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diff --git a/Aircraft_Structures_for_Engineering_Students/Chapter08.ipynb b/Aircraft_Structures_for_Engineering_Students/Chapter08.ipynb new file mode 100755 index 00000000..65ccbf76 --- /dev/null +++ b/Aircraft_Structures_for_Engineering_Students/Chapter08.ipynb @@ -0,0 +1,154 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:d4ab160ecba8745ef027bb167a7abbd97977707c483b1d0a639c7f068e2016a8"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 08: Columns"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.3 Pg.No.280"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from __future__ import division\n",
+ "import math\n",
+ "\n",
+ "E=75000 #youngs modulus(N/mm^2)\n",
+ "G=21000 #shear modulus (N/mm^2)\n",
+ "L=2 #length of column (m)\n",
+ "l1=75 #flange length (mm)\n",
+ "l2=37.5 #total length(mm)\n",
+ "t=2.5 #thickness(mm)\n",
+ "\n",
+ "A=t*(2*l2+l1) #observed from Fig 8.17\n",
+ "\n",
+ "#chapter 16 Ixx=bd^3/12+Ab^2\n",
+ "Ixx=2*l2*t*l2**2+t*l1**3/12\n",
+ "Iyy=2*t*l2**3/12\n",
+ "\n",
+ "I0=Ixx+Iyy\n",
+ "\n",
+ "#eqn 18.11 J=SUM((s*t^3)/3)\n",
+ "J=2*l2*t**3/3+l1*t**3/3\n",
+ "\n",
+ "Gama=t*l2**3*l1**2/24\n",
+ "Iyy=0.22*10**5\n",
+ "L=2*10**3\n",
+ "P_CRxx=math.pi**2*E*Ixx/L**2\n",
+ "P_CRyy=math.pi**2*E*Iyy/L**2\n",
+ "P_CRo=A/I0*(G*J+math.pi**2*E*Gama/L**2)\n",
+ "\n",
+ "print \"P_CRxx = %3.2e N\\n\"%(P_CRxx)\n",
+ "print \"P_CRyy = %0.1e N\\n\"%(P_CRyy)\n",
+ "print \"P_CRO = %0.2e N\\n\"%(P_CRo)\n",
+ "\n",
+ "print \"therefore buckling in the column due to axial load=%0.1e N\\n\"%(P_CRyy)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "P_CRxx = 6.51e+04 N\n",
+ "\n",
+ "P_CRyy = 4.1e+03 N\n",
+ "\n",
+ "P_CRO = 2.22e+04 N\n",
+ "\n",
+ "therefore buckling in the column due to axial load=4.1e+03 N\n",
+ "\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 8.4 Pg.No.282"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "from __future__ import division\n",
+ "import math\n",
+ "import numpy as np\n",
+ "from sympy import solve, symbols, pprint\n",
+ "from sympy import diff\n",
+ "P=symbols('P')\n",
+ "\n",
+ "E=70000 #youngs modulus (N/mm^2)\n",
+ "G=30000 #shear modulus (N/mm^2)\n",
+ "x_S=-76.2 #position of shear center(mm)\n",
+ "l1=l2=100 #lengths (mm)\n",
+ "t=2 #thickness(mm)\n",
+ "\n",
+ "x_bar=2*t*l1*50/(3*l1)/2\n",
+ "\n",
+ "A=600 #area (mm^2)\n",
+ "Ixx=1.17*10**6 #second moment of area (mm^4)\n",
+ "Iyy=0.67*10**6 #second moment of area (mm^4)\n",
+ "I0=5.32*10**6 # total second moment of area (mm^4)\n",
+ "J=800 #torsion constant (mm^4)\n",
+ "Gama=2488*10**6 #(mm^6)\n",
+ "L=10**3 #(mm)\n",
+ "\n",
+ "P_CRxx=math.pi**2*E*Ixx/L**2\n",
+ "P_CRyy=math.pi**2*E*Iyy/L**2\n",
+ "P_CRo=A/I0*(G*J+math.pi**2*E*Gama/L**2)\n",
+ "\n",
+ "fun=P**2*(1-A*x_S**2/I0)-P*(P_CRxx+P_CRo)+P_CRxx*P_CRo\n",
+ "solution = solve(fun, P)\n",
+ "print \"lowest value of critical load = %1.2e N\\n\"%(min(solution))"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "lowest value of critical load = 1.68e+05 N\n",
+ "\n"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
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