path: root/Solid_Mechanics_by_S._M._A._Kazimi/Chapter7.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter7-Beams and Bendings"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex2-pg234"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "import numpy\n",
      "#calculate sf and Bm\n",
      "import matplotlib\n",
      "from matplotlib import pyplot\n",
      "%matplotlib inline\n",
      "#initialization of variables\n",
      "s=3. #m\n",
      "n=60.\n",
      "p=50. #kg\n",
      "## calculations\n",
      "W=n*p\n",
      "Rc=W*2./s\n",
      "Rb=W-Rc\n",
      "dx = 0.001;\n",
      "x = numpy.linspace(0,s,3001)\n",
      "n = round(s/dx +1);\n",
      "n=int(n)\n",
      "Sx=numpy.zeros(n)\n",
      "Mx=numpy.zeros(n)\n",
      "i=0;\n",
      "for i in range (0,n):\n",
      "    Sx[i] = -Rb + Rc*x[i]**2./6.;\n",
      "    Mx[i] = Rb*x[i] - Rc*x[i]**3 /18.;\n",
      "\n",
      "##Results\n",
      "pyplot.plot(x,Sx);pyplot.title(\"Shear force diagram\");pyplot.xlabel(\"X (in m)\");pyplot.ylabel(\"Shear force (in kg)\");\n",
      "pyplot.show()\n",
      "pyplot.plot(x,Mx);pyplot.title(\"Bending Moment diagram\");pyplot.xlabel(\"X (in m)\");pyplot.ylabel(\"Bending Moment (in kg-m)\");\n",
      "pyplot.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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O0MysUtXXpzHDHngAtt0272gqS4sV+pKuA7YF7gcmAHMBAT2B/sABwIyI+E7nhNoxrtA3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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1d2b1f0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x5910590>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex8-pg249"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "##initialization of new variables\n",
      "#centriod of the section and momets of inertia and product of inertia about xx and yy axes and direction of principal axes and value of maximum and minimum\n",
      "b=10075 ##mm\n",
      "h=10 ##mm\n",
      "p1=7.5\n",
      "p2=9\n",
      "##part (a)\n",
      "ybar=1*p1*0.5+1*p2*5.5\n",
      "ybar=ybar/16.5\n",
      "xbar=1*p1*0.5+1*p1*4.75\n",
      "xbar=xbar/16.5\n",
      "print('part (a)')\n",
      "print'%s %.2f %s %.2f %s '%('\\n Centroid coordinates (x,y) = ',xbar,''and '',ybar,'cm')\n",
      "\n",
      "##part (b)\n",
      "Ixx=p1*1**3/12.+p1*1*(3.23-0.5)**2+1*p2**3/12.+p2*1*(5.5-3.23)**2\n",
      "Iyy=1*p1**3/12.+p1*1*(3.75-2.43)**2+p2*1**3/12.+p2*1*(2.43-0.5)**2\n",
      "Ixy=p1*1.32*2.73+9*(-1.93)*(-2.27)\n",
      "print('\\n part (b)')\n",
      "print'%s %.2f %s %.2f %s %.2f %s '%('\\n Moment of Areas: \\n Ixx = ',Ixx,' cm^4 \\n Iyy = ',Iyy,' cm^4' and'Ixy=',Ixy,'cm^4')\n",
      "\n",
      "##part (c)\n",
      "alpha=0.5*math.atan(2*Ixy/(Iyy-Ixx))\n",
      "alpha=alpha*180/math.pi\n",
      "print('\\n part (c)')\n",
      "print('\\n Direction of principal axes:')\n",
      "print'%s %.2f %s'%('\\n alpha = ',alpha,' degrees')\n",
      "\n",
      "##part (d)\n",
      "Iuu=(Ixx+Iyy)/2+math.sqrt((Iyy-Ixx)**2/4.+Ixy**2)\n",
      "Ivv=(Ixx+Iyy)/2-math.sqrt((Iyy-Ixx)**2/4.+Ixy**2)\n",
      "print('\\n part (d)')\n",
      "print'%s %.2f %s %.2f %s '%('\\n Iuu = ',Iuu,' cm^4 \\n Ivv = ',Ivv,' cm^4')\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "part (a)\n",
        "\n",
        " Centroid coordinates (x,y) =  2.39  3.23 cm \n",
        "\n",
        " part (b)\n",
        "\n",
        " Moment of Areas: \n",
        " Ixx =  163.65  cm^4 \n",
        " Iyy =  82.50 Ixy= 66.46 cm^4 \n",
        "\n",
        " part (c)\n",
        "\n",
        " Direction of principal axes:\n",
        "\n",
        " alpha =  -29.30  degrees\n",
        "\n",
        " part (d)\n",
        "\n",
        " Iuu =  200.94  cm^4 \n",
        " Ivv =  45.21  cm^4 \n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex10-pg256"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "##initialization of variables\n",
      "#determine bending stress and find the minimum radius \n",
      "Ys=17000. ##kg/cm^2\n",
      "E=2*10**6 ##kg/cm^2\n",
      "d1=1. ##mm\n",
      "d=1. ##cm\n",
      "##calculations: 1 cm\n",
      "R=E*d/(2*Ys)\n",
      "M=Ys*math.pi*d**3/32.\n",
      "## results\n",
      "print'%s %.2f %s'%(' daimeter wire:',d,'cm')\n",
      "print'%s %.2f %s'%('\\n Minimum radius = ',R,' cm')\n",
      "print'%s %.2f %s'%('\\n Bending Moment = ',M,' kg-cm')\n",
      "## calculations: 1 mm\n",
      "R1=R/(d1*10.)\n",
      "M1=M/(d1*1000.)\n",
      "## results\n",
      "print'%s %.2f %s'%('\\n  daimeter wire:',d1,'mm')\n",
      "print'%s %.2f %s'%('\\n Minimum radius = ',R1,' cm')\n",
      "print'%s %.2f %s'%('\\n Bending Moment = ',M1,' kg-cm')\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " daimeter wire: 1.00 cm\n",
        "\n",
        " Minimum radius =  58.82  cm\n",
        "\n",
        " Bending Moment =  1668.97  kg-cm\n",
        "\n",
        "  daimeter wire: 1.00 mm\n",
        "\n",
        " Minimum radius =  5.88  cm\n",
        "\n",
        " Bending Moment =  1.67  kg-cm\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex11-pg258"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate the section modulus per meter width of plate \n",
      "##initialization of variables\n",
      "import math\n",
      "t=0.5 ##cm\n",
      "s=2. ##m\n",
      "p1=7.5 ##cm\n",
      "p2=10. ##cm\n",
      "d=p2/2.\n",
      "D=1650. ##kg/cm**2\n",
      "## calculations\n",
      "## ab\n",
      "IxX=p1*t**3./12.+t*p1*d**2.\n",
      "## bc\n",
      "alpha=math.atan(3/4.)*57.3\n",
      "Ixx=t*(p1+d)**3./12.\n",
      "Iyy=0.\n",
      "Ixy=0.\n",
      "Iuu=Ixx*math.cos(alpha)**2+Iyy*math.sin(alpha)**2-Ixy*math.sin(2.*alpha)\n",
      "Ixx=Iuu+IxX\n",
      "IXX=Ixx*100./(2.*p1)\n",
      "Z=IXX/(d+t/2.)\n",
      "w=D*Z*8./(s**2*100.)\n",
      "w=w/1000.\n",
      "##Results\n",
      "print'%s %.2f %s'%('w = ',w,' tonne/m')\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "w =  5.50  tonne/m\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex12-pg261"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#find the total u.d load that can be supported \n",
      "##initialization of variables\n",
      "import math\n",
      "wb=10. ##cm\n",
      "wh=20. ##cm\n",
      "sb=0.5 ##cm\n",
      "sh=10. ##cm\n",
      "s=6. ##m\n",
      "fs=1650. ##kg/cm^2\n",
      "fw=150. ##kg/cm^2\n",
      "Es=2*10**6 ##kg/cm^2\n",
      "Ew=12*10**4 ##kg/cm^2\n",
      "\n",
      "##calculations\n",
      "## Method 1\n",
      "A=2*fs/(21.*Es)\n",
      "aw=2.*fw/(20.*Ew)\n",
      "a=min(A,aw)\n",
      "ss=a*Ew*wh/2.\n",
      "##Moment resistance of steel portion\n",
      "F=(fs+1573.)/2.*sb*sh\n",
      "k=sb/3*(fs+2*1573.)/(fs+1573.)\n",
      "Ms=2*F*(10.5-k)\n",
      "##Moment resistance of wooden portion\n",
      "F=ss*wb*wb/2.\n",
      "Mw=2*(F*(wb-wb/3.))\n",
      "M=Ms+Mw\n",
      "##Total udl supported\n",
      "W=M*8./(s*100.)\n",
      "\n",
      "##Results\n",
      "print('Using method 1')\n",
      "print'%s %.2f %s'%('\\n W = ',W,' kg')\n",
      "\n",
      "##Method 2\n",
      "nE=Es/Ew\n",
      "nf=fs/fw\n",
      "Is=2*(0+sb*sh*10.25**2)\n",
      "Iw=0.6*wh**3/12.\n",
      "I=Is+Iw\n",
      "W=fs*I*8./(s*100*10.5)\n",
      "\n",
      "##Results\n",
      "print('\\n Using method 2')\n",
      "print'%s %.2f %s'%('\\n W = ',W,' kg')\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Using method 1\n",
        "\n",
        " W =  3040.91  kg\n",
        "\n",
        " Using method 2\n",
        "\n",
        " W =  3039.40  kg\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex13-pg264"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate stiffness ratio \n",
      "##initialization of variables\n",
      "import math\n",
      "p=6. ##mm\n",
      "Ixx=2375. ##cm**4\n",
      "Es=2*10**6. ##kg/cm**2\n",
      "EAl=0.667*10**6 ##kg/cm**2\n",
      "d1=10.6 ##cm\n",
      "d2=10. ##cm\n",
      "## calculations\n",
      "I1=2.*(0.+p/10*10*10.3**2)\n",
      "I2=Ixx*EAl/Es\n",
      "I=I1+I2\n",
      "n=I/I2\n",
      "## results\n",
      "print'%s %.2f %s'%('stiffness ratio =  ',n,'')\n",
      "n1=Es*d1/(d2*EAl)\n",
      "print'%s %.2f %s'%('\\n Stress ration = ',n1,'')\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "stiffness ratio =   2.61 \n",
        "\n",
        " Stress ration =  3.18 \n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex14-pg269"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate shape factor \n",
      "##initilization of new variables\n",
      "import math\n",
      "wt=0.8 ##cm\n",
      "ft=1.4 ##cm\n",
      "w=10. ##cm\n",
      "y=20. ##cm\n",
      "## Sigma_y: yield stress is not given explicitly\n",
      "k1=wt*(40.-2*ft)/2.\n",
      "Zp=(14*19.3+k1*9.3)*2\n",
      "If=2*(w*ft**3/12+w*ft*19.3**2)\n",
      "Iw=wt*(40-2*ft)**3/12.\n",
      "I=Iw+If\n",
      "Z=I/y\n",
      "sf=Zp/Z\n",
      "##Results\n",
      "print'%s %.2f %s'%('shape factor =  ',sf,'')\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "shape factor =   1.18 \n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex15-pg270"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate elastic core \n",
      "##initilization of new variables\n",
      "import math\n",
      "wt=0.8 ##cm\n",
      "ft=1.4 ##cm\n",
      "w=10. ##cm\n",
      "y=20. ##cm\n",
      "T=750. ##T==750*sigma_y\n",
      "## calculations\n",
      "MpF=ft*w*(40-2*ft)\n",
      "c1=((40.-2*ft)/2)**2-(T-MpF)/wt\n",
      "c=math.sqrt(3*c1)\n",
      "## results\n",
      "print'%s %.2f %s'%('Elastic core of ',2*c,' cm depth is present')\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Elastic core of  26.71  cm depth is present\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex17-pg274"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#find stress at the inner side of the hook \n",
      "##initialization of new variables\n",
      "P=2000. ##kg\n",
      "a=4. ##cm\n",
      "b=1. ##cm\n",
      "d=7. ##cm\n",
      "r=3. ##cm\n",
      "## calculations\n",
      "A=(a+b)/2*d\n",
      "xbar=(a+b*2.)*d/(r*(a+b))\n",
      "rbar=r+xbar\n",
      "I=b*d**3/12.+r*d**3/12.\n",
      "Ixx=I-A*2.8**2\n",
      "e=Ixx/(rbar*A)\n",
      "f1=P*5.8*(xbar-0.62)/(A*0.62*r)\n",
      "f2=P*5.8*(-d+2.18)/(A*0.62*(5.18+d-2.18))\n",
      "str=P/A\n",
      "Str_i=f1+str\n",
      "Str_o=-f2-str\n",
      "##Results\n",
      "print'%s %.2f %s'%('stress at the inner side of the hook =',Str_i,' kg/cm^2 (tensile)')\n",
      "print'%s %.2f %s'%('\\n stress at the outer side of the hook = ',Str_o,' kg/cm^2 (compressive)')\n",
      "## approximations involved in the text\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "stress at the inner side of the hook = 891.18  kg/cm^2 (tensile)\n",
        "\n",
        " stress at the outer side of the hook =  401.03  kg/cm^2 (compressive)\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex20-pg281"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#  find Ratio of maximum bending stress in the stem and flange at various point\n",
      "##initialization of new variables\n",
      "import math\n",
      "t=1. ##cm\n",
      "a=40. ##cm\n",
      "A=236.\n",
      "## calculations\n",
      "ybar=a*t*0.5+(50-1)*4*0.5/(a*t+(50-1)*4)\n",
      "y1bar=1.25*a-ybar\n",
      "IAA=a*t**3/3.+(50-1)**3*4/12.+(50-1)*4*25.5**2\n",
      "Io=IAA-A*ybar**2.\n",
      "##part (1)\n",
      "r=y1bar/ybar\n",
      "## results\n",
      "print('Ratio of maximum bending stress in the stem and flange')\n",
      "print'%s %.2f %s'%('\\n Ratio = ',r,'')\n",
      "##part(2)\n",
      "## calculations\n",
      "r=(2/3.*388*29.56)-(2/3.*160*20.44)-(228*20.44)\n",
      "r=r/(2*2/3.*388*29.56)\n",
      "## results\n",
      "print('\\n Ratio of S.F in flange to total S.F')\n",
      "print'%s %.2f %s'%('\\n Ratio = ',r*100,' percent')\n",
      "## part (3)\n",
      "## calculations\n",
      "r=359.*200./Io\n",
      "## results\n",
      "print('\\n Ratio of maximum shear stress in the flange to average sher stress in the stem')\n",
      "print'%s %.2f %s'%('\\n Ratio =  ',r,'')\n",
      "##part (4)\n",
      "## calculations\n",
      "s=10 ##m\n",
      "r=r/0.922\n",
      "sigma=1650 ##kg/cm**2\n",
      "shear=945 ##kg/cm**2\n",
      "wsh=2*200*shear/(r*s)\n",
      "wsi=8*Io*sigma/(s**2*10*29.56)\n",
      "w=min(wsh,wsi)\n",
      "## results\n",
      "print'%s %.2f %s'%('\\n Maximum u.d.l. = ',w,' kg/m ')\n",
      "\n",
      "print('wrong moment of Inertia (Io) in the text and hence part (3) and part (4) are wrong')\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Ratio of maximum bending stress in the stem and flange\n",
        "\n",
        " Ratio =  1.45 \n",
        "\n",
        " Ratio of S.F in flange to total S.F\n",
        "\n",
        " Ratio =  5.27  percent\n",
        "\n",
        " Ratio of maximum shear stress in the flange to average sher stress in the stem\n",
        "\n",
        " Ratio =   1.05 \n",
        "\n",
        " Maximum u.d.l. =  30507.35  kg/m \n",
        "wrong moment of Inertia (Io) in the text and hence part (3) and part (4) are wrong\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex21-pg284"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#find the design force two cases\n",
      "##initialization of new variables\n",
      "import math\n",
      "a=30. ##cm\n",
      "t=2.5 ##cm\n",
      "S=15. ##cm\n",
      "s=5. ##Tonne\n",
      "## calculations\n",
      "I=a*a**3-25*25**3\n",
      "I=I/12.\n",
      "tau_zx=s*1000.*27.5*t*25/(4*35000.*t)\n",
      "FA=S*t*tau_zx\n",
      "tau_xy=s*1000.*a*t*27.5/(4.*35000.*t)\n",
      "FB=tau_xy*t*S\n",
      "##Results\n",
      "print'%s %.2f %s'%('case A \\n F = ',FA,' kg')\n",
      "print'%s %.2f %s'%('\\n case B \\n F= ',FB,' kg')\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "case A \n",
        " F =  920.76  kg\n",
        "\n",
        " case B \n",
        " F=  1104.91  kg\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex23-pg288"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate shear centre\n",
      "##initialization of variables\n",
      "import math\n",
      "h=40. ##cm\n",
      "b=10. ##cm\n",
      "t1=1.4 ##cm\n",
      "t2=0.8 ##cm\n",
      "Ixx=13989.5 ##cm^4\n",
      "##calculations\n",
      "e=b**2*h**2*t1/(4.*Ixx)*(1-t1/h-t1/b+t1**2/(b*h))*(1-t1/h)\n",
      "##Results\n",
      "print'%s %.2f %s'%('Shear center: \\n e = ',e,' cm')\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Shear center: \n",
        " e =  3.21  cm\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex33-pg303"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#calculate deflection\n",
      "##initialization of new variables\n",
      "import math\n",
      "L=50. ##cm\n",
      "k=15. ##cm\n",
      "I=200. ##cm^4\n",
      "II=40. ##cm^4\n",
      "d=30. ##cm\n",
      "Pd=40. ##cm\n",
      "E=0.6667*10**6 ##kg/cm^2\n",
      "##calculations\n",
      "delta=(100.*10./2*16.33+L*d*35+L*k/2.*25+d*k/2.*45)\n",
      "delta1=delta/E\n",
      "##Results\n",
      "print'%s %.2f %s'%('deflection = ',delta1*10**1,'mm')\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "deflection =  1.20 mm\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Ex39-pg312"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#design suitable I design section\n",
      "W=1\n",
      "L=6\n",
      "f=1650\n",
      "Z=305.9\n",
      "w=31.2\n",
      "z=8\n",
      "t=0.65\n",
      "d=22.5\n",
      "M=4.5*10**5\n",
      "##part(i)\n",
      "#maximum B.M\n",
      "BM= W*L**2/(z)\n",
      "SF=W*L/2\n",
      "print'%s %.2f %s %.2f %s '%('Bm=',Bm,''and '',SF,'')\n",
      "#part(ii)\n",
      "Z=M/f\n",
      "#part(iii)\n",
      "#for ISMB 225 having weight 31.2\n",
      "Z1=305.9\n",
      "print'%s %.2f %s'%('z=',Z1,'')\n",
      "#Additional Beam\n",
      "Bm=w*12/z\n",
      "Z2=Bm/f\n",
      "TZ=Z+Z2\n",
      "print'%s %.2f %s'%('TZ=',TZ,'')\n",
      "#thickness\n",
      "WA=t*d\n",
      "print'%s %.2f %s'%('WA=',WA,'')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Bm= 4.00  3.00  \n",
        "z= 305.90 \n",
        "TZ= 272.76 \n",
        "WA= 14.62 \n"
       ]
      }
     ],
     "prompt_number": 19
    }
   ],
   "metadata": {}
  }
 ]
}