From c7fe425ef3c5e8804f2f5de3d8fffedf5e2f1131 Mon Sep 17 00:00:00 2001 From: hardythe1 Date: Tue, 7 Apr 2015 15:58:05 +0530 Subject: added books --- Mechanics_of_Structures/Chapter6.ipynb | 491 +++++++++++++++++++++++++++++++++ 1 file changed, 491 insertions(+) create mode 100755 Mechanics_of_Structures/Chapter6.ipynb (limited to 'Mechanics_of_Structures/Chapter6.ipynb') diff --git a/Mechanics_of_Structures/Chapter6.ipynb b/Mechanics_of_Structures/Chapter6.ipynb new file mode 100755 index 00000000..70a08d4a --- /dev/null +++ b/Mechanics_of_Structures/Chapter6.ipynb @@ -0,0 +1,491 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:c177c52862f24e7aa2f65bd196b1696db90de567ae2d80d6061ed266557f0af1" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter6-Beams and bending part 3" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex1-pg215" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "#calculate The deflection at the free\n", + "l = 5.;## feet\n", + "W = 150.;## lb\n", + "w = 120.;## lb. per foot run\n", + "l1 = 3.;## feet\n", + "b = 3.;## inches\n", + "d = 6.;## inches\n", + "E = 1.5*10**6;## lb/in^2\n", + "I = (1./12.)*b*d**3;## in^4\n", + "y_B1 = (W*l**3)/(3.*E*I);## feet\n", + "y_B2 = (w*l1*l1**3)/(8.*E*I) + (l-l1)*(w*l1*l1**2)/(6.*E*I);## feet\n", + "y_B = (12**3)*(y_B1+y_B2);## inches\n", + "print'%s %.4f %s'%('The deflection at the free end =',y_B,'inches')\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The deflection at the free end = 0.1823 inches\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Ex2-pg218" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "#calculate 'Uniform distributed load\n", + "b = 4.;## inches\n", + "d = 9.;## inches\n", + "l = 12.;## feet\n", + "y_c = 1/4.;## inches\n", + "E = 1.5*10**6;## lb/in^2\n", + "I = (1/12.)*b*d**3;## in^4\n", + "W = y_c*384.*E*I/(5.*12**3.*l**3);## inches\n", + "print'%s %.d %s'%('Uniform distributed load, the beam should carry is, W =',W,'lb-wt');\n", + "\n", + "##there is an error in the answer given in text book\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Uniform distributed load, the beam should carry is, W = 2343 lb-wt\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex3-pg224" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "#calculate 'Uniform distributed load the beam should carry\n", + "b = 4.;## inches\n", + "d = 9.;## inches\n", + "l = 12.;## feet\n", + "y_c = 1/4.;## inches\n", + "E = 1.5*10**6;## lb/in^2\n", + "I = (1/12.)*b*d**3;## in^4\n", + "W = y_c*384.*E*I/(5.*12**3.*l**3);## inches\n", + "print'%s %.d %s'%('Uniform distributed load, the beam should carry is, W =',W,'lb-wt');\n", + "\n", + "##there is an error in the answer given in text book\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Uniform distributed load, the beam should carry is, W = 2343 lb-wt\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex4-pg225" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "#calculateThe deflection for a uniformly distributed load\n", + "d = 6.;## feet\n", + "l = 60.;## feet\n", + "f = 15./2.;## tons/in^2\n", + "E = 13000.;## tons/in^2\n", + "k1 = 2.*f/(12.*d);## k1 = M_r/I \n", + "k2 = k1/(l*12./8.);##k2 = W/I\n", + "y_c = (5./384.)*k2*l**3 *12**3 /E;## inches\n", + "##If the giredr is of constant deapth and uniform strength, it bends to an arc of a circle of radius R \n", + "R = E*d*12/(2*f);## inches\n", + "delta = (l*12)**2 /(8*R);## inches\n", + "print'%s %.2f %s'%('The deflection for a uniformly distributed load on it is,delta =',delta,'inches');\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The deflection for a uniformly distributed load on it is,delta = 1.04 inches\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex5-pg227" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "#calculate The ratio of deapth to span\n", + "f = 8.;##tons/in^2\n", + "E = 12800.;## tons/in^2\n", + "k1 = 1./480.;##central deflection = k = delta/l\n", + "k2 = (5./24.)*(f/E)/k1 ;##k2 = d/l = deapth to span ratio\n", + "print'%s %.3f %s'%('The ratio of deapth to span, d/l =',k2,'');\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The ratio of deapth to span, d/l = 0.062 \n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex6-pg228" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "#calculate 'A section with d and If the deapth of section is limited\n", + "w = 550.;## lb. per foot run\n", + "f = 1000.;## lb/in^2\n", + "l = 20.;## feet\n", + "d_limit = 15.;## inches\n", + "E = 1.5*10**6;## lb/in^2\n", + "##central ddeflection\n", + "delta = (1./2.);## inches\n", + "d = (5./24.)*(f/E)*20.*12./(1./(2.*20.*12.));## inches\n", + "M = w*l*l*12./8.;## lb-inches\n", + "b = M/(f*(1./6.)*d**2);## inches\n", + "print'%s %.d %s'%('A section with d =',round(d),'inches')\n", + "print'%s %.d %s'%('b =',round(b),'inches will do.')\n", + "f1 = (1./(2.*20.*12.))*(d_limit/(l*12.))*E/(5./24.);## lb/in^2\n", + "b = M/(f1*(1./6.)*d_limit**2);## inches\n", + "print'%s %.d %s'%('If the deapth of section is limited to',d_limit,'inches,then')\n", + "print'%s %.1f %s'%('f =',f1,'lb/in^2')\n", + "print'%s %.1f %s'%('b =',b,'inches');\n", + "\n", + "##tha answer is correct only, but it is approximated in the text book.\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "A section with d = 16 inches\n", + "b = 8 inches will do.\n", + "If the deapth of section is limited to 15 inches,then\n", + "f = 937.5 lb/in^2\n", + "b = 9.4 inches\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex7-pg235" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "#calculate The position of maximum deflection occurs and The maximum deflection and The deflection at the centre\n", + "l = 20.;## feet\n", + "b = 4.;## feet\n", + "W = 5.;## tons\n", + "d = 12.;## inches\n", + "h = 5.;## inches\n", + "I_xx = 220.;## in^4\n", + "E = 13000.;## tons/in^2\n", + "a = l-b;## feet\n", + "##for maximum deflection\n", + "x = math.sqrt((a**2 + 2.*a*b)/3.);## feet\n", + "y_max = x*12**3 *((a**2 + 2.*a*b) - x**2)/(6.*E*I_xx);## inches\n", + "##for deflection at the centre\n", + "x1 = 0.5*l;## inches\n", + "y_x1 = x1*12**3 *((a*82. + 2.*a*b) - x1*82.)/(6.*E*I_xx);## inches\n", + "print'%s %.2f %s'%('The position of maximum deflection occurs at x =',x,'feet')\n", + "print'%s %.4f %s'%('The maximum deflection is, y_max =',y_max,'inches');\n", + "print'%s %.3f %s'%('The deflection at the centre,',y_x1,'inches');\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The position of maximum deflection occurs at x = 11.31 feet\n", + "The maximum deflection is, y_max = 0.2917 inches\n", + "The deflection at the centre, 0.624 inches\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex8-pg236" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "#calculate The position of the maximum deflection and the maximum deflection\n", + "d = 12.;## inches\n", + "h = 5.;## inches\n", + "l = 20.;## feet\n", + "E = 13000.; ##tons/in**2\n", + "I_xx = 220.;## in**4\n", + "W = 4.;## tons\n", + "W1 = 3.;## tons\n", + "a = 15.;## feet\n", + "b = l-a;## feet\n", + "a1 = 16.;## feet \n", + "b1 = l-a1;## feet\n", + "K1 = (-2*W1*b1*l)/(W1*b1-W*b);\n", + "K2 = (W*b*a**2 + 2*a*W*b**2 + 2*W1*b1*l**2 - W1*b1*a1**2 -2*W1*a1*b1**2 +W1*b1*l**2)/(3*(W1*b1 - W*b));\n", + "x = -0.5*K1 + math.sqrt(-K2 + 0.25*K1**2);## feet\n", + "x1 = l-x;## feet\n", + "y_max = W*b*x*1728.*(a**2 +2*a*b -x**2)/(6.*E*I_xx*l) + W1*b1*x1*1728.*(a1**2 +2.*a1*b1 -x1**2)/(6.*E*I_xx*l);## inches\n", + "print'%s %.2f %s'%('The position of the maximum deflection is, x =',x,'feet.');\n", + "print'%s %.4f %s'%('And the maximum deflection is, y_max =',y_max,'inches');\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The position of the maximum deflection is, x = 10.26 feet.\n", + "And the maximum deflection is, y_max = 0.4488 inches\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex9-pg243" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "#calculate The position of the maximum deflection and the maximum deflection\n", + "b = 18.;## inches\n", + "d = 7.;## inches\n", + "w1 = 1.;## ton per foot run\n", + "w2 = 3.;## ton per foot run\n", + "I_xx = 1149.;## in**4\n", + "E = 13000.;## tons/in**2\n", + "R_A = 0.5*b + (b/3.);## tons\n", + "R_B = 0.5*b + (2.*b/3.);## tons\n", + "##integrating M = E*I*y'', to get E*I*y' and making y' = 0;, we get maximu deflection\n", + "x = 9.18;## by trial and error method\n", + "y_derivative = -R_A*0.5*x**3 + x**4 /6. +0.5*(2./3.)*(1./b)*(1./4.)*x**5 + 469.8;\n", + "y = -R_A*0.5*x**3 /3. + x**4 /24. +0.5*(2./3.)*(1./b)*(1./(4.*5.))*x**5 + 469.8*x;\n", + "y_max = y;## inches\n", + "print'%s %.2f %s'%('The position of maximum deflection from the end A, x =',x,'inches')\n", + "print'%s %.4f %s'%('Maximum deflection, y_max =',y_max*12**3 /(E*I_xx),'inches')\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The position of maximum deflection from the end A, x = 9.18 inches\n", + "Maximum deflection, y_max = 0.3164 inches\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex10-pg254" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "#calculate The position of the maximum deflection and the maximum deflection and stress induced\n", + "b = 18.;## inches\n", + "d = 6.;## inches\n", + "l = 16.;## feet\n", + "W = 2.;## tons\n", + "h = 1./2.;## inches\n", + "I_xx = 841.76;## in**4\n", + "E = 13000.;## tons/in**2\n", + "P = W + math.sqrt(2.*W*h*48.*E*I_xx/(l*12.)**3 + 2.*W);## tons\n", + "M_max = P*l*12./4.;## ton-inches\n", + "Z = 2.*I_xx/b ;## in**3\n", + "f = M_max/Z ;## tons/in**2\n", + "delta = P*(l*12.)**3 /(48.*E*I_xx);## inches\n", + "print'%s %.3f %s'%('The maximum instantaneous deflection delta =',delta,'inches') \n", + "print'%s %.3f %s'%('stress induced, f =',f,'tons/in**2');\n", + "##there is an error in the answer given in text book\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The maximum instantaneous deflection delta = 0.193 inches\n", + "stress induced, f = 7.362 tons/in**2\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex11-pg262" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "#calculate Number of plates required and Number of plates required and The initial radius to which the plates must be bent\n", + "l = 3.;## feet\n", + "b = 3.;## inches\n", + "t = 3./8.;## inches\n", + "W = 1500.;## lb.\n", + "f = 12.;## tons/in**2\n", + "E = 30.*10**6;## tons/in**2\n", + "M_max = W*l*12./4. ;## lb-inches\n", + "M_r = f*(1./6.)*b*t**2 *2240.;## lb-inches\n", + "n = M_max/M_r ;## no. of plates\n", + "n = round(n+1);\n", + "f = M_max/(n*(1./6.)*b*t**2);## lb/in**2\n", + "R = E/(2.*f/t) ;## inches\n", + "delta = (l*12.)**2 /(8.*R);## inches\n", + "print'%s %.d %s'%('Number of plates required, n =',n,'');\n", + "print'%s %.4f %s'%(' The central deflection, delta =',delta,'inch.');\n", + "print'%s %.3f %s'%('The initial radius to which the plates must be bent, R =',R,'inches');\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Number of plates required, n = 8 \n", + " The central deflection, delta = 0.6912 inch.\n", + "The initial radius to which the plates must be bent, R = 234.375 inches\n" + ] + } + ], + "prompt_number": 17 + } + ], + "metadata": {} + } + ] +} \ No newline at end of file -- cgit