From 92cca121f959c6616e3da431c1e2d23c4fa5e886 Mon Sep 17 00:00:00 2001 From: hardythe1 Date: Tue, 7 Apr 2015 15:58:05 +0530 Subject: added books --- .../Chapter16.ipynb | 280 +++++++++++++++++++++ 1 file changed, 280 insertions(+) create mode 100755 Aircraft_Structures_for_Engineering_Students/Chapter16.ipynb (limited to 'Aircraft_Structures_for_Engineering_Students/Chapter16.ipynb') diff --git a/Aircraft_Structures_for_Engineering_Students/Chapter16.ipynb b/Aircraft_Structures_for_Engineering_Students/Chapter16.ipynb new file mode 100755 index 00000000..72ff7ec3 --- /dev/null +++ b/Aircraft_Structures_for_Engineering_Students/Chapter16.ipynb @@ -0,0 +1,280 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:c3ab3016805321c8a28748b1937c77b2125357dfc661b20013df0624feaa950e" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 16: Bending of open and closed thin-walled beams \n" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.1 Pg. No.456" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Fig 16.6 Dimensions\n", + "from __future__ import division\n", + "import math\n", + "\n", + "#variable declaration\n", + "l=300 #length of I section (mm)\n", + "b=200 #width of I section beam (mm)\n", + "w1=25 #width of center section of I beam (mm)\n", + "w2=20 #width of upper and lower section of I beam (mm)\n", + "M=100*10**6 #moment applied in vertical plane (N*mm)\n", + "\n", + "#second moment of area Ixx\n", + "# Ixx=b*l^3/12\n", + "Ixx=b*l**3/12-(b-w1)*(l-w2-w2)**3/12\n", + "print \"\\nSecond moment of area of I section beam = %5.3e mm^4\"%(Ixx)\n", + "\n", + "#sigma_z=My/I reference 16.9\n", + "# @ \n", + "y=150\n", + "sigma_z=M*y/Ixx\n", + "print \"\\ndirect stress at the top of the I section (y=150) = %3.2f N/mm^2 (compression)\"%(sigma_z)\n", + "\n", + "# @\n", + "y=-150\n", + "sigma_z=M*y/Ixx\n", + "print \"\\ndirect stress at the bottom of the I section (y=-150) = %3.2f N/mm^2 (tension)\"%(sigma_z)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "Second moment of area of I section beam = 1.937e+08 mm^4\n", + "\n", + "direct stress at the top of the I section (y=150) = 77.45 N/mm^2 (compression)\n", + "\n", + "direct stress at the bottom of the I section (y=-150) = -77.45 N/mm^2 (tension)\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.2 Pg. No.457" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Fig 16.6 reference\n", + "from __future__ import division\n", + "import math\n", + "\n", + "#variable declaration\n", + "l=300 #length of I section (mm)\n", + "b=200 #width of I section beam (mm)\n", + "w1=25 #width of center section of I beam (mm)\n", + "w2=20 #width of upper and lower section of I beam (mm)\n", + "M=100*10**6 #moment applied in vertical plane (N*mm)\n", + "\n", + "# second moment of area\n", + "# Iyy=wb^3/12\n", + "Iyy=2*20*200**3/12+260*25**3/12\n", + "print \"\\nSecond moment of area of I section beam = %5.3e mm^4\"%(Iyy)\n", + "\n", + "#sigma_z=Mx/I \n", + "# @ \n", + "x=100\n", + "sigma_z=M*x/Iyy\n", + "print \"\\ndirect stress at the top of the I section (y=150) = %3.2f N/mm^2 (compression)\"%(sigma_z)\n", + "\n", + "# @\n", + "x=-100\n", + "sigma_z=M*x/Iyy\n", + "print \"\\ndirect stress at the bottom of the I section (y=-150) = %3.2f N/mm^2 (tension)\"%(sigma_z)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "Second moment of area of I section beam = 2.701e+07 mm^4\n", + "\n", + "direct stress at the top of the I section (y=150) = 370.30 N/mm^2 (compression)\n", + "\n", + "direct stress at the bottom of the I section (y=-150) = -370.30 N/mm^2 (tension)\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.3 Pg.No.458 " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from __future__ import division\n", + "import math\n", + "\n", + "#variable declaration\n", + "l=300 #length of I section (mm)\n", + "b=200 #width of I section beam (mm)\n", + "w1=25 #width of center section of I beam (mm)\n", + "w2=20 #width of upper and lower section of I beam (mm)\n", + "M=100*10**6 #moment applied in vertical plane (N*mm)\n", + "theta=30 #angle at which bending moment is applied(degree)\n", + "\n", + "Mx=M*math.cos(math.radians(30))\n", + "My=M*math.sin(math.radians(30))\n", + "\n", + "# sigma_z=Mx/Ixx*y+My/Iyy*x\n", + "# @top left hand corner\n", + "y=150\n", + "x=-100\n", + "sigma_z=Mx/Ixx*y-My/Iyy*x \n", + "print \"\\ndirect stress at the top left hand corner = %3.1f N/mm^2 (tension)\"%(sigma_z)\n", + "\n", + "# @ top right hand corner\n", + "x=100\n", + "y=150\n", + "sigma_z=Mx/Ixx*y-My/Iyy*x \n", + "print \"\\ndirect stress at the top right hand corner = %3.1f N/mm^2 (compression)\"%(sigma_z)\n", + "\n", + "alpha=math.atan(My*Ixx/Mx/Iyy)\n", + "print \"\\ninclination = %3.1f degree\\n\"%(alpha*180/math.pi)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "direct stress at the top left hand corner = 252.2 N/mm^2 (tension)\n", + "\n", + "direct stress at the top right hand corner = -118.1 N/mm^2 (compression)\n", + "\n", + "inclination = 76.4 degree\n", + "\n" + ] + } + ], + "prompt_number": 38 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 16.4 Pg.No.466" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# reference Fig 16.13\n", + "import math\n", + "from __future__ import division\n", + "#variable declaration\n", + "l=80 #length of one section (mm)\n", + "w=8 #thickness of each section (mm)\n", + "b1=40 #width of one section (mm)\n", + "b2=80 #width of other section (mm)\n", + "Mx=1500*10*3 #bending moment (N.mm)\n", + "My=0\n", + "\n", + "#centroid\n", + "# in this example C is taken at top surface x axis aligned to AB and y axis is \n", + "# aligned to E surface \n", + "y_bar=((b1+b2)*w*w/2+l*w*(w+l/2))/(l*w+(b1+b2)*w)\n", + "print \"\\ny coordinate of centroid = %3.1f mm\"%(y_bar)\n", + "\n", + "x_bar=((b1+b2)*w*((b1+b2)/2-b1+w/2)+l*w*(w/2))/(l*w+(b1+b2)*w)\n", + "print \"\\nx coordinate of centroid = %3.1f mm\"%(x_bar)\n", + "\n", + "#second area of moment\n", + "#IB=IC+Ab^2 IB=moment about any point,IC=moment about centroid, b=distace between both points\n", + "Ixx=(b1+b2)*w**3/12+(b1+b2)*w*(y_bar-w/2)**2+w*l**3/12+l*w*(w+l/2-y_bar)**2\n", + "print \"\\nsecond moment of area about x axis = %3.2e mm^4\"%(Ixx)\n", + "\n", + "Iyy=w*(b1+b2)**3/12+(b1+b2)*w*((b1+b2)/2-b1+w/2-x_bar)**2+l*w**3/12+l*w*(x_bar-w/2)**2\n", + "print \"\\nsecond moment of area about y axis = %3.2e mm^4\"%(Iyy)\n", + "\n", + "Ixy=(b1+b2)*w*(y_bar-w/2)*((b1+b2)/2-b1+w/2-x_bar)+l*w*(w+l/2-y_bar)*(x_bar-w/2)\n", + "print \"\\nsecond moment of area about x and y axis = %3.2e mm^4\"%(Ixy)\n", + "\n", + "Mx=15*10**5\n", + "def f(x,y):\n", + " return Mx*(Iyy*y-Ixy*x)/(Ixx*Iyy-Ixy**2)\n", + "sigma_z_max= f(-8,-66.4)\n", + "print \"\\nmaximum direct shear stress = %3.0f N/mm^2 (compressive)\\n\"%(sigma_z_max)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "y coordinate of centroid = 21.6 mm\n", + "\n", + "x coordinate of centroid = 16.0 mm\n", + "\n", + "second moment of area about x axis = 1.09e+06 mm^4\n", + "\n", + "second moment of area about y axis = 1.31e+06 mm^4\n", + "\n", + "second moment of area about x and y axis = 3.38e+05 mm^4\n", + "\n", + "maximum direct shear stress = -96 N/mm^2 (compressive)\n", + "\n" + ] + } + ], + "prompt_number": 62 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +} \ No newline at end of file -- cgit