path: root/Strength_Of_Materials_by_B_K_Sarkar/Chapter13.ipynb

{
 "metadata": {
  "name": "chapter 13 som.ipynb"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Chapter No.13:Shear Stress in Beams"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problem no 13.2,Page No.301"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "#W=10*w #KN/m #u.d.l\n",
      "sigma=805*10**6 #Pa  #Bending stress\n",
      "Tou=0.85*10**6 #Pa #Shear stress\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#M=W*L**2*10**-4*8**-1 #Max B.M\n",
      "#F=W*L*10**-2*2**-1 #Max S.F\n",
      "#y=h*2**-1 #depth\n",
      "#A-b*h #Area of c/s\n",
      "\n",
      "#Now using relation we get\n",
      "#sigma=M*h*(2*I)**-1   #Bending stress\n",
      "\n",
      "#AFter substituitng values we get\n",
      "#805*10**6=w*l**2*h*(16*10**5*I)**-1   #Equation 1\n",
      "\n",
      "#Again using the relation we get \n",
      "#tou=F*A*y_bar*(I*b)**-1  #shear atress\n",
      "\n",
      "#AFter substituitng values we get\n",
      "#0.85*10**6=w*L*h**2*(16*10**5*I)**-1  #Equation 2\n",
      "\n",
      "#Dividing equation 1 & 2 we get\n",
      "#L*h**-1=10\n",
      "#Let L*h**-1=Z\n",
      "z=10\n",
      "\n",
      "#Result\n",
      "print\"The Ratio of span to depth ratio is\",round(z,2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Ratio of span to depth ratio is 10.0\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problem no 13.3,Page No.302"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "%matplotlib  inline\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "L=2 #m #span\n",
      "w=20*10**3 #N/m #u.d.L\n",
      "b=12.5 #cm #width of Flange\n",
      "t=2.5 #cm #flange thickness\n",
      "w_t=2.5 #cm #web thickness\n",
      "D=20  #cm #Overall depth\n",
      "w_d=17.5 #m #Depth of web\n",
      "\n",
      "#Calculations\n",
      "\n",
      "F=w*L*2**-1 #N #Max S.F\n",
      "a_1=b*t #Area of flange\n",
      "a_2=w_d*w_t #Area of web\n",
      "y_1=t*2**-1 #C.G of flange\n",
      "y_2=w_d*2**-1+t #C.G of web\n",
      "\n",
      "#C.G of c/s\n",
      "Y=(a_1*y_1+a_2*y_2)*(a_1+a_2)**-1 \n",
      "\n",
      "#M.I about N.A\n",
      "I=b*t**3*12**-1+b*t*(Y-y_1)**2+w_t*w_d**3*12**-1+w_t*w_d*(y_2-Y)**2 \n",
      "\n",
      "#Shear Stress in flange at the junction with web\n",
      "#Let tou(Shear stress)=S \n",
      "#Change in the notifications of Shear Stress For convenience\n",
      "S_1=(F*a_1*(Y-y_1)*10**-6)*(I*10**-8*b*10**-2)**-1*10**-3 \n",
      "\n",
      "#Shear Stress in web at the junction with flange \n",
      "S_2=(F*a_1*(Y-y_1)*10**-6)*(I*10**-8*w_t*10**-2)**-1*10**-3 \n",
      "\n",
      "#Max Shear Stres at N.A\n",
      "S_max=(F*(a_1*(Y-y_1)+(w_t*(Y-t))*((Y-t)*2**-1))*10**-6)*(I*10**-8*w_t*10**-2)**-1*10**-3\n",
      "\n",
      "#Result\n",
      "print\"The Max shear stress in the beam is\",round(X_max,2),\"KN/m**2\"\n",
      "\n",
      "print\"Shear stress distribution Diagram\"\n",
      "\n",
      "#Plotting the Shear stress distribution Diagram\n",
      "\n",
      "X_1=[0,2.5,2.5,4.58,15.42]\n",
      "Y_1=[0,S_1,S_2,S_max,0]\n",
      "Z_1=[0,0,0,0,0]\n",
      "plt.plot(X_1,Y_1,X_1,Z_1)\n",
      "plt.xlabel(\"Length x in m\")\n",
      "plt.ylabel(\"Shear Stress in kN/m**2\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Max shear stress in the beam is 5644.64 KN/m**2\n",
        "Shear stress distribution Diagram\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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YgL+/v6XYxMTEEBoaytGjRwkJCSEmJgaA1NRUVq1aRWpqKomJiURHR1sun6ZNm0ZsbCxp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\nQXGxnirXvz9Mnw6ffipFQwh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       "text": [
        "<matplotlib.figure.Figure at 0x57624b0>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problem no 13.4,Page No.303"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "F=100*10**3 #N #Shear Force\n",
      "I=11340*10**-8 #m**4 #M.I\n",
      "b=20 #cm #width of Flange\n",
      "t=5 #cm #thickness of flange\n",
      "w_d=20 #cm #Depth of web\n",
      "w_t=5 #cm #thickness of web\n",
      "\n",
      "#Calculations\n",
      "\n",
      "a_1=b*t #cm**2 #Area of flange\n",
      "a_2=w_d*w_t #cm**2 #Area of web\n",
      "y_1=t*2**-1 #cm #C.G of flange\n",
      "y_2=t+w_d*2**-1\n",
      "\n",
      "#C.G of C/s\n",
      "Y=(a_1*y_1+a_2*y_2)*(a_1+a_2)**-1\n",
      "\n",
      "#Shear Stress in flange at the junction with web\n",
      "#Let tou(Shear stress)=S \n",
      "#Change in the notifications of Shear Stress For convenience\n",
      "S_1=(F*a_1*(Y-y_1)*10**-6)*(I*b*10**-2)**-1*10**-3 \n",
      "\n",
      "#Shear Stress in web at the junction with flange \n",
      "S_2=(F*a_1*(Y-y_1)*10**-6)*(I*w_t*10**-2)**-1*10**-3 \n",
      "\n",
      "#Max Shear Stres at N.A\n",
      "S_max=(F*(a_1*(Y-y_1)+(w_t*(Y-t))*((Y-t)*2**-1))*10**-6)*(I*w_t*10**-2)**-1*10**-3\n",
      "\n",
      "#Result\n",
      "print\"Shear Stress in flange at the junction with web\",round(S_1,2),\"KN/m**2\"\n",
      "print\"Shear Stress in web at the junction with flange\",round(S_2,2),\"KN/m**2\"\n",
      "print\"Max Shear Stres at N.A\",round(S_max,2),\"KN/m**2\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Shear Stress in flange at the junction with web 2755.73 KN/m**2\n",
        "Shear Stress in web at the junction with flange 11022.93 KN/m**2\n",
        "Max Shear Stres at N.A 11642.97 KN/m**2\n"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problem no 13.5,Page No.304"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "from scipy.integrate import quad\n",
      "\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "D=50 #cm #Overall depth\n",
      "b=19 #cm #width of flange\n",
      "t=2.5 #cm #Thickness of Flange\n",
      "w_t=1.5 #cm #Web thickness\n",
      "w_d=45 #cm #web thickness\n",
      "F=400*10**3 #N #Shear Force\n",
      "I=64500*10**-8 #m**4 #M.I\n",
      "\n",
      "#Calculations  (Part-1)\n",
      " \n",
      "a_1=b*t #cm**2 #Area of flange\n",
      "a_2=w_d*w_t #cm**2 #Area of web\n",
      "y_1=t*2**-1 #cm #C.G of flange\n",
      "y_2=t+w_d*2**-1\n",
      "\n",
      "#As section is symmetrical \n",
      "Y=D*2**-1 #cm\n",
      "\n",
      "#Shear Stress in flange at the junction with web\n",
      "#Let tou(Shear stress)=S \n",
      "#Change in the notifications of Shear Stress For convenience\n",
      "S_1=(F*a_1*(Y-y_1)*10**-6)*(I*b*10**-2)**-1*10**-3 \n",
      "\n",
      "#Shear Stress in web at the junction with flange \n",
      "S_2=(F*a_1*(Y-y_1)*10**-6)*(I*w_t*10**-2)**-1*10**-3 \n",
      "\n",
      "#Max Shear Stres at N.A\n",
      "S_max=(F*(a_1*(Y-y_1)+(w_t*(Y-t))*((Y-t)*2**-1))*10**-6)*(I*w_t*10**-2)**-1*10**-3\n",
      "\n",
      "#Calculations (Part-2)\n",
      "\n",
      "#consider a strip in the flange of thickness dy at a distance y from N.A \n",
      "\n",
      "#S=F*(b*(Y-y)*(Y+y)*2**-1*10**-6)*(I*b*10**-2)**-1\n",
      "#after substituting values we get\n",
      "#S=625-y**2*(3225*10**-8)**-1\n",
      "\n",
      "#shear force carried by small strip\n",
      "#F_1=625-y**2*(3225*10**-8)**-1*b*dy*10**-4\n",
      "\n",
      "#Now Integrating above Equation we get\n",
      "def integrand(y, a, b):\n",
      "       return 625-y**2\n",
      "a =625\n",
      "b =-1\n",
      "I = quad(integrand, 22.5, 25, args=(a,b))\n",
      "\n",
      "#Shear force carried by one flange\n",
      "F_1=19*3225**-1*10**4*I[0]\n",
      "\n",
      "#Shear force carried by two flange\n",
      "F_2=2*F_1\n",
      "\n",
      "#Shear force carried by web\n",
      "F_3=F-F_2\n",
      "\n",
      "#Result\n",
      "print\"The shear Force int the section is\",round(S_max,2),\"Pa\"\n",
      "print\"Total Shear Force in the web is\",round(F_3,2),\"N\"\n",
      "\n",
      "\n",
      "print\"Shear stress distribution Diagram\"\n",
      "\n",
      "#Plotting the Shear stress distribution Diagram\n",
      "\n",
      "X_1=[0,2.5,2.5,25,47.5,47.5,50]\n",
      "Y_1=[0,S_1,S_2,S_max,S_2,S_1,0]\n",
      "Z_1=[0,0,0,0,0,0,0]\n",
      "plt.plot(X_1,Y_1,X_1,Z_1)\n",
      "plt.xlabel(\"Length x in m\")\n",
      "plt.ylabel(\"Shear Stress in kN/m**2\")\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The shear Force int the section is 62338.5 MPa\n",
        "Total Shear Force in the web is 382202.84 N\n",
        "Shear stress distribution Diagram\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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LC/n2t7/NxIkTeeyxx5o08+7duwNQWVlJdXU1119/PRkZGSQlJQGQlJTE5s2b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\nUERExC0UKCIi4hYKFBERcYv/D6L3iyTClBJuAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5633a10>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problem no 13.6,Page No.305"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "F=5*10**3 #N #shea Force\n",
      "b=20 #cm #width of Flange\n",
      "t=6 #cm #Thickness of flange\n",
      "w_d=20 #cm #depth of web\n",
      "w_t=6 #cm #thickness of web\n",
      "X=700 #N #Shear Looad\n",
      "\n",
      "#Calculations\n",
      "\n",
      "a_1=b*t #cm**2 #Area ofFlange\n",
      "a_2=w_d*w_t #cm**2 #Area of web\n",
      "y_1=t*2**-1 #cm #C.G of Flange\n",
      "y_2=t+w_d*2**-1 #cm #C.G of Web\n",
      "\n",
      "Y=(a_1*y_1+a_2*y_2)*(a_1+a_2)**-1\n",
      "\n",
      "#M.I about N.A\n",
      "I=b*t**3*12**-1+b*t*(Y-y_1)**2+w_t*w_d**3*12**-1+w_t*w_d*(y_2-Y)**2 \n",
      "\n",
      "#Shear Force per metre Length in Plane of contact of two Planks \n",
      "#Let Shear Force per metre Length=F_1 \n",
      "F_1=(F*a_1*(Y-y_1)*10**-6)*(I*10**-8)**-1\n",
      "\n",
      "#Spacing of nails\n",
      "s=X*F_1**-1*100\n",
      "\n",
      "#Result\n",
      "print\"The spacing of nails along the Length of beam is\",round(s,2),\"cm\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The spacing of nails along the Length of beam is 2.6 cm\n"
       ]
      }
     ],
     "prompt_number": 74
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problem no 13.7,Page No.306"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "L=3 #m #span\n",
      "d=5 #cm #depth of each plank\n",
      "b=15 #cm #width of plank\n",
      "d_1=1.9 #cm #Diameter of bolt\n",
      "s=12.5 #cm #spacing of bolt\n",
      "w=3.3*10**3 #N.m #u.d.l\n",
      "\n",
      "#Calculations\n",
      "\n",
      "#Shear Force at 1.5m from support\n",
      "F=w*1.5\n",
      "\n",
      "I=b*(5*d)**3*12**-1 #M.I\n",
      "A=pi*4**-1*d_1**2 #area of Bolt\n",
      "Y=5*d*2**-1 #C.G of beam\n",
      "y_1=d*2**-1 #c.G of top plank\n",
      "\n",
      "#Shear Force per metre Length \n",
      "F_1=F*b*d*(Y-y_1)*10**-6*(I*10**-8)**-1\n",
      "\n",
      "#Load carried by bolt\n",
      "W_1=F_1*s*10**-2\n",
      "\n",
      "#shear stress\n",
      "X_1=W_1*(round(A,3))**-1*10**+4\n",
      "\n",
      "#Shear Force per metre Length \n",
      "F_2=F*b*2*d*((d+y_1)-Y*10**-6)*(I*10**-8)**-1*10**-6\n",
      "\n",
      "#Load carried by bolt\n",
      "W_2=F_2*s*10**-2\n",
      "\n",
      "#shear stress\n",
      "X_2=W_2*(A*10**-4)**-1*10**-3\n",
      "\n",
      "#Reult\n",
      "print\"Shear stress in a bolt Located at 1.5 m from support is\",round(X_2,2),\"KN/m**2\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Shear stress in a bolt Located at 1.5 m from support is 12570.13 KN/m**2\n"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problem no 13.8,Page No.307"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\\\n",
      "\n",
      "b=15 #cm #width of plank\n",
      "t=2.5 #cm #thickness of planf\n",
      "F_1=1250 #N #Shear Force\n",
      "F_2=5*10**3 #shaear force transmitted by screw\n",
      "d=15 #cm #Depth of plank\n",
      "D=20 #cm  #Overall depth\n",
      "\n",
      "#Calculations\n",
      "\n",
      "Y=D*2**-1  #C.G of beam\n",
      "y_1=t*2**-1 #C.G of flange\n",
      "\n",
      "I=((b*D**3)-(D*2**-1*b**3))*12**-1 #cm**4 #M.I\n",
      "\n",
      "#Shear Stress in the Flange at 7.5 cm from N.A\n",
      "X_1=F_2*b*t*(Y-y_1)*10**-6*(I*10**-8*d*10**-2)**-1*10**-3\n",
      "\n",
      "#Shear Stress in the web at 7.5 cm from N.A\n",
      "X_2=X_1*d*(2*t)**-1\n",
      "\n",
      "#shear stress at N.A\n",
      "X_max=F_2*(b*t*(Y-y_1)+2*t*d*2**-1*d*4**-1)*10**-6*(I*10**-8*2*t*10**-2)**-1*10**-3\n",
      "\n",
      "#horizontal shear force per pitch length to the shearing strength of two bolts we have\n",
      "#X_h=X_2*10**3*2*t*10**-2*p\n",
      "\n",
      "#Equating horizontal shear force per pitch length to the shearing strength of two bolts we have\n",
      "p=F_1*2*(X_2*10**3*2*t*10**-2)**-1*10**2\n",
      "\n",
      "#Result\n",
      "print\"The Min spacing of screw along the beam is\",round(p,2),\"cm\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Min spacing of screw along the beam is 10.95 cm\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problem no 13.9,Page No.308"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "L=4 #m #span\n",
      "w=80*10**3 #N/m #u.d.l\n",
      "D=35 #cm #Overall depth\n",
      "b=15 #cm #width of Flange\n",
      "t=2.5 #cm #Thickness of flange\n",
      "w_d=30 #cm #Depth of web\n",
      "w_t=1.2 #cm #thickness of web\n",
      "\n",
      "#Calculations\n",
      "\n",
      "R_a=R_b=160 #KN #Reactions at supports\n",
      "\n",
      "#Shear FOrce at 1m from left support\n",
      "F=R_a*10**3-w\n",
      "\n",
      "M=R_a*10**3-w*2**-1 #B.M at 1m From support\n",
      "\n",
      "I=(b*D**3-((b-w_t)*w_d**3))*12**-1 #cm**4\n",
      "\n",
      "y=w_d*2**-1\n",
      "sigma=M*I**-1*y #N/m**2\n",
      "\n",
      "#Shear stress in Flange at the junction with web\n",
      "X_1=w*b*t*(w_d*2**-1+t*2**-1)*10**-6*(I*10**-8*b*10**-2)**-1*10**-3\n",
      "\n",
      "#Shear stress in web at the junction with Flange \n",
      "X_2=X_1*15*1.2**-1\n",
      "\n",
      "#Result\n",
      "print\"The Magnitude of Bending is\",round(sigma,2),\"N/m**2\"\n",
      "print\"Shear stress in web at the junction with Flange\",round(X_1,2),\"KN/m**2\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Magnitude of Bending is 79.84 N/m**2\n",
        "Shear stress in web at the junction with Flange 1441.64 KN/m**2\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Problem no 13.10,Page No.309"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import math\n",
      "\n",
      "#Initilization of variables\n",
      "\n",
      "b=25 #cm #width of top FLange\n",
      "t=5 #cm #thickness of top Flange\n",
      "D=35 #cm #Depth of overall section\n",
      "w_d=25 #cm #depth of web\n",
      "w_t=5 #cm #thickness of web\n",
      "t_1=5 #cm #thickness of bottom Flange\n",
      "b_1=15 #cm #width of bottom Flange\n",
      "sigma=17.5*10**6\n",
      "F=100*10**3 #N #S.F\n",
      "\n",
      "#Calculations\n",
      "\n",
      "a_1=b*t #area of top flange\n",
      "a_2=w_d*w_t #area of web\n",
      "a_3=b_1*t_1 #area of bottom Flange\n",
      "y_1=t*2**-1 #C.G of top flange\n",
      "y_3=D-(t_1*2**-1) #C.G of bottom Flange \n",
      "y_2=D*2**-1 #c.G of Web\n",
      "\n",
      "Y=(a_1*y_1+a_2*y_2+a_3*y_3)*(a_1+a_2+a_3)**-1\n",
      "\n",
      "I=b*t**3*12**-1+b*t*(Y-y_1)**2+w_t*w_d**3*12**-1+w_t*w_d*(D*2**-1-Y)**2+b_1*t_1**3*12**-1+b_1*t_1*(y_3-Y)**2\n",
      "\n",
      "M=sigma*I*10**-8*(Y*10**-2)**-1 #B.M\n",
      "\n",
      "#Shear Stress in upper Flange at the junction with web\n",
      "S_1=F*b*t*(Y-y_1)*10**-6*(I*10**-8*b*10**-2)**-1*10**-3\n",
      "\n",
      "#Shear Stress in web at the junction with upper Flange \n",
      "S_2=S_1*b*t**-1\n",
      "\n",
      "#Max shear stress at the N.A\n",
      "S=F*(b*t*(Y-y_1)+w_t*(Y-t)*(Y-t)*2**-1)*10**-6*(I*10**-8*w_t*10**-2)**-1*10**-3\n",
      "\n",
      "#Shear Stress in Lower Flange at the junction with web\n",
      "S_3=F*(a_3*(D-Y-t_1*2**-1))*10**-6*(I*10**-8*b_1*10**-2)**-1*10**-3\n",
      "\n",
      "#Shear Stress in web at the junction with Lower Flange \n",
      "S_4=S_3*b_1*t_1**-1\n",
      "\n",
      "#Result\n",
      "print\"The Bending Moment section can take is\",round(M,2),\"N-m\"\n",
      "print\"The shear stress Distribution Diagram\"\n",
      "\n",
      "#Plotting the Shear stress distribution Diagram\n",
      "\n",
      "X_1=[0,5,5,15.19,30,30,35]\n",
      "Y_1=[0,S_1,S_2,S,S_3,S_4,0]\n",
      "Z_1=[0,0,0,0,0,0,0]\n",
      "plt.plot(X_1,Y_1,X_1,Z_1)\n",
      "plt.xlabel(\"Length x in m\")\n",
      "plt.ylabel(\"Shear Stress in kN/m**2\")\n",
      "plt.show()\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The Bending Moment section can take is 57821.07 N-m\n",
        "The shear stress Distribution Diagram\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Dx1mEcDft2sH778OuXfDss3pHI8T5LrrkSE2Lo3bLw17ffPMNM2fOpKKiAl9fX9544w2q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\noJRixowZBAUF8eCDD9qOx8b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/Pz+llFLvvfeeGj16tFJKqeLiYtWlSxe1du1apdT5G3EZ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\nu0jiEEIIYRdJHEIIIezy/0Du21HzYcG/AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5641790>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}