From 73b0bffc1781c6cf1eec459813767508da507c33 Mon Sep 17 00:00:00 2001 From: hardythe1 Date: Mon, 28 Jul 2014 14:01:58 +0530 Subject: adding book --- Mechanics_of_Materials/APPENDIX_A.ipynb | 366 ++++++++++++++++++++++++++++++++ 1 file changed, 366 insertions(+) create mode 100755 Mechanics_of_Materials/APPENDIX_A.ipynb (limited to 'Mechanics_of_Materials/APPENDIX_A.ipynb') diff --git a/Mechanics_of_Materials/APPENDIX_A.ipynb b/Mechanics_of_Materials/APPENDIX_A.ipynb new file mode 100755 index 00000000..b7a1f860 --- /dev/null +++ b/Mechanics_of_Materials/APPENDIX_A.ipynb @@ -0,0 +1,366 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "APPENDIX A:Geomatric Properties of an Area" + ] + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example A.1:Page no. 786" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Given\n", + "#From fig. A-4(a) The given dimensions are\n", + "l1=8 #inch\n", + "l2=3 #inch\n", + "l3=10 #inch\n", + "l4=5 #inch\n", + "l5=11.5 #inch\n", + "l6=2 #inch\n", + "\n", + "#calculation\n", + "ymean1=((l4*l3*l6)+(l5*l2*l1))/((l3*l6)+(l2*l1))\n", + "#From fig. A-4(b)\n", + "l1_=-8 #inch\n", + "l2_=3 #inch\n", + "l3_=10 #inch\n", + "l4_=-1.5 #\n", + "l5_=2 #inch\n", + "ymean2=((l4_*l2_*-l1_)+(l1_*l3_*l5_))/((l2_*-l1_)+(l3_*l5_))\n", + "d=ymean1-ymean2 #Depth of beam\n", + "#From fig. A-4(c)\n", + "la=8 #inch\n", + "lb=6.5 #inch\n", + "lc=10 #inch\n", + "ld=13 #\n", + "le=5 #inch\n", + "lf=3 #inch\n", + "ymean3=((lb*ld*la)-2*(le*lc*lf))/((ld*la-2*(lc*lf)))\n", + "print\"Location of centroid in fig (a)is\",ymean1,\"inch\" \n", + "print\"Location of centroid in fig (b)is\",ymean2,\"inch\"\n", + "print\"Location of centroid in fig (c)is\",ymean3,\"inch\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Location of centroid in fig (a)is 8.54545454545 inch\n", + "Location of centroid in fig (b)is -4.45454545455 inch\n", + "Location of centroid in fig (c)is 8.54545454545 inch\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example A.2:Page no 789" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Given\n", + "#Dimension in the fig.A-7 a\n", + "#The given dimensions are\n", + "l1=8 #inch\n", + "l2=8.55 #inch\n", + "l3=10 #inch\n", + "l4=5 #inch\n", + "l5=1.5 #inch\n", + "l6=2 #inch\n", + "l7=4.45 #inch\n", + "\n", + "#Calculation\n", + "Ix1=(1/12.0*l6*l3**3)\n", + "A1=l6*l3\n", + "dy1=(l2-l4)\n", + "Ix2=(1/12.0*l1*(l5+l5)**3)\n", + "A2=l1*(l5+l5)\n", + "dy2=(l7-l5)\n", + "I1=(Ix1+A1*dy1**2)+(Ix2+A2*dy2**2)\n", + "print I1\n", + "\n", + "#Dimension in the fig.A-7 b\n", + "l1_= 13 #inch\n", + "l2_= 3 #inch\n", + "l3_=10 #inch\n", + "l4_=5 #inch\n", + "l5_= 2 #inch\n", + "l6_= 6.5 #inch\n", + "l7_=4.45 #inch\n", + "l8_=8.55 #inch\n", + "l9_=6.5 #inch\n", + "\n", + "Ix1_=(1/12.0*l1_*(l2_+l5+l2_)**3)\n", + "A1_=l1_*(l2_+l5+l2_)\n", + "dy1_=(l8_-l9_)\n", + "Ix2_=(1/12.0*l2_*(l3_)**3)\n", + "A2_=l2_*(l3_)\n", + "dy2_=(l7_-l4_)\n", + "I2=(Ix1+A1*dy1**2)+(Ix2+A2*dy2**2)\n", + "\n", + "#Result\n", + "print\"Moment of inertia for fig a is\",round(I1,0),\"inch**4\"\n", + "print\"Moment of inertia for fig a is\",round(I2,0),\"inch**4\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "645.576666667\n", + "645.576666667\n", + "Moment of inertia for fig a is 646.0 inch**4\n", + "Moment of inertia for fig a is 646.0 inch**4\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example A.3 Page no: 790" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Given\n", + "#From fig A-8(a)\n", + "#The given dimensions are\n", + "l1=100 #mm\n", + "l2=400 #mm\n", + "l3=600 #mm\n", + "dx=250 #mm\n", + "dy=200 #mm\n", + "\n", + "#Calculation\n", + "#Rectangle A:\n", + "Ix1=(1/12.0*l1*(l2-l1)**3)\n", + "Ady=(l1*(l2-l1)*dy**2)\n", + "Ix=(Ix1+Ady)\n", + "Iy1=(1/12.0*(l2-l1)*l1**3)\n", + "Adx=(l1*(l2-l1)*dx**2)\n", + "Iy=(Iy1+Adx)\n", + "\n", + "#Rectangle B:\n", + "Ix_=(1/12.0*l3*l1**3)\n", + "Iy_=(1/12.0*l1*l3**3)\n", + "\n", + "#Rectangle C\n", + "Ix3=(1/12.0*l1*(l2-l1)**3)\n", + "Ady_=(l1*(l2-l1)*200**2)\n", + "Ix3_=(Ix3+Ady_)\n", + "Iy3=(1/12.0*(l2-l1)*l1**3)\n", + "Adx_=(l1*(l2-l1)*dx**2)\n", + "Iy3_=(Iy3+Adx)\n", + "\n", + "#Total Moment of inertia\n", + "Itx=(Ix+Ix_+Ix3_)\n", + "Ity=(Iy+Iy_+Iy3_)\n", + "\n", + "#Result\n", + "print\"Moment of inertia across x is \",Itx,\"mm**4\"\n", + "print\"Moment of inertia across y is \",Ity,\"mm**4\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Moment of inertia across x is 2900000000.0 mm**4\n", + "Moment of inertia across y is 5600000000.0 mm**4\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example A.4 :page no. 793" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Given\n", + "#From fig A-12 a\n", + "#The given length of sides are\n", + "l1=100 #mm\n", + "l2=300 #mm\n", + "dy=200 #mm\n", + "dx=250 #mm\n", + "\n", + "#Calculation\n", + "#Rectangle A\n", + "Ixy1=0\n", + "A1=l1*l2\n", + "Ixy1=Ixy1+A1*(-dx)*dy\n", + "\n", + "#Rectangle B\n", + "Ixy2=0\n", + "A2=0\n", + "Ixy2=Ixy2+A2*dx*dy\n", + "\n", + "#Rectangle D\n", + "Ixy3=0\n", + "A3=l1*l2\n", + "Ixy3=Ixy3+A3*(dx)*(-dy)\n", + "Ixy=Ixy1+Ixy2+Ixy3\n", + "\n", + "#Result\n", + "print\"The moment of inertia is\",Ixy,\"mm**4\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The moment of inertia is -3000000000 mm**4\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example A.5 :page no. 796" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#Given\n", + "#From fig A-15 and From Example A.3 and A.4\n", + "Ix=2.9*10**9 #moment of inertia along x\n", + "Iy=5.6*10**9 #moment of inertia along y\n", + "Ixy=-3*10**9 #moment of inertia along xy\n", + "\n", + "#Calculation\n", + "import math\n", + "#Using eq. A11\n", + "import math\n", + "thetaP1=1/2.0*math.atan(-Ixy*2/(Ix-Iy))*100\n", + "#As shown in fig. A-15\n", + "thetaP2=-32.9 #degree\n", + "Imax=(Ix+Iy)/2.0+math.sqrt((((Ix-Iy)/2.0)**2)+Ixy**2)\n", + "Imin=(Ix+Iy)/2.0-math.sqrt((((Ix-Iy)/2.0)**2)+Ixy**2)\n", + "\n", + "#Result\n", + "print\"Maximum moment of inertia is\",Imax,\"mm**4\"\n", + "print\"Minimum moment of inertia is\",Imin,\"mm**4\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum moment of inertia is 7539756829.92 mm**4\n", + "Minimum moment of inertia is 960243170.081 mm**4\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 3, + "metadata": {}, + "source": [ + "Example A.6 :page no. 799" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#given\n", + "#From fig. A-17 a and Example A.3 and A.4\n", + "Ix=2.9*10**9 #mm**4, moment of inertia\n", + "Iy=5.6*10**9\n", + "Ixy=-3*10**9\n", + "\n", + "#Calculation\n", + "import math\n", + "d=(Ix+Iy)/2.0 #distance of centre of circle \n", + "#from fig A-17 b\n", + "BC=1.35\n", + "AB=3\n", + "CA=math.sqrt(BC**2+AB**2)\n", + "\n", + "#the circle intersect the I axis at point (7.54,0) and (0.960,0) hence\n", + "Imax=7.54*(10**9) #mm**4\n", + "Imin=0.960*(10**9) #mm**4\n", + "thetap1=1/2.0*(180-(math.atan(AB/BC))*180/math.pi)\n", + "\n", + "#Result\n", + "print\"The maximum moment of inertia is\",Imax,\"mm**4\"\n", + "print\"The minimum moment of inertia is\",Imin,\"mm**4\"\n", + "print\"The angle is \",round(thetap1,1)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The maximum moment of inertia is 7540000000.0 mm**4\n", + "The minimum moment of inertia is 960000000.0 mm**4\n", + "The angle is 57.1\n" + ] + } + ], + "prompt_number": 33 + } + ], + "metadata": {} + } + ] +} \ No newline at end of file -- cgit