{
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  "signature": "sha256:54c92a13ce853ac5fe5325a355c839b097f01e81340aa957e3602b8ea43de184"
 },
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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter8-Axisymmetrically Loaded Members"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex1-pg239"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate pressure and for longitudinal stress \n",
      "di=0.3 ##m\n",
      "de=0.4 ##m\n",
      "v=0.3\n",
      "sigmathetamax=250*10**6 ##Pa\n",
      "p0=0.\n",
      "pi=0.\n",
      "\n",
      "##solution a:\n",
      "a=0.15\n",
      "b=0.2\n",
      "r=a\n",
      "##sigmathetamax=pi*((b**2+a**2)/(b**2-a**2))\n",
      "pi=sigmathetamax*((b**2-a**2.)/(b**2+a**2.))\n",
      "print'%s %.2f %s'%(\"in Pa is= \",pi,\"\")\n",
      "\n",
      "##solution b:\n",
      "r=a\n",
      "##sigmathetamax=-2*p0*(b**2/(b**2-a**2))\n",
      "p0=-(-sigmathetamax)*((b**2.-a**2.)/(2.*b**2.))\n",
      "print'%s %.2f %s'%(\"in Pa is= \",p0,\"\")\n",
      "\n",
      "##solution c:\n",
      "u=((a**3*pi)/(b**2-a**2))*(0.7+1.3*(b**2./a**2.))\n",
      "print'%s %.2f %s'%(\"in per E meter is= \",u,\"\")\n",
      "sigmaz=(pi*a**2-p0*b**2)/(b**2-a**2)\n",
      "print'%s %.2f %s'%(\"for longitudinal stress is\",sigmaz,\"\")\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "in Pa is=  70000000.00 \n",
        "in Pa is=  54687500.00 \n",
        "in per E meter is=  40650000.00 \n",
        "for longitudinal stress is -35000000.00 \n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex2-pg241"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate pressure \n",
      "sigmayp=340. ##MPa\n",
      "tauyp=sigmayp/2. ##MPa\n",
      "print'%s %.2f %s'%(\"in MPa is=\",tauyp,\"\")\n",
      "a=0.1 ##m\n",
      "b=0.15 ##m\n",
      "v=0.3 \n",
      "##pi=4*p0\n",
      "##sigmatheta=(pi*(a**2+b**2)-2*p0*b**2)/(b**2-a**2)\n",
      "##sigmatheta=1.7*pi\n",
      "\n",
      "##sloution a: maxi principal stress theory\n",
      "sigmatheta=1.7\n",
      "pi=sigmayp/sigmatheta\n",
      "print'%s %.2f %s'%(\"in MPa is= \",pi,\"\")\n",
      "\n",
      "##sloution b: maxi shearing stress theory\n",
      "##(sigmatheta-sigmar)/2=1.35*pi\n",
      "pi=tauyp/1.35\n",
      "print'%s %.2f %s'%(\"in MPa is= \",pi,\"\")\n",
      "\n",
      "##solution c: energy of distortion theory\n",
      "sigmar=-1\n",
      "sigmayp1=math.sqrt(sigmatheta**2+sigmar**2-sigmatheta*sigmar)##*pi\n",
      "print(sigmayp1)\n",
      "pi=sigmayp/sigmayp1\n",
      "print'%s %.2f %s'%(\"in MPa is=\",pi,\"\")\n",
      "\n",
      "##solution d: maxi principal strain theory\n",
      "##(sigmatheta-v*sigmar)/E=sigmayp/E\n",
      "pi=sigmayp/(sigmatheta-v*sigmar)\n",
      "print'%s %.2f %s'%(\"in MPa is= \",pi,\"\")\n",
      "\n",
      "##solution e: octahedral shearing stress theory:\n",
      "pi=(math.sqrt(2.)*sigmayp)/math.sqrt((sigmatheta-sigmar)**2.+sigmar**2.+(-sigmatheta)**2)\n",
      "print'%s %.2f %s'%(\"in MPa is= \",pi,\"\")\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "in MPa is= 170.00 \n",
        "in MPa is=  200.00 \n",
        "in MPa is=  125.93 \n",
        "2.36431808351\n",
        "in MPa is= 143.80 \n",
        "in MPa is=  170.00 \n",
        "in MPa is=  143.80 \n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex3-pg243"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate contact pressure and tangential stresses in the outer cylinder\n",
      "a=0.15 ##m\n",
      "b=0.2 ##m\n",
      "c=0.25 ##m\n",
      "E=200*10**9. ##Pa\n",
      "delta=0.0001 ##m\n",
      "140 ##MPa\n",
      "\n",
      "p=((E*delta)/8.)*(((b**2.-a**2.)*(c**2.-b**2.))/(2.*(b**2.)*(c**2.-a**2.)))\n",
      "print'%s %.2f %s'%(\"the contact pressure in Pa is= \",p,\"\") ## textbook ans is wrong\n",
      "\n",
      "p=12.3*10**6\n",
      "sigmatheta=p*((b**2+c**2.)/(c**2.-b**2.)) ## where r=0.2\n",
      "print'%s %.2f %s'%(\"tangential stresses in the outer cylinder in Pa is= \",sigmatheta,\"\")\n",
      "sigmatheta1=(2*p*b**2)/(c**2-b**2) ## where r=0.25\n",
      "print'%s %.2f %s'%(\"tangential stresses in the outer cylinder in Pa is= \",sigmatheta1,\"\")\n",
      "sigmatheta3=-(2*p*b**2)/(b**2-a**2) ## where r=0.15\n",
      "print'%s %.2f %s'%(\"tangential stresses in the inner cylinder in Pa is= \",sigmatheta3,\"\")\n",
      "sigmatheta4=-p*((b**2.+a**2.)/(b**2.-a**2.)) ## where r=0.2\n",
      "print'%s %.2f %s'%(\"tangential stresses in the inner cylinder in Pa is= \",sigmatheta4,\"\")\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the contact pressure in Pa is=  307617.19 \n",
        "tangential stresses in the outer cylinder in Pa is=  56033333.33 \n",
        "tangential stresses in the outer cylinder in Pa is=  43733333.33 \n",
        "tangential stresses in the inner cylinder in Pa is=  -56228571.43 \n",
        "tangential stresses in the inner cylinder in Pa is=  -43928571.43 \n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex4-pg246"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate radial displacement of disk and shaft\n",
      "dn=0.1 ##m\n",
      "do=0.5 ##m\n",
      "t=0.08 ##m\n",
      "w=6900*(2*math.pi/60.) ##rpm\n",
      "row=7.8*10**3##Ns**2/m**4\n",
      "E=200*10**9 ##Pa\n",
      "v=0.3\n",
      "b=0.05\n",
      "c=0.25\n",
      "\n",
      "\n",
      "##solution a:\n",
      "##ud=((0.05*3.3*0.7)*(0.0025+0.0625-(1.3/3.3)*0.0025+(1.3/0.7)*0.0625)*row*w**2)/(8*E)\n",
      "ud=((0.05*3.3*0.7)*(b**2+c**2-(1.3/3.3)*b**2+(1.3/0.7)*c**2))/(8)\n",
      "print'%s %.4f %s'%(\"radial displacement of the disk in meter is= \",ud,\"\")\n",
      "\n",
      "##us=((0.05*0.7)*(3.3*0.0025-1.3*0.0025)*row*w**2)/(8*E)\n",
      "us=((0.05*0.7)*(3.3*b**2-1.3*b**2))/(8)\n",
      "print'%s %.6f %s'%(\"radial displacement of the shaft in meter is= \",us,\"\")\n",
      "delta=(ud-us)*row*w**2./E\n",
      "print(delta)\n",
      "\n",
      "##solution b:\n",
      "##p=E*delta*(c**2-b**2)/(2*b*c**2)\n",
      "p=E*delta*(c**2-b**2)/(2*b*c**2)\n",
      "print'%s %.2f %s'%(\"in Pa is= \",p,\"\")\n",
      "sigmathetamax=p*(c**2+b**2)/(c**2-b**2)\n",
      "print'%s %.2f %s'%(\"in Pa is= \",sigmathetamax,\"\")\n",
      "\n",
      "##solution c:\n",
      "sigmathetamax=3.3*(b**2.+c**2.-(1.9/3.3)*b**2.+c**2.)*row*w**2./8.\n",
      "print'%s %.2f %s'%(\"in Pa is= \",sigmathetamax,\"\")\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "radial displacement of the disk in meter is=  0.0026 \n",
        "radial displacement of the shaft in meter is=  0.000022 \n",
        "5.24957318528e-05\n",
        "in Pa is=  100791805.16 \n",
        "in Pa is=  109191122.25 \n",
        "in Pa is=  211764600.73 \n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex5-pg250"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate sigma theta and sigma \n",
      "ti=0.075 ##m\n",
      "to=0.015##m\n",
      "a=0.05##m\n",
      "b=0.25##m\n",
      "delta=0.05 ##mm\n",
      "w=6900*(2*math.pi/60.) ##rpm\n",
      "s=1.\n",
      "row=7.8*10**3##Ns**2/m**4\n",
      "E=200. ##GPa\n",
      "\n",
      "##solution a:\n",
      "t1=ti*a**s\n",
      "print'%s %.4f %s'%(\"t1 is=\",t1,\"\")\n",
      "t1=to*b**2.\n",
      "print'%s %.4f %s'%(\"t1 is=\",t1,\"\")\n",
      "##(ti/to)=(t1*a**-s)/(t1*b**-s)=(b/a)**s\n",
      "c=(b/a)**s\n",
      "\n",
      "(ti/to)==c\n",
      "print'%s %.2f %s'%(\"ti/t0 is=\",c,\"\")\n",
      "m1=-0.5+math.sqrt((0.5)**2+(1+0.3*1))\n",
      "print'%s %.2f %s'%(\"m1 is=\",m1,\"\")\n",
      "m2=-0.5-math.sqrt((0.5)**2.+(1.+0.3*1.))\n",
      "print'%s %.2f %s'%(\"m2 is=\",m2,\"\")\n",
      "\n",
      "##sigmar=0=(c1/t1)*(0.05)**m1+(c2/t1)*(0.05)**(m2)-0.00176*row*w**2     ## r=0.05\n",
      "##sigmar=0=(c1/t1)*(0.25)**m1+(c2/t1)*(0.25)**(m2)-0.0439*row*w**2     ## r=0.25\n",
      "\n",
      "c1=t1*0.12529*row*w**2.\n",
      "print'%s %.2f %s'%(\"c1 is=\",c1,\"\")\n",
      "c2=t1*-6.272*10**-5*row*w**2\n",
      "print'%s %.2f %s'%(\"c2 is=\",c2,\"\")\n",
      "\n",
      "r=0.05\n",
      "sigmar=(0.12529*r**0.745-6.272*10**-5*r**(-1.745)-0.70*r**2)##*row*w**2\n",
      "print'%s %.5f %s'%(\"sigmar is= \",sigmar,\"\")\n",
      "\n",
      "sigmatheta=(0.09334*r**0.745+1.095*10**-4*r**(-1.745)-0.40*r**2)##*row*w**2\n",
      "print'%s %.2f %s'%(\"sigmatheta is= \",sigmatheta,\"\")\n",
      "\n",
      "##solution b:\n",
      "r=0.05\n",
      "##ur=(r*sigmatheta)/E\n",
      "ur=(r*sigmatheta)\n",
      "print'%s %.7f %s'%(\"ur is= \",ur,\"\")\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "t1 is= 0.0037 \n",
        "t1 is= 0.0009 \n",
        "ti/t0 is= 5.00 \n",
        "m1 is= 0.74 \n",
        "m2 is= -1.74 \n",
        "c1 is= 478341.11 \n",
        "c2 is= -239.46 \n",
        "sigmar is=  0.00001 \n",
        "sigmatheta is=  0.03 \n",
        "ur is=  0.0014711 \n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex6-pg251"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "#calculate pressure\n",
      "b=0.25 ##m\n",
      "w=6900.*(2*math.pi/60.) ##rpm\n",
      "t1=0.075 ##m\n",
      "t2=0.015 ##m\n",
      "row=7.8*10**3##Ns**2/m**4\n",
      "c1=t1\n",
      "\n",
      "x=t2/t1\n",
      "print(x)\n",
      "\n",
      "##(t2/t1)==(c1*exp(-(row*w**2/2*sigma)*b**2))/c1\n",
      "##exp(-(row*w**2/2*sigma)*b**2)=x\n",
      "##log(x)=-(row*w**2*b**2/2*sigma)\n",
      "y=2.*math.log(x)\n",
      "print(y)\n",
      "sigma=-(row*w**2.*b**2.)/y\n",
      "print'%s %.2f %s'%(\"in Pa is= \",sigma,\"\")\n",
      "\n",
      "##t=c1*exp(-row*(w**2/2*sigma)*r**2)\n",
      "z=row*(w**2./(2.*sigma))\n",
      "print(z)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.2\n",
        "-3.21887582487\n",
        "in Pa is=  79072562.70 \n",
        "25.7510065989\n"
       ]
      }
     ],
     "prompt_number": 2
    }
   ],
   "metadata": {}
  }
 ]
}