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{
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"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter3-Two-Dimensional problems in elasticity"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex5-pg83"
]
},
{
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"collapsed": false,
"input": [
"import math\n",
"#calculate alpha and semiaxes of elliptical contaact area and max contact pressure\n",
"E=210. ##GPa\n",
"v=0.3\n",
"r1=0.4 ##m radius\n",
"r2=0.3 ##m cross radius\n",
"P=90. ##kN compression load\n",
"\n",
"\n",
"m=4./((1./r1)+(1./r2))\n",
"print'%s %.2f %s'%(\"m\",m,\"\")\n",
"A=(1/2.)*((1./r1)+(1./r2))\n",
"print'%s %.2f %s'%(\"A\",A,\"\")\n",
"B=(1/2.)*((1./r1)-(1./r2))\n",
"print'%s %.2f %s'%(\"B\",B,\"\")\n",
"coss=(((1./r1)-(1./r2))/((1./r1)+(1./r2)))\n",
"print'%s %.2f %s'%(\"cos aplha is= \",coss,\"\")\n",
"n=(4.*E*10**9.)/(3.*(1.-v**2.))\n",
"print'%s %.3e %s'%(\"n is \",n,\"\")\n",
"s=math.acos(coss)*57.3\n",
"print'%s %.2f %s'%(\" s is alpha value = \",s,\"\") ## ans is 81.79degree but here since cosa is in negative we get ans as 98.21\n",
"ca=1.1040 ## from the interpolating table\n",
"cb=0.9112 ## from the interpolating table\n",
"a=ca*(90000.*m/n)**(0.33)\n",
"print'%s %.4f %s'%(\"semiaxes of the elliptical contact area in meter is= \",a,\"\")\n",
"b=cb*(90000*m/n)**(0.33)\n",
"print'%s %.4f %s'%(\"semiaxes of the elliptical contact area in meter is= \",b,\"\")\n",
"sigmac=1.5*(90000./(math.pi*a*b))\n",
"print'%s %.3e %s'%(\"max contact pressure in Pa is= \",sigmac,\"\") ## text book ans is wrong\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"m 0.69 \n",
"A 2.92 \n",
"B -0.42 \n",
"cos aplha is= -0.14 \n",
"n is 3.077e+11 \n",
" s is alpha value = 98.22 \n",
"semiaxes of the elliptical contact area in meter is= 0.0068 \n",
"semiaxes of the elliptical contact area in meter is= 0.0056 \n",
"max contact pressure in Pa is= 1.125e+09 \n"
]
}
],
"prompt_number": 1
}
],
"metadata": {}
}
]
}
|
