diff options
Diffstat (limited to 'Aircraft_Structures_for_Engineering_Students/Chapter23.ipynb')
| -rwxr-xr-x | Aircraft_Structures_for_Engineering_Students/Chapter23.ipynb | 390 |
1 files changed, 390 insertions, 0 deletions
diff --git a/Aircraft_Structures_for_Engineering_Students/Chapter23.ipynb b/Aircraft_Structures_for_Engineering_Students/Chapter23.ipynb new file mode 100755 index 00000000..a5e90903 --- /dev/null +++ b/Aircraft_Structures_for_Engineering_Students/Chapter23.ipynb @@ -0,0 +1,390 @@ +{
+ "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": {}
+ }
+ ]
+}
\ No newline at end of file |