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diff --git a/Mechanics_of_Structures/Chapter12.ipynb b/Mechanics_of_Structures/Chapter12.ipynb new file mode 100755 index 00000000..794c3e4e --- /dev/null +++ b/Mechanics_of_Structures/Chapter12.ipynb @@ -0,0 +1,850 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:f6a5fb5a9bb50976164cfcdf430ee1b396b67dbf2ffbf7763fc02510b90290d3"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "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": {}
+ }
+ ]
+}
\ No newline at end of file |