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diff --git a/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter4.ipynb b/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter4.ipynb new file mode 100644 index 00000000..cf156252 --- /dev/null +++ b/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter4.ipynb @@ -0,0 +1,447 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:9aca5229d39ed9fee3ce40f1f1dab6ba8b884ebc52bfe9bb1467df97ee1f15bb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 4:Torsion"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.2 page number 183"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#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"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The maximum shear due to torsion is 152.87 Mpa\n",
+ "stress tensor matrix [[ 0. 153. 0.]\n",
+ " [ 153. 0. 0.]\n",
+ " [ 0. 0. 0.]]\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.3 page number 184"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#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"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The maximum shear due to torsion is 43.15 Mpa\n",
+ "The minimum shear due to torsion is 34.52 Mpa\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4 page number 187"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#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"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Diameter of the shaft used is 15.26 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.5 page number 188"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#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"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Diameter of the shaft1 is 6.87 mm\n",
+ "The Diameter of the shaft2 is 0.702590481015 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.7 page number 193"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#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 \" "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The maximum angle rotated is 0.0232628450106 radians \n"
+ ]
+ }
+ ],
+ "prompt_number": 37
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.9 Pagenumber 196"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#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"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "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"
+ ]
+ }
+ ],
+ "prompt_number": 39
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.12 Pagenumber 202"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#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"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The allowable torsion on the 8 bolt combination 27129600.0 N-m\n"
+ ]
+ }
+ ],
+ "prompt_number": 49
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.15 page number 211"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#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"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "the Equivalent Torsion constant is 1.97 in4\n"
+ ]
+ }
+ ],
+ "prompt_number": 57
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.16 page number 214"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#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\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The maximum shear due to torsion is 345.23 Mpa\n",
+ "The minimum shear due to torsion is 276.18 Mpa\n"
+ ]
+ }
+ ],
+ "prompt_number": 58
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |