path: root/Mechanics_of_Structures_by_S._B._Junnarkar/Chapter12.ipynb

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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter12-Shafts and springs in torsion"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex1-pg450"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate The maximum intensity of shear stress induced and The angle of twist in degree\n",
      "d = 3.;##inches\n",
      "HP = 120.;##horse power\n",
      "RPM = 180.;\n",
      "l = 25.;##feet\n",
      "N = 12.*10**6.;## lb/in**2\n",
      "T = 33000.*HP/(2.*math.pi*RPM);##  lb-feet\n",
      "f_s = 16*T*12/(math.pi*d**3.);## lb/in**2\n",
      "theta = f_s*l*12./(0.5*d*N);## radian\n",
      "print'%s %.d %s'%('The maximum intensity of shear stress induced is f_s =',f_s,' lb/in**2');\n",
      "print'%s %.2f %s'%('The angle of twist in degrees is theta = ',theta*180/math.pi,'');\n",
      "\n",
      "##there is a minute error in the answer given in textbook.\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The maximum intensity of shear stress induced is f_s = 7925  lb/in**2\n",
        "The angle of twist in degrees is theta =  7.57 \n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex2-pg451"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate H.P transmitted is\n",
      "D = 2.;## inches\n",
      "N = 150.;## RPM\n",
      "f_s = 9000.;## lb/in^2\n",
      "M_r = f_s*(math.pi/16.)*D**3.;## lb-inches\n",
      "HP = M_r*2.*math.pi*N/(12.*33000.);##\n",
      "print'%s %.2f %s'%('H.P transmitted is',HP,'');\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "H.P transmitted is 33.65 \n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex3-pg451"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate Suitable diameter \n",
      "HP = 80.;\n",
      "N = 200.;## RPM\n",
      "m = 30/100.;\n",
      "f = 12000.;## lb/in^2\n",
      "T = HP*33000./(2.*math.pi*N);## lb-feet\n",
      "T_max = (1+m)*T;## lb-feet\n",
      "D = (T_max*12.*16./(math.pi*f))**(1/3.);## inches\n",
      "print'%s %.3f %s'%('Suitable diameter is D =',D,'inches');\n",
      "\n",
      "##the answer is approximated in the textbook.\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Suitable diameter is D = 2.405 inches\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex4-pg451"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#check whether it is satisfactory or not for given st A shaft',round(D),'inches external diameter and',round(d),' inches internal diameter\n",
      "HP = 750.;\n",
      "N = 90.;## RPM\n",
      "m = 40/100.;\n",
      "f = 12000.;## lb/in^2\n",
      "t = 1.;## inch\n",
      "T = HP*33000./(2.*math.pi*N);## lb-inches\n",
      "T_max = (1.+m)*T;## lb-inches\n",
      "##On solving (4*t)D^3 - (6*t^2)D^2 +(4*t^3 -(16*M/f*%pi))D -t^4 = 0, we get D\n",
      "D = 7.6;##inches\n",
      "d = D - 2.;##inches\n",
      "print'%s %.d %s %d %s '%('A shaft',round(D),'inches external diameter and',round(d),' inches internal diameter will be satisfactory.');\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "A shaft 8 inches external diameter and 6  inches internal diameter will be satisfactory. \n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex5-pg452"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate'D = ',round(D1),' inches will be suitable for the shaft\n",
      "RPM = 180.;## RPM\n",
      "HP = 130.;\n",
      "f = 9000.;## lb/in^2\n",
      "alpha = 1.;##degree\n",
      "l = 10.;## feet\n",
      "N = 6000.;## tons/in^2\n",
      "T = 33000.*HP/(2*math.pi*RPM);## lb-feet\n",
      "D1 = (16*T*12/(f*math.pi))**(1/3);## inches\n",
      "D2 = (T*12*l*12*32*alpha*180/(math.pi*N*math.pi*2240.))**(1/4.);## inches\n",
      "if D1 > D2 :\n",
      "    print'%s %.d %s'%('D = ',round(D1),' inches will be suitable for the shaft');\n",
      "else:\n",
      "    print'%s %.d %s'%('D =',round(D2),'inches will be suitable for the shaft');\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "D = 4 inches will be suitable for the shaft\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex6-pg453"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate 'The saving in weight per foot run and percentage saving\n",
      "HP = 3000.;\n",
      "RPM = 60.;\n",
      "f = 12000.;##lb/in^2\n",
      "rho = 480.;##lb. per sq. foot\n",
      "k = 3./4.;## k = d/D \n",
      "T = HP*33000.*12./(2.*math.pi*RPM);## lb-inches\n",
      "D1 = (T*16/(f*math.pi))**(1/3.);##inches\n",
      "D2 = (T/((1.+k**2.)*(1.-k**2.)*math.pi*f/16.))**(1/3.);##inches\n",
      "d = k*D2;## inches\n",
      "w1 = 0.25*math.pi*D1**2 *rho/144. ;## lb-wt\n",
      "w2 = 0.25*math.pi*(D2+d)*(D2-d)*rho/144. ;## lb-wt\n",
      "w = w1-w2;## lb-wt\n",
      "n = (w/w1)*100.;\n",
      "print'%s %.d %s'%('The saving in weight per foot run is w =',w,' lb-wt');\n",
      "print'%s %.2f %s'%('Percentage saving is ',n,'');\n",
      "\n",
      "##there is a minute error in the answer given in textbook.\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The saving in weight per foot run is w = 138  lb-wt\n",
        "Percentage saving is  43.62 \n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex7-pg454"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate T1 and T2 \n",
      "l1 = 3.;## feet\n",
      "d1 = 1.;## feet\n",
      "l2 = 9.;## feet\n",
      "M = 200.;## lb-wt\n",
      "l = 9.;## inches\n",
      "N = 12.*10**6;## lb/in^2\n",
      "k = l2/l1;\n",
      "T1 = M/(1.+k);## lb-feet\n",
      "T2 = k*T1;## lb-feet\n",
      "f_s = T2*12./(math.pi/16.);## lb/in^2\n",
      "theta = f_s*l/(0.5*d1*N);## radians\n",
      "print'%s %.d %s %.d %s '%('T1 =',T1,'lb-feet, T2 = ',T2,' lb-feet');\n",
      "print'%s %.d %s'%('f_s = ',f_s,' lb/in^2');\n",
      "print'%s %.4f %s %.3f %s'%(' theta = ',theta,' radian ,  theta    = ',theta*180/math.pi,' degrees');\n",
      "##there is a minute error in the answer given in twxtbook\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "T1 = 50 lb-feet, T2 =  150  lb-feet \n",
        "f_s =  9167  lb/in^2\n",
        " theta =  0.0138  radian ,  theta    =  0.788  degrees\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex8-pg456"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate forces \n",
      "D = 5.;## inches\n",
      "HP = 120.;\n",
      "RPM = 150.;\n",
      "b = 5.;## inches\n",
      "h = 1.;##inch\n",
      "n = 6.;## no. of bolts\n",
      "d = 3/4.;## inches\n",
      "T = HP*33000.*12./(2.*math.pi*RPM);## lb-inches\n",
      "f_s = T*16./(math.pi*27.);\n",
      "f_k = T/(b*h*2.*d);\n",
      "f_b = T/(n*0.25*math.pi*d**2 * b);## lb-inches\n",
      "print'%s %.d %s %d %s %d %s'%('f_s =',f_s,'lb/in^2, f_k =',f_k,'lb/in^2, f_b =',f_b,' lb/in^2');\n",
      "\n",
      "##there are errors given in the answers given in the textbook\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "f_s = 9510 lb/in^2, f_k = 6722 lb/in^2, f_b = 3804  lb/in^2\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex9-pg460"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate 'Maximum strain  energys\n",
      "d = 4.;##inches\n",
      "T = 30.;## ton-inches\n",
      "M = 20.;##ton-inches\n",
      "m = 1/0.3;\n",
      "f_s = 16.*T/(math.pi*d**3);## tons/in^2\n",
      "f_b = 32*M/(math.pi*d**3);## tons/in^2\n",
      "theta = 0.5*math.atan(T/M);## radians\n",
      "theta1 = theta*180./math.pi;\n",
      "theta2 = theta1+90.;\n",
      "f1 = 0.5*f_b + math.sqrt(f_s**2 + 0.25*f_b**2);## tons/in^2\n",
      "f2 = 0.5*f_b - math.sqrt(f_s**2 + 0.25*f_b**2);## tons/in^2\n",
      "Ee = f1 - (f2/m);## tons/in^2\n",
      "f = math.sqrt(f1**2 + f2**2 - 2*f1*f2/m);## tons/in^2\n",
      "print'%s %.3f %s'%('Maximum strain is Ee = ',Ee,' tons/in^2');\n",
      "print'%s %.3f %s'%(' Maximum strain energy is f = ',f,' tons/in^2');\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Maximum strain is Ee =  4.844  tons/in^2\n",
        " Maximum strain energy is f =  4.995  tons/in^2\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex10-pg461"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate diameter of the shaft in all  different cases\n",
      "HP = 80.;\n",
      "RPM = 120.;\n",
      "b = 10.;## feet\n",
      "h = 3.;## feet\n",
      "F = 8000.;## lb-wt\n",
      "m = 4.;\n",
      "T = HP*33000.*12./(2.*math.pi*RPM*2240.);## ton-inches\n",
      "M = F*h*(b-h)*12./(b*2240.);## ton-inches\n",
      "##(i) The major principal stress f1 is given by\n",
      "f1 = 6;## tons/in^2\n",
      "d1 = ((M+math.sqrt(M**2 + T**2))*16/(math.pi*f1))**(1/3.);## inches\n",
      "\n",
      "##(ii) If f_s_dash is the maximum intensity of shear stress\n",
      "f_s_dash = 3;## tons/in^2\n",
      "d2 = (math.sqrt(M**2 + T**2) * 16./(math.pi*f_s_dash))**(1/3.);## inches\n",
      "\n",
      "##(iii) If e is the major principal strain\n",
      "Ee = 6.;## tons/in^2\n",
      "d3 = (((1.-(1./m))*M + (1.+(1./m))*math.sqrt(M**2 + T**2))*16./(math.pi*Ee))**(1/3.);## inches\n",
      "\n",
      "##(iv) If f is the direct stress which, acting alone will produce the same maximum strain energy \n",
      "f = 6.;## tons/in^2\n",
      "d4 = ((math.sqrt(4*M**2 + 2.*(m+1.)*(T**2)/m))*16./(math.pi*f))**(1/3.);## inches\n",
      "print'%s %.3f %s %.3f %s %.3f %s %.3f %s'%('The diameter of the shaft in different cases will be, (i) d = ',d1,' inches,(ii) d = ',d2,' inches  , (iii) d = ',d3,' inches  ,(iv) d = ',d4,'inches');\n",
      "##there are round-off errors in the answers given in textbook.\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The diameter of the shaft in different cases will be, (i) d =  5.365  inches,(ii) d =  5.384  inches  , (iii) d =  5.370  inches  ,(iv) d =  5.370 inches\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex11-pg463"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate The maximum principal stress and The maximum shear intensity and maximum strain\n",
      "D = 12.;## inches\n",
      "d = 6.;## inches\n",
      "HP = 2400.;\n",
      "RPM = 80.;\n",
      "M = 40.;## ton-feet\n",
      "P = 25.;## tons\n",
      "PR = 0.3;##poisson's ratio\n",
      "A = 0.25*math.pi*(D**2 - d**2);## in**2\n",
      "Z = (math.pi/32)*(D**4 - d**4)/D;## in**3\n",
      "J = (math.pi/16)*(D**4 - d**4)/D;## in**3\n",
      "p_0 = P/A ;## ton/in**2\n",
      "p_b = M*12/Z ;## tons/in**2\n",
      "f_b = p_0 + p_b;##tons/in**2\n",
      "f_s = HP*33000*12/(2*math.pi*RPM*2240*J);## tons/in**2\n",
      "theta = 0.5*math.atan(2*f_s/f_b);## radians\n",
      "theta1 = theta*180/math.pi;## degrees\n",
      "theta2 = theta1+90;##degrees\n",
      "f_1 = 0.5*f_b + math.sqrt(f_s**2 + 0.25*f_b**2);##tons/in**2\n",
      "f_2 = 0.5*f_b - math.sqrt(f_s**2 + 0.25*f_b**2);##tons/in**2\n",
      "f = math.sqrt(0.25*f_b**2 + f_s**2);## tons/in**2\n",
      "Ee = f_1 - PR*f_2;## tons/in**2\n",
      "print'%s %.2f  %s %.2f %s'%('The maximum principal stresse are f_1 = ',f_1,' tons/in**2.,compressive ,  f_2 = ',-f_2,' tons/in**2., tensile');\n",
      "print'%s %.1f %s %.1f %s'%('theta1 = ',theta1,' degrees,theta2 =',theta2,'degrees');\n",
      "print'%s %.1f %s '%(' The maximum shear intensity = ',f,'tons/in**2');\n",
      "print'%s %.3f %s'%(' Maximum strain is, Ee =',Ee,'tons/in**2');\n",
      "\n",
      "##there are minute errors in the answers given in textbook.\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The maximum principal stresse are f_1 =  4.78   tons/in**2.,compressive ,  f_2 =  1.47  tons/in**2., tensile\n",
        "theta1 =  29.0  degrees,theta2 = 119.0 degrees\n",
        " The maximum shear intensity =  3.1 tons/in**2 \n",
        " Maximum strain is, Ee = 5.226 tons/in**2\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex12-pg466"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate 'The size of the shaft and angle of the twist in the shaft for a length \n",
      "RPM = 180.;\n",
      "P = 10.;## tons\n",
      "v = 25.;## feet per minute\n",
      "n = 64/100.;## efficiency of the crane\n",
      "f = 5500.;## lb/in^2\n",
      "l = 10.;## feet\n",
      "N = 12*10**6.;## lb/in^2\n",
      "W = P*v*2240./n;## ft-lbs\n",
      "T = W*12./(2.*math.pi*RPM);## lb-inches\n",
      "s = (T/(0.208*f))**(1/3.);## inches\n",
      "theta = 7.11*T*l*12.*180./(math.pi*N*s**4.);## degrees\n",
      "print'%s %.3f %s'%('The size of the shaft is s = ',s,' inches');\n",
      "print'%s %.1f %s %.2f %s'%('The angle of the twist in the shaft for a length of ',l,' feet, theta =',theta,' degrees');\n",
      "##there is a round-off error in the answer given in textbook.\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The size of the shaft is s =  2.010  inches\n",
        "The angle of the twist in the shaft for a length of  10.0  feet, theta = 2.32  degrees\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex13-pg469"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate Shear stress induced  and  Shear stress induced  and  Energy stored\n",
      "d = 3/8.;## inches\n",
      "n = 12.;##no. of complete turns\n",
      "D = 4.;## inches\n",
      "W = 50.;## lb-wt\n",
      "N = 12*10**6;## lb/in^2\n",
      "T = W*0.5*D;## lb-inches\n",
      "f_s = T*16./(math.pi*d*83);##lb/in^2\n",
      "delta = 64.*W*(D**3 /8.)*n/(N*d**4.);## inches\n",
      "E = 0.5*W*delta;## inch-lbs\n",
      "print'%s %.d %s'%('Shear stress induced is f_s =',f_s,' lb/in^2');\n",
      "print'%s %.3f %s'%(' Deflection under the pull is delta = ',delta,' inches');\n",
      "print'%s %.3f %s'%(' Energy stored = ',E,' lb-inches');\n",
      "\n",
      "##there is a minute error in the answer given in textbook.\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Shear stress induced is f_s = 16  lb/in^2\n",
        " Deflection under the pull is delta =  1.295  inches\n",
        " Energy stored =  32.363  lb-inches\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex14-pg469"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate The number of springs required\n",
      "W = 2.;## tons\n",
      "v = 4.;## miles per hour\n",
      "n = 18.;## no. of coils\n",
      "delta = 9.;## inches\n",
      "N = 6000.;## tons/in^2\n",
      "d = 1.;## inch\n",
      "D = 8.;## inches\n",
      "KE = 12.*(W*(v*44./30.)**2.)/(2.*32.);## inch-tons\n",
      "P = (delta*N*d**4)/(64.*n*(0.5*D)**3);## tons\n",
      "E = 0.5*P*delta;## inch-tons\n",
      "m = KE/E ;## no. of springs required\n",
      "print'%s %.d %s'%('The number of springs required m =',round(m),'');\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The number of springs required m = 4 \n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex15-470"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate height of drop\n",
      "W = 5.;## cwt\n",
      "n = 18.;## no. of coils\n",
      "delta = 9.;## inches\n",
      "d = 1.;## inch\n",
      "D = 8.;## inches\n",
      "N = 6000.;## tons/in^2\n",
      "P = (delta*N*d**4.)/(64.*n*(0.5*D)**3);## tons\n",
      "h = (0.5*P*delta*20./W)-delta;## inches\n",
      "print'%s %.3f %s'%('The height of drop h = ',h,' inches');\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The height of drop h =  4.184  inches\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex16-pg471"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate  Maximum possible axial load and  Deflection, delta\n",
      "s = 1/4.;## inch\n",
      "n = 12.;## no. of coils\n",
      "D = 3.;## inches\n",
      "f_s = 45000.;## lb/in^2\n",
      "N = 12*10**6;## lb/in^2\n",
      "T = 0.208*f_s*s**3;## lb-inches\n",
      "W = T/(0.5*D);## lb-wt\n",
      "theta = 7.11*T*math.pi*D*12./(N*s**4);##rdaians\n",
      "delta = 0.5*D*theta;## inches\n",
      "print'%s %.1f %s'%('Maximum possible axial load is W = ',W,' lb-wt');\n",
      "print'%s %.3f %s'%(' Deflection, delta = ',delta,' inches');\n",
      "\n",
      "##there is a minute error in the answer given in textbook.\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Maximum possible axial load is W =  97.5  lb-wt\n",
        " Deflection, delta =  3.763  inches\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex17-pg472"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate The bending stresses\n",
      "d = 3/8.;## inches\n",
      "n = 12.;##no. of complete turns\n",
      "D = 4.;## inches\n",
      "W = 50.;## lb-wt\n",
      "N = 12.*10**6;## lb/in^2\n",
      "E = 30.*10**6;## lb/in^2\n",
      "M = 75.;## lb-inches\n",
      "I = (math.pi/64.)*d**4;## in^4\n",
      "Z = 2.*I/d;## in^3\n",
      "f = M/Z ;## lb/in^2\n",
      "phi = M*math.pi*D*12./(E*I);## radians\n",
      "n_ = (phi/(2*math.pi)) + n;## increase in no. of turns\n",
      "print'%s %.d %s'%('The bending stress is f = ',f,' lb/in^2');\n",
      "print'%s %.3f %s'%(' n_new = ',n_,' turns');\n",
      "\n",
      "##there are minute errors in the answers given in textbook.\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The bending stress is f =  14486  lb/in^2\n",
        " n_new =  12.062  turns\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex18-pg476"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate The maximum intensity of shear stress and 'Deflection\n",
      "d = 3/8.;## inches\n",
      "n = 12.;##no. of complete turns\n",
      "D = 4.;## inches\n",
      "W = 50.;## lb-wt\n",
      "N = 12.*10**6.;## lb/in^2\n",
      "alpha = 15*math.pi/180.;## degrees\n",
      "E = 30.*10**6.;## lb/in^2\n",
      "T = W*0.5*D*math.cos(alpha);## lb-inches\n",
      "M = W*0.5*D*math.sin(alpha);## lb-inches\n",
      "J = math.pi*d**4 /32.;## in^4\n",
      "I = math.pi*d**4 /64.;## in^4\n",
      "delta = 64.*W*((D/2.)**3.)*n/math.cos(alpha)*((math.cos(alpha)**2.)/N + (2.*math.sin(alpha)**2.)/E)/d**4. ;## inches\n",
      "f = 32.*W*0.5*D*math.sin(alpha)/(math.pi*d**3) ;## lb/in^2\n",
      "f_s = T*16./(math.pi*d**3);## lb/in^2\n",
      "f_1 = 0.5*f + math.sqrt(f_s**2. + 0.25*f**2.);## lb/in^2\n",
      "f_2 = 0.5*f - math.sqrt(f_s**2. + 0.25*f**2.);## lb/in^2\n",
      "f_s_dash = math.sqrt(f_s**2. + 0.25*f**2.);## lb/in^2\n",
      "print'%s %.3f %s'%('Deflection, delta = ',delta,' inches');\n",
      "print'%s %.d %s %.d %s'%(' f = ',f,' lb/in^2, f_s = ',f_s,' lb/in^2');\n",
      "print'%s %.d %s'%('The maximum intensity of shear stress =',f_s_dash,' lb/in^2');\n",
      "\n",
      "##there are calculation errors in the answers given in textbook\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Deflection, delta =  1.322  inches\n",
        " f =  4999  lb/in^2, f_s =  9328  lb/in^2\n",
        "The maximum intensity of shear stress = 9657  lb/in^2\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex19-pg477"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate 'Angle of rotation and 'Angle of rotation\n",
      "d = 3/8.;## inches\n",
      "n = 12.;##no. of complete turns\n",
      "D = 4.;## inches\n",
      "M = 75.;## lb-inches\n",
      "N = 12.*10**6.;## lb/in**2\n",
      "alpha = 15*math.pi/180.;## degrees\n",
      "E = 30.*10.**6.;## lb/in**2\n",
      "phi_dash = (64./d**4.)*M*0.5*D*n/math.cos(alpha)*((2.*(math.cos(alpha))**2.)/E + ((math.sin(alpha))**2)/N);## radians\n",
      "DELTA = 64.*M*((0.5*D)**2.)*n*math.sin(alpha)*((1./N) - (2./E))/d**4.;## inches\n",
      "print'%s %.2f %s %.3f %s'%('Angle of rotation phi_dash = ',phi_dash,' radians or ',phi_dash*180/math.pi,' degrees');\n",
      "print'%s %.4f %s '%(' The axial deflection = ',DELTA,' inches');\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Angle of rotation phi_dash =  0.41  radians or  23.422  degrees\n",
        " The axial deflection =  0.0503  inches \n"
       ]
      }
     ],
     "prompt_number": 15
    }
   ],
   "metadata": {}
  }
 ]
}