{ "metadata": { "name": "chapter 8.ipynb" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "CHAPTER 8: FORCES IN BEAMS" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.8-1, Page no 118" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "#Initilization of variables\n", "R_A=100 #N\n", "R_B=200 #N\n", "\n", "#Calculations\n", "#Shear force at 2m\n", "V=100 #N\n", "#Moment at 2m\n", "M=R_A*2 #N.m\n", "\n", "#Result\n", "print'The shear force at 2m is +',round(V),\"N\"\n", "print'The moment at 2m is +',round(M),\"N-m\" \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The shear force at 2m is + 100.0 N\n", "The moment at 2m is + 200.0 N-m\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.8-2, Page no 118" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "#Initilization of variables\n", "#length matrix\n", "L1=[0,3.99,4,5.99,6] #m\n", "#Bending moment matrix\n", "B=[0,400,400,0.00001,0] #N.m\n", "#Shear force plotting\n", "#Here the left side and right side lengths are considered as close as 4 to keep up with right and left distinctions\n", "L=[0,3.99,4,5.99,6]\n", "S=[100,100,-200,-200,0]\n", "g=[0,0,0,0,0]\n", "\n", "#Calculations cum Result\n", "d=transpose(L1)\n", "e=transpose(S)\n", "plt.plot(d,B)\n", "xlabel('distance (m)')\n", "ylabel('B.M (N.m)')\n", "plt.show()\n", "plt.plot(L,e,L,g)\n", "xlabel('distance (m)')\n", "ylabel('S.F (N)')\n", "plt.show()\n", "\n", "print'The graphs are the solutions'\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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3/qygoABfX996j1E7EETTLVgA//ynGgZdumhdjRCua84cuPNOeOop6NhR62rq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\n5xrc3mX+dhv70JpwXuXl5Yw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"text": [ "" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "The graphs are the solutions\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.8-3, Page no 119" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "#Initilization of variables\n", "w=196 #N/m\n", "M_app=4000 #N.m\n", "L=6 #m\n", "\n", "#Calculations\n", "#Taking Moment about Point L and equating it to 0\n", "R_r=(M_app+w*L*L*0.5)/(3*L) #N\n", "#Taking Moment about Point R and equating it to 0\n", "R_l= ((((2*L)+(L/2))*(w*L))-(M_app))/(3*L) #N\n", "#finding point of zero shear\n", "a=R_l*w**-1\n", "#defining x\n", "x0=[0,18]\n", "x=[0,0.5,1,1.5,2,2.5,3,3.5,a,4,4.5,5,5.5,6] #for 0" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "The value of reactions are: R_l= 757.0 N and R_r= 418.0 N\n", "The point of maximum bending moment is 3.86 meters from left support and maximum bending moment is 1462.0 N.m\n", "The bending moment and shear force diagrams have been plotted\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 8.8-4, Page no 121" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "#Initlization of variables\n", "F1=2000 #lb\n", "w=100 #lb/ft\n", "\n", "#Calculations\n", "R_r=(-F1*5+w*14*13)/20 #lb\n", "R_l=(F1*25+w*14*7)/20 #lb\n", "#Shear Force matrix\n", "V=[-2000,-2000,990,990,-410,0] #lb\n", "#Bending Moment matrix\n", "B=[0,-10000,-10000,-4060,840,0]\n", "#Length matrix for shear force\n", "X_v=[0,5,5.0001,11,20.89999,20.9]\n", "#Length matrix for bendimg moment\n", "X_b=[0,4.99,5,11,19.9,20.9]\n", "g=[0,0,0,0,0,0]\n", "\n", "#Plotting of SFD & BMD.\n", "d=transpose(X_v)\n", "e=transpose(V)\n", "plt.plot(d,B)\n", "xlabel('distance (ft)')\n", "ylabel('B.M (lb.ft)')\n", "plt.show()\n", "plt.plot(X_b,e,X_b,g)\n", "xlabel('distance (ft)')\n", "ylabel('S.F (lb)')\n", "plt.show()\n", "\n", "#Result\n", "print'The bending Moment and Shear Force diagrams have been plotted'\n", "#Note\n", "#The textbook does not specify the span and hence there seems to be a disagreement between the textbook and python solution.here the values have just been plotted\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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Z2YwaNYrQ0FDCw8OJiIhg27ZtlJaWUlFRQUJCAgBjx45l9erVAKxZs4a0tDQA\nhg0bxpYtWyxYotqlqCjX6hL8hj48ztC6OEPr4vJZfk5lyZIlpKSkALBv3z4cDof7MYfDQUlJSZXp\ndrudkpISAEpKSmjTpg0AISEhNG7cmIMHD/pwCURE5LQQb71wUlISZWVlVabPnj2bIUOGAPD0009T\nr1497rrrLm+VUck/3zaoffcdNGtmdRUiEqi8FiqbNm264OOvv/4669evr3S4ym63U1RU5P67uLgY\nh8OB3W53HyI7e/rpefbu3cu1117LiRMnOHz4MM3O86nZvn171q1T29NpNtssq0vwG7NmaV2cpnVx\nhtaFqX379jV6vtdC5UJycnJ45pln+OCDD6hfv757empqKnfddRdTp06lpKQEl8tFQkICNpuNRo0a\nsW3bNhISEli6dCmTJ092z5OZmUn37t1ZuXIl/fr1O+97fvfddz5ZNhGRYGYzDN9fY+10Ojl+/Lh7\nj6JHjx6kp6cD5uGxJUuWEBISwsKFCxkwYABgthSPGzeOY8eOkZKSwvPPPw+YLcVjxowhPz+f5s2b\ns3z5csLDw329SCIigkWhIiIigcny7i9fyMnJISoqCqfTybx586wux1Lh4eF06tSJuLg4d4t2sLj3\n3nsJCwsjJibGPe3gwYMkJSURGRlJcnIyhw4dsrBC3znfupg5cyYOh4O4uDji4uLc14IFsqKiIvr0\n6UPHjh254YYb3EdAgnG7qG5d1HS7CPg9lZMnT3L99dezefNm7HY7//Iv/8KyZcvo0KGD1aVZol27\ndmzfvv28zQyBbuvWrTRo0ICxY8fy5ZdfAvD4449zzTXX8PjjjzNv3jx+/PFH5s6da3Gl3ne+dTFr\n1iwaNmzI1KlTLa7Od8rKyigrK6Nz584cOXKErl27snr1al577bWg2y6qWxdvv/12jbaLgN9TycvL\nIyIigvDwcEJDQxk5ciTZ2dlWl2WpAP8eUa1evXrRtGnTStPOvng2LS3NfVFtoDvfuoDg2zZatWpF\n586dAWjQoAEdOnSgpKQkKLeL6tYF1Gy7CPhQOfviSDhzQWWwstls9O/fn/j4eF555RWry7FceXk5\nYWFhAISFhVFeXm5xRdZatGgRsbGxjB8/PigO+ZytsLCQ/Px8unXrFvTbxel10b17d6Bm20XAh4pN\nQ/JW8vHHH5Ofn8+GDRt44YUX2Lp1q9Ul+Q2bzRbU28vEiRPZvXs3n3/+Oa1bt+aRRx6xuiSfOXLk\nCMOGDWNExqemAAAGDUlEQVThwoU0bNiw0mPBtl0cOXKEO+64g4ULF9KgQYMabxcBHyrnXlBZVFRU\naciXYNO6dWsAWrRowdChQ8nLy7O4ImuFhYW5R34oLS2lZcuWFldknZYtW7o/QCdMmBA028Zvv/3G\nsGHDGDNmDLfddhsQvNvF6XUxevRo97qo6XYR8KESHx+Py+WisLCQ48ePk5WVRWpqqtVlWeLnn3+m\noqICgKNHj7Jx48ZK3T/B6PTFswCZmZnu/5GCUWlpqfv3VatWBcW2YRgG48ePJzo6moceesg9PRi3\ni+rWRY23CyMIrF+/3oiMjDTat29vzJ492+pyLLNr1y4jNjbWiI2NNTp27Bh062LkyJFG69atjdDQ\nUMPhcBhLliwxDhw4YPTr189wOp1GUlKS8eOPP1pdpk+cuy4yMjKMMWPGGDExMUanTp2MW2+91Sgr\nK7O6TK/bunWrYbPZjNjYWKNz585G586djQ0bNgTldnG+dbF+/foabxcB31IsIiK+E/CHv0RExHcU\nKiIi4jEKFRER8RiFioiIeIxCRUREPEahIiIiHqNQEbmAmTNnMn/+fACeeuqpSre/Pld2djZff/21\nr0qrYt26dcycOROAH374gW7dutG1a1c++ugj/vrXv7qfV15eTkpKikVVSqBTqIhcwNljPs2aNava\n21WDebVxQUGBL8o6r/nz5zNx4kQAtmzZQqdOndi+fTsOh8N9Z1UwhyBp2rQpO3bssKpUCWAKFZFz\nPP3001x//fX06tWLb775xh0s48aN45133gFg+vTpdOzYkdjYWB577DE++eQT1q5dy2OPPUaXLl3Y\ntWsXr7zyCgkJCXTu3Jk77riDY8eOuV9nypQp9OzZk/bt27tfE2DevHl06tSJzp0782//9m8A7Ny5\nk0GDBhEfH0/v3r355ptvqtRcVFTE8ePHCQsL4/PPP2fatGlkZ2cTFxfH9OnT2blzJ3FxcUybNg0w\nhyFZtmyZV9ejBCmfXP8vUkt89tlnRkxMjHHs2DHjp59+MiIiIoz58+cbhmEY48aNM9555x1j//79\nxvXXX++e5/Dhw5UeP+3AgQPu32fMmGEsWrTIMAzDSEtLM4YPH24YhmEUFBQYERERhmGYwwndeOON\nxrFjxwzDMNxDg/Tt29dwuVyGYRjGp59+avTt27dK3cuWLTMeeOAB99+vv/668eCDDxqGYRiFhYXG\nDTfcUOn5u3btMhISEmq8fkQuJsTqUBPxJ1u3buX222+nfv361K9f/7yDjzZp0oT69eszfvx4Bg8e\nzODBg92PGWeNevTll18yY8YMDh8+zJEjRxg4cCBgHlI7PUBhhw4d3Pfq2Lx5M/feey/169d3v8+R\nI0f45JNPuPPOO92ve/z48So17d271z0C9ek6TtdinGckptatW1NYWHjJ60XkUilURM5is9kqfQif\n+4FsGAZ169YlLy+PLVu2sHLlShYvXuw+gX/2OZhx48axZs0aYmJiyMzMJDc31/1YvXr1qrzHue8N\ncOrUKZo0aUJ+fv5Faz973ovd/8MwjKC6R4j4js6piJyld+/erF69ml9++YWKigrWrVtX5TlHjx7l\n0KFDDBo0iGeffZYvvvgCgIYNG/LTTz+5n3fkyBFatWrFb7/9xptvvnnRD/GkpCRee+0197mXH3/8\nkUaNGtGuXTtWrlwJmGHwv//7v1Xmbdu2rfv+H6efd1rDhg3dtzw4rbS0lLZt215sdYjUmEJF5Cxx\ncXGMGDGC2NhYUlJSSEhIqPS4zWajoqKCIUOGEBsbS69evXjuuecAGDlyJM888wxdu3Zl165d/OUv\nf6Fbt27cdNNNdOjQocrrnPv7gAEDSE1NJT4+nri4OHcr81tvvUVGRgadO3fmhhtuYM2aNVXq7tmz\nZ6VurrPvVti8eXN69uxJTEyM+0R9Xl4evXv3/r2rS6QKDX0vEiD69u3LW2+9VencSnXuvvtuHn30\nUeLi4nxQmQQT7amIBIhHH32UF1988aLP+/777zl06JACRbxCeyoiIuIx2lMRERGPUaiIiIjHKFRE\nRMRjFCoiIuIxChUREfEYhYqIiHjM/wMjUibUs6KdhgAAAABJRU5ErkJggg==\n", "text": [ "" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "The bending Moment and Shear Force diagrams have been plotted\n" ] } ], "prompt_number": 6 } ], "metadata": {} } ] }