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Diffstat (limited to 'Aircraft_Structures_for_Engineering_Students/Chapter23.ipynb')
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diff --git a/Aircraft_Structures_for_Engineering_Students/Chapter23.ipynb b/Aircraft_Structures_for_Engineering_Students/Chapter23.ipynb deleted file mode 100755 index a5e90903..00000000 --- a/Aircraft_Structures_for_Engineering_Students/Chapter23.ipynb +++ /dev/null @@ -1,390 +0,0 @@ -{
- "metadata": {
- "name": "",
- "signature": "sha256:38d29ad436c9255138372fb573a0261c5aeb8d664f2491fbf03a71e42b1c4783"
- },
- "nbformat": 3,
- "nbformat_minor": 0,
- "worksheets": [
- {
- "cells": [
- {
- "cell_type": "heading",
- "level": 1,
- "metadata": {},
- "source": [
- "Chapter 23: Wings"
- ]
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 23.1 Pg.No.609"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from __future__ import division\n",
- "from sympy import solve, symbols, pprint\n",
- "import math\n",
- "y=symbols('y')\n",
- "\n",
- "B1=B6=2580\n",
- "B2=B5=3880 #Boom areas (mm^2)\n",
- "B3=B4=3230\n",
- "\n",
- "l1=200\n",
- "l2=230 #dimensions shown in Fig 23.3 (mm)\n",
- "l3=165\n",
- "\n",
- "Mx=300*10**6 #bending moment (N.mm)\n",
- "My=0\n",
- "\n",
- "Ixx=2*(B1*l3**2+B2*l2**2+B3*l1**2)\n",
- "sigma_z=Mx/Ixx*y\n",
- "\n",
- "print \"direct stress in booms sigma_z = %s\" %(sigma_z)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "direct stress in booms sigma_z = 0.370651791174781*y\n"
- ]
- }
- ],
- "prompt_number": 8
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 23.2 Pg.No.612"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from __future__ import division\n",
- "from sympy import solve, symbols, pprint\n",
- "import math\n",
- "import numpy as np\n",
- "\n",
- "T=11.3*10**6 # torque applied (N.mm)\n",
- "G_REF=27600 #(N/mm^2)\n",
- "A1=258000\n",
- "A2=355000 #areas in table\n",
- "A3=161000\n",
- "\n",
- "#t*12=G/G_REF*t\n",
- "t12=24200/G_REF*1.22\n",
- "t12i=27600/G_REF*2.03\n",
- "t13=t24=24200/G_REF*1.22 #G and thickness taken from table ex23.2 Pg.No.612\n",
- "t35=t46=t56=20700/G_REF*0.92\n",
- "t34=27600/G_REF*1.63\n",
- "\n",
- "# del12=ds/t*12\n",
- "del12=1650/t12\n",
- "del12i=508/t12i\n",
- "del13=del24=775/t13\n",
- "del34=380/t34 #lengths taken from table\n",
- "del35=del46=508/t35\n",
- "del56=254/t56\n",
- "\n",
- "\n",
- "a=np.array([[del12+del12i,-del12i,0,-2*A1*G_REF],[-del12i,del12i+del13+del24+del34,-del34,-2*A2*G_REF],[0,-del34,del35+del46+del34+del56,-2*A3*G_REF],[A1,A2,A3,0]])\n",
- "b=np.array([0,0,0,5.65*10**6])\n",
- "x=np.linalg.solve(a,b)\n",
- "print \"shear stress distribution is as follows\"\n",
- "print \"q1=%1.1f N/mm\"%(x[0])\n",
- "print \"q2=%1.1f N/mm\"%(x[1])\n",
- "print \"q3=%1.1f N/mm\\n\"%(x[2])\n",
- "print \"dO_dz=%1.2e \"%(x[3])"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "shear stress distribution is as follows\n",
- "q1=7.1 N/mm\n",
- "q2=8.9 N/mm\n",
- "q3=4.2 N/mm\n",
- "\n",
- "dO_dz=7.36e-07 \n"
- ]
- }
- ],
- "prompt_number": 27
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 23.3 Pg.No.616"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from __future__ import division\n",
- "from sympy import solve, symbols, pprint\n",
- "import math\n",
- "import numpy as np\n",
- "\n",
- "A1=265000\n",
- "A2=213000\n",
- "A3=413000\n",
- "\n",
- "G_REF=27600\n",
- "Sy=86.8*10**3\n",
- "t78=3*27600/27600*1.22\n",
- "del78=1270/t78\n",
- "t12=t56=1.22\n",
- "del12=del56=1023/t12\n",
- "t23=1.63\n",
- "del23=1274/t23\n",
- "t34=2.03\n",
- "del34=2200/t34\n",
- "del38=57\n",
- "del84=95\n",
- "del87=347\n",
- "del27=68\n",
- "del75=106\n",
- "del16=330/1.63\n",
- "Ixx=809*10**6 #From example 23.1\n",
- "\n",
- "qb27=-99.4;qb16=-45.5;qb65=0;qb57=95.5;qb38=-69.8;qb48=69\n",
- "\n",
- "\n",
- "a=np.array([ [del34+del84+del38,-del38,0,-2*A1*G_REF], [-del38,del23+del38+del87+del27,-del27,-2*A2*G_REF], [0,-del27,del56+del27+del75+del12+del16,-2*A3*G_REF], [2*A1,2*A2,2*A3,0] ])\n",
- "b=np.array([-10488,-2561,7426,19736700])\n",
- "x=np.linalg.solve(a,b)\n",
- "\n",
- "qs01=5.5\n",
- "qs02=10.2\n",
- "qs03=16.5\n",
- "\n",
- "q34=qs01\n",
- "q23=qs02\n",
- "q12=qs03\n",
- "q61=-qb16+qs03\n",
- "q57=qb57-qs03\n",
- "q72=-qb27-qs02\n",
- "q48=qb48+qs01\n",
- "q83=-qb38-qs01\n",
- "\n",
- "print \"shear flows distribution is as follows :\"\n",
- "print \"q34=%1.2f N/mm\"%(q34)\n",
- "print \"q23=q87=%1.2f N/mm\"%(q23)\n",
- "print \"q12=q56=%1.2f N/mm\"%(q12)\n",
- "print \"q61=%1.2f N/mm\"%(q61) \n",
- "print \"q57=%1.2f N/mm\"%(q57)\n",
- "print \"q72=%1.2f N/mm\"%(q72)\n",
- "print \"q48=%1.2f N/mm\"%(q48)\n",
- "print \"q83=%1.2f N/mm\\n\"%(q83)\n",
- "\n",
- "print \"rate of twist = %1.1e rad/mm\"%(x[3])"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "shear flows distribution is as follows :\n",
- "q34=5.50 N/mm\n",
- "q23=q87=10.20 N/mm\n",
- "q12=q56=16.50 N/mm\n",
- "q61=62.00 N/mm\n",
- "q57=79.00 N/mm\n",
- "q72=89.20 N/mm\n",
- "q48=74.50 N/mm\n",
- "q83=64.30 N/mm\n",
- "\n",
- "rate of twist = 1.1e-06 rad/mm\n"
- ]
- }
- ],
- "prompt_number": 8
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 23.4 Pg.No.618 "
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from __future__ import division\n",
- "from sympy import solve, symbols, pprint\n",
- "import math\n",
- "import numpy as np\n",
- "\n",
- "#Boom areas\n",
- "B=[600,900,600,600,900,600]\n",
- "Pz=[0,0,0,0,0,0]\n",
- "y=[54.56,54.56,54.56,-54.56,-54.56,-54.56]\n",
- "Ixx=4*600*90**2+2*900*90**2\n",
- "Ixy=0\n",
- "Mx=1.65*10**6\n",
- "My=0\n",
- "\n",
- "a=np.array([[1700,-1520],[72000,144000]])\n",
- "b=np.array([3942,690726])\n",
- "x=np.linalg.solve(a,b)\n",
- "print \"\\nqs0I = %2.1f N/mm\\n\"%(x[0])\n",
- "print \"\\nqs0II = %2.1f N/mm\\n\"%(x[1])"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "\n",
- "qs0I = 4.6 N/mm\n",
- "\n",
- "\n",
- "qs0II = 2.5 N/mm\n",
- "\n"
- ]
- }
- ],
- "prompt_number": 21
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 23.5 Pg.No.622"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from __future__ import division\n",
- "from sympy import solve, symbols, pprint\n",
- "import math\n",
- "import numpy as np\n",
- "from sympy import integrate\n",
- "z=symbols('z')\n",
- "\n",
- "E=69000 #youngs modulus (N/mm^2)\n",
- "G=25900 #shear modulus (N/mm^2)\n",
- "t=2 #thickness (mm)\n",
- "B=[650,1300,650,650,1300,650] #boom area\n",
- "q0=[9.6,-5.8,50.3,-5.8,9.6,54.1,73.6]\n",
- "Sy0=44.5*10**3\n",
- "Sy1=1\n",
- "Mx0=-44.5*10**3*(2000-z)\n",
- "Mx1=-(2000-z)\n",
- "Ixx=81.3*10**6\n",
- "int_q0q1_Gt=1/G/t/Sy0*(q0[0]**2*250*t+q0[1]**2*500*t+q0[2]**2*250+q0[5]**2*250+q0[6]**2*250)\n",
- "\n",
- "delta=integrate(Mx0*Mx1/E/Ixx,(z,0,2000))+integrate(int_q0q1_Gt,(z,0,2000))\n",
- "print \"deflection at free end of the two cell = %2.2f mm\"%(delta)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "deflection at free end of the two cell = 23.58 mm\n"
- ]
- }
- ],
- "prompt_number": 70
- },
- {
- "cell_type": "heading",
- "level": 2,
- "metadata": {},
- "source": [
- "Example 23.6 Pg.No.624"
- ]
- },
- {
- "cell_type": "code",
- "collapsed": false,
- "input": [
- "from sympy import solve, symbols, pprint\n",
- "import math\n",
- "import numpy as np\n",
- "from sympy import integrate\n",
- "\n",
- "T=10*10**6 #torque subjected (N.mm)\n",
- "l1=800 \n",
- "l2=200 #lengths shown in Fig23.17 (mm)\n",
- "l3=1500\n",
- "A=l2*l1\n",
- "\n",
- "\n",
- "q=T/2/A\n",
- "S=T/l1\n",
- "q1=S/l2\n",
- "P=S*l3/2/l2\n",
- "\n",
- "a=np.array([[1,-1],[1,1]])\n",
- "b=np.array([31.3,62.5])\n",
- "q=np.linalg.solve(a,b)\n",
- "\n",
- "print \"shear flow :\"\n",
- "print \"q1=%2.2f N/mm\"%(q1)\n",
- "print \"q2=%2.2f N/mm\"%(q[0])\n",
- "print \"q3=%2.2f N/mm\\n\"%(q[1])\n",
- "\n",
- "print \"flange loads :\"\n",
- "print \"P(st.4500) = 0\"\n",
- "print \"P(st.3000) = %2.2f N (compression)\"%(l3*q[0]-l3*q[1])\n",
- "print \"P(st.2250) = %2.1f\"%(46875-l3/2*q1)"
- ],
- "language": "python",
- "metadata": {},
- "outputs": [
- {
- "output_type": "stream",
- "stream": "stdout",
- "text": [
- "shear flow :\n",
- "q1=62.50 N/mm\n",
- "q2=46.90 N/mm\n",
- "q3=15.60 N/mm\n",
- "\n",
- "flange loads :\n",
- "P(st.4500) = 0\n",
- "P(st.3000) = 46950.00 N (compression)\n",
- "P(st.2250) = 0.0\n"
- ]
- }
- ],
- "prompt_number": 84
- }
- ],
- "metadata": {}
- }
- ]
-}
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