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| author | hardythe1 | 2015-05-05 14:21:39 +0530 |
|---|---|---|
| committer | hardythe1 | 2015-05-05 14:21:39 +0530 |
| commit | 435840cef00c596d9e608f9eb2d96f522ea8505a (patch) | |
| tree | 4c783890c984c67022977ca98432e5e4bab30678 /Materials_Science/Chapter07.ipynb | |
| parent | aa1863f344766ca7f7c20a395e58d0fb23c52130 (diff) | |
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diff --git a/Materials_Science/Chapter07.ipynb b/Materials_Science/Chapter07.ipynb new file mode 100755 index 00000000..82a2c634 --- /dev/null +++ b/Materials_Science/Chapter07.ipynb @@ -0,0 +1,724 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:c09a61f5f13016fbda07546fd7ab3e30960d55a34ee491901311869fc5da9a32"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter07:Mechanical Tests of Metals"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex7.1:pg-146"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Example 7.1 : shear modulus of the material\n",
+ " \n",
+ "#given data :\n",
+ "E=210 # youngs's modulus in GN/m**2\n",
+ "v=0.3 # poisson ratio\n",
+ "G=E/(2*(1+v)) # shear modulus\n",
+ "\n",
+ "print \"shear modulus,G(GN/m**2) = \",round(G,2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "shear modulus,G(GN/m**2) = 80.77\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex7.2:pg-152"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Example 7.2 : young's modulus of elasticity,yield point stress, ultimate stress and percentage elongation\n",
+ " \n",
+ "#given data :\n",
+ "d=40.0*10**-3 #in m\n",
+ "W=40.0*10**3 # load in N\n",
+ "del_l=3.04*10**-5 # in m\n",
+ "L=200.0*10**-3 # in m\n",
+ "load_max=242.0*10**3 #in N\n",
+ "l=249*10.0**-3 # length of specimen in m\n",
+ "l0=(d+L) # in m\n",
+ "A=(math.pi*d**2)/4.0\n",
+ "\n",
+ "b=W/A\n",
+ "\n",
+ "epsilon=del_l/L\n",
+ "\n",
+ "E=(b/epsilon)\n",
+ "\n",
+ "print\"young modulus,E(N/m**2) = \",E\n",
+ "\n",
+ "Y_load=161*10**3\n",
+ "\n",
+ "Y_stress=Y_load/A\n",
+ "\n",
+ "print \"yield point stress,Y_stress(N/m**2) = \",Y_stress\n",
+ "\n",
+ "U_stress=load_max/A\n",
+ "\n",
+ "print \"ultimate stress,U_stress(N/m**2) = \",U_stress\n",
+ "\n",
+ "p_elongation=((l-l0)/l0)*100\n",
+ "\n",
+ "print \"percentage elongation,p_elongation(%) = \",p_elongation\n",
+ "#percentage elongation is calculated wrong in textbook\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "young modulus,E(N/m**2) = 2.09414398805e+11\n",
+ "yield point stress,Y_stress(N/m**2) = 128119729.189\n",
+ "ultimate stress,U_stress(N/m**2) = 192577481.141\n",
+ "percentage elongation,p_elongation(%) = 3.75\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex7.3.a:pg-153"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Example 7.3.a: yield point stress\n",
+ " \n",
+ "\n",
+ "yl=40.0 #yeild load in kN\n",
+ "ml=71.5 #maximum load in kN\n",
+ "fl=50.5 #fracture load in kN\n",
+ "glf=79.5 #gauge length of fratture in mm\n",
+ "st=7.75*10**-4 #strain at load of 20kN\n",
+ "d=12.5 #specimen diamtere in mm\n",
+ "sl=62.5 #specimen length in mm\n",
+ "A=(math.pi*(d*10**-3)**2)/4.0 # in meter square\n",
+ "ylp=((yl*10.0**3)/(A)) #yeild point stress in N/m**2\n",
+ "print \"yeild point stress in N/m**2 is \",ylp \n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "yeild point stress in N/m**2 is 325949323.452\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex7.3.b:pg-153"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Example 7.3.b: ultimate tensile strength\n",
+ " \n",
+ "yl=40.0 #yeild load in kN\n",
+ "ml=71.5 #maximum load in kN\n",
+ "fl=50.5 #fracture load in kN\n",
+ "glf=79.5 #gauge length of fratture in mm\n",
+ "st=7.75*10**-4 #strain at load of 20kN\n",
+ "d=12.5 #specimen diamtere in mm\n",
+ "sl=62.5 #specimen length in mm\n",
+ "A=(math.pi*(d*10**-3)**2)/4.0 # in meter square\n",
+ "ylp=((yl*10.0**3)/(A)) #yeild point stress in N/m**2\n",
+ "uts=((ml*10.0**3)/(A)) #ultimate tensile strangth in N/m**2\n",
+ "print uts,\"is ultimate tensile strangth in N/m**2\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "582634415.671 is ultimate tensile strangth in N/m**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex7.3.c:pg153"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Example 7.3.c: percentage elongation\n",
+ " \n",
+ "yl=40 #yeild load in kN\n",
+ "ml=71.5 #maximum load in kN\n",
+ "fl=50.5 #fracture load in kN\n",
+ "glf=79.5 #gauge length of fratture in mm\n",
+ "st=7.75*10**-4 #strain at load of 20kN\n",
+ "d=12.5 #specimen diamtere in mm\n",
+ "sl=62.5 #specimen length in mm\n",
+ "a=(math.pi*d*10**-3)**2/4 # in meter square\n",
+ "pel=((glf-sl)/sl)*100 #percentage elongation\n",
+ "print pel,\"% is percentage elongation\"\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "27.2 % is percentage elongation\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex7.3.d:pg-153"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Example 7.3.d:modulus of elasticity\n",
+ "import math\n",
+ "yl=40 #yeild load in kN\n",
+ "ml=71.5 #maximum load in kN\n",
+ "fl=50.5 #fracture load in kN\n",
+ "glf=79.5 #gauge length of fratture in mm\n",
+ "st=7.75*10**-4 #strain at load of 20kN\n",
+ "d=12.5 #specimen diamtere in mm\n",
+ "sl=62.5 #specimen length in mm\n",
+ "A=(math.pi*(d*10**-3)**2)/4.0 # in meter square\n",
+ "ylp=((yl*10**3)/(A)) #yeild point stress in N/m**2\n",
+ "uts=((ml*10**3)/(A)) #ultimate tensile strangth in N/m**2\n",
+ "pel=((glf-sl)/sl)*100 #percentage elongation\n",
+ "strss=((20*10**3)/A) #stress at 20kN in N/m**2\n",
+ "mel=strss/st #modulus of elasticity in N/m**2\n",
+ "print round(mel,2),\"is modulus of elasticity in N/m**2\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "2.10289886098e+11 is modulus of elasticity in N/m**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex7.3.e:pg153"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Example 7.3.e: yield point stress\n",
+ "import math\n",
+ "yl=40.0 #yeild load in kN\n",
+ "ml=71.5 #maximum load in kN\n",
+ "fl=50.5 #fracture load in kN\n",
+ "glf=79.5 #gauge length of fratture in mm\n",
+ "st=7.75*10**-4.0 #strain at load of 20kN\n",
+ "d=12.5 #specimen diamtere in mm\n",
+ "sl=62.5 #specimen length in mm\n",
+ "A=(math.pi*(d*10**-3)**2)/4.0 # in meter square\n",
+ "ylp=((yl*10**3)/(A)) #yeild point stress in N/m**2\n",
+ "uts=((ml*10**3)/(A)) #ultimate tensile strangth in N/m**2\n",
+ "pel=((glf-sl)/sl)*100 #percentage elongation\n",
+ "strss=((20*10**3)/A) #stress at 20kN in N/m**2\n",
+ "mel=strss/st #modulus of elasticity in N/m**2\n",
+ "mrs=((ylp*10**-3)**2/(2*mel)) #modulus of resilience \n",
+ "print mrs,\" is modulus of resilience\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "0.252610725675 is modulus of resilience\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex7.3.f:pg-153"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Example 7.3.f: fracture stress\n",
+ " \n",
+ "yl=40 #yeild load in kN\n",
+ "ml=71.5 #maximum load in kN\n",
+ "fl=50.5 #fracture load in kN\n",
+ "glf=79.5 #gauge length of fratture in mm\n",
+ "st=7.75*10**-4 #strain at load of 20kN\n",
+ "d=12.5#specimen diamter in mm\n",
+ "sl=62.5 #specimen length in mm\n",
+ "A=(math.pi*(d*10**-3)**2.0)/4 # in meter square\n",
+ "ylp=((yl*10**3)/(A)) #yeild point stress in N/m**2\n",
+ "uts=((ml*10**3)/(A)) #ultimate tensile strangth in N/m**2\n",
+ "pel=((glf-sl)/sl)*100 #percentage elongation\n",
+ "strss=((20*10.0**3)/A) #stress at 20kN in N/m**2\n",
+ "mel=strss/st #modulus of elasticity in N/m**2\n",
+ "mrs=((ylp*10**-3)**2.0/(2*mel)) #modulus of resilience \n",
+ "fs=((fl*10.0**3)/(A)) #fracture stress in N/m**2\n",
+ "print fs,\"is fracture stress in N/m**2\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "411511020.858 is fracture stress in N/m**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex7.3.g:pg153"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "# Example 7.3.g: modulus of toughness\n",
+ " \n",
+ "yl=40.0 #yeild load in kN\n",
+ "ml=71.5 #maximum load in kN\n",
+ "fl=50.5 #fracture load in kN\n",
+ "glf=79.5 #gauge length of fratture in mm\n",
+ "st=7.75*10**-4 #strain at load of 20kN\n",
+ "d=12.5 #specimen diamtere in mm\n",
+ "sl=62.5 #specimen length in mm\n",
+ "A=(math.pi*(d*10**-3)**2)/4 # in meter square\n",
+ "ylp=((yl*10**3)/(A)) #yeild point stress in N/m**2\n",
+ "uts=((ml*10**3)/(A)) #ultimate tensile strangth in N/m**2\n",
+ "pel=((glf-sl)/sl)*100 #percentage elongation\n",
+ "strss=((20*10**3)/A) #stress at 20kN in N/m**2\n",
+ "mel=strss/st #modulus of elasticity in N/m**2\n",
+ "mrs=((ylp*10**-3)**2/(2*mel)) #modulus of resilience \n",
+ "fs=((fl*10**3)/(A)) #fracture stress in N/m**2\n",
+ "mth=((ylp+uts)*(pel/100))/2 #modulus of toughness in N/m**2\n",
+ "print mth,\" is modulus of toughness in N/m**2\"\n",
+ "#percentage reduction in area is not calulated in the textbook\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "123567388.521 is modulus of toughness in N/m**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex7.4:pg-155"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "#Example 7.4 : true breaking stress and nominal breaking stress \n",
+ " \n",
+ "\n",
+ "#given data :\n",
+ "d1=12.7; # in mm\n",
+ "B_load=14;# in K-N\n",
+ "A1=(math.pi*d1**2)/4;# original cross section area\n",
+ "d2=7.87; # in mm\n",
+ "A2=(math.pi*d2**2)/4;# final cross sction area\n",
+ "T_stress=B_load/A2;\n",
+ "print T_stress*1000,\" is true breaking stress,T_stress in (N/mm**2) \"\n",
+ "N_stress=B_load/A1;\n",
+ "print N_stress*1000,\" is nominal breaking stress,N_stress in (N/mm**2) \"\n",
+ "#true breaking stress unit is wrong in the textbook\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "287.798608363 is true breaking stress,T_stress in (N/mm**2) \n",
+ "110.517413518 is nominal breaking stress,N_stress in (N/mm**2) \n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex7.5.a:pg-155"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Example 7.5.a: yield point stress\n",
+ " \n",
+ "\n",
+ "yl=34.0;#yeild load in kN\n",
+ "ul=61.0;#ultimate load in kN\n",
+ "fl=78.0;#final length in mm\n",
+ "glf=60.0;#gauge length of fratture in mm\n",
+ "fd=7.0;#final diamtere in mm\n",
+ "d=12.0;#specimen diamtere in mm\n",
+ "sl=62.5;#specimen length in mm\n",
+ "A=(math.pi*(d)**2)/4;# in meter square\n",
+ "ylp=((yl*10**3)/(A));# yeild point stress in N/mm**2\n",
+ "print floor(ylp),\" is yeild point stress in N/mm**2\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "300.0 is yeild point stress in N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex7.5.b:pg-155"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Example 7.5.b: ultimate tensile stress\n",
+ " \n",
+ "\n",
+ "yl=34.0;#yeild load in kN\n",
+ "ul=61.0;#ultimate load in kN\n",
+ "fl=78.0;#final length in mm\n",
+ "glf=60.0;#gauge length of fratture in mm\n",
+ "fd=7.0;#final diamtere in mm\n",
+ "d=12.0;#specimen diamtere in mm\n",
+ "sl=62.5;#specimen length in mm\n",
+ "A=(math.pi*(d)**2)/4;# in meter square\n",
+ "uts=((ul*10**3)/(A));#ultimate tensile strangth in N/mm**2\n",
+ "print uts,\" is ultimate tensile strangth in N/mm**2\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "539.358418256 is ultimate tensile strangth in N/mm**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex7.5.c:pg-155"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Example 7.5.c: percentage reduction\n",
+ " \n",
+ " \n",
+ "yl=34;#yeild load in kN\n",
+ "ul=61;#ultimate load in kN\n",
+ "fl=78;#final length in mm\n",
+ "glf=60;#gauge length of fratture in mm\n",
+ "fd=7;#final diamtere in mm\n",
+ "d=12;#specimen diamtere in mm\n",
+ "sl=62.5;#specimen length in mm\n",
+ "A=(math.pi*(d)**2)/4;# in mm square\n",
+ "A1=(math.pi*(fd)**2)/4;# in mm square\n",
+ "pr=(A-A1)/A;# reduction\n",
+ "print round(pr*100,2),\"% is percentage reduction\"\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "65.97 % is percentage reduction\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex7.5.d:pg-155"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Example 7.5.d: percentage elonagtion\n",
+ " \n",
+ "\n",
+ "yl=34.0;#yeild load in kN\n",
+ "ul=61.0;#ultimate load in kN\n",
+ "fl=78.0;#final length in mm\n",
+ "glf=60.0;#gauge length of fratture in mm\n",
+ "fd=7.0;#final diamtere in mm\n",
+ "d=12.0;#specimen diamtere in mm\n",
+ "sl=62.5;#specimen length in mm\n",
+ "A=(math.pi*(d)**2)/4;# in mm square\n",
+ "A1=(math.pi*(fd)**2)/4;# in mm square\n",
+ "pr=(fl-glf)/glf;# elongation\n",
+ "print round(pr*100,2),\"% is percentage elongtion \"\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "30.0 % is percentage elongtion \n"
+ ]
+ }
+ ],
+ "prompt_number": 24
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex7.6:pg-156"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Example 7.6 : strain \n",
+ " \n",
+ "\n",
+ "#given data :\n",
+ "b=44.5*10**3;#force\n",
+ "E=1.1*10**5;# in N/mm**2\n",
+ "A=15.2*19.1# in mm**2\n",
+ "epsilon=b/(A*E);\n",
+ "print \"strain,epsilon (mm) = \",epsilon"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "strain,epsilon (mm) = 0.00139344672963\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex7.7:pg-156"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Example 7.7 :stress and strain \n",
+ " \n",
+ "\n",
+ "#given data :\n",
+ "sigma=450;#in MPa\n",
+ "epsilon=0.63;\n",
+ "sigma_t=sigma*(1+epsilon);\n",
+ "print \"true stress,sigma_t(MPa) = \",sigma_t\n",
+ "epsilon_t=math.log(1+epsilon);\n",
+ "print \"true strain,epsilon_t(MPa) = \",epsilon_t\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "true stress,sigma_t(MPa) = 733.5\n",
+ "true strain,epsilon_t(MPa) = 0.488580014819\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex7.8:pg-157"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Example 7.8: which part has a greater stress\n",
+ " \n",
+ "l=24.0;#length in mm\n",
+ "b=30;#breadth in mm\n",
+ "ld=7000;#load in kg\n",
+ "sd=10;#steel bar diamtere in mm\n",
+ "sl=5000.0;#load in kg\n",
+ "al=ld/(l*b);#stress on aluminium bar in kg/mm**2\n",
+ "a=((math.pi*sd**2)/4.0);#area in mm**2\n",
+ "slb=sl/a;#stress on steel bar in kg/mm**2\n",
+ "print\"stress on aluminium bar is \",round(al,2),\" kg/mm**2 is less than stress on steel bar \",round(slb,2),\" kg/mm**2 \"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "stress on aluminium bar is 9.72 kg/mm**2 is less than stress on steel bar 63.66 kg/mm**2 \n"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
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