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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": {}
+ }
+ ]
+}
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