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{
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"name": "",
"signature": "sha256:217b3507f45091d99aa496d838ab43e552e1e20629747bd44a2cad35220ffe6a"
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"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 24: Fuselage frames and wing ribs"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 24.1 Pg.No.638"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import numpy\n",
"import math\n",
"#reference Fig 42.2\n",
"l1=250 #length of each section(mm)\n",
"l2=200 #length of DK(mm)\n",
"l3=100 #length of KH(mm)\n",
"F1=4000\n",
"F2=5000 #forces as shown in Fig 24.1\n",
"theta=60 #force angle from DH (degree)\n",
"\n",
"#solve (i) and (ii) equation\n",
"a=numpy.array([[1,-1],[200,100]])\n",
"b=numpy.array([13.8564,2000])\n",
"q=numpy.linalg.solve(a,b)\n",
"q1=q[0]\n",
"q2=q[1]\n",
"q3=F1*math.cos(math.radians(theta))/(l2+l3)\n",
"q4=F1*math.cos(math.radians(theta))/(l2+l3)+F2/(l2+l3)\n",
"P_A=l1*q1+l1*q3+l1*q4\n",
"P_E=-l1*q2-l1*q3-l1*q4\n",
"P=3464.1\n",
"M_AE=F2*l1+F1/2*3*l1-P*50\n",
"\n",
"P_A=M_AE/(l2+l3)+P/2\n",
"P_E=-M_AE/(l2+l3)+P/2\n",
"\n",
"print \"shear flow as shown in Fig 24.1\\n\"\n",
"print \"q1=%2.2f N/mm\\n\"%(q1)\n",
"print \"q2=%2.2f N/mm\\n\"%(q2)\n",
"print \"q3=%2.2f N/mm\\n\"%(q3)\n",
"print \"q4=%2.2f N/mm\\n\"%(q4)\n",
"\n",
"print \"Stiffener load at point A = %2.2f N/mm(tension)\\n\"%(P_A)\n",
"print \"Stiffener load at point E = %2.2f N/mm(compression)\\n\"%(P_E) #in book another method is also explained"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"shear flow as shown in Fig 24.1\n",
"\n",
"q1=11.29 N/mm\n",
"\n",
"q2=-2.57 N/mm\n",
"\n",
"q3=6.67 N/mm\n",
"\n",
"q4=23.33 N/mm\n",
"\n",
"Stiffener load at point A = 10321.37 N/mm(tension)\n",
"\n",
"Stiffener load at point E = -6857.27 N/mm(compression)\n",
"\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 24.2 Pg.No.645"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import numpy as np\n",
"import math\n",
"\n",
"A1=50000\n",
"A2=95000 #area shown in Fig 24.13(mm^2)\n",
"A3=95000\n",
"\n",
"A4=46000\n",
"A5=49000 #area shown in Fig 24.11 (mm^2)\n",
"\n",
"F1=12000\n",
"F2=15000 #forces shown in Fig 24.9 (N)\n",
"\n",
"l1=l3=300\n",
"l2=320 #lengths and angle shown in Fig 24.9\n",
"alpha=15\n",
"\n",
"#solve equation (i)&(iii)\n",
"a=np.array([[600,-600],[190000,290000]])\n",
"b=np.array([12000,440000])\n",
"q=np.linalg.solve(a,b)\n",
"q12=q[0]\n",
"q23=q[1]\n",
"q31=(F2+l1*q23)/l1\n",
"print \"shear flows are shown in Fig 24.9 (flanges)\"\n",
"print \"q12=%2.2f N/mm\"%(q12)\n",
"print \"q23=%2.2f N/mm\"%(q23)\n",
"print \"q31=%2.2f N/mm\\n\"%(q31)\n",
"\n",
"Sy_1=7*l3\n",
"Px4=Px2=2*A1*7/l1\n",
"Py2=Py4=Px4*math.tan(math.radians(alpha))\n",
"q1=(2100-2*625.2)/l1\n",
"P2=P4=(Px4**2+Py4**2)**0.5\n",
"P5=P6=2*((A1+A4)*7-A5*13)/l2\n",
"q2=(7*l1+7*10-13*10)/l2\n",
"q3=(6.4*l2+F2)/l2\n",
"\n",
"M3=2*((A1+A2)*7-A2*13)+F2*l1\n",
"Px1=Px3=M3/l1\n",
"Py1=Py3=3626.2\n",
"P1=P3=(Px1**2+Py1**2)**.5\n",
"q3=(17100-2*Py1)/l1\n",
"\n",
"print \"Loads in webs \"\n",
"print \"P4=P2=%2.2f N\"%(P2)\n",
"print \"P6=P5=%2.2f N\"%(P6)\n",
"print \"P3=P1=%2.2f N\\n\"%(P1)\n",
"\n",
"print \"shear flow in webs\"\n",
"print \"q1=%2.2f N/mm\"%(q1)\n",
"print \"q2=%2.2f N/mm\"%(q2)\n",
"print \"q3=%2.2f N/mm (this value is given at the end of example)\"%(q3)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"shear flows are shown in Fig 24.9 (flanges)\n",
"q12=13.00 N/mm\n",
"q23=-7.00 N/mm\n",
"q31=43.00 N/mm\n",
"\n",
"Loads in webs \n",
"P4=P2=2415.64 N\n",
"P6=P5=218.75 N\n",
"P3=P1=14010.73 N\n",
"\n",
"shear flow in webs\n",
"q1=2.83 N/mm\n",
"q2=6.38 N/mm\n",
"q3=32.83 N/mm (this value is given at the end of example)\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
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