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{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter2-Strain and stress -strain relations"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex1-pg38"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#calculate radius of circle and principal stresses and distance between o and c and strain and shear strain and maxi shear stress\n",
"radius=((math.sqrt(195**2.+130**2.))*10**(-6.));\n",
"print'%s %.5f %s'%(\"radius of the circle in degree = \",radius,\"\")\n",
"theta1=(math.atan(130./195.))*57.3\n",
"print'%s %.2f %s'%(\"pricipal stresses in degree\",theta1,\"\");## print'%s %.2f %s'%laying result\n",
"epsilonx=510.*10**(-6.)\n",
"epsilony=120.*10**(-6.)\n",
"epsilon=(epsilonx+epsilony)/2.\n",
"print'%s %.5f %s'%(\"distance between O and c=\",epsilon,\"\")\n",
"\n",
"##solution a\n",
"angle=60.- theta1\n",
"print'%s %.2f %s'%(\"angle of ACA1 in degree = \",angle,\"\")## print'%s %.2f %s'%laying result\n",
"epsilonx1=epsilon+radius*math.cos(26.3/57.3)\n",
"print'%s %.5f %s'%(\"strains in x axis= \",epsilonx1,\"\")## print'%s %.2f %s'%laying result\n",
"epsilony1=epsilon-radius*math.cos(26.3/57.3)\n",
"print'%s %.5f %s'%(\"strains in y axis= \",epsilony1,\"\")## print'%s %.2f %s'%laying result\n",
"gammaxy=-2*(radius*math.sin(26.3/57.3))\n",
"print'%s %.5f %s'%(\"shear strain\",gammaxy,\"\")## print'%s %.2f %s'%laying result\n",
"\n",
"##solution b\n",
"epsilon1=epsilon+radius\n",
"print'%s %.5f %s'%(\"strains in x axis= \",epsilon1,\"\")## print'%s %.2f %s'%laying result\n",
"epsilon2=epsilon-radius\n",
"print'%s %.5f %s'%(\"strains in x axis= \",epsilon2,\"\")## print'%s %.2f %s'%laying result\n",
"\n",
"##solution c\n",
"gammamax=-+468*10**(-6)\n",
"print'%s %.5f %s'%(\"maxi shear stress= \",gammamax,\"\")\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"radius of the circle in degree = 0.00023 \n",
"pricipal stresses in degree 33.69 \n",
"distance between O and c= 0.00031 \n",
"angle of ACA1 in degree = 26.31 \n",
"strains in x axis= 0.00053 \n",
"strains in y axis= 0.00010 \n",
"shear strain -0.00021 \n",
"strains in x axis= 0.00055 \n",
"strains in x axis= 0.00008 \n",
"maxi shear stress= -0.00047 \n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex2-pg46"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#calculate value of epsilon and gamma\n",
"epsilon0=190.*10**(-6)\n",
"epsilon60=200.*10**(-6)\n",
"epsilon120=-300.*10**(-6)\n",
"E=200.## GPa\n",
"v=0.3\n",
"epsilonx=epsilon0\n",
"print'%s %.4f %s'%(\"value of epsilonx is= \",epsilonx,\"\")\n",
"\n",
"## epsilon60=((epsilonx+epsilony)/2)-((epsilonx-epsilony)/4)+(gammaxy*sqrt(3))/4 eqn 1\n",
"## epsilon120=((epsilonx+epsilony)/2)-((epsilonx-epsilony)/4)-(gammaxy*sqrt(3))/4 eqn 2\n",
"\n",
"epsilony=(2.*(epsilon60+epsilon120)-epsilon0)/3.\n",
"print'%s %.4f %s'%(\"value of epsilony is= \",epsilony,\"\")\n",
"gammaxy=(2./math.sqrt(3.))*(epsilon60-epsilon120)## from eqn 1 and eqn 2\n",
"print'%s %.5f %s'%(\"value of gammaxy is= \",gammaxy,\"\")\n",
"epsilon1=((epsilonx+epsilony)/2.)+math.sqrt(((epsilonx-epsilony)/2.)**2.+(gammaxy/2.)**2.)## epsilony value is in negative so the sign changes in the eqn\n",
"print'%s %.5f %s'%(\"value of epsilon1 is= \",epsilon1,\"\")\n",
"epsilon2=((epsilonx+epsilony)/2.)-math.sqrt(((epsilonx-epsilony)/2.)**2+(gammaxy/2.)**2.)##epsilony value is in negative so the sign changes in the eqn\n",
"print'%s %.4f %s'%(\"value of epsilon2 is= \",epsilon2,\"\")\n",
"\n",
"gammamax=(2.*10**-6)*math.sqrt(((epsilonx-epsilony)/2.)**2.+(gammaxy/2.)**2)\n",
"print'%s %.3e %s'%(\"max shear strain is= \",gammamax,\"\")\n",
"thetap=math.atan((577./320.)/2.)*57.3\n",
"print'%s %.2f %s'%(\"orientations of principal axes is= \",thetap,\"\") ## or\n",
"thetap1=math.atan((577./320.)*2.)*57.\n",
"print'%s %.2f %s'%(\"orientations of principal axes is= \",thetap1,\"\")\n",
"sigma1=(200.*10**9/(1.-0.09))*(epsilon1+0.3*epsilon2)\n",
"print'%s %.2f %s'%(\"plane stresss is Pa= \",sigma1,\"\")\n",
"sigma2=(200*10**3/(1-0.09))*(epsilon2+0.3*epsilon1)\n",
"print'%s %.2f %s'%(\"plane stresss is MPa= \",sigma2,\"\")\n",
"\n",
"taumax=(200.*10**9./(2.*(1.+0.3)))*gammamax\n",
"print'%s %.2f %s'%(\"plane stresss is MPa= \",taumax,\"\")\n",
"#error in orientationd of principal axes because of round off error \n",
"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"value of epsilonx is= 0.0002 \n",
"value of epsilony is= -0.0001 \n",
"value of gammaxy is= 0.00058 \n",
"value of epsilon1 is= 0.00036 \n",
"value of epsilon2 is= -0.0003 \n",
"max shear strain is= 6.601e-10 \n",
"orientations of principal axes is= 42.04 \n",
"orientations of principal axes is= 74.12 \n",
"plane stresss is Pa= 59348428.75 \n",
"plane stresss is MPa= -42.21 \n",
"plane stresss is MPa= 50.78 \n"
]
}
],
"prompt_number": 3
}
],
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}
]
}
|
