{
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter5-Bending of Beams"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex1-pg128"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#calculate meter and sigma \n",
"Mz=11000. ##Nm\n",
"A1=0.13*0.02 ##m\n",
"A2=0.15*0.02 ##m\n",
"z1=0.01 ##m\n",
"z2=0.075 ##m\n",
"yA=0.043 ##m\n",
"zA=-0.106 ##m\n",
"yB=-0.063 ##m\n",
"zB=0.\n",
"\n",
"##location of the centroid\n",
"z=(A1*z1+A2*z2)/(A1+A2)\n",
"print'%s %.2f %s'%(\"in meter is= \",z,\"\")\n",
"\n",
"Iz=(0.02*(0.13)**3)/12.+ (0.13*0.02*(0.04)**2)+(0.15*(0.02)**3.)/12.+ (0.15*0.02*(0.035)**2.)\n",
"print'%s %.5f %s'%(\"Iz in meter^4 is= \",Iz,\"\")\n",
"Iy=(0.02*(0.13)**3)/12.+ (0.13*0.02*(0.04)**2)+(0.15*(0.02)**3)/.12+ (0.15*0.02*(0.035)**2.)\n",
"print'%s %.5f %s'%(\"Iy in meter^4 is= \",Iy,\"\")\n",
"Iyz=0+A1*0.04*(-0.035)+0+A2*(-0.035)*0.03\n",
"print'%s %.2f %s'%(\"Iyz in meter^4 is= \",Iyz,\"\")\n",
"##thetap=(atand((-2*Iyz)/(Iz-Iy)))/2\n",
"##print'%s %.2f %s'%(thetap)\n",
"I1=(Iz+math.sqrt(0.+(6.79*10**-6)**2.))\n",
"print'%s %.5f %s'%(\"I1 in meter^4 is= \",I1,\"\")\n",
"I2=(Iz-math.sqrt(0+(6.79*10**-6)**2))\n",
"print'%s %.6f %s'%(\"I2 in meter^4 is= \",I2,\"\")\n",
"My1=11000.*math.sin(45/57.3)\n",
"print'%s %.2f %s'%(\"My1 in Nm is\",My1,\"\")\n",
"Mz1=11000*math.sin(45/57.3)\n",
"print'%s %.2f %s'%(\"Mz1 in Nm is\",Mz1,\"\")\n",
"\n",
"sigmaxA=((My1*(zA))/I1)-((Mz1*yA)/I2)\n",
"print'%s %.2f %s'%(\"sigmaxA in MPa is\",sigmaxA,\"\")\n",
"sigmaxB=0-((My1*yB)/I2)\n",
"print'%s %.2f %s'%(\"sigmaxB in MPa is\",sigmaxB,\"\")\n",
"\n",
"My=0.\n",
"y=((Mz*Iyz)*z)/(Mz*Iy) ##.......equal to z=-1.71y\n",
"print'%s %.3f %s'%(\"y\",y,\"\")\n",
"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"in meter is= 0.04 \n",
"Iz in meter^4 is= 0.00001 \n",
"Iy in meter^4 is= 0.00002 \n",
"Iyz in meter^4 is= -0.00 \n",
"I1 in meter^4 is= 0.00002 \n",
"I2 in meter^4 is= 0.000005 \n",
"My1 in Nm is 7777.72 \n",
"Mz1 in Nm is 7777.72 \n",
"sigmaxA in MPa is -114417761.50 \n",
"sigmaxB in MPa is 101941050.82 \n",
"y -0.014 \n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex4-144"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#calculate the distance \n",
"import scipy\n",
"from scipy import integrate\n",
"t=1.25 ##mm\n",
"y=15.87 ##mm\n",
"z=5.28 ##mm\n",
"Iy=4765.62 ##mm**4\n",
"Iz=21054.69 ##mm**4\n",
"Iyz=3984.37 ##mm**4\n",
"thetap=13.05 ##degree\n",
"Iy1=3828.12 ##mm**4\n",
"Iz1=21953.12##mm**4\n",
"s=12.5\n",
"\n",
"##tau=(Vy/Iz1*t)*s*t(19.55+s*asind(13.05)/2)....equation 1\n",
"##F1=integrate((tau*t)ds)\n",
"def fun(s):\n",
"\ty=(0)\n",
"\treturn y\n",
"x=scipy.integrate.quad(fun,0,1)\n",
"x=x[0]\n",
"##F1=0.0912*Vy1 substituting the value of tau we get F1\n",
"##Vy1*ez1=37.5*F1 substituting the value of F1 we get ez1\n",
"ez1=37.5*0.0912\n",
"print'%s %.2f %s'%(\"the distance in mm is= \",ez1,\"\")\n",
"\n",
"##tau=(Vz1/Iy1*t)*s*t(12.05-s*asind(13.05)/2)....equation 2\n",
"##F1=integrate((tau*t)ds)\n",
"def fun(s):\n",
"\ty=(0)\n",
"\treturn y\n",
"x=scipy.integrate.quad(fun,0,1)\n",
"x=x[0]\n",
"\n",
"##F1=0.204*Vz1 substituting the value of tau we get F1\n",
"##Vz1*ey1=37.5*F1 substituting the value of F1 we get ez1\n",
"ey1=37.5*0.204\n",
"print'%s %.2f %s'%(\"the distance in mm is= \",ey1,\"\")\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"the distance in mm is= 3.42 \n",
"the distance in mm is= 7.65 \n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex5-pg154"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#calculate stress and meter\n",
"import scipy\n",
"from scipy import integrate\n",
"P=70. ##kN\n",
"c=0.05##m\n",
"c1=c\n",
"c2=c\n",
"R=0.1+0.05\n",
"A=0.005\n",
"\n",
"##m=(-1/(2*c))*integrate((y/R+y)dy)\n",
"def fun(c):\n",
"\ty=(-c)\n",
"\treturn y\n",
"\n",
"x=scipy.integrate.quad(fun,0,1)\n",
"m=-1.+(R/2.*c)*math.log((R+c)/(R-c))\n",
"print'%s %.2f %s'%(\"m\",m,\"\")\n",
"##m=(-1/(2*c))*integrate((y/R)-(y**2/R**2)+(y**3/R**3)-(y**4/R**4)+.....)dy)\n",
"m=-1+(3/2.)*math.log(2.)\n",
"print'%s %.3f %s'%(\"m\",m,\"\")\n",
"\n",
"M=P*R\n",
"print'%s %.2f %s'%(\"M\",M,\"\")\n",
"sigmatheta1=(-P*c2)/(m*A*(R-c1))\n",
"print'%s %.2f %s'%(\"stress in Pa is= \",sigmatheta1,\"\")\n",
"sigmatheta2=(P*c2)/(m*A*(R+c2))\n",
"print'%s %.2f %s'%(\"stress in Pa is= \",sigmatheta2,\"\")\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"m -1.00 \n",
"m 0.040 \n",
"M 10.50 \n",
"stress in Pa is= -176230.22 \n",
"stress in Pa is= 88115.11 \n"
]
}
],
"prompt_number": 1
}
],
"metadata": {}
}
]
}