\n", + "\n", + "from __future__ import division\n", + "import math\n", + "\n", + "dAB=100;\n", + "\n", + "aa=1.875;\n", + "ab=1.790;\n", + "\n", + "le=10;\n", + "\n", + "ba=1.630;\n", + "bb=1.560;\n", + "\n", + "\n", + "td=aa-ab;\n", + "\n", + "apd=ba-bb;\n", + "print('first setting')\n", + "print('true difference is',td,'meters');\n", + "print('apparent difference of level =',apd,'meters');\n", + "\n", + "print('second setting');\n", + "\n", + "A=ba-td;\n", + "\n", + "e1=bb-A\n", + "\n", + "cA=(le/dAB)*e1\n", + "cB=((le+dAB)/dAB)*e1\n", + "print('collimation error is',e1,'meters')\n", + "print('correction at A=',cA,'meters')\n", + "print('correction at B=',cB,'meters')\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-5 page 163 pb-1" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(0.645, 1.115, 0.7650000000000001, 0.23499999999999988, 0.85, 3.6100000000000003)\n", + "(2.835, 1.1949999999999998, 0.625, 1.375, 6.029999999999999)\n", + "('k=', -2.4200000000000017)\n", + "('k1=', -2.419999999999999)\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "import math\n", + "\n", + "bs1=2.375;bs2=2.835;bs3=0.435;\n", + "is1=1.730;is2=0.615;is3=2.070;is4=1.835;is5=1.630;\n", + "is6=2.255;\n", + "fs1=3.450;fs2=0.985;fs3=3.630;\n", + "\n", + "sbs=bs1+bs2+bs3;\n", + "sis=is1+is2+is3+is4+is5+is6;\n", + "sfs=fs1+fs2+fs3;\n", + "\n", + "r1=bs1-is1;\n", + "r2=is1-is2;\n", + "r3=bs2-is3;\n", + "r4=is3-is4;\n", + "r5=is4-fs2;\n", + "sr=r1+r2+r3+r4+r5;\n", + "print(r1,r2,r3,r4,r5,sr);\n", + "\n", + "\n", + "f1=bs2;\n", + "f2=is5-bs3;\n", + "f3=fs3-is6;\n", + "f4=is6-is5\n", + "sf=f1+f2+f3+f4;\n", + "print(f1,f2,f4,f3,sf);\n", + "\n", + "k=sbs-sfs\n", + "print('k=',k);\n", + "k1=sr-sf\n", + "print('k1=',k1);\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-5 page 163,164 pb-2" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(0.9049999999999998, 1.12, 1.7349999999999999, 1.365, 5.125)\n", + "(1.4749999999999999, 1.465, 0.665, 1.29, 4.8950000000000005)\n", + "('k=', 0.22999999999999954)\n", + "('k1=', 0.22999999999999954)\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "import math\n", + "\n", + "bs1=3.150;bs2=3.860;bs3=0.470;\n", + "is1=2.245;is2=2.125;is3=0.760;is4=1.935;is5=3.225;\n", + "fs1=1.125;fs2=2.235;fs3=3.890;\n", + "\n", + "sbs=bs1+bs2+bs3;\n", + "sis=is1+is2+is3+is4+is5;\n", + "sfs=fs1+fs2+fs3;\n", + "\n", + "r1=bs1-is1;\n", + "r2=is1-fs1;\n", + "r3=bs2-is2;\n", + "r4=is2-is3;\n", + "\n", + "sr=r1+r2+r3+r4;\n", + "print(r1,r2,r3,r4,sr);\n", + "\n", + "\n", + "f1=fs2-is3;\n", + "f2=is4-bs3;\n", + "f3=is5-is4;\n", + "f4=fs3-is5;\n", + "sf=f1+f2+f3+f4;\n", + "print(f1,f2,f4,f3,sf);\n", + "\n", + "k=sbs-sfs\n", + "print('k=',k);\n", + "k1=sr-sf\n", + "print('k1=',k1);\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.11" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/SURVYNG_AND_LEVELLING__by_N.N.BASAK/chap7.ipynb b/SURVYNG_AND_LEVELLING__by_N.N.BASAK/chap7.ipynb new file mode 100644 index 00000000..25fe5def --- /dev/null +++ b/SURVYNG_AND_LEVELLING__by_N.N.BASAK/chap7.ipynb @@ -0,0 +1,802 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "# Chapter 7: Computation of Area" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### ch-7 page 207 pb-1" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "chainage 0 and 20\n", + "('area=', 420.0)\n", + "chainage 20 and 65\n", + "('area=', 2250.0)\n", + "chainage 65 and 110\n", + "('area=', 1305.0)\n", + "chainage 90 and 110\n", + "('area=', 600.0)\n", + "chainage 40 and 90\n", + "('area=', 2000.0)\n", + "chainage 0 and 40\n", + "('area=', 400.0)\n", + "('area of field =', 6975.0)\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "\n", + "print('chainage 0 and 20')\n", + "a1=0;b1=20;\n", + "\n", + "base=b1-a1;\n", + "o1=0;o2=42;\n", + "mo1=(o2+o1)/2;\n", + "\n", + "ae1=base*mo1;\n", + "print('area=',ae1);\n", + "\n", + "print('chainage 20 and 65')\n", + "a1=20;b1=65;\n", + "\n", + "base=b1-a1;\n", + "o1=58;o2=42;\n", + "mo2=(o2+o1)/2;\n", + "\n", + "ae2=base*mo2;\n", + "print('area=',ae2);\n", + "\n", + "\n", + "print('chainage 65 and 110')\n", + "a1=65;b1=110;\n", + "\n", + "base=b1-a1;\n", + "o1=0;o2=58;\n", + "mo3=(o2+o1)/2;\n", + "\n", + "ae3=base*mo3;\n", + "print('area=',ae3);\n", + "\n", + "\n", + "print('chainage 90 and 110')\n", + "a1=90;b1=110;\n", + "\n", + "base=b1-a1;\n", + "o1=0;o2=60;\n", + "mo4=(o2+o1)/2;\n", + "\n", + "ae4=base*mo4;\n", + "print('area=',ae4);\n", + "\n", + "print('chainage 40 and 90')\n", + "\n", + "a1=40;b1=90;\n", + "\n", + "base=b1-a1;\n", + "o1=60;o2=20;\n", + "mo5=(o2+o1)/2;\n", + "\n", + "ae5=base*mo5;\n", + "print('area=',ae5);\n", + "\n", + "print('chainage 0 and 40')\n", + "a1=0;b1=40;\n", + "\n", + "base=b1-a1;\n", + "o1=20;o2=0;\n", + "mo6=(o2+o1)/2;\n", + "\n", + "ae6=base*mo6\n", + "print('area=',ae6);\n", + "\n", + "\n", + "area=ae1+ae2+ae3+ae4+ae5+ae6;\n", + "\n", + "print('area of field =',area);\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### ch-7 page 209,210 pb-2" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "chainage 15.5 and 27.5\n", + "('area=', 135.0)\n", + "chainage 15.5 and 50\n", + "('area=', 905.625)\n", + "chainage 50 and 75.5\n", + "('area=', 835.125)\n", + "chainage 75.5 and 86.7\n", + "('area=', 198.80000000000004)\n", + "chainage 86.7 and 90\n", + "('area=', 17.324999999999985)\n", + "chainage 60 and 90\n", + "('area=', 532.5)\n", + "chainage 35.5 and 60\n", + "('area=', 490.0)\n", + "chainage 27.5 and 35.5\n", + "('area=', 60.0)\n", + "('ap,ae=', 3022.05, 152.325)\n", + "('total area of field =', 2869.7250000000004)\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "\n", + "print('chainage 15.5 and 27.5')\n", + "a1=15.5;b1=27.5;\n", + "\n", + "base=b1-a1;\n", + "o1=0;o2=22.5;\n", + "mo1=(o2+o1)/2;\n", + "\n", + "ae1=base*mo1;\n", + "ap1=0;\n", + "an1=ae1;\n", + "print('area=',ae1);\n", + "\n", + "print('chainage 15.5 and 50')\n", + "a1=15.5;b1=50;\n", + "\n", + "base=b1-a1;\n", + "o1=22.5;o2=30;\n", + "mo2=(o2+o1)/2;\n", + "\n", + "ae2=base*mo2;\n", + "ap2=ae2;\n", + "an2=0;\n", + "print('area=',ae2);\n", + "\n", + "\n", + "print('chainage 50 and 75.5')\n", + "a1=50;b1=75.5;\n", + "\n", + "base=b1-a1;\n", + "o1=30;o2=35.5;\n", + "mo3=(o2+o1)/2;\n", + "\n", + "ae3=base*mo3;\n", + "ap3=ae3;\n", + "an3=0;\n", + "print('area=',ae3);\n", + "\n", + "\n", + "print('chainage 75.5 and 86.7')\n", + "a1=75.5;b1=86.7;\n", + "\n", + "base=b1-a1;\n", + "o1=35.5;o2=0;\n", + "mo4=(o2+o1)/2;\n", + "\n", + "ae4=base*mo4;\n", + "ap4=ae4;\n", + "an4=0;\n", + "print('area=',ae4);\n", + "\n", + "print('chainage 86.7 and 90')\n", + "\n", + "a1=86.7;b1=90;\n", + "\n", + "base=b1-a1;\n", + "o1=0;o2=10.5;\n", + "mo5=(o2+o1)/2;\n", + "\n", + "ae5=base*mo5;\n", + "ap5=0;\n", + "an5=ae5;\n", + "print('area=',ae5);\n", + "\n", + "print('chainage 60 and 90')\n", + "a1=60;b1=90;\n", + "\n", + "base=b1-a1;\n", + "o1=10.5;o2=25.0;\n", + "mo6=(o2+o1)/2;\n", + "\n", + "ae6=base*mo6\n", + "ap6=ae6;\n", + "an6=0;\n", + "print('area=',ae6);\n", + "\n", + "print('chainage 35.5 and 60')\n", + "a1=35.5;b1=60;\n", + "\n", + "base=b1-a1;\n", + "o1=25;o2=15;\n", + "mo7=(o2+o1)/2;\n", + "\n", + "ae7=base*mo7\n", + "ap7=ae7;\n", + "an7=0;\n", + "print('area=',ae7);\n", + "\n", + "print('chainage 27.5 and 35.5')\n", + "a1=27.5;b1=35.5;\n", + "\n", + "base=b1-a1;\n", + "o1=15;o2=0;\n", + "mo8=(o2+o1)/2;\n", + "\n", + "ae8=base*mo8\n", + "ap8=ae8;\n", + "an8=0\n", + "print('area=',ae8);\n", + "\n", + "an=an1+an2+an3+an4+an5+an6+an7+an8;\n", + "ap=ap1+ap2+ap3+ap4+ap5+ap6+ap7+ap8;\n", + "\n", + "area=ap-an;\n", + "print('ap,ae=',ap,an)\n", + "print('total area of field =',area);\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-7 page 214 pb-1" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mid ordinate rule\n", + "('required area is', 188.0, 'square meters')\n", + "average ordinate rule\n", + "('required area is', 161.14285714285714, 'sqare meters')\n", + "trapezoidal rule\n", + "('required area is ', 188.0, 'square meters')\n", + "simpsons rule\n", + "('required area is ', 196.66666666666669, 'square meters')\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "\n", + "dis=10;\n", + "a=0;g=0;\n", + "b=2.5;c=3.5;d=5;e=4.6;f=3.2;\n", + "\n", + "print('Mid ordinate rule');\n", + "\n", + "h1=(a+b)/2;\n", + "h2=(b+c)/2;\n", + "h3=(c+d)/2;\n", + "h4=(d+e)/2;\n", + "h5=(e+f)/2;\n", + "h6=(f+g)/2;\n", + "area=dis*(h1+h2+h3+h4+h5+h6);\n", + "\n", + "print('required area is',area,'square meters');\n", + "\n", + "print('average ordinate rule');\n", + "dis=10;\n", + "p=6;\n", + "bl=dis*p;\n", + "no=7;\n", + "\n", + "\n", + "area2=bl*(a+b+c+d+e+f+g)/no;\n", + "\n", + "print('required area is',area2,'sqare meters');\n", + "\n", + "print('trapezoidal rule');\n", + "\n", + "\n", + "area3=(dis/2)*(2*(a+b+c+d+e+f+g));\n", + "\n", + "print('required area is ',area3,'square meters');\n", + "print('simpsons rule');\n", + "\n", + "area4=(dis/3)*(4*(b+d+f)+2*(c+e));\n", + "print('required area is ',area4,'square meters');\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-7 page 216 pb-2" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "trapezoidal rule\n", + "('required area is ', 820.125, 'square meters')\n", + "simpsons rule\n", + "(756.0, 57.375)\n", + "('required area is ', 813.375, 'square meters')\n" + ] + } + ], + "source": [ + "#ch-7 page 216 pb-2\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "print('trapezoidal rule');\n", + "\n", + "o1=3.5;o2=4.3;o3=6.75;o4=5.25;o5=7.5;o6=8.8;o7=7.9;\n", + "o8=6.4;o9=4.4;o10=3.25;\n", + "\n", + "dis=15;\n", + "\n", + "area1=(dis/2)*(o1+o10+(2*(o2+o3+o4+o5+o6+o7+o8+o9)));\n", + "\n", + "print('required area is ',area1,'square meters');\n", + "\n", + "print('simpsons rule')\n", + "\n", + "A1=dis/3*(o1+o9+4*(o2+o4+o6+o8)+2*(o3+o5+o7));\n", + "\n", + "A2=dis/2*(o10+o9);\n", + "\n", + "area2=A1+A2;\n", + "print(A1,A2)\n", + "\n", + "print('required area is ',area2,'square meters');\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### cha 7 page -216 pb-3" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "trapezoidal rule\n", + "(89.5, 106.49999999999999, 158.0)\n", + "('total area=', 354.0, 'meters')\n", + "simpsons rule\n", + "(89.66666666666667, 102.33333333333333, 157.33333333333334)\n", + "('total area is ', 349.33333333333337, 'meters')\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "o1=2.5;o2=3.8;o3=4.6;o4=5.2;o5=6.1;o6=4.7;o7=5.8;o8=3.9;o9=2.20;\n", + "\n", + "d1=5;\n", + "d2=10;\n", + "d3=20;\n", + "\n", + "\n", + "print('trapezoidal rule')\n", + "\n", + "del1=(d1/2)*(o1+o5+2*(o2+o3+o4));\n", + "del2=(d2/2)*(o5+o7+2*(o6));\n", + "del3=(d3/2)*(o7+o9+2*(o8));\n", + "\n", + "total1=del1+del2+del3;\n", + "print(del1,del2,del3)\n", + "\n", + "print('total area=',total1,'meters');\n", + "\n", + "print('simpsons rule')\n", + "\n", + "de1=(d1/3)*(o1+o5+4*(o2+o4)+2*(o3));\n", + "de2=(d2/3)*(o5+o7+4*(o6));\n", + "de3=(d3/3)*(o7+o9+4*(o8));\n", + "\n", + "\n", + "total2=de1+de2+de3;\n", + "print(de1,de2,de3)\n", + "\n", + "print('total area is ',total2,'meters')\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### cha 7 page -225 pb-1" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('A=', 748.0)\n", + "('required area is', 748.0, 'meters')\n" + ] + } + ], + "source": [ + "#cha 7 page -225 ;pb-1\n", + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "ir=9.377;\n", + "fr=3.336;\n", + "m=100;\n", + "c=23.521;\n", + "\n", + "n=1;\n", + "\n", + "a1=m*(fr-ir+10*(n)+c);\n", + "\n", + "a2=m*(fr-ir-10*(n)+c);\n", + "\n", + "print('A=',a2);\n", + "print('required area is',a2,'meters');\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### cha 7 page -225,226 pb-2" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('A=', 81460.00000000001)\n", + "('required area is', 81460.00000000001, 'meters')\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "ir=8.652;\n", + "fr=6.798;\n", + "c=20;\n", + "m=100;\n", + "n=1;\n", + "\n", + "sc=100;\n", + "\n", + "a2=m*(fr-ir-10*(n)+c);\n", + "\n", + "a2=a2*sc;\n", + "\n", + "print('A=',a2);\n", + "print('required area is',a2,'meters');\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### cha 7 page -226 pb-3" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('required area is', 9747.499999999998, 'meters')\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "ir=4.855;\n", + "fr=8.754;\n", + "m=100;\n", + "\n", + "n=0;\n", + "c=0;\n", + "sc=25\n", + "a=m*(fr-ir)\n", + "a=a*sc;\n", + "print('required area is',a,'meters');\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### cha-7 page-226 pb-4" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "case 1\n", + "('A=', 100.0)\n", + "('M=', 100.0)\n", + "case 2\n", + "('required area is', 1347.0)\n", + "('area of zero circle is', 2122.0)\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "print('case 1')\n", + "\n", + "ir=3.415;\n", + "fr=4.415;\n", + "n=0;\n", + "c=0;\n", + "sc=16; #1cm^2=16m^2;\n", + "h=10000;\n", + "ag=0.16*h;\n", + "\n", + "am=ag/sc;\n", + "print('A=',am);\n", + "\n", + "m=am/(fr-ir);\n", + "\n", + "print('M=',m);\n", + "\n", + "print('case 2');\n", + "\n", + "fr_ir=2.25;\n", + "c=21.22;\n", + "n=1\n", + "\n", + "a1=m*(fr_ir-10+c);\n", + "print('required area is',a1);\n", + "\n", + "area=m*c;\n", + "\n", + "print('area of zero circle is',area);\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### cha-7 page-227 pb-5" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('area of zero circle is', 1221.0, 'square centimeters')\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "l=10;b=15;\n", + "a1=l*b;\n", + "\n", + "ir=0.686;\n", + "fr=9.976;\n", + "n=2;\n", + "m=100;\n", + "\n", + "marea=150;\n", + "\n", + "c=(marea/100)+10.710;\n", + "\n", + "area=m*c;\n", + "print('area of zero circle is',area,'square centimeters');\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### cha-7 page-228 pb-6" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "case 1\n", + "('area of figure is', 705.0, 'square cm')\n", + "case 2\n", + "('area of figure is', -1357.0, 'sq cm')\n", + "('C=', 20.62)\n", + "('area of zero circle is', 2062.0, 'square cm')\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "print('case 1')\n", + "n=1;\n", + "c=0;\n", + "m=100;\n", + "fr=4.825;\n", + "ir=7.775;\n", + "area1=m*(fr-ir+10*n)\n", + "\n", + "print('area of figure is',area1,'square cm');\n", + "\n", + "print('case 2')\n", + "fr=8.755;\n", + "ir=2.325;\n", + "m=100;\n", + "n=2;\n", + "area2=m*(fr-ir-10*n+c)\n", + "\n", + "print('area of figure is',area2,'sq cm')\n", + "c=(area1/m)+13.570;\n", + "print('C=',c)\n", + "\n", + "areac=m*c;\n", + "print('area of zero circle is',areac,'square cm');\n", + "\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.11" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/SURVYNG_AND_LEVELLING__by_N.N.BASAK/chap8.ipynb b/SURVYNG_AND_LEVELLING__by_N.N.BASAK/chap8.ipynb new file mode 100644 index 00000000..197ff573 --- /dev/null +++ b/SURVYNG_AND_LEVELLING__by_N.N.BASAK/chap8.ipynb @@ -0,0 +1,713 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "# Chapter 8: Computation of volume" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### cha-8 page-241 pb-1" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(10.215, 14.84375, 28.433749999999996, 34.375, 23.633750000000003, 16.23375, 9.58375)\n", + "by trapezoidal rule\n", + "('V=', 5096.775, 'meter cube')\n", + "by prismoidal rule\n", + "('V=', 5143.25, 'meter cube')\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "h1=0.90;h2=1.25;h3=2.15;h4=2.50;h5=1.85;h6=1.35;h7=0.85;\n", + "\n", + "b=10;\n", + "sh=1.5;\n", + "\n", + "h=40;\n", + "\n", + "d1=(b+(sh*h1))*h1;\n", + "d2=(b+(sh*h2))*h2;\n", + "d3=(b+(sh*h3))*h3;\n", + "d4=(b+(sh*h4))*h4;\n", + "d5=(b+(sh*h5))*h5;\n", + "d6=(b+(sh*h6))*h6;\n", + "d7=(b+(sh*h7))*h7;\n", + "\n", + "print(d1,d2,d3,d4,d5,d6,d7)\n", + "print('by trapezoidal rule');\n", + "v=(h/2)*(d1+d7+2*(d2+d3+d4+d5+d6));\n", + "print('V=',v,'meter cube');\n", + "\n", + "print('by prismoidal rule');\n", + "\n", + "v1=(h/3)*(d1+d7+4*(d2+d4+d6)+2*(d3+d5));\n", + "\n", + "print('V=',v1,'meter cube');\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### cha-8 page-241,242 pb-2" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(19.736842105263158, 29.487179487179485, 19.047619047619047, 23.214285714285715)\n", + "(7.125, 11.845, 7.68, 13.78, 16.5, 7.125)\n", + "from chainage 0 to 50\n", + "(70.3125, 179.3165955128205)\n", + "from chainage 50 to 100\n", + "(78.74925714285715, 174.63782051282053)\n", + "from chainage 100 to 150\n", + "(73.14285714285714, 213.2455)\n", + "from chainage 150 to 200\n", + "(221.13535714285715, 159.94642857142858)\n", + "from chainage 200 to 250\n", + "590.625\n", + "('total cutting =', 1033.9649714285715)\n", + "('total fitting=', 727.1463445970695)\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "h1=0.75;h2=1.15;h3=0.80;h4=1.30;h5=1.5;h6=0.75\n", + "b=8;sh=2;\n", + "\n", + "x1=(50*h1)/(h1+h2);\n", + "x2=(50*h2)/(h2+h3);\n", + "x3=(50*h3)/(h4+h3);\n", + "x4=(50*h4)/(h4+h5);\n", + "print(x1,x2,x3,x4);\n", + "\n", + "a1=(b+(sh*h1))*h1;\n", + "a2=(b+(sh*h2))*h2;\n", + "a3=(b+(sh*h3))*h3;\n", + "a4=(b+(sh*h4))*h4;\n", + "a5=(b+(sh*h5))*h5;\n", + "a6=(b+(sh*h6))*h6;\n", + "print(a1,a2,a3,a4,a5,a6)\n", + "\n", + "print('from chainage 0 to 50');\n", + "c1=(a1/2)*(x1);\n", + "f1=(a2/2)*(x2+0.79);\n", + "print(c1,f1);\n", + "\n", + "\n", + "\n", + "print('from chainage 50 to 100');\n", + "f2=(a2/2)*(x2);\n", + "c2=(a3/2)*(x3+1.46);\n", + "print(c2,f2);\n", + "\n", + "print('from chainage 100 to 150');\n", + "c3=(a3/2)*(x3);\n", + "f3=(a4/2)*(30.95);\n", + "print(c3,f3);\n", + "\n", + "print('from chainage 150 to 200');\n", + "f4=(a4/2)*(x4);\n", + "c4=(a5/2)*(x4+3.59);\n", + "print(c4,f4);\n", + "\n", + "print('from chainage 200 to 250');\n", + "c5=((a1+a5)/2)*50;\n", + "\n", + "print(c5);\n", + "\n", + "tc=c1+c2+c3+c4+c5;\n", + "tf=f1+f2+f3+f4;\n", + "\n", + "print('total cutting =',tc);\n", + "print('total fitting=',tf);\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### cha-8 page-244 pb-3" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(26.25, 11.5625, 8.5025, 15.9225, 22.44, 30.9225, 6.5625)\n", + "('volume=', 5472.125)\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "h=50;\n", + "h1=2.50;h2=1.25;h3=0.95;h4=1.65;h5=2.20;h6=2.85;h7=0.75;\n", + "b=8;sh=1;\n", + "\n", + "\n", + "a1=(b+(sh*h1))*h1;\n", + "a2=(b+(sh*h2))*h2;\n", + "a3=(b+(sh*h3))*h3;\n", + "a4=(b+(sh*h4))*h4;\n", + "a5=(b+(sh*h5))*h5;\n", + "a6=(b+(sh*h6))*h6;\n", + "a7=(b+(sh*h7))*h7;\n", + "\n", + "print(a1,a2,a3,a4,a5,a6,a7);\n", + "\n", + "v=(h/3)*(a1+a7+4*(a2+a4+a6)+2*(a3+a5));\n", + "\n", + "\n", + "print('volume=',v);\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### cha-8 page-245 pb-4" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "according to trapezoidal rule\n", + "('volume =', 330375.0)\n", + "according to prismoidal rule\n", + "('volume =', 330250.0)\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "a1=2050;a2=8400;a3=16300;a4=24600;a5=31500;\n", + "\n", + "h=5;\n", + "\n", + "print('according to trapezoidal rule')\n", + "\n", + "v1=(h/2)*(a1+a5+2*(a2+a3+a4));\n", + "\n", + "print('volume =',v1);\n", + "\n", + "print('according to prismoidal rule')\n", + "\n", + "v2=(h/3)*(a1+a5+4*(a2+a4)+2*(a3));\n", + "\n", + "print('volume =',v2)\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### cha-8 page-245,246 pb-5" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "bottom section\n", + "('area A1=', 1200)\n", + "mid section\n", + "('area A2=', 2000.0)\n", + "top section\n", + "('area A3=', 30000)\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "print('bottom section')\n", + "L=40;\n", + "B=30;\n", + "a1=L*B;\n", + "print('area A1=',a1)\n", + "\n", + "print('mid section')\n", + "b=40;\n", + "sh=2.5;\n", + "\n", + "l=L+2*2*sh;\n", + "b=B+2*2*sh;\n", + "a2=l*b;\n", + "print('area A2=',a2);\n", + "\n", + "print('top section')\n", + "sh=5;\n", + "\n", + "l1=L+2*sh;\n", + "b1=B*2*2*sh;\n", + "a3=l1*b1;\n", + "print('area A3=',a3)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### cha-8 page-246,247 pb-6" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "first section\n", + "(6.666666666666666, 5.454545454545455)\n", + "('area A1=', 20.36363636363636)\n", + "second section\n", + "(7.777777777777778, 6.363636363636363)\n", + "('area A2=', 33.494949494949495)\n", + "third section\n", + "(8.88888888888889, 7.2727272727272725)\n", + "('area A3=', 48.64646464646465)\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "b=8;\n", + "h=2;\n", + "n=10;\n", + "s=1;\n", + "\n", + "print('first section');\n", + "b1=(b/2)+((n*s)/(n-s))*(h+(b/(2*n)));\n", + "b2=(b/2)+((n*s)/(n+s))*(h-(b/(2*n)));\n", + "\n", + "a1=0.5*((((b/(2*s))+h))*(b1+b2)-((b*b)/(2*s)));\n", + "print(b1,b2)\n", + "\n", + "print('area A1=',a1);\n", + "\n", + "print('second section');\n", + "b=8;h=3;n=10;s=1;\n", + "\n", + "\n", + "b1=(b/2)+((n*s)/(n-s))*(h+(b/(2*n)));\n", + "b2=(b/2)+((n*s)/(n+s))*(h-(b/(2*n)));\n", + "\n", + "a2=0.5*((((b/(2*s))+h))*(b1+b2)-((b*b)/(2*s)));\n", + "print(b1,b2)\n", + "\n", + "print('area A2=',a2);\n", + "\n", + "print('third section');\n", + "b=8;h=4;n=10;s=1;\n", + "\n", + "\n", + "b1=(b/2)+((n*s)/(n-s))*(h+(b/(2*n)));\n", + "b2=(b/2)+((n*s)/(n+s))*(h-(b/(2*n)));\n", + "\n", + "a3=0.5*((((b/(2*s))+h))*(b1+b2)-((b*b)/(2*s)));\n", + "print(b1,b2)\n", + "\n", + "print('area A3=',a3);\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### cha-8 page-247,248 pb-7" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "first section\n", + "(6.666666666666667, 5.454545454545454)\n", + "('area A1=', 11.36363636363636)\n", + "second section\n", + "(8.75, 5.833333333333333)\n", + "('area A2=', 26.041666666666664)\n", + "third section\n", + "(7.428571428571429, 5.777777777777778)\n", + "('area A3=', 17.920634920634917)\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "b=10;\n", + "h=1;\n", + "n=10;\n", + "s=1;\n", + "\n", + "print('first section');\n", + "b1=(b/2)+((n*s)/(n-s))*(h+(b/(2*n)));\n", + "b2=(b/2)+((n*s)/(n+s))*(h-(b/(2*n)));\n", + "\n", + "a1=0.5*((((b/(2*s))+h))*(b1+b2)-((b*b)/(2*s)));\n", + "print(b1,b2)\n", + "\n", + "print('area A1=',a1);\n", + "\n", + "print('second section');\n", + "b=10;h=2;n=5;s=1;\n", + "\n", + "\n", + "b1=(b/2)+((n*s)/(n-s))*(h+(b/(2*n)));\n", + "b2=(b/2)+((n*s)/(n+s))*(h-(b/(2*n)));\n", + "\n", + "a2=0.5*((((b/(2*s))+h))*(b1+b2)-((b*b)/(2*s)));\n", + "print(b1,b2)\n", + "\n", + "print('area A2=',a2);\n", + "\n", + "print('third section');\n", + "b=10;h=1.5;n=8;s=1;\n", + "\n", + "\n", + "b1=(b/2)+((n*s)/(n-s))*(h+(b/(2*n)));\n", + "b2=(b/2)+((n*s)/(n+s))*(h-(b/(2*n)));\n", + "\n", + "a3=0.5*((((b/(2*s))+h))*(b1+b2)-((b*b)/(2*s)));\n", + "print(b1,b2)\n", + "\n", + "print('area A3=',a3);\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### cha-8 page-248 pb-8" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "at station 1\n", + "('area=', 14.25)\n", + "at station 2\n", + "('area=', 18.975)\n", + "('v=', 830.625, 'cp=', 0.20833333333333262)\n", + "('correct volume =', 830.4166666666666)\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "print('at station 1');\n", + "h=1;h1=2.55;h2=0.95;b=9;b1=7.5;b2=5.25;\n", + "w1=b1+b2\n", + "a=(((h/2)*(b1+b2))+((b/4)*(h1+h2)));\n", + "print('area=',a)\n", + "\n", + "print('at station 2');\n", + "h=1.5;h1=2.8;h2=1.35;b=9;b1=8.1;b2=4.75;\n", + "\n", + "a1=(((h/2)*(b1+b2))+((b/4)*(h1+h2)));\n", + "d=50;\n", + "k=10.01;\n", + "v=(d/2)*(a+a1);\n", + "w2=b1+b2\n", + "print('area=',a1)\n", + "h2=1;\n", + "h1=1.5;\n", + "cp=(d/12)*(h1-h2)*(w2-w1);\n", + "\n", + "\n", + "cv=v-cp;\n", + "print('v=',v,'cp=',cp)\n", + "print('correct volume =',cv);\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### cha-8 page-249 pb-9" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "section 1\n", + "(7.03125, 1.0416666666666667)\n", + "section 2\n", + "(9.03125, 0.375)\n", + "('vc=', 401.5625, 'vf=', 35.41666666666667)\n", + "('corrected volume (in cutting)=', 400.5208333333333)\n", + "('corrected volume(in filling)', 34.027777777777786)\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "print('section 1')\n", + "b=10;n=5;s=1;s1=2;\n", + "d=50;h1=0.5;h2=0.7;\n", + "\n", + "ac=0.5*(((0.5*b+n*h1)*(0.5*b+n*h1))/(n-s));\n", + "\n", + "af=0.5*(((0.5*b-n*h1)*(0.5*b-n*h1))/(n-s1));\n", + "\n", + "print(ac,af)\n", + "\n", + "\n", + "print('section 2')\n", + "\n", + "\n", + "ac1=0.5*(((0.5*b+n*h2)*(0.5*b+n*h2))/(n-s));\n", + "\n", + "af1=0.5*(((0.5*b-n*h2)*(0.5*b-n*h2))/(n-s1));\n", + "D=50;\n", + "print(ac1,af1)\n", + "vc=((ac+ac1)/2)*D;\n", + "vf=((af+af1)/2)*D;\n", + "\n", + "print('vc=',vc,'vf=',vf);\n", + "\n", + "D=50;\n", + "pcc=(D/(12*(n-s)))*(n*n*(h1-h2)*(h1-h2));\n", + "\n", + "\n", + "pcf=(D/(12*(n-s1)))*(n*n*(h1-h2)*(h1-h2));\n", + "\n", + "\n", + "cvc=vc-pcc;\n", + "cvf=vf-pcf;\n", + "\n", + "print('corrected volume (in cutting)=',cvc);\n", + "\n", + "print('corrected volume(in filling)',cvf)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### cha-8 page-251 pb-10" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "at station 1\n", + "(40.2, 82.475)\n", + "('area =', 21.137499999999996)\n", + "at station 2\n", + "(53.7, 105.675)\n", + "('area =', 25.987499999999997)\n", + "volume by average end area rule\n", + "('volume=', 1178.1249999999998)\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "a1=0;a2=3.0;\n", + "b1=2.20;b2=5.50;\n", + "c1=1.75;c2=3.0;\n", + "d1=1.5;d2=0;\n", + "e1=4.75;e2=5.25;\n", + "f1=6.40;f2=7.30;\n", + "g1=0;g2=3.0;\n", + "\n", + "print('at station 1')\n", + "sp=(e1*d2)+(f1*e2)+(d2*f2)+(c1*d2)+(b1*c2)+(a1*b2);\n", + "\n", + "sq=(e2*d1)+(e1*f2)+(f1*g2)+(d1*c2)+(c1*b2)+(b1*a2);\n", + "\n", + "area1=0.5*(sp-sq)\n", + "area1=abs(area1);\n", + "print(sp,sq)\n", + "print('area =',area1)\n", + "\n", + "a1=0;a2=3.0;\n", + "b1=3.1;b2=5.25;\n", + "c1=2.20;c2=3.0;\n", + "d1=2;d2=0;\n", + "e1=5.25;e2=6;\n", + "f1=7.40;f2=8.5;\n", + "g1=0;g2=3.0;\n", + "print('at station 2')\n", + "sp1=(e1*d2)+(f1*e2)+(d2*f2)+(c1*d2)+(b1*c2)+(a1*b2);\n", + "\n", + "sq1=(d1*e2)+(e1*f2)+(f1*g2)+(d1*c2)+(c1*b2)+(b1*a2);\n", + "print(sp1,sq1)\n", + "\n", + "\n", + "area2=0.5*(sp1-sq1)\n", + "area2=abs(area2);\n", + "print('area =',area2)\n", + "\n", + "print('volume by average end area rule')\n", + "v=50*((area1+area2)/2);\n", + "print('volume=',v)\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.11" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/SURVYNG_AND_LEVELLING__by_N.N.BASAK/chap9.ipynb b/SURVYNG_AND_LEVELLING__by_N.N.BASAK/chap9.ipynb new file mode 100644 index 00000000..3153bd76 --- /dev/null +++ b/SURVYNG_AND_LEVELLING__by_N.N.BASAK/chap9.ipynb @@ -0,0 +1,502 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "# Chapter 9: Theodolite Traversing" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-9 page 302 pb-1" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(65.11978202514794, -63.50741753704864, -51.91315691660193)\n", + "(38.20554919114786, 168.9587462008847, -30.579186368382416)\n", + "(50.300792428502625, -176.58510902365015)\n", + "('distance DA=', 183.60955979422673)\n", + "('bearing of DA=', 74.10023981818601)\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "l1=75.5;\n", + "l2=180.5\n", + "l3=60.25\n", + "\n", + "t1=30.4;t2=69.4;t3=30.5;\n", + "t2=180-t2;\n", + "t3=180-t3;\n", + "\n", + "Lc1=l1*math.cos(t1*(math.pi/180))\n", + "Lc2=l2*math.cos(t2*(math.pi/180))\n", + "Lc3=l3*math.cos(t3*(math.pi/180))\n", + "\n", + "Ls1=l1*math.sin(t1*(math.pi/180))\n", + "Ls2=l2*math.sin(t2*(math.pi/180))\n", + "Ls3=-l3*math.sin(t3*(math.pi/180))\n", + "\n", + "print(Lc1,Lc2,Lc3);\n", + "print(Ls1,Ls2,Ls3);\n", + "Lc4=-Lc1-Lc2-Lc3;\n", + "Ls4=-Ls1-Ls2-Ls3;\n", + "\n", + "print(Lc4,Ls4);\n", + "\n", + "t4=-math.atan(Ls4/Lc4);\n", + "t4=t4*(180/math.pi);\n", + "\n", + "l4=math.sqrt(Lc4*Lc4+Ls4*Ls4);\n", + "\n", + "print('distance DA=',l4);\n", + "print('bearing of DA=',t4);\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-9 page 304 pb-2" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('length of DA is', 145.80634036039953, 'or', 12.053659639600497)\n", + "when length of DA ,L=145.8\n", + "('bearing at AB is=N', 82.44640641462031)\n", + "when length of DA ,L=12.04\n", + "0.999661660714\n", + "('bearing at AB is=N', 1.4904797844587976)\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "l1=100;\n", + "l2=80;\n", + "l3=60;\n", + "\n", + "t2=39.5;t3=40.5;t4=49.75;\n", + "\n", + "L2=l2*math.cos(t2*(math.pi/180));\n", + "L3=l3*math.cos(t3*(math.pi/180));\n", + "\n", + "D2=l2*math.sin(t2*(math.pi/180));\n", + "D3=l3*math.sin(t3*(math.pi/180));\n", + "\n", + "l41=(157.86+math.sqrt(157.86*157.86-4*1757.5))/2;\n", + "l42=(157.86-math.sqrt(157.86*157.86-4*1757.5))/2;\n", + "\n", + "print('length of DA is',l41,'or',l42);\n", + "\n", + "print('when length of DA ,L=145.8')\n", + "\n", + "k=math.cos(t4*(math.pi/180))\n", + "k1=(L2+L3-(k*l41))/100;\n", + "t1=math.acos(k1);\n", + "t1=t1*(180/(math.pi))\n", + "print('bearing at AB is=N',t1)\n", + "\n", + "\n", + "print('when length of DA ,L=12.04')\n", + "\n", + "k=math.cos(t4*(math.pi/180))\n", + "k1=(L2+L3-(k*l42))/100;\n", + "k1=k1+0.004;\n", + "t11=math.acos(k1);\n", + "t11=t11*(180/(math.pi))\n", + "print(k1)\n", + "print('bearing at AB is=N',t11)\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-9 page 305 pb-3" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('latitude of AB,CD,DE are', 86.59373062437335, -57.03044742000232, -25.250000000000007)\n", + "('Depature of AB,CD,DE are', 51.00760547755076, -48.708603624763775, -43.73428289111415)\n", + "(-4.313283204371025, 41.43528103832716)\n", + "('length of BC=', 348.51410778926174)\n", + "('length of EA=', 317.28203276885586)\n" + ] + } + ], + "source": [ + "#ch-9 page 305 pb-3\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "l1=100.5;l3=75;l4=50.5;\n", + "t1=30.5;t2=45;t3=40.5;t4=60;t5=40.25;\n", + "\n", + "\n", + "L1=l1*math.cos(t1*(math.pi/180))\n", + "L3=-l3*math.cos(t3*(math.pi/180))\n", + "L4=-l4*math.cos(t4*(math.pi/180))\n", + "\n", + "print('latitude of AB,CD,DE are',L1,L3,L4);\n", + "D1=l1*math.sin(t1*(math.pi/180))\n", + "D3=-l3*math.sin(t3*(math.pi/180))\n", + "D4=-l4*math.sin(t4*(math.pi/180))\n", + "print('Depature of AB,CD,DE are',D1,D3,D4);\n", + "\n", + "L2_L5=-(L1+L3+L4);\n", + "D2_D5=-(D1+D3+D4);\n", + "print(L2_L5,D2_D5)\n", + "\n", + "k=0.117;\n", + "l5=(L2_L5+D2_D5)/(k);\n", + "\n", + "k1=0.763;\n", + "\n", + "l2=(k1*l5)-L2_L5;\n", + "l2=l2/0.707;\n", + "\n", + "print('length of BC=',l2);\n", + "print('length of EA=',l5);\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-9 page 307 pb-4" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('latitudes of AQ,QR,RB are', 65.21958064293187, -61.02257873940248, -36.93176700776003)\n", + "('Depature of AQ,QR,RB are', 38.03493526693723, 52.118205878497236, -65.27667719549248)\n", + "('length of AB=', 41.114514530539196, 'meters')\n" + ] + } + ], + "source": [ + "#ch-9 page 307 pb-4\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "l1=75.5;l2=80.25;l3=75;\n", + "t1=30.25;t2=40.5;t3=60.5;\n", + "\n", + "\n", + "L1=l1*math.cos(t1*(math.pi/180))\n", + "L2=-l2*math.cos(t2*(math.pi/180))\n", + "L3=-l3*math.cos(t3*(math.pi/180))\n", + "print('latitudes of AQ,QR,RB are',L1,L2,L3);\n", + "\n", + "\n", + "D1=l1*math.sin(t1*(math.pi/180))\n", + "D2=l2*math.sin(t2*(math.pi/180))\n", + "D3=-l3*math.sin(t3*(math.pi/180))\n", + "print('Depature of AQ,QR,RB are',D1,D2,D3);\n", + "\n", + "L4=-(L1+L2+L3);\n", + "D4=-(D1+D2+D3);\n", + "\n", + "l4=math.sqrt(L4*L4+(D4*D4));\n", + "\n", + "print('length of AB=',l4,'meters');\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-9 page 308 pb-5" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('latitudes of BQ,QP,PA are', -96.23556979807799, -172.32583208830516, -61.552945012933385)\n", + "('Depature of BQ,QP,PA are', 115.71069572705566, -101.50767259214082, -108.79446199248746)\n", + "('length of AB=', 343.3992171422471, 'meters')\n", + "('bearing of AB=', 15.989201746570728)\n", + "('PAB=', 44.51079825342927, 'QBA=', 66.23920174657073)\n" + ] + } + ], + "source": [ + "#ch-9 page 308 pb-5\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "l1=150.5;l2=200;l3=125;\n", + "t1=50.25;t2=30.5;t3=60.5;\n", + "\n", + "\n", + "L1=-l1*math.cos(t1*(math.pi/180))\n", + "L2=-l2*math.cos(t2*(math.pi/180))\n", + "L3=-l3*math.cos(t3*(math.pi/180))\n", + "print('latitudes of BQ,QP,PA are',L1,L2,L3);\n", + "\n", + "\n", + "D1=l1*math.sin(t1*(math.pi/180))\n", + "D2=-l2*math.sin(t2*(math.pi/180))\n", + "D3=-l3*math.sin(t3*(math.pi/180))\n", + "print('Depature of BQ,QP,PA are',D1,D2,D3);\n", + "\n", + "L4=-(L1+L2+L3);\n", + "D4=-(D1+D2+D3);\n", + "\n", + "l4=math.sqrt(L4*L4+(D4*D4));\n", + "\n", + "print('length of AB=',l4,'meters');\n", + "\n", + "t4=math.atan(D4/L4);\n", + "t4=t4*(180/math.pi);\n", + "print('bearing of AB=',t4);\n", + "\n", + "PAB=t3-t4;\n", + "QBA=t1+t4;\n", + "\n", + "print('PAB=',PAB,'QBA=',QBA);\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-9 page 308 pb-6" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('latitudes of AB,BC,CD,DE are', 121.76738460229168, 106.68654829016975, -133.98333444865727, 19.805712703281312)\n", + "('Depature of AB,BC,CD,DE are', 45.52695956373076, 186.6627451151656, 78.9222154403895, 118.35427218446777)\n", + "('length of EA=', 444.4100422146986, 'meters')\n", + "('bearing of EA=', 75.09947760257306)\n", + "('bearing from F to C is =', 5.818201574554788)\n", + "('distance from F to C is =', 172.2028708809785)\n" + ] + } + ], + "source": [ + "#ch-9 page 308 pb-6\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "l1=130;l2=215;l3=155.5;l4=120;\n", + "t1=20.5;t2=60.25;t3=30.5;t4=80.5;\n", + "\n", + "\n", + "L1=l1*math.cos(t1*(math.pi/180))\n", + "L2=l2*math.cos(t2*(math.pi/180))\n", + "L3=-l3*math.cos(t3*(math.pi/180))\n", + "L4=l4*math.cos(t4*(math.pi/180))\n", + "print('latitudes of AB,BC,CD,DE are',L1,L2,L3,L4);\n", + "\n", + "\n", + "D1=l1*math.sin(t1*(math.pi/180))\n", + "D2=l2*math.sin(t2*(math.pi/180))\n", + "D3=l3*math.sin(t3*(math.pi/180))\n", + "D4=l4*math.sin(t4*(math.pi/180))\n", + "print('Depature of AB,BC,CD,DE are',D1,D2,D3,D4);\n", + "\n", + "L5=-(L1+L2+L3+L4);\n", + "D5=-(D1+D2+D3+D4);\n", + "\n", + "l5=math.sqrt(L5*L5+(D5*D5));\n", + "\n", + "print('length of EA=',l5,'meters');\n", + "\n", + "t5=math.atan(D5/L5);\n", + "t5=t5*(180/math.pi);\n", + "print('bearing of EA=',t5);\n", + "\n", + "FA=l5/2;\n", + "l6=FA;\n", + "t6=t5;\n", + "L6=-l6*math.cos(t6*(math.pi/180))\n", + "D6=-l6*math.sin(t6*(math.pi/180))\n", + "\n", + "L7=-(L1+L2+L6)\n", + "D7=-(D1+D2+D6)\n", + "\n", + "t7=math.atan(D7/L7);\n", + "t7=t7*(180/math.pi);\n", + "print('bearing from F to C is =',t7);\n", + "\n", + "l7=math.sqrt(L7*L7+(D7*D7));\n", + "\n", + "print('distance from F to C is =',l7);\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### ch-9 page 308 pb-7" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('latitudes of AB,DE,EA are', 362.50000000000006, -538.0859250785912, -574.3378222288467)\n", + "('Depature of AB,DE,EA are', 627.8684177437179, -782.9198791909149, -27.587423899772766)\n", + "('t2-t3=', 100.07865810778766)\n", + "('Bearing of BC is', 63.0)\n", + "('Bearing of CD is', 37.12098009569709)\n" + ] + } + ], + "source": [ + "#ch-9 page 308 pb-7\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "l1=725;l2=1050;l3=1250;l4=950;l5=575;\n", + "t1=60;t4=55.5;t5=2.75;\n", + "\n", + "\n", + "L1=l1*math.cos(t1*(math.pi/180))\n", + "L4=-l4*math.cos(t4*(math.pi/180))\n", + "L5=-l5*math.cos(t5*(math.pi/180))\n", + "print('latitudes of AB,DE,EA are',L1,L4,L5);\n", + "\n", + "\n", + "D1=l1*math.sin(t1*(math.pi/180))\n", + "D4=-l4*math.sin(t4*(math.pi/180))\n", + "D5=-l5*math.sin(t5*(math.pi/180))\n", + "print('Depature of AB,DE,EA are',D1,D4,D5);\n", + "\n", + "t2_t3=math.acos(0.1750);\n", + "t2_t3=180-(t2_t3*(180/math.pi));\n", + "\n", + "print('t2-t3=',t2_t3);\n", + "\n", + "t3=math.asin(0.6035);\n", + "t3=t3*(180/math.pi);\n", + "t2=t2_t3-t3;\n", + "t2=math.ceil(t2);\n", + "\n", + "print('Bearing of BC is',t2);\n", + "print('Bearing of CD is',t3);\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.11" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/SURVYNG_AND_LEVELLING__by_N.N.BASAK/chapter1.ipynb b/SURVYNG_AND_LEVELLING__by_N.N.BASAK/chapter1.ipynb new file mode 100644 index 00000000..2c3b3b69 --- /dev/null +++ b/SURVYNG_AND_LEVELLING__by_N.N.BASAK/chapter1.ipynb @@ -0,0 +1,1473 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "# Chapter 1: Introduction\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### Problem1, pg 25" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "true length= 327.4905\n" + ] + } + ], + "source": [ + "\n", + "\n", + "l=20; #chain length\n", + "e=0.03; #error\n", + "l1=l+e; #L'\n", + "ml=327; #measured length\n", + "truel=(l1/l)*(ml) #true length\n", + "print (\"true length=\",truel)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### Problem2, pg 25" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "amount of error= 0.20083682008368697\n" + ] + } + ], + "source": [ + "\n", + "\n", + "l1=20; #chain 1 length\n", + "e=0.05; #error\n", + "l11=l1+e; \n", + "ml1=1200; #measured lenght\n", + "tl=(l11/l1)*ml1; #true lenght of line\n", + "\n", + "l2=30; #chain 2 length\n", + "ml2=1195; #measured length\n", + "\n", + "l21=(tl/ml2)*l2; \n", + "ae=l21-l2; #amount of error\n", + "print('amount of error=',ae)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### Problem3, pg 25" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "true length1= 901.35\n", + "true length 2= 678.3750000000001\n", + "true distance= 1579.7250000000001\n" + ] + } + ], + "source": [ + "\n", + "\n", + "l1=20\n", + "e=(0.06/2) #consider mean elongation\n", + "l11=l1+e;\n", + "ml=900;\n", + "tl=(l11/l1)*ml;\n", + "print('true length1=',tl)\n", + "l2=20;\n", + "e2=(0.06+0.14)/2;\n", + "l21=20+e2;\n", + "ml2=1575-ml;\n", + "\n", + "tl2=(l21/l2)*ml2;\n", + "print('true length 2=',tl2)\n", + "td=tl+tl2;\n", + "print('true distance=',td)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### Problem4, pg26" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "distance between stations on map= 35.0 centimeters\n", + "true distance on ground = 1750.0 meters\n" + ] + } + ], + "source": [ + "\n", + "\n", + "s=100;\n", + "dsm=3500;\n", + "adsm=dsm/s;\n", + "\n", + "print('distance between stations on map=',adsm,'centimeters')\n", + "\n", + "actuals=50;\n", + "td=adsm*actuals;\n", + "\n", + "print('true distance on ground =',td,'meters')\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### Problem 5, pg 26" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "actual area present= 132.01840894148586 square cm\n", + "true area= 212286.9217619987 square meters\n" + ] + } + ], + "source": [ + "\n", + "\n", + "present=19.5\n", + "actual=20;\n", + "cm1=actual/present;\n", + "cm12=(actual*actual)/(present*present);\n", + "pm=125.5;\n", + "apm=pm*cm12;\n", + "print('actual area present=',apm,'square cm');\n", + "\n", + "cm=40;\n", + "cm2=cm*cm;\n", + "\n", + "area=cm2*apm;\n", + "scale=(20.05*20.05)/(20*20);\n", + "ta=scale*area;\n", + "print('true area=',ta,'square meters');\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### Problem 6, pg 27" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " for n=1\n", + "the temperature correction is 0.00396 meters\n", + "the pull corretion is 0.002380952380952381 meters\n", + "the sag correction is -0.0026680499999999995 meters\n", + "the total correction is 0.0036729023809523816 meters\n", + "the true length is 780.0954954619046\n", + " for n=2\n", + "the temperature correction is 0.00396 meters\n", + "the pull corretion is 0.002380952380952381 meters\n", + "the sag correction is -0.0006670124999999999 meters\n", + "the total correction is 0.005673939880952382 meters\n", + "the true length is 780.1475224369049\n" + ] + } + ], + "source": [ + "\n", + "\n", + "from __future__ import division\n", + "\n", + "L=30;\n", + "t0=20;\n", + "p0=10;\n", + "pm=15;\n", + "tm=32;\n", + "a=0.03;\n", + "al=11/(1000000);\n", + "E=2.1*(1000000);\n", + "w=0.693;\n", + "ml=780;\n", + "n=1;\n", + "print(' for n=1')\n", + "ct=al*L*(tm-t0);\n", + "print('the temperature correction is',ct,'meters');\n", + "\n", + "cp=(pm-p0)*L/(a*E);\n", + "print('the pull corretion is ',cp,' meters');\n", + "\n", + "cs=-L*w*w/(24*pm*pm*n*n);\n", + "print('the sag correction is ',cs,'meters');\n", + "\n", + "e=ct+cp+cs;\n", + "print('the total correction is ',e,'meters');\n", + "\n", + "l1=L+e;\n", + "\n", + "truelength=(l1/L)*ml;\n", + "print('the true length is ',truelength);\n", + "\n", + "n=2;\n", + "\n", + "print(' for n=2')\n", + "ct=al*L*(tm-t0);\n", + "print('the temperature correction is',ct,'meters');\n", + "\n", + "cp=(pm-p0)*L/(a*E);\n", + "print('the pull corretion is ',cp,' meters');\n", + "\n", + "cs=-L*w*w/(24*pm*pm*n*n);\n", + "print('the sag correction is ',cs,'meters');\n", + "\n", + "e=ct+cp+cs;\n", + "print('the total correction is ',e,'meters');\n", + "\n", + "l1=L+e;\n", + "\n", + "truelength=(l1/L)*ml;\n", + "print('the true length is ',truelength);\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### Problem 7, pg 28" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the temperature correction is 0.0021999999999999997 meters\n", + "the pull corretion is -0.002380952380952381 meters\n", + "the sag correction is -0.0013333333333333335 meters\n", + "the total correction is -0.001514285714285715 meters\n", + "the horizontal distance is 19.998485714285714\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "\n", + "L=20;\n", + "t0=20;\n", + "p0=15;\n", + "p=10;\n", + "tm=30;\n", + "a=0.02;\n", + "al=11/(1000000);\n", + "E=2.1*(1000000);\n", + "w=0.4;\n", + "\n", + "n=1;\n", + "ct=al*L*(tm-t0);\n", + "print('the temperature correction is',ct,'meters');\n", + "\n", + "cp=(p-p0)*L/(a*E);\n", + "print('the pull corretion is ',cp,' meters');\n", + "\n", + "cs=-L*w*w/(24*p*p*n*n);\n", + "print('the sag correction is ',cs,'meters');\n", + "\n", + "e=ct+cp+cs;\n", + "print('the total correction is ',e,'meters');\n", + "\n", + "hd=L+e;\n", + "\n", + "print('the horizontal distance is ',hd);\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### Problem 8, pg 29" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "for p=5 case\n", + "the temperature correction is 0.00165 meters\n", + "the pull corretion is 0.0 meters\n", + "the sag correction is -0.02178 meters\n", + "the total correction is -0.020130000000000002 meters\n", + "the horizontal distance is 29.97987\n", + "for p=11 case\n", + "the temperature correction is 0.00165 meters\n", + "the pull corretion is 0.004285714285714286 meters\n", + "the sag correction is -0.0045000000000000005 meters\n", + "the total correction is 0.001435714285714285 meters\n", + "the horizontal distance is 30.001435714285716\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "\n", + "L=30;\n", + "t0=20;\n", + "p0=5;\n", + "tm=25;\n", + "a=0.02;\n", + "al=11/(1000000);\n", + "E=2.1*(1000000);\n", + "float(E);\n", + "float(al);\n", + "w1=22;\n", + "w=0.66;\n", + "n=1;\n", + "\n", + "p=5;\n", + "print('for p=5 case');\n", + "\n", + "ct=al*L*(tm-t0);\n", + "float(ct);\n", + "print('the temperature correction is',ct,'meters');\n", + "\n", + "cp=(p-p0)*L/(a*E);\n", + "print('the pull corretion is ',cp,' meters');\n", + "\n", + "cs=-L*w*w/(24*p*p*n*n);\n", + "print('the sag correction is ',cs,'meters');\n", + "\n", + "e=ct+cp+cs;\n", + "print('the total correction is ',e,'meters');\n", + "\n", + "hd=L+e;\n", + "\n", + "print('the horizontal distance is ',hd);\n", + "\n", + "p=11;\n", + "print('for p=11 case');\n", + "\n", + "ct=al*L*(tm-t0);\n", + "print('the temperature correction is',ct,'meters');\n", + "\n", + "cp=(p-p0)*L/(a*E);\n", + "print('the pull corretion is ',cp,' meters');\n", + "\n", + "cs=-L*w*w/(24*p*p*n*n);\n", + "print('the sag correction is ',cs,'meters');\n", + "\n", + "e=ct+cp+cs;\n", + "print('the total correction is ',e,'meters');\n", + "\n", + "hd=L+e;\n", + "\n", + "print('the horizontal distance is ',hd);\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### Problem 9, pg 30" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the temperature correction is 0.00264 meters\n", + "the pull corretion is 0.003492063492063492 meters\n", + "the sag correction is -0.001171875 meters\n", + "the total correction is 0.004960188492063492 meters\n", + "the true length is 680.1686464087301\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "\n", + "L=20;\n", + "t0=20;\n", + "p0=5;\n", + "pm=16;\n", + "tm=32;\n", + "a=0.03;\n", + "al=11/(1000000);\n", + "E=2.1*(1000000);\n", + "w=0.6;\n", + "ml=680;\n", + "n=1;\n", + "\n", + "\n", + "ct=al*L*(tm-t0);\n", + "print('the temperature correction is',ct,'meters');\n", + "\n", + "cp=(pm-p0)*L/(a*E);\n", + "print('the pull corretion is ',cp,' meters');\n", + "\n", + "cs=-L*w*w/(24*pm*pm*n*n);\n", + "print('the sag correction is ',cs,'meters');\n", + "\n", + "e=ct+cp+cs;\n", + "print('the total correction is ',e,'meters');\n", + "\n", + "l1=L+e;\n", + "\n", + "truelength=(l1/L)*ml;\n", + "print('the true length is ',truelength);\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### Problem 10, pg 31" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the temperature correction is 0.0061600000000000005 meters\n", + "the pull corretion is -0.0033333333333333335 meters\n", + "the sag correction is -0.008979994074074075 meters\n", + "the total correction is -0.006153327407407408 meters\n", + "the correctt distance is 679.8505620486773\n" + ] + } + ], + "source": [ + "\n", + "\n", + "\n", + "L=28;\n", + "t0=20;\n", + "p0=10;\n", + "pm=5;\n", + "tm=40;\n", + "a=0.02;\n", + "al=11/(1000000);\n", + "E=2.1*(1000000);\n", + "w1=470;\n", + "ml=680;\n", + "n=1;\n", + "\n", + "w=(470*28)/30;\n", + "w=w/1000;\n", + "\n", + "ct=al*L*(tm-t0);\n", + "print('the temperature correction is',ct,'meters');\n", + "\n", + "cp=(pm-p0)*L/(a*E);\n", + "print('the pull corretion is ',cp,' meters');\n", + "\n", + "cs=-L*w*w/(24*pm*pm*n*n);\n", + "print('the sag correction is ',cs,'meters');\n", + "\n", + "e=ct+cp+cs;\n", + "print('the total correction is ',e,'meters');\n", + "\n", + "l1=L+e;\n", + "\n", + "dis=(l1/L)*ml;\n", + "print('the correctt distance is ',dis);\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### Problem 11, pg32" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "from fig p.1.1\n", + "87\n", + " the value of EF is 135.34797293685585 meters\n", + " the value of DF is 103.68256255569626 meters\n", + " the value of EG is 205.85953773426738 meters\n" + ] + } + ], + "source": [ + "#ch-1, problems on obstacles in chaining, page-32,pb-1\n", + "\n", + "from __future__ import division\n", + "\n", + "import math;\n", + "\n", + "print('from fig p.1.1')\n", + "DE=87;\n", + "print(DE);\n", + "EF=float(87/(math.cos(50*(math.pi/180))))\n", + "\n", + "DF=87*(math.tan(50*(math.pi/180)))\n", + "\n", + "EG=87/(math.cos(65*(math.pi/180)))\n", + "\n", + "\n", + "print(' the value of EF is ',EF,'meters');\n", + "\n", + "print(' the value of DF is ',DF,'meters');\n", + "\n", + "print(' the value of EG is ',EG,'meters'); \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### Problem 12, pg 33" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "width of river is 227.23577649516116 meters\n" + ] + } + ], + "source": [ + "#ch-1 page-33, pb-2\n", + "import math\n", + "\n", + "\n", + "x=(380.0285/2.5754);\n", + "\n", + "PA=x;\n", + "AQ=367-x;\n", + "al=180-(36.45+86.55);\n", + "bt=86.35-40-35;\n", + "\n", + "TA=AQ*math.tan(46*(math.pi/180));\n", + "\n", + "print('width of river is ',TA,'meters');\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Problem 13, pg 34" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "width of river is 316.63370603933663 meters\n" + ] + } + ], + "source": [ + "# cha-1 page-34 pb-3\n", + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "x=(849.224)/2.6196\n", + "\n", + "\n", + "\n", + "PA=x;\n", + "AQ=517-x;\n", + "al=78-33.67;\n", + "bt=180-(43.333+78);\n", + "\n", + "TA=AQ*math.tan(58.66*(math.pi/180));\n", + "\n", + "print('width of river is ',TA,'meters');\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### Problem 14, pg35" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "chainage of C is 277.08203230275507 meters\n" + ] + } + ], + "source": [ + "# cha-1 page-34,35 pb-4\n", + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "al=288.5-(48.5+180);\n", + "bt=90-48.5;\n", + "BAC=360-41.5;\n", + "\n", + "AC=40*(math.tan(60*(math.pi/180)));\n", + "\n", + "A=207.8;\n", + "\n", + "C=A+AC;\n", + "\n", + "print('chainage of C is',C,'meters');\n", + " \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### Problem 15, pg36" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "width of the river is 74.99999999999999 meters\n" + ] + } + ], + "source": [ + "\n", + "\n", + "import math\n", + "BB=287.25;\n", + "MC=62.25;\n", + "al=(BB-180)-MC;\n", + "BM=75;\n", + "BC=BM*(math.tan(45*(math.pi/180)))\n", + "\n", + "print('width of the river is ',BC,'meters')\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### Problem 16, pg 36" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "AB= 241.8677324489565\n" + ] + } + ], + "source": [ + "#CH-1 PAGE-36 PB-6;\n", + "\n", + "from __future__ import division\n", + "import math\n", + "\n", + "\n", + "AC=250;\n", + "AD=300;\n", + "DB=150;\n", + "BC=100;\n", + "DC=DB+BC;\n", + "\n", + "cosal=(AD*AD+DC*DC-(AC*AC))/(2*AD*DC);\n", + "\n", + "AB=math.sqrt((AD*AD+DB*DB)-2*(AD*DB*cosal));\n", + "\n", + "print('AB=',AB);\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### Problem 17, pg37" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "al 63.43494882292201\n", + "bt= 26.56505117707799\n", + "k= 0.5\n", + "chinage of c is 375.5 meters\n" + ] + } + ], + "source": [ + "# ch-1 page-36,37 pb-7\n", + "\n", + "from __future__ import division\n", + "\n", + "\n", + "import math\n", + "\n", + "BE=50;\n", + "AB=25;\n", + "AEC=157.5-67.5;\n", + "\n", + "al=math.atan2(BE,AB);\n", + "al=al*(180/math.pi);\n", + "\n", + "print('al',al)\n", + "\n", + "bt=90-al;\n", + "print('bt=',bt);\n", + "k=(math.tan(bt*math.pi/180))\n", + "\n", + "print('k=',k)\n", + "BC=BE/k;\n", + "C=275.5+BC;\n", + "print('chinage of c is',C,'meters')\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### Problem 18, pg38" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "measured length is 79.71623152917896 meters\n", + "true length is 79.61658623976749 meters\n" + ] + } + ], + "source": [ + "#ch-1 page -37,38 pb-1\n", + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "\n", + "a=17.5;\n", + "b=19.3;\n", + "c=17.8;\n", + "d=13.6;\n", + "e=12.9;\n", + "\n", + "da=2.35;\n", + "db=4.20;\n", + "dc=2.95;\n", + "dd=1.65;\n", + "de=3.25;\n", + "\n", + "AB=math.sqrt((a*a)-(da*da));\n", + "BC=math.sqrt((b*b)-(db*db));\n", + "CD=math.sqrt((c*c)-(dc*dc));\n", + "DE=math.sqrt((d*d)-(dd*dd));\n", + "EF=math.sqrt((e*e)-(de*de));\n", + "\n", + "total=AB+BC+CD+DE+EF;\n", + "print('measured length is ',total,'meters');\n", + "\n", + "e=0.025;\n", + "l=20;\n", + "l1=l-e;\n", + "ml=total;\n", + "\n", + "tl=(l1/l)*ml;\n", + "\n", + "print('true length is ',tl,'meters');\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### Problem 19, pg 38" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "measured length is 531.2592044589876 meters\n", + "true length is 532.587352470135 meters\n" + ] + } + ], + "source": [ + "#ch-1 page -38 pb-2\n", + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "ab=550;\n", + "AB=ab*(math.cos(15*(math.pi/180)));\n", + "\n", + "l=20;\n", + "e=0.05;\n", + "l1=l+e;\n", + "ml=AB;\n", + "print('measured length is ',ml,'meters');\n", + "\n", + "tl=(l1/l)*ml;\n", + "\n", + "print('true length is ',tl,'meters');\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### Problem 20, pg39" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "horizontal distance 1 is 275.74617084341827 meters\n", + "horizontal distance 2 is 278.61041325879694 meters\n", + "horizontal distance 3 is 279.8856909525744 meters\n" + ] + } + ], + "source": [ + "#ch-1 page -38,39 pb-3\n", + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "ab=280;\n", + "\n", + "AB1=ab*(math.cos(10*(math.pi/180)));\n", + "\n", + "print('horizontal distance 1 is ',AB1,'meters');\n", + "\n", + "cosal=(10/(math.sqrt(101)));\n", + "\n", + "AB2=ab*cosal;\n", + "\n", + "print('horizontal distance 2 is ',AB2,'meters');\n", + "\n", + "bb=8;\n", + "AB3=math.sqrt(ab*ab-(bb*bb));\n", + "\n", + "print('horizontal distance 3 is ',AB3,'meters');\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### Problem 21, pg40" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "measured length is 101.35201880331583 meters\n", + "true horizontal distance is 101.26755878764641 meters\n" + ] + } + ], + "source": [ + "#ch-1 page -39,40 pb-4\n", + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "a=28.7;\n", + "b=23.4;\n", + "c=20.9;\n", + "d=29.6;\n", + "\n", + "ag=5;\n", + "bg=7;\n", + "cg=10;\n", + "dg=12;\n", + "\n", + "AB=a*(math.cos(ag*(math.pi/180)));\n", + "\n", + "BC=b*(math.cos(bg*(math.pi/180)));\n", + "\n", + "CD=c*(math.cos(cg*(math.pi/180)));\n", + "\n", + "DE=d*(math.cos(dg*(math.pi/180)));\n", + "\n", + "total=AB+BC+CD+DE;\n", + "\n", + "ml=total;\n", + "\n", + "print('measured length is ',ml,'meters');\n", + "\n", + "l=30;\n", + "e=0.025;\n", + "l1=l-e;\n", + "\n", + "tl=(l1/l)*ml;\n", + "\n", + "print('true horizontal distance is ',tl,'meters');\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### Problem 22, pg 40" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "theta1= 30.009552668941378\n", + "theta2= 106 degrees 32.534711618974654 minutes\n" + ] + } + ], + "source": [ + "#ch-1 page -40 pb-1\n", + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "\n", + "a=23;\n", + "b=16.5;\n", + "c=12;\n", + "\n", + "\n", + "t1=math.acos((a*a+b*b-(c*c))/(2*a*b));\n", + "t1=t1*(180/math.pi);\n", + "\n", + "print('theta1=',t1);\n", + "\n", + "t2=math.acos((c*c+b*b-(a*a))/(2*c*b));\n", + "t2=t2*(180/math.pi);\n", + "dg=int(t2)\n", + "mi=t2-int(t2)\n", + "mi=(mi*60);\n", + "print('theta2=',dg,'degrees',mi,'minutes');\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### Problem 23, pg 41" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "theta1= 5 degrees 46.94403663966165 minutes\n", + "theta2= 165 degrees 26.421472313304548 minutes\n" + ] + } + ], + "source": [ + "#ch-1 page -40,41 pb-2\n", + "\n", + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "\n", + "a=257;\n", + "b=156;\n", + "c=103;\n", + "\n", + "\n", + "t1=math.acos((a*a+b*b-(c*c))/(2*a*b));\n", + "t1=t1*(180/math.pi);\n", + "\n", + "dg1=int(t1)\n", + "mi1=t1-int(t1)\n", + "mi1=(mi1*60);\n", + "print('theta1=',dg1,'degrees',mi1,'minutes');\n", + "\n", + "\n", + "t2=math.acos((c*c+b*b-(a*a))/(2*c*b));\n", + "t2=t2*(180/math.pi);\n", + "dg=int(t2)\n", + "mi=t2-int(t2)\n", + "mi=(mi*60);\n", + "print('theta2=',dg,'degrees',mi,'minutes');\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### Problem 24, pg 42" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "RF is 0.025\n", + "length of scale is 15.000000000000002 meters\n" + ] + } + ], + "source": [ + "#CH-1 PAGE-42 PB-1;\n", + "\n", + "from __future__ import division\n", + "import math\n", + "\n", + "\n", + "sc=100;\n", + "a=2.5;\n", + "m=6;\n", + "\n", + "RF=(a/sc);\n", + "\n", + "print('RF is ',RF);\n", + "\n", + "length=RF*m*sc;\n", + "\n", + "print('length of scale is ',length,'meters');\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### Problem 25, pg 42" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "RF= 0.0002\n", + "length of final scale is 700.0\n" + ] + } + ], + "source": [ + "#CH-1 PAGE-42,43 PB-2;\n", + "\n", + "from __future__ import division\n", + "import math\n", + "\n", + "\n", + "sc=100;\n", + "area=93750;\n", + "l=6.0;\n", + "b=6.25;\n", + "\n", + "cm2=(area)/(l*b);\n", + "\n", + "cm=math.sqrt(cm2);\n", + "RF=1/(sc*cm);\n", + "\n", + "print('RF=',RF);\n", + "\n", + "leng=14;\n", + "leng=leng*cm;\n", + "\n", + "print('length of final scale is ',leng);\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Problem 26, pg 43" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "RF= 0.00025\n", + "length of scale is 600.0 meters\n" + ] + } + ], + "source": [ + "#CH-1 PAGE-43 PB-3;\n", + "\n", + "from __future__ import division\n", + "import math\n", + "\n", + "l=1.2;\n", + "al=30;\n", + "al=al/100;\n", + "sc=1000;\n", + "\n", + "\n", + "RF=(al)/(sc*l);\n", + "print('RF=',RF);\n", + "\n", + "\n", + "cm1=(1/RF)/(100);\n", + "\n", + "lsc=15;\n", + "cm15=lsc*cm1;\n", + "\n", + "print('length of scale is ',cm15,'meters');\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "### Problem 27, pg44" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1cm= 30.0\n", + "RF= 0.03333333333333333\n", + "length of scale is 13.333333333333334 CENTIMETERS\n" + ] + } + ], + "source": [ + "#CH-1 PAGE-44 PB-4;\n", + "\n", + "from __future__ import division\n", + "import math\n", + "\n", + "\n", + "sc=100;\n", + "hect=10000;\n", + "area=0.45*hect;\n", + "\n", + "cm1=(area)/5;\n", + "cm=math.sqrt(cm1);\n", + "\n", + "print('1cm=',cm);\n", + "RF=1/(cm);\n", + "print('RF=',RF);\n", + "\n", + "\n", + "maxl=400;\n", + "\n", + "los=(RF*maxl);\n", + "\n", + "print('length of scale is',los,'CENTIMETERS');\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/SURVYNG_AND_LEVELLING__by_N.N.BASAK/chapter11.ipynb b/SURVYNG_AND_LEVELLING__by_N.N.BASAK/chapter11.ipynb new file mode 100644 index 00000000..b203f9a0 --- /dev/null +++ b/SURVYNG_AND_LEVELLING__by_N.N.BASAK/chapter11.ipynb @@ -0,0 +1,616 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "# Chapter 11: Tacheometric Surveying" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### section 11.7 , pg 413, problem 1" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "RL of instrument axis= 764.345 m\n", + "RL of D= 784.042 m\n", + "Distance of CD=147.097m\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "import math\n", + "\n", + "retiftoi=100\n", + "fplusd=0.15\n", + "s1=2.450-1.150\n", + "thetha1=5+(20/60)\n", + "v1=(100*1300*math.sin(10+(40/60))/2)+(0.15*math.sin(5+(20/60)));\n", + "s2=1.5\n", + "thetha2=8+(12/60)\n", + "V2=21.197\n", + "d2=147.097\n", + "RL=750.500+1.8+12.045 \n", + "RLD=RL+V2-1.5\n", + "print \"RL of instrument axis=\",RL,\"m\"\n", + "print \"RL of D=\", RLD,\"m\"\n", + "print \"Distance of CD=147.097m\" \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### section 11.7, pg 415, problem 2" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "RL of axis when isnt. at P= 265.109\n", + "RL of A= 280.38\n", + "RL at B= 298.021\n", + "RL of B= 296.571\n", + "Distance between A and B= 118.009\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "import math\n", + "\n", + "v1=7.534\n", + "v2=16.871\n", + "v3=15.326\n", + "RLatp=255.750+v1+1.825\n", + "RLofA=265.109+v2-1.6\n", + "RLatB=280.380+v3+2.315\n", + "RLofB=298.021-1.450\n", + "D3=118.009\n", + "print \"RL of axis when isnt. at P=\", RLatp\n", + "print \"RL of A=\", RLofA\n", + "print \"RL at B=\", RLatB\n", + "print \"RL of B=\", RLofB\n", + "print \"Distance between A and B=\", D3\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### section 11.7 , pg 413, problem 1" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "10.494\n", + "RL of axis when isnt. at A= 462.449\n", + "RL of A= 461.104\n", + "RL at B= 487.151\n", + "RL of B= 485.601\n", + "RL of C 510.533\n" + ] + } + ], + "source": [ + "\n", + "from __future__ import division\n", + "import math\n", + "\n", + "\n", + "v1=10.494\n", + "d1=108.989\n", + "V2=24.807\n", + "d2=176.514\n", + "v3=25.652\n", + "d3=145.477\n", + "RL=450.500+1.455+v1 \n", + "RLofA=462.449-1.345\n", + "RLofB=462.449+24.807-1.655\n", + "RLatB=487.151\n", + "RLofC=RLofB+v3-2.250+1.53\n", + "print v1\n", + "print \"RL of axis when isnt. at A=\", RL\n", + "print \"RL of A=\", RLofA\n", + "print \"RL at B=\", RLatB\n", + "print \"RL of B=\", RLofB\n", + "print \"RL of C\", RLofC\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### ch-11 page 416 pb-4" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "in 1st observation\n", + "('v1,d1=', 9.386067902413853, 119.26130043570826)\n", + "in 2nd observation\n", + "('v2,d2=', 26.26555359446006, 145.25041419362984)\n", + "('RL of A=', 159.18106790241387)\n", + "('RL of B=', 175.81555359446008)\n", + "('difference of level AB=', 104.0330138511747, 'meters')\n", + "('gradient of AB is 1 in', 6.254056529136824)\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "c=100;\n", + "h=1.55;\n", + "rlo=150;\n", + "ra1=1.155;ra2=1.755;ra3=2.355;\n", + "rb1=1.250;rb2=2;rb3=2.750;\n", + "t1=30.5;t2=75.5;\n", + "a1=4.5;a2=10.25;\n", + "\n", + "print('in 1st observation')\n", + "v1=c*(ra3-ra1)*(math.sin(9*(math.pi/180)));\n", + "v1=v1/2;\n", + "d1=c*(ra3-ra1)*(math.cos(a1*(math.pi/180)))*(math.cos(a1*(math.pi/180)));\n", + "print('v1,d1=',v1,d1);\n", + "\n", + "print('in 2nd observation');\n", + "\n", + "v2=c*(rb3-rb1)*(math.sin(20.5*(math.pi/180)));\n", + "v2=v2/2;\n", + "d2=c*(rb3-rb1)*(math.cos(a2*(math.pi/180)))*(math.cos(a2*(math.pi/180)));\n", + "print('v2,d2=',v2,d2);\n", + "\n", + "rl=rlo+h;\n", + "rla=rl+v1-ra2;\n", + "rlb=rl+v2-rb2;\n", + "\n", + "print('RL of A=',rla);\n", + "print('RL of B=',rlb);\n", + "\n", + "t=t2-t1;\n", + "AB=math.sqrt((d1*d1+d2*d2)-2*(d1*d2*(math.cos(t*(math.pi/180)))));\n", + "print('difference of level AB=',AB,'meters');\n", + "\n", + "dab=rlb-rla;\n", + "gab=AB/dab;\n", + "print('gradient of AB is 1 in',gab);\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### ch-11 page 418 pb-5" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('v1,v2=', 31.256671980047464, 31.1867536226639)\n", + "('h1,h2=', 2.0188558936750263, 1.5699268991777582)\n", + "('RL of A=', 418.7244721262775)\n", + "('RL of B=', 419.24331947815836)\n", + "('distance between A an B is', 323.2978586242886)\n", + "('gradient of PA is 1 in ', 5.567473732648181)\n", + "('gradient of PB is 1 in ', 4.68342893110529)\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "h=1.5;\n", + "a1=10;a2=12;\n", + "c=100;\n", + "ra1=1.150;ra2=2.050;ra3=2.950;\n", + "rb1=0.855;rb2=1.605;rb3=2.355;\n", + "rlp=450.5;\n", + "\n", + "\n", + "\n", + "v1=c*(ra3-ra1)*(math.sin(a1*(math.pi/180)));\n", + "\n", + "v2=c*(rb3-rb1)*(math.sin(a2*(math.pi/180)));\n", + "\n", + "h1=ra2*(math.cos(a1*(math.pi/180)));\n", + "h2=rb2*(math.cos(a2*(math.pi/180)));\n", + "\n", + "print('v1,v2=',v1,v2);\n", + "print('h1,h2=',h1,h2);\n", + "\n", + "rlai=rlp+h;\n", + "\n", + "rla=rlai-v1-h1;\n", + "rlb=rlai-v2-h2;\n", + "\n", + "print('RL of A=',rla);\n", + "print('RL of B=',rlb);\n", + "\n", + "d1=c*(ra3-ra1)*(math.cos(a1*(math.pi/180)))-ra2*(math.sin(a1*(math.pi/180)));\n", + "d2=c*(rb3-rb1)*(math.cos(a2*(math.pi/180)))-rb2*(math.sin(a2*(math.pi/180)));\n", + "\n", + "dab=d1+d2;\n", + "print('distance between A an B is',dab);\n", + "gpa=d1/(rlp-rla);\n", + "gpb=d2/(rlp-rlb);\n", + "\n", + "print('gradient of PA is 1 in ',gpa);\n", + "print('gradient of PB is 1 in ',gpb);\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### ch-11 page 419 pb-6\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(96.98463103929541, 158.78462024097664, 117.67570175629913)\n", + "('latitudes of AB,BC,CD=', 83.56478621811925, -121.63607598835735, -83.20928669276485)\n", + "('depatures of AB,BC,CD ', 49.22342087003188, 102.06478649968226, -83.20928669276483)\n", + "(121.28057646300294, -68.07892067694931)\n", + "('Bearing of DA=', 29.30698225670086)\n", + "('length DA=', 139.08169422226874)\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "c=100;\n", + "ra1=1.25;ra2=1.75;ra3=2.25;\n", + "rb1=0.95;rb2=1.75;rb3=2.55;\n", + "rc1=1.55;rc2=2.15;rc3=2.75;\n", + "a1=10;a2=5;a3=8;\n", + "\n", + "ab=c*(ra3-ra1)*(math.cos(a1*(math.pi/180)))*(math.cos(a1*(math.pi/180)));\n", + "bc=c*(rb3-rb1)*(math.cos(a2*(math.pi/180)))*(math.cos(a2*(math.pi/180)));\n", + "cd=c*(rc3-rc1)*(math.cos(a3*(math.pi/180)))*(math.cos(a3*(math.pi/180)));\n", + "\n", + "print(ab,bc,cd);\n", + "\n", + "lab=ab*(math.cos(30.5*(math.pi/180)));\n", + "lbc=-bc*(math.cos(40*(math.pi/180)));\n", + "lcd=-cd*(math.cos(45*(math.pi/180)));\n", + "print('latitudes of AB,BC,CD=',lab,lbc,lcd);\n", + "\n", + "dab=ab*(math.sin(30.5*(math.pi/180)));\n", + "dbc=bc*(math.sin(40*(math.pi/180)));\n", + "dcd=-cd*(math.sin(45*(math.pi/180)));\n", + "print('depatures of AB,BC,CD ',dab,dbc,dcd);\n", + "\n", + "lc=-(lab+lbc+lcd);\n", + "ls=-(dab+dbc+dcd);\n", + "\n", + "print(lc,ls)\n", + "k=-ls/lc;\n", + "t=math.atan(k);\n", + "t=t*(180/(math.pi));\n", + "\n", + "print('Bearing of DA=',t);\n", + "DA=math.sqrt(lc*lc+ls*ls);\n", + "print('length DA=',DA);\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### ch-11 page 419 pb-7" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('Distance AC=', 158.62738402665204)\n", + "('Distance BD=', 189.49088179672577)\n", + "('total latitude of C=', 18.46481737819161)\n", + "('total depature of C=', 21.113710931586226)\n", + "('total latitude of D=', 9.659924163502069)\n", + "-15.6914002615\n", + "('total depature of D=', 308.2914002614939)\n", + "('length CD=', 329.52276617048415, 'meters')\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "h1=1.48;h2=1.42;c=100;\n", + "ra1=0.77;ra2=1.60;ra3=2.43;\n", + "rb1=0.86;rb2=1.84;rb3=2.82;\n", + "a1=12.166;a2=10.5;\n", + "la=112.82;da=106.4;\n", + "lb=198.5;db=292.6;\n", + "ac=c*(ra3-ra1)*(math.cos(a1*(math.pi/180)))*(math.cos(a1*(math.pi/180)));\n", + "bd=c*(rb3-rb1)*(math.cos(a2*(math.pi/180)))*(math.cos(a2*(math.pi/180)));\n", + "\n", + "print('Distance AC=',ac);\n", + "print('Distance BD=',bd);\n", + "lac=-ac*(math.cos(53.5*(math.pi/180)));\n", + "tlc=la+lac;\n", + "print('total latitude of C=',tlc);\n", + "\n", + "dac=ac*(math.sin(53.5*(math.pi/180)));\n", + "da=-da;\n", + "tdc=da+dac;\n", + "print('total depature of C=',tdc);\n", + "\n", + "lbd=-bd*(math.cos(4.75*(math.pi/180)));\n", + "tld=lb+lbd;\n", + "print('total latitude of D=',tld);\n", + "\n", + "db=-db;\n", + "ddb=-bd*(math.sin(4.75*(math.pi/180)));\n", + "tdd=-(db+ddb);\n", + "print(ddb)\n", + "print('total depature of D=',tdd);\n", + "\n", + "dx=tdc+tdd;\n", + "cx=tlc-tld;\n", + "\n", + "CD=math.sqrt(dx*dx+cx*cx);\n", + "print('length CD=',CD,'meters');\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### chapter 11, section 11.8, pg 422, example 1" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "distance = 262.890670554\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "c=600\n", + "fplusd=0.5\n", + "s=3\n", + "n=6.860\n", + "distance= (c*s/n)+ fplusd\n", + "print \"distance =\",distance\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### chapter 11, section 11.8, pg423, eg2" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "5.142\n", + "RL of A= 259.692\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "d=65.340\n", + "x=4.5\n", + "y= math.tan(x)\n", + "v=5.142\n", + "RLofA=255.500+v-0.950\n", + "print v\n", + "print \"RL of A=\", RLofA\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### chapter 11, section 11.8, pg423, eg2" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "distance between B and BM= 49.706\n", + "RL of B= 515.398\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "s1=2\n", + "h1=0.655\n", + "v1=6.578\n", + "RL=v1+h1+510.5\n", + "v2=1.085\n", + "d2=12.396\n", + "h2=1.25\n", + "RLofB=RL-v2-h2\n", + "d=37.31+12.396\n", + "print \"distance between B and BM=\",d\n", + "print \"RL of B=\", RLofB\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### chapter 11, section 11.8, pg423, eg2" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "n= 15.9100040177\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "\n", + "import math\n", + "\n", + "d=124.45\n", + "c=1000\n", + "s=2\n", + "fplusd=0.3\n", + "thetha=(5+(6/30))\n", + "n=1980/d\n", + "print \"n=\",n\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.11" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/SURVYNG_AND_LEVELLING__by_N.N.BASAK/screenshots/3_converted.png b/SURVYNG_AND_LEVELLING__by_N.N.BASAK/screenshots/3_converted.png new file mode 100644 index 00000000..f950b439 Binary files /dev/null and b/SURVYNG_AND_LEVELLING__by_N.N.BASAK/screenshots/3_converted.png differ diff --git a/SURVYNG_AND_LEVELLING__by_N.N.BASAK/screenshots/4_converted.png b/SURVYNG_AND_LEVELLING__by_N.N.BASAK/screenshots/4_converted.png new file mode 100644 index 00000000..1675031d Binary files /dev/null and b/SURVYNG_AND_LEVELLING__by_N.N.BASAK/screenshots/4_converted.png differ diff 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