From 79c59acc7af08ede23167b8455de4b716f77601f Mon Sep 17 00:00:00 2001 From: hardythe1 Date: Thu, 11 Jun 2015 17:31:11 +0530 Subject: add books --- Solid_Mechanics_by_S._M._A._Kazimi/Chapter9.ipynb | 895 ++++++++++++++++++++++ 1 file changed, 895 insertions(+) create mode 100755 Solid_Mechanics_by_S._M._A._Kazimi/Chapter9.ipynb (limited to 'Solid_Mechanics_by_S._M._A._Kazimi/Chapter9.ipynb') diff --git a/Solid_Mechanics_by_S._M._A._Kazimi/Chapter9.ipynb b/Solid_Mechanics_by_S._M._A._Kazimi/Chapter9.ipynb new file mode 100755 index 00000000..ff92969f --- /dev/null +++ b/Solid_Mechanics_by_S._M._A._Kazimi/Chapter9.ipynb @@ -0,0 +1,895 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:9a9db8433ab57f1254bcf525f290f9e1ef0d063ac15516708405e3ee93106db3" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter9-Combined Stresses" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex1-pg361" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#calculate values of R at A,B,C\n", + "##initialization of variables\n", + "import math\n", + "##case (a)\n", + "A=72.9 ##cm^2\n", + "Iy=633 ##cm^4\n", + "Ix=1199. ##cm^4\n", + "t=24./(5.*Ix)+13.5/(5.*Iy)\n", + "r=1/(A*t)\n", + "print'%s %.2f %s'%('case (a) \\n r = ',r,' cm')\n", + "## case (b)\n", + "t=24./(5.*Ix)-13.5/(5.*Iy)\n", + "r=1/(A*t)\n", + "print'%s %.2f %s'%('\\n case (b) \\n r = ',r,' cm')\n", + "##case (c)\n", + "t=-24./(5.*Ix)+13.5/(5.*Iy)\n", + "r=1./(A*t)\n", + "print'%s %.2f %s'%('\\n case (a) \\n r =',r,' cm')\n", + "print'%s %.2f %s'%('\\n So the load is to be placed on the leg OD, at a distance of ',r,' cm from O' )\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "case (a) \n", + " r = 1.66 cm\n", + "\n", + " case (b) \n", + " r = -52.34 cm\n", + "\n", + " case (a) \n", + " r = 52.34 cm\n", + "\n", + " So the load is to be placed on the leg OD, at a distance of 52.34 cm from O\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex3-pg365" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#calculate steel height and Width\n", + "##initialization of variables\n", + "import math\n", + "b=14. ##cm\n", + "d=20. ##cm\n", + "rx=8.46 ##cm\n", + "ry=2.99 ##cm\n", + "## calculations\n", + "ex=2.*rx**2/d\n", + "ey=2*ry**2/b\n", + "h=2*ex\n", + "w=2*ey\n", + "## results\n", + "print'%s %.2f %s %.2f %s '%('for steel height=',h,' cm and width=',w,' cm')\n", + "## ISHB 225\n", + "b=22.5 ##cm\n", + "d=22.5 ##cm\n", + "rx=9.8 ##cm\n", + "ry=4.96 ##cm\n", + "## calculations\n", + "ex=2*rx**2/d\n", + "ey=2*ry**2/b\n", + "h=2*ex\n", + "w=2*ey\n", + "## results\n", + "print'%s %.2f %s %.2f %s '%('\\n for an ISHB height=',h,' cm and width=',w,' cm')\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "for steel height= 14.31 cm and width= 2.55 cm \n", + "\n", + " for an ISHB height= 17.07 cm and width= 4.37 cm \n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex4-pg366" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#calculate Safe load\n", + "##initialization of variables\n", + "import math\n", + "t=280. ##kg/cm^2\n", + "c=840. ##kg/cm^2\n", + "xbar=7.5 ##cm from AB\n", + "A=210. ##cm^2\n", + "## calculations\n", + "e=50.+xbar ##cm\n", + "Iyy=7433. ##cm^2\n", + "k=(1./210.+e*xbar/Iyy)\n", + "P=t/k\n", + "k1=(-1./210.+e*(xbar+5.)/Iyy)\n", + "P1=c/k1\n", + "P_safe=min(P1,P)\n", + "## results\n", + "print'%s %.2f %s'%('The safe load is ',P_safe,' kg')\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The safe load is 4460.00 kg\n" + ] + } + ], + "prompt_number": 26 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex5-pg367" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#calcualte compression and tension\n", + "##initialization of the variables\n", + "import math\n", + "s=1.6 ##m\n", + "s1=4. ##m\n", + "pi=28. ##degrees\n", + "w=16. ##kg/m^2\n", + "p=100. ##kg/m^2\n", + "pl=20. ##cm\n", + "pb=10. ##cm\n", + "r=500. ##kg/m^3\n", + "## calculations\n", + "pi=pi*math.pi/180 ##radians\n", + "W=w*s+(r*pl*pb/(100.*100.))\n", + "P=p*s\n", + "L=P+W*math.cos(pi)\n", + "Mx=L*s1**2*100./8.\n", + "sigma_1=Mx*6./(pb*pl**2)\n", + "My=W*math.sin(pi)*s1**2*100./8.\n", + "sigma_2=My*6./(pl*pb**2)\n", + "sigma1=sigma_1+sigma_2\n", + "## results\n", + "print'%s %.2f %s %.2f %s '%('Due to bending in the noth the planes, D experiences maximum \\n compression of ',sigma1,' kg/cm^2 and B has maximum tension of ',sigma1,' kg/cm^2')\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Due to bending in the noth the planes, D experiences maximum \n", + " compression of 67.46 kg/cm^2 and B has maximum tension of 67.46 kg/cm^2 \n" + ] + } + ], + "prompt_number": 27 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex6-pg369" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#calculate maximum stresses\n", + "##initialization of the problems\n", + "import math\n", + "s=1.6 ##m\n", + "s1=4. ##m\n", + "pi=28. ##degrees\n", + "w=16. ##kg/m^2\n", + "p=100. ##kg/m^2\n", + "pl=20. ##cm\n", + "pb=10. ##cm\n", + "r=500. ##kg/m^3\n", + "Zx=54.8 ##cm^3\n", + "Zy=3.9 ##cm^3\n", + "## calculations\n", + "pi=pi*math.pi/180. ##radians\n", + "W=w*s+8.1\n", + "P=p*s\n", + "L=P+W*math.cos(pi)\n", + "Mx=L*s1**2*100./8.\n", + "sigma_1=Mx/Zx\n", + "My=W*math.sin(pi)*s1**2*100./8.\n", + "sigma_2=My/Zy\n", + "sigma=sigma_1+sigma_2\n", + "## results\n", + "print'%s %.2f %s'%('Maximum stresses are ',sigma,' kg/cm^2, tension or compression')\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum stresses are 1503.88 kg/cm^2, tension or compression\n" + ] + } + ], + "prompt_number": 28 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex7-pg369" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#calculate strain gauge \n", + "##initialization of variables\n", + "import math\n", + "s=1.6 ##m\n", + "s1=4. ##m\n", + "pi=28. ##degrees\n", + "w=16. ##kg/m^2\n", + "p=100. ##kg/m^2\n", + "pl=20. ##cm\n", + "pb=10. ##cm\n", + "r=500. ##kg/m^3\n", + "sg=5. ##cm\n", + "E=12*10**4\n", + "pi=pi*math.pi/180 ##radians\n", + "## calculations\n", + "W=w*s+(r*pl*pb/(100.*100.))\n", + "P=p*s\n", + "L=P+W*math.cos(pi)\n", + "Mx=L*s1**2*100/8.\n", + "sigma_1=Mx*6./(pb*pl**2)\n", + "My=W*math.sin(pi)*s1**2*100/8.\n", + "sigma_2=My*6./(pl*pb**2)\n", + "st=sigma_1*sg/10.\n", + "Ts=st-sigma_2\n", + "ez=Ts/E\n", + "## results\n", + "print'%s %.2e %s'%('The strain gauge, aligned to the z axis will give compression strain of ',ez,'')\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The strain gauge, aligned to the z axis will give compression strain of 1.56e-04 \n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex8-pg371" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#calcualte bending stress and shearing stress\n", + "##initialization of variables\n", + "import math\n", + "P=3. ##tonne/m\n", + "s=6. ##m\n", + "l=50. ##cm\n", + "b=20. ##cm\n", + "k=0.5 ##m\n", + "##calculations\n", + "R=P*s/2.\n", + "sf=R-k*P\n", + "bm=R*k-P*k**2/2.\n", + "tau_xy=1.5*sf*1000./(l*b)\n", + "tau_max=tau_xy\n", + "str=bm*s*10**5/(b*l*l)\n", + "\n", + "## consider the line a-a\n", + "\n", + "sigma_x=str*12.5/25.\n", + "sigma_y=0.\n", + "tau_xy=tau_xy*(1.-(12.5/25.)**2)\n", + "\n", + "sigma_1=(sigma_x+sigma_y)/2.+math.sqrt((1/2*(sigma_x-sigma_y))**2+tau_xy**2)\n", + "sigma_2=(sigma_x+sigma_y)/2.-math.sqrt((1/2*(sigma_x-sigma_y))**2+tau_xy**2)\n", + "\n", + "print'%s %.2f %s %.2f %s '%('For the line a-a the bending stress and shearing stress are \\n respectively ',sigma_x,' kg/cm^2'and'',tau_xy,'kg/cm^2 ')\n", + "print'%s %.2f %s %.2f %s '%('\\n The principal stresses are ',sigma_1,' kg/cm^2 (tension)' and '',sigma_2,'kg/cm^2 (compression) ')\n", + "\n", + "##consider the line c-c\n", + "print'%s %.2f %s %.2f %s '%('\\n For the line c-c the bending stress and shearing stress are \\n respectively ',sigma_x,' kg/cm^2'and '',tau_xy,' kg/cm^2 ')\n", + "print'%s %.2f %s %.2f %s '%('\\n The principal stresses are ',sigma_2,' kg/cm^2 (compression)'and '',sigma_1,' kg/cm^2 (tension) ')\n", + "\n", + "##for the line b-b\n", + "tau_xy=tau_max\n", + "sigma_x=0.\n", + "sigma_y=0.\n", + "sigma_1=(sigma_x+sigma_y)/2.+math.sqrt((1./2.*(sigma_x-sigma_y))**2+tau_xy**2)\n", + "sigma_2=(sigma_x+sigma_y)/2.-math.sqrt((1./2.*(sigma_x-sigma_y))**2+tau_xy**2)\n", + "## results\n", + "print'%s %.7f %s %.2f %s '%('\\n For the line b-b the bending stress and shearing stress are \\n respectively ',sigma_x,' kg/cm^2'and '',tau_xy,' kg/cm^2 ')\n", + "print'%s %.2f %s %.2f %s '%('\\n The principal stresses are ',sigma_1,' kg/cm^2 (tension)'and'',sigma_2,' kg/cm^2 (compression) ')\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "For the line a-a the bending stress and shearing stress are \n", + " respectively 24.75 8.44 kg/cm^2 \n", + "\n", + " The principal stresses are 20.81 3.94 kg/cm^2 (compression) \n", + "\n", + " For the line c-c the bending stress and shearing stress are \n", + " respectively 24.75 8.44 kg/cm^2 \n", + "\n", + " The principal stresses are 3.94 20.81 kg/cm^2 (tension) \n", + "\n", + " For the line b-b the bending stress and shearing stress are \n", + " respectively 0.0000000 11.25 kg/cm^2 \n", + "\n", + " The principal stresses are 11.25 -11.25 kg/cm^2 (compression) \n" + ] + } + ], + "prompt_number": 29 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex9-pg372" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#calculate tension and principal stress\n", + "##initialization of variables\n", + "import math\n", + "P=3. ##tonne/m\n", + "s=6. ##m\n", + "l=50. ##cm\n", + "b=20. ##cm\n", + "k=0.5 ##m\n", + "##calculations\n", + "R=P*s/2.\n", + "sf=R-k*P\n", + "bm=R*k-P*k**2/2.\n", + "tau_xy=1.5*sf*1000./(l*b) ##max shear stress\n", + "tau_max=tau_xy \n", + "str=bm*s*10**5/(b*l*l) ##max bending stress\n", + "\n", + "## consider the line a-a\n", + "\n", + "sigma_x=str*12.5/25.\n", + "sigma_y=0.\n", + "tau_xy=tau_xy*(1.-(12.5/25.)**2)\n", + "\n", + "sigma_1=(sigma_x+sigma_y)/2.+math.sqrt((1/2.*(sigma_x-sigma_y))**2+tau_xy**2)\n", + "sigma_2=(sigma_x+sigma_y)/2-math.sqrt((1/2.*(sigma_x-sigma_y))**2+tau_xy**2)\n", + "\n", + "theta=1/2.*math.atan(2.*tau_xy/(sigma_x-sigma_y))*57.3\n", + "sigma_p=sigma_1/math.cos(theta)\n", + "P=sigma_p*2.*l*b/(3.*1000.)\n", + "print'%s %.2f %s'%('A prestressing force of ',P,' Tonne must be applied to balance the tension at a-a')\n", + "\n", + "##At bottom point D or C\n", + "pre_str=P*2.*1000./(l*b)\n", + "net=str-pre_str\n", + "print('\\n At bottom point D or C')\n", + "print'%s %.2f %s'%('\\n Net tension = ',net,' kg/cm^2 ')\n", + "\n", + "##consider the line b-b\n", + "pre_str=P\n", + "sigma_x=pre_str\n", + "sigma_y=0.\n", + "tau_xy=tau_max\n", + "sigma_1=(sigma_x+sigma_y)/2.+math.sqrt((1./2.*(sigma_x-sigma_y))**2+tau_xy**2)\n", + "sigma_2=(sigma_x+sigma_y)/2.-math.sqrt((1./2.*(sigma_x-sigma_y))**2+tau_xy**2)\n", + "print('\\n At section b-b')\n", + "print'%s %.2f %s '%('\\n pre-stress=',pre_str,' kg/cm^2')\n", + "print'%s %.2f %s %.2f %s '%('\\n principal stresses are ',sigma_1,''and'',sigma_2,' kg/cm^2 ')\n", + "\n", + "##for the line c-c\n", + "sigma_x=str*12.5/25.\n", + "sigma_y=0.\n", + "tau_xy=tau_xy*(1-(12.5/25.)**2)\n", + "sigma_1=(sigma_x+sigma_y)/2.+math.sqrt((1./2.*(sigma_x-sigma_y))**2+tau_xy**2)\n", + "sigma_2=(sigma_x+sigma_y)/2.-math.sqrt((1./2.*(sigma_x-sigma_y))**2+tau_xy**2)\n", + "pre_str=pre_str/2.\n", + "net=sigma_1+pre_str\n", + "sigma_x=net\n", + "sigma_y=0.\n", + "sigma_1=(sigma_x+sigma_y)/2.+math.sqrt((1./2.*(sigma_x-sigma_y))**2+tau_xy**2)\n", + "sigma_2=(sigma_x+sigma_y)/2.-math.sqrt((1./2.*(sigma_x-sigma_y))**2+tau_xy**2)\n", + "## results\n", + "print('\\n At section c-c')\n", + "print'%s %.2f %s'%('\\n the direct stress is ',net,' kg/cm^2')\n", + "print'%s %.2f %s'%('\\n pre-stress =',pre_str,' kg/cm^2')\n", + "print'%s %.2f %s %.2f %s '%('\\n principal stresses are',sigma_1,'kg/cm^2'and '',sigma_2,'kg/cm^2')\n", + "print('wrong calculations in the thext for some parts')\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "A prestressing force of -136.43 Tonne must be applied to balance the tension at a-a\n", + "\n", + " At bottom point D or C\n", + "\n", + " Net tension = 322.36 kg/cm^2 \n", + "\n", + " At section b-b\n", + "\n", + " pre-stress= -136.43 kg/cm^2 \n", + "\n", + " principal stresses are 0.92 -137.35 kg/cm^2 \n", + "\n", + " At section c-c\n", + "\n", + " the direct stress is -40.86 kg/cm^2\n", + "\n", + " pre-stress = -68.22 kg/cm^2\n", + "\n", + " principal stresses are 1.67 -42.54 kg/cm^2 \n", + "wrong calculations in the thext for some parts\n" + ] + } + ], + "prompt_number": 30 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex10-pg373" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#calculate sigma and Tau\n", + "##initialization of variables\n", + "import math\n", + "b=2. ##cm\n", + "h=2. ##cm\n", + "T=2000. ##kg-cm\n", + "V=250. ##kg\n", + "M=2000. ##kg-cm\n", + "## calculations\n", + "Mmax=M*6./(b*h*b)\n", + "Vmax=3.*V/(2.*b*h)\n", + "Zt=0.208*b**2*h\n", + "Tmax=T/(Zt)\n", + "\n", + "sigma=Mmax\n", + "print('points A,B,')\n", + "print'%s %.2f %s'%('\\n sigma=',sigma,' kg/cm^2 (tension)')\n", + "print('\\n points C,D,')\n", + "print'%s %.2f %s'%('\\n sigma=',sigma,' kg/cm^2 (cmpression)')\n", + "tau=Vmax+Tmax\n", + "print('\\n point E')\n", + "print'%s %.2f %s'%('\\n tau=',tau,'kg/cm^2 shear')\n", + "tau=Vmax-Tmax\n", + "print'%s %.2f %s'%('\\n tau=',tau,' kg/cm^2 shear')\n", + "## at G\n", + "sigma_x=sigma\n", + "sigma_y=0.\n", + "tau_xy=Tmax\n", + "sigma_1=(sigma_x+sigma_y)/2.+math.sqrt((1./2.*(sigma_x-sigma_y))**2+tau_xy**2)\n", + "sigma_2=(sigma_x+sigma_y)/2.-math.sqrt((1./2.*(sigma_x-sigma_y))**2+tau_xy**2)\n", + "## results\n", + "print('\\n at point G')\n", + "print'%s %.2f %s'%('\\n sigma_1 = ',sigma_1,' kg/cm^2 (tension)')\n", + "print'%s %.2f %s'%('\\n sigma_2 = ',sigma_2,' kg/cm^2 (compression)')\n", + "\n", + "print('Question was asked only to find out at A,B,C,D,E,F and G')\n", + "print(' And in book Ans worng')\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "points A,B,\n", + "\n", + " sigma= 1500.00 kg/cm^2 (tension)\n", + "\n", + " points C,D,\n", + "\n", + " sigma= 1500.00 kg/cm^2 (cmpression)\n", + "\n", + " point E\n", + "\n", + " tau= 1295.67 kg/cm^2 shear\n", + "\n", + " tau= -1108.17 kg/cm^2 shear\n", + "\n", + " at point G\n", + "\n", + " sigma_1 = 2166.73 kg/cm^2 (tension)\n", + "\n", + " sigma_2 = -666.73 kg/cm^2 (compression)\n", + "Question was asked only to find out at A,B,C,D,E,F and G\n", + " And in book Ans worng\n" + ] + } + ], + "prompt_number": 31 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex11-pg374" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#calculate total shear and bending stress and principal stress\n", + "##initialization of variables\n", + "import math\n", + "w=10. ##cm\n", + "s=2.8 ##m\n", + "P=1. ##tonne\n", + "Ft=1.4 ##cm\n", + "Wt=0.8 ##cm\n", + "Ix=13989.5 ##cm^4\n", + "Z=699.5 ##cm^3\n", + "## calculations\n", + "BM= 2.8 \n", + "T=P*1000*8.21\n", + "SF=P*1000.\n", + "BS=BM*10**5/(Z)\n", + "sigmaXA=BS*18.6/20.\n", + "K=w*Ft*19.3+18.6*Wt*9.3\n", + "tau_xy_C=SF/(Ix*Wt)*K\n", + "tau_xy_A=tau_xy_C*(w*Ft*19.3)/K \n", + "tau_xy_B=tau_xy_A*0.5*Wt/w\n", + "sigmaXB=sigmaXA*19.3/20.\n", + "\n", + "tau_max=3*Ft*8210./(w*Ft**3+37.2*Wt**3)\n", + "tau_A=3*Wt*8210./(w*Ft**3+37.2*Wt**3)\n", + "\n", + "##For point A\n", + "Shear=tau_xy_A-tau_A\n", + "sigma_x=sigmaXA\n", + "sigma_y=0.\n", + "tau_xy=Shear\n", + "sigma_1=(sigma_x+sigma_y)/2.+math.sqrt((1./2.*(sigma_x-sigma_y))**2+tau_xy**2)\n", + "sigma_2=(sigma_x+sigma_y)/2.-math.sqrt((1./2.*(sigma_x-sigma_y))**2+tau_xy**2)\n", + "\n", + "print('For point A')\n", + "print'%s %.2f %s'%('\\n Total shear= ',Shear,' kg/cm^2 ')\n", + "print'%s %.2f %s'%('\\n Bending stress = ',sigma_x,' kg/cm^2 (Compr.)')\n", + "print'%s %.2f %s %.2f %s '%('\\n Principal stresses are ',sigma_1,'(tension)kg/cm^2 'and'' ,sigma_2,'(comp.) kg/cm^2 ')\n", + "\n", + "##For point B\n", + "print('\\n FOr point B')\n", + "print'%s %.2f %s'%('\\n Bending shear stress is ',tau_xy_B,' k/cm^2')\n", + "sigmaXB=BS*19.3/20.\n", + "sigma_x=sigmaXB\n", + "sigma_y=0.\n", + "tau_xy=tau_max\n", + "sigma_1=(sigma_x+sigma_y)/2.+math.sqrt((1./2.*(sigma_x-sigma_y))**2+tau_xy**2)\n", + "sigma_2=(sigma_x+sigma_y)/2.-math.sqrt((1./2.*(sigma_x-sigma_y))**2+tau_xy**2)\n", + "print'%s %.2f %s %.2f %s '%('\\n Principal stresses are ',sigma_1,' (tension) kg/cm^2'and'',sigma_2,' (comp.) kg/cm^2 ')\n", + "print('Answers in the text are approximations')\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "For point A\n", + "\n", + " Total shear= -399.72 kg/cm^2 \n", + "\n", + " Bending stress = 372.27 kg/cm^2 (Compr.)\n", + "\n", + " Principal stresses are 627.07 -254.80 (comp.) kg/cm^2 \n", + "\n", + " FOr point B\n", + "\n", + " Bending shear stress is 0.97 k/cm^2\n", + "\n", + " Principal stresses are 959.64 -573.36 (comp.) kg/cm^2 \n", + "Answers in the text are approximations\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex12-pg380" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#calcualte permissible stress and developed stress\n", + "##initialization of variables\n", + "import math\n", + "b=10. ##cm\n", + "h=10. ##cm\n", + "P=5. ##tonne\n", + "e=1. ##cm\n", + "E=12*10**4 ##kg/cm^2\n", + "str=130. ## kg/cm^2\n", + "n=3.\n", + "L=2. ##m\n", + "## calculations\n", + "L=L*100. ##cm\n", + "Pcr=math.pi**2*E*b*h**3/(12.*L**2.)\n", + "Pcr=Pcr/1000.\n", + "Smax=-P*1000./(b*h)-(P*1000.*1.*5.*12./10**4)*1./(1.-(n*P/Pcr))\n", + "## results\n", + "print'%s %.2f %s'%('permissible stress = ',str,' kg/cm^2')\n", + "print'%s %.2f %s'%('\\n develoed stress = ',Smax,' kg/cm^2')\n", + "print('\\n Since it is below the permissible stress, the design is safe')\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "permissible stress = 130.00 kg/cm^2\n", + "\n", + " develoed stress = -126.52 kg/cm^2\n", + "\n", + " Since it is below the permissible stress, the design is safe\n" + ] + } + ], + "prompt_number": 33 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex13-pg381" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "##initializatio of variables\n", + "#calculate Smax and percentage error\n", + "## linked to 9.13\n", + "b=10. ##cm\n", + "h=10. ##cm\n", + "P=5. ##tonne\n", + "e=1. ##cm\n", + "E=12.*10**4 ##kg/cm^2\n", + "str=130. ## kg/cm^2\n", + "n=3.\n", + "L=2. ##m\n", + "## calculations\n", + "L=L*100. ##cm\n", + "Pcr=math.pi**2*E*b*h**3/(12*L**2)\n", + "Pcr=Pcr/1000.\n", + "Smax=-P*1000./(b*h)-(P*1000.*1.*5.*12./10**4)*1./(1.-(n*P/Pcr))\n", + "Smax=abs(Smax)\n", + "\n", + "rr=b*h**3/(12.*100.)\n", + "Smax_se=P*1000./(b*h)*(1+e*5/rr*(1./math.cos(math.pi/2.*math.sqrt(n*P/Pcr))))\n", + "Perror=(Smax-Smax_se)/Smax\n", + "Perror=Perror*100.\n", + "Perror=abs(Perror)\n", + "## results\n", + "print'%s %.2f %s'%('Using secent formula, stress obtained is ',Smax_se,' kg/cm^2')\n", + "print'%s %.2f %s'%('\\n hence, the percentage error ',Perror,'')\n", + "## approximate answees in the text\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Using secent formula, stress obtained is 138.45 kg/cm^2\n", + "\n", + " hence, the percentage error 9.43 \n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex14-pg382" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "##initialization of variables\n", + "#calculate maximum stress developed\n", + "P=400. ##kg/m\n", + "L=10. ##m\n", + "F=10. ##tonne\n", + "n=3.\n", + "Ixx=5943.1 ##cm^4\n", + "A=52.03 ##cm^2\n", + "rx=10.69 ##cm\n", + "E=2*10**6 ##kg/cm^2\n", + "## calculations\n", + "Pcr=math.pi**2*E*Ixx/((L*100.)**2.)\n", + "Pcr=Pcr/1000.\n", + "e=P*L**2/(8*F*1000.)\n", + "g=e*12.5*100./rx**2\n", + "Smax=F*1000./A*(1.+g*1./(1-n*(F/Pcr)))\n", + "## results\n", + "print'%s %.2f %s'%('The maximum stress developed is ',Smax,' kg/cm^2')\n", + "\n", + "print('approximate calculations involved in the text book')\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The maximum stress developed is 1604.54 kg/cm^2\n", + "approximate calculations involved in the text book\n" + ] + } + ], + "prompt_number": 35 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Ex15-pg383" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "#calculate maximum stress developed\n", + "##initialization of variables\n", + "import math\n", + "## linked to 9_14\n", + "## calculations\n", + "P=400. ##kg/m\n", + "L=10. ##m\n", + "F=10. ##tonne\n", + "n=3.\n", + "Ixx=5943.1 ##cm^4\n", + "A=52.03 ##cm^2\n", + "rx=10.69 ##cm\n", + "E=2*10**6 ##kg/cm^2\n", + "Pcr=math.pi**2.*E*Ixx/((L*100.)**2)\n", + "Pcr=Pcr/1000.\n", + "e=P*L**2./(8.*F*1000.)\n", + "g=e*12.5*100./rx**2.\n", + "Smax=F*1000./A*(1+g*1./(1.+n*(F/Pcr)))\n", + "## results\n", + "print'%s %.2f %s'%('The maximum stress developed is ',Smax,' kg/cm^2')\n", + "\n", + "print('approximate answer in the text')\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The maximum stress developed is 1029.29 kg/cm^2\n", + "approximate answer in the text\n" + ] + } + ], + "prompt_number": 36 + } + ], + "metadata": {} + } + ] +} \ No newline at end of file -- cgit