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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 21: Wing spars and box beams"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 21.1 Pg.No.585"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "from scipy import integrate\n",
      "import math\n",
      "\n",
      "Mx=20*10**6         #internal bending moment (N.mm)\n",
      "Sy=-20*10**3           #force applied(N)\n",
      "l1=400\n",
      "l2=300                #lengths of webs respectively from left to right in Fig 21.2\n",
      "l3=200\n",
      "\n",
      "#Ixx=I_C+Ab^2\n",
      "Ixx=2*l1*150**2+2*l2**3/12\n",
      "y=150\n",
      "sigma_z1=Mx*y/Ixx\n",
      "sigma_z2=-Mx*y/Ixx\n",
      "\n",
      "Pz1=sigma_z1*l1\n",
      "Pz2=sigma_z2*l1\n",
      "\n",
      "#from fig 21.1 and 21.2\n",
      "del_y1_by_del_z=-0.05\n",
      "del_y2_by_del_z=0.05\n",
      "Syw=Sy-Pz1*del_y1_by_del_z-Pz2*del_y2_by_del_z\n",
      "\n",
      "# equ 21.6 qs=-Syw/Ixx*integrate(t_D*y*ds+B1*Y1) from 0 to s\n",
      "fn=lambda s:300-2*s\n",
      "\n",
      "def shear(s):\n",
      "    return -Syw/Ixx*(integrate.quad(fn, 0, s)[0]+400*150)\n",
      "print \"maximum value of shear flow @s=150mm =%2.1f N/mm\\n\"%(shear(150.0))\n",
      "print \"value of shear @s=0mm = %2.1f N/mm\\n\"%(shear(0))\n",
      "print \"value of shear @s=300 mm = %2.1f N/mm\\n\"%(shear(300))\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "maximum value of shear flow @s=150mm =53.8 N/mm\n",
        "\n",
        "value of shear @s=0mm = 39.1 N/mm\n",
        "\n",
        "value of shear @s=300 mm = 39.1 N/mm\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 21.2 Pg.No.589"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "from sympy import symbols\n",
      "import math\n",
      "\n",
      "Sy=100*10**6             #load applied in y direction (N)\n",
      "Sx=0                     #load in x direction (N)\n",
      "y=[0.3,0.3,0.3,-0.3,-0.3,-0.3]\n",
      "B=[900,1200,900,900,1200,900]  #boom area\n",
      "dx_dz=[0.1,0,-0.1,-0.1,0,0.1]\n",
      "dy_dz=[-0.05,-0.05,-0.05,0.05,0.05,0.05]\n",
      "Er=[0.6,0,0.6,0.6,0,0.6]            \n",
      "nr=[0.3,0.3,0.3,0.3,0.3,0.3]\n",
      "Mx=-Sy*2\n",
      "My=-Sx*2\n",
      "Ixy=0\n",
      "Ixx=4*900*300**2+2*1200*300**2\n",
      "Pzr=[0]*6\n",
      "Pxr=[0]*6                #array initialization\n",
      "Pyr=[0]*6\n",
      "Pr=[0]*6\n",
      "print \"Boom \\t Pzr(kN) \\t dx_dz \\t dy_dz \\t Pxr(kN) \\t Pyr(kN) \\t Pr(kN)\"\n",
      "for i in range (0,6):\n",
      "    Pzr[i]=Mx*y[i]/Ixx*B[i]\n",
      "    Pxr[i]=Pzr[i]*dx_dz[i]                 #Pr is not correct in (7) column in book\n",
      "    Pyr[i]=Pzr[i]*dy_dz[i]\n",
      "    Pr[i]=(Pzr[i]**2+Pxr[i]**2+Pyr[i]**2)**0.5\n",
      "    if Pzr[i]>0 :\n",
      "        print \"%1.0f \\t %3.0f \\t\\t %1.1f \\t %1.2f \\t %2.0f \\t\\t %1.1f \\t\\t %3.1f\"%(i+1,Pzr[i],dx_dz[i],dy_dz[i],Pxr[i],Pyr[i],Pr[i])\n",
      "    else:\n",
      "        print \"%1.0f \\t %3.0f \\t\\t %1.1f \\t %1.2f \\t %2.0f \\t\\t %1.1f \\t\\t %3.1f\"%(i+1,Pzr[i],dx_dz[i],dy_dz[i],Pxr[i],Pyr[i],-Pr[i])\n",
      "       \n",
      "Sxw=0\n",
      "Syw=66.6*10**3\n",
      "qb16=0        #open section here\n",
      "qb12=qb16-Syw/Ixx*B[0]*300\n",
      "qb23=qb12-Syw/Ixx*B[1]*300\n",
      "qb34=qb23-Syw/Ixx*B[2]*300\n",
      "qb45=qb23\n",
      "qb56=qb12\n",
      "qs0=-97\n",
      "\n",
      "\n",
      "print \"\\n\\nqb16 = %3.1f N/mm\"%(qb16)\n",
      "print \"qb12 = %3.1f N/mm\"%(qb12)\n",
      "print \"qb23 = %3.1f N/mm\"%(qb23)\n",
      "print \"qb34 = %3.1f N/mm\"%(qb34)\n",
      "print \"qb45 = %3.1f N/mm\"%(qb45)\n",
      "print \"qb56 = %3.1f N/mm\"%(qb56)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Boom \t Pzr(kN) \t dx_dz \t dy_dz \t Pxr(kN) \t Pyr(kN) \t Pr(kN)\n",
        "1 \t -100 \t\t 0.1 \t -0.05 \t -10 \t\t 5.0 \t\t -100.6\n",
        "2 \t -133 \t\t 0.0 \t -0.05 \t -0 \t\t 6.7 \t\t -133.5\n",
        "3 \t -100 \t\t -0.1 \t -0.05 \t 10 \t\t 5.0 \t\t -100.6\n",
        "4 \t 100 \t\t -0.1 \t 0.05 \t -10 \t\t 5.0 \t\t 100.6\n",
        "5 \t 133 \t\t 0.0 \t 0.05 \t  0 \t\t 6.7 \t\t 133.5\n",
        "6 \t 100 \t\t 0.1 \t 0.05 \t 10 \t\t 5.0 \t\t 100.6\n",
        "\n",
        "\n",
        "qb16 = 0.0 N/mm\n",
        "qb12 = -33.3 N/mm\n",
        "qb23 = -77.7 N/mm\n",
        "qb34 = -111.0 N/mm\n",
        "qb45 = -77.7 N/mm\n",
        "qb56 = -33.3 N/mm\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 21.3 Pg.No.593\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "from sympy import symbols\n",
      "import numpy as np\n",
      "import math\n",
      "yr=symbols('yr')\n",
      "\n",
      "Mx=-100*1.9*10**6                #bending moment(N.mm)\n",
      "Ixx=4*900*295**2+2*1200*295**2      #second moment of area (mm^4)\n",
      "sigma_zr=Mx/Ixx*yr\n",
      "P1_1=P3_1=-0.364*295*900\n",
      "P4_1=P6_1=0.364*295*900\n",
      "P2_1=-0.364*295*1200\n",
      "P5_1=0.364*295*1200\n",
      "\n",
      "Mx=-100*2.1\n",
      "Ixx=4*900*305**2+2*1200*305**2\n",
      "sigma_zr=Mx/Ixx*yr\n",
      "P1_2=P3_2=-0.376*305*900\n",
      "P4_2=P6_2=0.376*305*900\n",
      "P2_2=-0.376*305*1200\n",
      "P5_2=0.376*305*1200\n",
      "\n",
      "deltaP1=deltaP3=(P1_1-P1_2)/200\n",
      "deltaP4=deltaP6=-(P4_1-P4_2)/200\n",
      "deltaP2=(P2_1-P2_2)/200\n",
      "deltaP5=(P5_1-P5_2)/200\n",
      "\n",
      "a=np.array([[1,-1,0,0,0,0],[0,1,-1,0,0,0],[0,0,1,-1,0,0],[0,0,0,1,-1,0],[0,0,0,0,1,-1],[600*300*2,2*600*300,600*600,0,0,600*600]])\n",
      "\n",
      "b=np.array([43.8,32.85,-32.85,-43.8,-32.85,600*10**5])\n",
      "q=np.linalg.solve(a,b)\n",
      "print \"shear flow distribution :\"\n",
      "print \"q12 = %2.1f N/mm\"%(q[0])\n",
      "print \"q23 = %2.1f N/mm\"%(q[1])\n",
      "print \"q34 = %2.1f N/mm\"%(q[2])\n",
      "print \"q45 = %2.1f N/mm\"%(q[3])\n",
      "print \"q56 = %2.1f N/mm\"%(q[4])\n",
      "print \"q61 = %2.1f N/mm\\n\"%(q[5])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "shear flow distribution :\n",
        "q12 = 63.6 N/mm\n",
        "q23 = 19.8 N/mm\n",
        "q34 = -13.1 N/mm\n",
        "q45 = 19.8 N/mm\n",
        "q56 = 63.6 N/mm\n",
        "q61 = 96.4 N/mm\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 41
    }
   ],
   "metadata": {}
  }
 ]
}