{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 6: Mechanical Properties of Metal"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 6.1 Page No 140"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"E=110*10**3 #Young's modulus of Copper in MPa\n",
"sigma=276.0 #Applied stress in MPa\n",
"lo=305.0 #Original length in mm\n",
"\n",
"dl=sigma*lo/E\n",
"\n",
"print\"Elongation obtained is \",round(dl,2),\"mm\"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Elongation obtained is 0.77 mm\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 6.2 Page No 142"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"del_d=-2.5*10**-3 #Deformation in dia in mm\n",
"d0=10.0 #Initial dia in mm\n",
"v=0.34 #Poisson ratio for brass\n",
"\n",
"ex=del_d/d0\n",
"ez=-ex/v\n",
"E=97*10**3 #Modulus of elasticity in MPa\n",
"sigma=ez*E\n",
"F=sigma*math.pi*(d0**2)/4.0\n",
"\n",
"print\"Applied force is \",round(F,0),\"N\"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Applied force is 5602.0 N\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 6.3 Page No 146"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"si2=150 # in MPa\n",
"si1=0\n",
"e2=0.0016\n",
"e1=0\n",
"d0=12.8*10**-3 #Initial Diameter in m\n",
"\n",
"E=(si2-si1)/(e2-e1)\n",
"\n",
"A0=math.pi*d0**2/4.0\n",
"sig=450*10**6 #tensile strength in MPa\n",
"F=sig*A0\n",
"l0=250 #Initial lengt in mm\n",
"e=0.06 #strain\n",
"dl=e*l0\n",
"\n",
"print\"Modulus of elasticity is \",round(E/10**3,1),\"GPa\"\n",
"print\"From the graph the Yield strength is\",l0,\"MPa\"\n",
"print\"Maximum load sustained is \",round(F,0),\"N/n\"\n",
"print\"Change in length is \",dl,\"mm\"\n",
"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Modulus of elasticity is 93.8 GPa\n",
"From the graph the Yield strength is 250 MPa\n",
"Maximum load sustained is 57906.0 N/n\n",
"Change in length is 15.0 mm\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 6.4 Page No 153"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"di=12.8 #Initial dia in mm\n",
"df=10.7 #Final dia in mm\n",
"\n",
"import math\n",
"RA = ((di**2-df**2)/di**2)*100\n",
"Ao=math.pi*di**2*10**-6/4.0\n",
"sig=460*10**6 #Tensile strength\n",
"\n",
"F=sig*Ao\n",
"\n",
"Af=math.pi*df**2/4.0\n",
"sig_t=F/Af\n",
"\n",
"print\"percent reduction in area is \",round(RA,0),\"%\"\n",
"print\"True stress is \",round(sig_t,1),\"MPa\"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"percent reduction in area is 30.0 %\n",
"True stress is 658.3 MPa\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 6.5 Page No 153"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"sig_t=415 #True stress in MPa\n",
"et=0.1 #True strain\n",
"K=1035.0 # In MPa\n",
"\n",
"n=(math.log(sig_t)-math.log(K))/math.log(et)\n",
"\n",
"print\"Strain - hardening coefficient is \",round(n,2)\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Strain - hardening coefficient is 0.4\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 6.6 Page No 162"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"n=4.0 #No of points\n",
"T1=520\n",
"T2=512\n",
"T3=515\n",
"T4=522\n",
"\n",
"Tav=(T1+T2+T3+T4)/n\n",
"s=(((T1-Tav)**2+(T2-Tav)**2+(T3-Tav)**2+(T4-Tav)**2)/(n-1))**(0.5)\n",
"\n",
"print\"The average Tensile strength is\",round(Tav,0),\"MPa\"\n",
"print\"The standard deviation is\",round(s,1),\"MPa\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The average Tensile strength is 517.0 MPa\n",
"The standard deviation is 4.6 MPa\n"
]
}
],
"prompt_number": 22
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Design Example 6.1 ,Page No 164"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"sig_y=310.0 #Minimum yield strength in MPa\n",
"N=5.0 # Conservative factor of safety\n",
"\n",
"F=220000/2.0 #Two rods must support half of the total force\n",
"sig_w=sig_y/N\n",
"d=2*math.sqrt(F/(math.pi*sig_w))\n",
"\n",
"print\"Diameter of each of the two rods is \",round(d,1),\"mm\"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Diameter of each of the two rods is 47.5 mm\n"
]
}
],
"prompt_number": 18
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}