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diff --git a/Solid_Mechanics/Chapter10.ipynb b/Solid_Mechanics/Chapter10.ipynb new file mode 100755 index 00000000..cfa3510e --- /dev/null +++ b/Solid_Mechanics/Chapter10.ipynb @@ -0,0 +1,381 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:f6a72f4cc57a2a0246e1148374d652bdc5837f696dab36422b01926c78183403"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter10-Introduction To Energy Methods"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex3-pg400"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#calculate lift using Energy method\n",
+ "##initialization of variables\n",
+ "import math\n",
+ "L=6000. ##cm\n",
+ "L1=150. ##cm\n",
+ "T=90. ##W\n",
+ "Ip=math.pi*10**4./32.\n",
+ "E=2*10**6 ##kg/cm^2\n",
+ "G=E/2.5\n",
+ "A=3. ##cm^2\n",
+ "delta=0.5\n",
+ "##calculations\n",
+ "U=L/(2.*E*A)+(T*T*L1/(2.*G*Ip))\n",
+ "## U=0.5*W*delta\n",
+ "W=0.25/U\n",
+ "##results\n",
+ "print'%s %.2f %s'%('W = ',W,' kg')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "W = 196.31 kg\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex4-pg400"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#find deflection under a load of one tonne at end\n",
+ "##initialization of variabes\n",
+ "import math\n",
+ "cA=10. ##cm^2\n",
+ "wA=5. ##cm^2\n",
+ "P=1. ##tonne\n",
+ "E=2*10**6 ##kg/cm^2\n",
+ "P=P*1000. ##kg\n",
+ "## calculations\n",
+ "U_up=P**2*200./(2.*E*cA)*1./math.sqrt(3)*(2.+4.+6.+8.+10.+12.)\n",
+ "U_do=P**2*200./(2.*E*cA)*1./math.sqrt(3)*(1.+3.+5.+7.+9.+11.+13./2.)\n",
+ "U_web=P**2*200./(2.*E*wA)*1./math.sqrt(3)*(2.*13.)\n",
+ "U=U_up+U_do+U_web\n",
+ "delta=U*2./(P)\n",
+ "## results\n",
+ "print'%s %.2f %s'%('deflection = ',delta,' cm')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "deflection = 0.79 cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex5-pg402"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#calculate deflection of loaded end due to same load of one tonne\n",
+ "a=2*10**8\n",
+ "b=69282032.302\n",
+ "c=136.5\n",
+ "d=28\n",
+ "aa=5\n",
+ "bb=15\n",
+ "BC=16.77\n",
+ "cc=56000\n",
+ "dd=1300\n",
+ "ee=20*10**6\n",
+ "\n",
+ "\n",
+ "#part(a)\n",
+ "AB=a*c/(b) #\n",
+ "print'%s %.2f %s'%('energy stored in Bd due to axial force ',AB,'kg-cm')\n",
+ "\n",
+ "#Part(b)\n",
+ "Ubc=(b*b*aa)/(bb*bb)\n",
+ "UB=BC*100./(4.*10.)\n",
+ "UBC=Ubc*UB\n",
+ "Bc=730 \n",
+ "print'%s %.2f %s'%('energy stored in Bd due to axial force ',Bc,'kg-cm')\n",
+ "\n",
+ "#part(c)\n",
+ "AB=394 #\n",
+ "print'%s %.2f %s'%('energy stored in Bd due to axial force ',AB,'kg-cm')\n",
+ "\n",
+ "\n",
+ "#part(d)\n",
+ "Ebc=d*2/bb\n",
+ "\n",
+ "\n",
+ "#assuming that only chord memeber are taking axial stress then\n",
+ "\n",
+ "BD=(cc/bb)**2*(dd/4*ee)\n",
+ "BD1=227 \n",
+ "print'%s %.2f %s'%('energy stored in Bd due to axial force ',BD1,'kg-cm')\n",
+ "#total energy\n",
+ "TE=BD1+AB+Bc+AB\n",
+ "delta=(2*TE)/(1000.)\n",
+ "print'%s %.2f %s'%('total energy stored in Bd due to axial force ',delta,'kg-cm')"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "energy stored in Bd due to axial force 394.04 kg-cm\n",
+ "energy stored in Bd due to axial force 730.00 kg-cm\n",
+ "energy stored in Bd due to axial force 394.00 kg-cm\n",
+ "energy stored in Bd due to axial force 227.00 kg-cm\n",
+ "total energy stored in Bd due to axial force 3.49 kg-cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex7-pg406"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#calculate stresses in steel and stress in cloth laminate\n",
+ "##initialization of variables\n",
+ "import math\n",
+ "L=1. ##m\n",
+ "w=10. ##kg\n",
+ "h=50. ##cm\n",
+ "A=1. ##cm^2\n",
+ "E=2*10**6 ##kg/cm^2\n",
+ "Ar=1 ##cm^2\n",
+ "Ec=3*10**4 ##kg/cm^2\n",
+ "## For steel\n",
+ "D=w*L*100./(A*E)\n",
+ "P=w*(1+math.sqrt(1.+(2.*h/D)))\n",
+ "print'%s %.2f %s'%('Stress in steeel = ',P,' kg/cm^2 ')\n",
+ "\n",
+ "## for cloth laminate\n",
+ "D=w*L*100./(A*Ec)\n",
+ "P=w*(1+math.sqrt(1.+(2.*h/D)))\n",
+ "print'%s %.2f %s'%('\\n Stress in cloth laminate = ',P,' kg/cm^2 ')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Stress in steeel = 4482.15 kg/cm^2 \n",
+ "\n",
+ " Stress in cloth laminate = 557.81 kg/cm^2 \n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex8-pg407"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#calculate maximum stress in wood and divers feet in all parts\n",
+ "##initialization of variables\n",
+ "import math\n",
+ "w=64. ##kg\n",
+ "H=60. ##cm\n",
+ "b=40. ##cm\n",
+ "h=5. ##cm\n",
+ "E=0.12*10**6 ##kg/cm^2\n",
+ "Es=2*10**6 ##kg/cm^2\n",
+ "## for part (a) and (b)\n",
+ "I=b*h**3./12.\n",
+ "D=4.*w*120**3/(E*I)\n",
+ "P=w*(1+math.sqrt(1.+(2.*H/D)))\n",
+ "str=P*240.*6./(b*h**2.)\n",
+ "print('part (a) and (b)')\n",
+ "print'%s %.2f %s'%('\\n Maximum stress in wood = ',str,' kg/cm^2')\n",
+ "print'%s %.2f %s'%('\\n Max. force on divers feet =',P,' kg')\n",
+ "\n",
+ "##for part (c)\n",
+ "Ixx=I*E/Es\n",
+ "Zxx=19.4 ##cm^2\n",
+ "Ixx=72.7 ##cm^4\n",
+ "D=4*w*120**3/(Es*Ixx)\n",
+ "P=w*(1+math.sqrt(1.+(2.*H/D)))\n",
+ "str=P*240./Zxx\n",
+ "## results\n",
+ "print('\\n part (c)')\n",
+ "print'%s %.2f %s'%('\\n Maximum stress in steel = ',str,' kg/cm^2')\n",
+ "print'%s %.2f %s'%('\\n Max. force on divers feet =',P,' kg')\n",
+ "print('\\n Hence wood is better than steel')\n",
+ "\n",
+ "print('wrong calculations in some parts')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "part (a) and (b)\n",
+ "\n",
+ " Maximum stress in wood = 443.86 kg/cm^2\n",
+ "\n",
+ " Max. force on divers feet = 308.24 kg\n",
+ "\n",
+ " part (c)\n",
+ "\n",
+ " Maximum stress in steel = 5826.84 kg/cm^2\n",
+ "\n",
+ " Max. force on divers feet = 471.00 kg\n",
+ "\n",
+ " Hence wood is better than steel\n",
+ "wrong calculations in some parts\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex11-pg414"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#calculate central deflection\n",
+ "##initialization of variables\n",
+ "import math\n",
+ "A=100. ##cm^2\n",
+ "E=2*10**6 ##kg/cm^2\n",
+ "## calculations\n",
+ "D=1093.5*10**6/(E*A)\n",
+ "## 1093.5 from the table\n",
+ "## results\n",
+ "print'%s %.2f %s'%('Central deflection = ',D,' mm')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Central deflection = 5.47 mm\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex12-pg415"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#calculate deflection\n",
+ "##initialization of variables\n",
+ "import math\n",
+ "T=30. ##degree celcius\n",
+ "alpha=0.0000117 ## per degree celcius\n",
+ "##AB\n",
+ "L=6. ##m\n",
+ "dl=T*alpha*L\n",
+ "df=0.375 ##kg\n",
+ "tot=dl*df\n",
+ "##BC\n",
+ "dl=T*alpha*L\n",
+ "df=0.375 ##kg\n",
+ "tot=tot+dl*df\n",
+ "##CD\n",
+ "dl=T*alpha*L\n",
+ "df=0.75 ##kg\n",
+ "tot=tot+dl*df\n",
+ "tot=tot*100.*2.\n",
+ "## results\n",
+ "print'%s %.2f %s'%('The deflection is ',tot,' cm')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The deflection is 0.63 cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
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