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+{

+ "metadata": {

+  "name": "",

+  "signature": "sha256:4defd5409de6787753d9afa80f45fd44de9564eee21481b5ef4ed48087f19bda"

+ },

+ "nbformat": 3,

+ "nbformat_minor": 0,

+ "worksheets": [

+  {

+   "cells": [

+    {

+     "cell_type": "heading",

+     "level": 1,

+     "metadata": {},

+     "source": [

+      "Chapter5-Bending of Beams"

+     ]

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Ex1-pg128"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "import math\n",

+      "#calculate meter and sigma \n",

+      "Mz=11000. ##Nm\n",

+      "A1=0.13*0.02 ##m\n",

+      "A2=0.15*0.02 ##m\n",

+      "z1=0.01 ##m\n",

+      "z2=0.075 ##m\n",

+      "yA=0.043 ##m\n",

+      "zA=-0.106 ##m\n",

+      "yB=-0.063 ##m\n",

+      "zB=0.\n",

+      "\n",

+      "##location of the centroid\n",

+      "z=(A1*z1+A2*z2)/(A1+A2)\n",

+      "print'%s %.2f %s'%(\"in meter is= \",z,\"\")\n",

+      "\n",

+      "Iz=(0.02*(0.13)**3)/12.+ (0.13*0.02*(0.04)**2)+(0.15*(0.02)**3.)/12.+ (0.15*0.02*(0.035)**2.)\n",

+      "print'%s %.5f %s'%(\"Iz in meter^4 is= \",Iz,\"\")\n",

+      "Iy=(0.02*(0.13)**3)/12.+ (0.13*0.02*(0.04)**2)+(0.15*(0.02)**3)/.12+ (0.15*0.02*(0.035)**2.)\n",

+      "print'%s %.5f %s'%(\"Iy in meter^4 is= \",Iy,\"\")\n",

+      "Iyz=0+A1*0.04*(-0.035)+0+A2*(-0.035)*0.03\n",

+      "print'%s %.2f %s'%(\"Iyz in meter^4 is= \",Iyz,\"\")\n",

+      "##thetap=(atand((-2*Iyz)/(Iz-Iy)))/2\n",

+      "##print'%s %.2f %s'%(thetap)\n",

+      "I1=(Iz+math.sqrt(0.+(6.79*10**-6)**2.))\n",

+      "print'%s %.5f %s'%(\"I1 in meter^4 is= \",I1,\"\")\n",

+      "I2=(Iz-math.sqrt(0+(6.79*10**-6)**2))\n",

+      "print'%s %.6f %s'%(\"I2 in meter^4 is= \",I2,\"\")\n",

+      "My1=11000.*math.sin(45/57.3)\n",

+      "print'%s %.2f %s'%(\"My1 in Nm is\",My1,\"\")\n",

+      "Mz1=11000*math.sin(45/57.3)\n",

+      "print'%s %.2f %s'%(\"Mz1 in Nm is\",Mz1,\"\")\n",

+      "\n",

+      "sigmaxA=((My1*(zA))/I1)-((Mz1*yA)/I2)\n",

+      "print'%s %.2f %s'%(\"sigmaxA in MPa is\",sigmaxA,\"\")\n",

+      "sigmaxB=0-((My1*yB)/I2)\n",

+      "print'%s %.2f %s'%(\"sigmaxB in MPa is\",sigmaxB,\"\")\n",

+      "\n",

+      "My=0.\n",

+      "y=((Mz*Iyz)*z)/(Mz*Iy) ##.......equal to z=-1.71y\n",

+      "print'%s %.3f %s'%(\"y\",y,\"\")\n",

+      "\n",

+      "\n"

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "in meter is=  0.04 \n",

+        "Iz in meter^4 is=  0.00001 \n",

+        "Iy in meter^4 is=  0.00002 \n",

+        "Iyz in meter^4 is=  -0.00 \n",

+        "I1 in meter^4 is=  0.00002 \n",

+        "I2 in meter^4 is=  0.000005 \n",

+        "My1 in Nm is 7777.72 \n",

+        "Mz1 in Nm is 7777.72 \n",

+        "sigmaxA in MPa is -114417761.50 \n",

+        "sigmaxB in MPa is 101941050.82 \n",

+        "y -0.014 \n"

+       ]

+      }

+     ],

+     "prompt_number": 3

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Ex4-144"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "import math\n",

+      "#calculate the distance \n",

+      "import scipy\n",

+      "from scipy import integrate\n",

+      "t=1.25 ##mm\n",

+      "y=15.87 ##mm\n",

+      "z=5.28 ##mm\n",

+      "Iy=4765.62 ##mm**4\n",

+      "Iz=21054.69 ##mm**4\n",

+      "Iyz=3984.37 ##mm**4\n",

+      "thetap=13.05 ##degree\n",

+      "Iy1=3828.12 ##mm**4\n",

+      "Iz1=21953.12##mm**4\n",

+      "s=12.5\n",

+      "\n",

+      "##tau=(Vy/Iz1*t)*s*t(19.55+s*asind(13.05)/2)....equation 1\n",

+      "##F1=integrate((tau*t)ds)\n",

+      "def fun(s):\n",

+      "\ty=(0)\n",

+      "\treturn y\n",

+      "x=scipy.integrate.quad(fun,0,1)\n",

+      "x=x[0]\n",

+      "##F1=0.0912*Vy1                   substituting the value of tau we get F1\n",

+      "##Vy1*ez1=37.5*F1                 substituting the value of F1 we get ez1\n",

+      "ez1=37.5*0.0912\n",

+      "print'%s %.2f %s'%(\"the distance in mm is= \",ez1,\"\")\n",

+      "\n",

+      "##tau=(Vz1/Iy1*t)*s*t(12.05-s*asind(13.05)/2)....equation 2\n",

+      "##F1=integrate((tau*t)ds)\n",

+      "def fun(s):\n",

+      "\ty=(0)\n",

+      "\treturn y\n",

+      "x=scipy.integrate.quad(fun,0,1)\n",

+      "x=x[0]\n",

+      "\n",

+      "##F1=0.204*Vz1                   substituting the value of tau we get F1\n",

+      "##Vz1*ey1=37.5*F1                 substituting the value of F1 we get ez1\n",

+      "ey1=37.5*0.204\n",

+      "print'%s %.2f %s'%(\"the distance in mm is= \",ey1,\"\")\n",

+      "\n"

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "the distance in mm is=  3.42 \n",

+        "the distance in mm is=  7.65 \n"

+       ]

+      }

+     ],

+     "prompt_number": 2

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Ex5-pg154"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "import math\n",

+      "#calculate stress and meter\n",

+      "import scipy\n",

+      "from scipy import integrate\n",

+      "P=70. ##kN\n",

+      "c=0.05##m\n",

+      "c1=c\n",

+      "c2=c\n",

+      "R=0.1+0.05\n",

+      "A=0.005\n",

+      "\n",

+      "##m=(-1/(2*c))*integrate((y/R+y)dy)\n",

+      "def fun(c):\n",

+      "\ty=(-c)\n",

+      "\treturn y\n",

+      "\n",

+      "x=scipy.integrate.quad(fun,0,1)\n",

+      "m=-1.+(R/2.*c)*math.log((R+c)/(R-c))\n",

+      "print'%s %.2f %s'%(\"m\",m,\"\")\n",

+      "##m=(-1/(2*c))*integrate((y/R)-(y**2/R**2)+(y**3/R**3)-(y**4/R**4)+.....)dy)\n",

+      "m=-1+(3/2.)*math.log(2.)\n",

+      "print'%s %.3f %s'%(\"m\",m,\"\")\n",

+      "\n",

+      "M=P*R\n",

+      "print'%s %.2f %s'%(\"M\",M,\"\")\n",

+      "sigmatheta1=(-P*c2)/(m*A*(R-c1))\n",

+      "print'%s %.2f %s'%(\"stress in Pa is= \",sigmatheta1,\"\")\n",

+      "sigmatheta2=(P*c2)/(m*A*(R+c2))\n",

+      "print'%s %.2f %s'%(\"stress in Pa is= \",sigmatheta2,\"\")\n"

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "m -1.00 \n",

+        "m 0.040 \n",

+        "M 10.50 \n",

+        "stress in Pa is=  -176230.22 \n",

+        "stress in Pa is=  88115.11 \n"

+       ]

+      }

+     ],

+     "prompt_number": 1

+    }

+   ],

+   "metadata": {}

+  }

+ ]

+}
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