{
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"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": {}
}
]
}