diff options
Diffstat (limited to 'Mechanics_of_Materials_by_Pytel_and_Kiusalaas/Chapter04_3.ipynb')
-rwxr-xr-x | Mechanics_of_Materials_by_Pytel_and_Kiusalaas/Chapter04_3.ipynb | 460 |
1 files changed, 460 insertions, 0 deletions
diff --git a/Mechanics_of_Materials_by_Pytel_and_Kiusalaas/Chapter04_3.ipynb b/Mechanics_of_Materials_by_Pytel_and_Kiusalaas/Chapter04_3.ipynb new file mode 100755 index 00000000..c3a3650e --- /dev/null +++ b/Mechanics_of_Materials_by_Pytel_and_Kiusalaas/Chapter04_3.ipynb @@ -0,0 +1,460 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:917bb07406192d85aadde0267447c880e5f0a4926ac5c228682662420223d03b" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 04:Shear and Moment in Beams" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.4.1, Page No:103" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "%matplotlib inline\n", + "\n", + "#Variable Decleration\n", + "F1=14 #Force in kN\n", + "F2=28 #Force in kN\n", + "l1=2 #Length in m\n", + "l2=3 #Length in m\n", + "Ra=18 #Reaction at point A in kN\n", + "Rb=24 #Reaction at point D in kN\n", + "\n", + "#Calculations\n", + "#Part(1)\n", + "#Applying the summation of force in y in segment AB\n", + "V_ab=Ra # Shear in part AB in kN\n", + "#Moment is in the variable form M=18x kN.m\n", + "#Segment BC\n", + "V_bc=Ra-F1 #Shear in the segment BC in kN\n", + "#Moment in the form M=4x+28 kN.m\n", + "#Segment CD\n", + "V_cd=Ra-F1-F2 #Shear in the segment CD in kN\n", + "#Moment in the form -24x+168 kN.m\n", + "\n", + "#Importing the plotting libraries and computing the plots\n", + "import matplotlib.pyplot as plt\n", + "\n", + "#Result\n", + "print \"The Shear Force and Bending Moment Diagrams are the results\"\n", + "#Plotting the SHear Force Diagram\n", + "\n", + "X1=[0,l1,l1+0.0000000001,l1+l2,l1+l2+0.0000000001,l1+l2+l1]\n", + "Y1=[V_ab,V_ab,V_bc,V_bc,V_cd,V_cd]\n", + "Z1=[0,0,0,0,0,0]\n", + "plt.plot(X1,Y1,X1,Z1)\n", + "plt.xlabel(\"Length x in m\")\n", + "plt.ylabel(\"Shear Force in kN\")\n", + "plt.show()\n", + "\n", + "#Plotting the Bendimg Moment Diagram\n", + "\n", + "Y2=[0,36,48,0]\n", + "X2=[0,l1,l1+l2,l1+l2+l1]\n", + "Z2=[0,0,0,0]\n", + "plt.plot(X2,Y2)\n", + "plt.xlabel(\"Lenght in m\")\n", + "plt.ylabel(\"Bending Moment in kN.m\")\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Shear Force and Bending Moment Diagrams are the results\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEPCAYAAACtCNj2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAFypJREFUeJzt3XuUpVV95vHvA8goqAHUAcQewQTN6PKCF6JR44kSgjMG\nZRxFE40iy3GWUeNEHQXHUDFZa5iYOGZMcKkoIUbJiBeEoEhr+hhMEC9cRC4KSq9FoyAGFMQLSP/m\nj/P2m7KmqvpUV53adaq+n7XO8j3vpc6vW/o8tfe7371TVUiSBLBb6wIkSWuHoSBJ6hkKkqSeoSBJ\n6hkKkqSeoSBJ6jULhSSbkmxJckWSryV5Tbd/vySbk3wjyflJ9mlVoyRtNGn1nEKSA4ADqurSJPcG\nvgI8BzgO+F5V/WmSNwL7VtWbmhQpSRtMs5ZCVd1YVZd22z8ErgIOAo4GTu9OO51RUEiSVsGauKeQ\n5GDgMOAiYP+quqk7dBOwf6OyJGnDaR4KXdfRR4Hfr6rbZx+rUd+W83BI0irZo+WHJ7kHo0D4QFWd\n1e2+KckBVXVjkgOB785znUEhSbugqrLY8ZajjwK8D7iyqt4x69DZwEu67ZcAZ829FqCqpvZ10kkn\nNa/B+tvXYf3T95rm2qvG+126ZUvhycCLgK8muaTbdwJwMvDhJMcDW4HntylPkjaeZqFQVZ9n4ZbK\nEatZiyRppPmN5o1oMBi0LmFZrL8t629nmmsfV7OH15YjSU1j3ZLUUhJqrd5oliStPYaCJKlnKEiS\neoaCJKnX9Inm5ciit0o0SfvuC7fc0roKSZMwtaHg4KN2DGRp/bL7SJLUMxQkST1DQZLUMxQkST1D\nQZLUMxQkST1DQZLUMxQkSb2moZDk/UluSnL5rH0zSbYluaR7HdWyRknaSFq3FE4D5n7pF/D2qjqs\ne53XoC5J2pCahkJVXQDcOs8hJ1KQpAZatxQW8uoklyV5X5J9WhcjSRvFWpwQ713AW7vtPwb+HDh+\n7kkzMzP99mAw2BBrp0rSUgyHQ4bD4ZKuab5Gc5KDgXOq6pHjHnON5rYSZ6mVptFUrtGc5MBZb48B\nLl/oXEnSymrafZTkDOBpwP2TXA+cBAySPIbRKKTrgFc0LFGSNpTm3Ue7wu6jtuw+kqbTVHYfSZLa\nMRQkST1DQZLUMxQkST1DQZLUMxQkST1DQZLUMxQkST1DQZLUMxQkST1DQZLUMxQkST1DQZLUMxQk\nST1DQZLUMxQkSb2moZDk/UluSnL5rH37Jdmc5BtJzk+yT8saJWkjad1SOA04as6+NwGbq+qhwGe7\n95KkVdA0FKrqAuDWObuPBk7vtk8HnrOqRUnSBta6pTCf/avqpm77JmD/lsVI0kayR+sCFlNVlWTe\nJeJnZmb67cFgwGAwWKWqJGk6DIdDhsPhkq5J1bzfuasmycHAOVX1yO791cCgqm5MciCwpap+ec41\n1brujSwB//ql6ZOEqspi56zF7qOzgZd02y8BzmpYiyRtKE1bCknOAJ4G3J/R/YM/BD4BfBj4d8BW\n4PlV9f0519lSaMiWgjSdxmkpNO8+2hWGQluGgjSdprX7SJLUiKEgSeoZCpKknqEgSeoZCpKknqEg\nSeoZCpKknqEgSeoZCpKknqEgSeoZCpKknqEgSeoZCpKknqEgSeoZCpKk3oJrNCfZssChAqiqp0+k\nIklSMwuGAvCGWds7llR5IvBG4LsTq6iTZCtwG3A3cFdVHT7pz5SkjW7BUKiqL+/YTjIA/gdwL+AV\nVfWpyZdGAYOqumUVPkuSxOItBZIcBbwZuBP4k6paqEtpUhZdNk6StLIWXKM5yZeABwB/BlzY7e5P\nrqqLJ1pY8i3gB4y6j95dVe+ddcw1mhtyjWZpOo2zRvNiLYU7utdzu9dcv76M2sbx5Kr6TpIHAJuT\nXF1VF+w4ODMz0584GAwYDAYTLkeSpstwOGQ4HC7pmgVbCv0JyW5VtX3OvntW1U+WXOEuSnIS8MOq\n+vPuvS2FhmwpSNNpnJbCOM8pnDrnh94b+ORyCtuZJHsluU+3vTdwJHD5JD9TkjReKNyQ5BSAJPsC\n5wMfmGhVsD9wQZJLgYuAv6+q8yf8mZK04e20+wggyduA+wKPA06uqo9MurCd1GP3UUN2H0nTaZzu\no8VGH+24uVyMhoa+BfgScB5QVfWxFax1SQyFtvbbD269tXUVmlb77gu3+PRRE8sNhb9m1hBURsEw\ne0jqcStQ4y4xFKTpZUuznWWFwlpmKEjTy1BoZ6VGH0mSNghDQZLUMxQkSb1FJ8SD0dPLjKa5OHjW\n+VVVb51gXZKkBnYaCsAngO8DXwFWbWoLSdLqGycUDqqq35x4JZKk5sa5p/DPSR418UokSc2NM0vq\nVcAvAdcBP+12V1U1CwqfU5Cml88ptLPc9RR2eOYK1SNJWuMWDIUk962q24DbVrEeSVJDi7UUzgD+\nI3AxPz8HEt37h0yqKElSG859JGlVeU+hnamd+yjJUUmuTnJNkje2rkeSNoo111JIsjvwdeAI4AZG\nazi8sKqumnWOLQVpStlSaGdaWwqHA9dW1daqugv4O+DZjWuSpA1hrFBI8tQkx3XbD0hyyARrOgi4\nftb7bd0+SdKE7TQUkswA/x04odu1J/C3E6zJhqUkNTLOw2vHAIcxmhCPqrohyX0mWNMNwKZZ7zcx\nai38nAxmdYsdDEyy7SJp5cxA/qh1ERvEdcDWpV0yTij8tKq2J6Mv4SR7L7WuJfoycGiSg4FvA8cC\nL5x7Ug1tUEjTyBvN7ez4Hl/MOPcUzkzybmCfJP8F+Cxw6jJrW1BV/Qx4FfBp4Erg/84eeSRJmpyx\nhqQmORI4snv76araPNGqdl6PQ1KlKWVLoZ1xhqSOM0vqIcCNVfXj7v29gP2rautKFbpUhoI0vQyF\ndlbqOYWPAHfPer+92ydJWmfGCYXdq+rOHW+q6qfAPSZXkiSplXFC4XtJ+ieKu+3vTa4kSVIr49xT\n+CXgg8ADu13bgBdX1bUTrm2xmrynIE0p7ym0s+yV17rJ6f5rVf3KjgfWqur2FaxRkrSGLBoKVXV3\nkqdk9Ku5YSBJ69w4TzRfCnwiyZnAj7p9VVUfm1xZkqQWxgmFewK3AE+fs99QkKR1Zs0tsjMObzRL\n08sbze2syMNrSTYl+XiSm7vXR5M8aOXKlCStFeM8p3AacDajIakPBM7p9kmS1plxnlO4rKoevbN9\nq8nuI2l62X3UzkrNffQvSV6cZPckeyR5ET7RLEnr0jih8DLg+cCNwHeA5wHHTbIoSVIbC3YfJXli\nVX1hlesZi91H0vSy+6id5XYfvWvWD7pwxaraiSQzSbYluaR7HbVany1JG904D6/B6AG21VLA26vq\n7av4mZIkFg+F3ZPsB2TWdq+qbplgXTtfXVqStOIWu6ewldFv7TD6kp59YlXVQyZSUHISoxvZPwC+\nDLyuqr4/5xzvKUhTynsK7azIGs2TkGQzcMA8h94MfAG4uXv/x8CBVXX8nOsNBWlKGQrtLHs9hUmp\nqt8Y57wkpzJ6gvr/MzMz028PBgMGg8FKlCZJ68ZwOGQ4HC7pmjU3IV6SA6vqO932fwOeUFW/Pecc\nWwrSlLKl0M6abSnsxP9K8hhG9zCuA17RuB5J2jAWbSkk2QO4oqoetnol7ZwtBWl62VJoZ9lzH1XV\nz4Crkzx4RSuTJK1J43Qf7QdckeSLwB3dvqqqoydXliSphXFC4S0Tr0KStCasudFH4/CegjS9vKfQ\nzkotx/mkJF9K8sMkdyXZnuS2lStTkrRWjLOewl8Cvw1cw2hivOOBUyZZlCSpjXFCgaq6Bti9qu6u\nqtMAp7OWpHVonBvNdyT5N8BlSf6U0QpszmIqSevQOC2F3+3OexXwI+BBwHMnWZQkqY2xRh8l2QvY\nVFVfn3xJO+foI2l6OfqonZUafXQ0cAnw6e79YUnOXpkSJUlryTjdRzPArwC3AlTVJcBEFtiRJLU1\nTijcNXflM2D7JIqRJLU1zuijK5L8DrBHkkOB1wD/PNmyJEktjNNSeDXwCOCnwBnAbcBrJ1mUJKkN\n5z6StKocfdTOSo0+eliS9ybZnGRL9/qHZRb2vCRXJLk7yWPnHDshyTVJrk5y5HI+R5K0NOPcUzgT\neBdwKnB3t2+5OX85cAzw7tk7kzwcOBZ4OHAQ8JkkD60qb2xL0ioYJxTuqqp3reSHVtXVMGrKzPFs\n4IyqugvYmuRa4HDgCyv5+ZKk+S3YfZRkvyT3A85J8ntJDuz27ZdkvwnV80Bg26z32xi1GCRJq2Cx\nlsLF/Hw30etnbRc7eYAtyWbggHkOnVhV54xd4QJdVTMzM/32YDBgMBgs4UdK0vo3HA4ZDodLuqbp\n6KMkW4DXVdXF3fs3AVTVyd3784CTquqiOdc5+kiaUo4+amdZo4+SPCHJgbPevyTJ2Un+zwp3H80u\n8GzgBUn2THIIcCjwxRX8LEnSIhYbkvoeRg+skeTXgJOB0xk9vPae5XxokmOSXA88ETg3yacAqupK\n4MPAlcCngFfaJJCk1bNg91GSy6rq0d32XwE3V9XM3GMt2H0kTS+7j9pZ7sNruye5R7d9BLBl1rFx\nhrJKkqbMYl/uZwCfS/I9RiuuXQDQTYo3d9ZUSdI6sOjooyRPYjSs9PyquqPb91Dg3jtGDLVg95E0\nvew+amec7iMnxJO0qgyFdlZkQjxJ0sZhKEiSeoaCJKlnKEiSeoaCJKlnKEiSeoaCJKlnKEiSeoaC\nJKlnKEiSeoaCJKlnKEiSek1CIcnzklyR5O4kj521/+AkP05ySfc6pUV9krRRtVos53LgGODd8xy7\ntqoOW+V6JEk0CoWquhpG07hKktaOtXhP4ZCu62iY5Cmti5GkjWRiLYUkmxmt2jbXiVV1zgKXfRvY\nVFW3dvcazkryiKq6fe6JMzMz/fZgMGAwGCy/aElaR4bDIcPhcEnXNF15LckW4HULLe250HFXXpOm\nlyuvtTMtK6/1BSa5f5Ldu+2HAIcC32pVmCRtNK2GpB6T5HrgicC5ST7VHXoacFmSS4AzgVdU1fdb\n1ChJG1HT7qNdZfeRNL3sPmpnWrqPJElrhKEgSeoZCpKknqEgSeoZCpKknqEgSeoZCpKknqEgSeoZ\nCpKknqEgSeoZCpKknqEgSeoZCpKknqEgSeoZCpKknqEgSeq1WnntbUmuSnJZko8l+YVZx05Ick2S\nq5Mc2aI+SdqoWrUUzgceUVWPBr4BnACQ5OHAscDDgaOAU5LYmpGkVdLkC7eqNlfV9u7tRcCDuu1n\nA2dU1V1VtRW4Fji8QYmStCGthd/CXwZ8stt+ILBt1rFtwEGrXpEkbVB7TOoHJ9kMHDDPoROr6pzu\nnDcDd1bVhxb5UfMu8T0zM9NvDwYDBoPBLtcqSevRcDhkOBwu6ZpUzfudO3FJXgq8HHhGVf2k2/cm\ngKo6uXt/HnBSVV0059pqVbek5UnAf75tJKGqstg5rUYfHQW8AXj2jkDonA28IMmeSQ4BDgW+2KJG\nSdqIJtZ9tBPvBPYENicBuLCqXllVVyb5MHAl8DPglTYJJGn1NOs+Wg67j6TpZfdRO2u2+0iStDYZ\nCpKknqEgSeoZCpKknqEgSeoZCpKknqEgSeoZCpKknqEgSeoZCpKknqEgSeoZCpKknqEgSeoZCpKk\nnqEgSeo1WWQnyduAZwF3At8EjquqHyQ5GLgKuLo79cKqemWLGiVNxr77jtZU0NrUqqVwPvCIqno0\n8A3ghFnHrq2qw7rXugyEpS6kvdZYf1vTXv/HPjakiql8bdkyvbWPu7BRk1Coqs1Vtb17exHwoBZ1\ntDLt/6itvy3rb2eaax/XWrin8DLgk7PeH5LkkiTDJE9pVZQkbUQTu6eQZDNwwDyHTqyqc7pz3gzc\nWVUf6o59G9hUVbcmeSxwVpJHVNXtk6pTkvSvUo1W0E7yUuDlwDOq6icLnLMFeF1VXTxnv8t+S9Iu\nqKpFb/O3Gn10FPAG4GmzAyHJ/YFbq+ruJA8BDgW+Nff6nf2hJEm7pklLIck1wJ7ALd2uC6vqlUme\nC/wRcBewHfjDqjp31QuUpA2qWfeRJGntWQujj5YkyVFJrk5yTZI3tq5nKZK8P8lNSS5vXcuuSLIp\nyZYkVyT5WpLXtK5pKZLcM8lFSS5NcmWS/9m6pqVKsns3Ou+c1rUsVZKtSb7a1f/F1vUsVZJ9knwk\nyVXdfz9PbF3TuJI8rPt73/H6wUL/fqeqpZBkd+DrwBHADcCXgBdW1VVNCxtTkqcCPwT+pqoe2bqe\npUpyAHBAVV2a5N7AV4DnTMvfP0CSvarqR0n2AD4PvL6qPt+6rnEl+QPgccB9quro1vUsRZLrgMdV\n1S07PXkNSnI68Lmqen/338/eVfWD1nUtVZLdGH1/Hl5V1889Pm0thcMZPfG8taruAv4OeHbjmsZW\nVRcAt7auY1dV1Y1VdWm3/UNGU5I8sG1VS1NVP+o29wR251/va615SR4E/AfgVGBaB1tMZd1JfgF4\nalW9H6CqfjaNgdA5AvjmfIEA0xcKBwGz/yDbun1aZd08VYcxeiJ9aiTZLcmlwE3Alqq6snVNS/C/\nGY3a276zE9eoAj6T5MtJXt66mCU6BLg5yWlJLk7y3iR7tS5qF70A+NBCB6ctFKanr2sd67qOPgL8\nftdimBpVtb2qHsNoapVfSzJoXNJYkjwL+G5VXcKU/rYNPLmqDgOeCfxe1506LfYAHgucUlWPBe4A\n3tS2pKVLsifwW8CZC50zbaFwA7Bp1vtNjFoLWiVJ7gF8FPjbqjqrdT27qmv6nws8vnUtY/pV4Oiu\nX/4M4OlJ/qZxTUtSVd/p/vdm4OOMuoOnxTZgW1V9qXv/EUYhMW2eCXyl+/9gXtMWCl8GDk1ycJd4\nxwJnN65pw0gS4H3AlVX1jtb1LFWS+yfZp9u+F/AbwCVtqxpPVZ1YVZuq6hBGzf9/qKrfbV3XuJLs\nleQ+3fbewJHA1IzCq6obgeuTPLTbdQRwRcOSdtULGf1SsaAmTzTvqqr6WZJXAZ9mdJPwfVM28uUM\n4GnA/ZJcz+jhvNMal7UUTwZeBHw1yY4v0xOq6ryGNS3FgcDp3eiL3YAPVNVnG9e0q6atK3V/4OOj\n3yvYA/hgVZ3ftqQlezXwwe4X0m8CxzWuZ0m6MD6C0fRCC583TUNSJUmTNW3dR5KkCTIUJEk9Q0GS\n1DMUJEk9Q0GS1DMUJEk9Q0HrSpKJTruR5LXdg28r+nlJfmvapoLX+uRzClpXktxeVfeZ4M+/Dnh8\nVf3LanyetNpsKWjdS/KLST7Vzc75j0ke1u3/6yR/keSfknyzWw52x0yqp3SLqZyf5Nwkz03yakZT\nhW9J8tlZP/9PuoV7Lkzyb+f5/HckeUu3/ZtJPjfPOS9N8s7F6ppz/sHdYlOnJfl6kg8mObK75htJ\nnrBSf3/aWAwFbQTvAV5dVY9nNPX0KbOOHVBVTwaeBZzc7ftPwIOr6t8DLwaeBFRVvRP4NjCoqmd0\n5+7NaI3xxwD/yPxTCJwAHJvk14G/AF46zzlzm+zz1TXXLwJ/Bvwy8DDg2O6a1wMnLnCNtKipmvtI\nWqpumu8nAWd28+7AaIEdGH0RnwVQVVcl2b/b/xTgw93+m5JsWeQj7qyqc7vtrzCaZO/nVNWPu/UD\nLmA03fh1Oyl7obrmuq6qruj+nFcAn+n2fw04eCefIc3LUNB6txvw/W4e//ncOWt7R2rUrG3mbM91\n16zt7Sz8b+pRwM2MvyjUfHXN9dM5n33nrG3/bWuX2H2kda2qbgOuS/KfYTT9d5JH7eSyfwKe2527\nP6OZbXe4HbjvUmpI8mDgDxitVPfMJPOtIzCtC+donTEUtN7sleT6Wa/XAr8DHN8tw/k1YPaC9zXP\n9kcZLapyJfAB4GJgx3q87wHOm3Wjee71P3dvoFuD4lTgdd2c/McDp3bTL7PItQttz71mofcOK9Qu\ncUiqNI8ke1fVHUnux2gd6l+tqu+2rkuaNPsdpfn9fbdK257AWw0EbRS2FCRJPe8pSJJ6hoIkqWco\nSJJ6hoIkqWcoSJJ6hoIkqff/AEcEKyYmBQ6RAAAAAElFTkSuQmCC\n", + "text": [ + "<matplotlib.figure.Figure at 0x10bc70310>" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAEPCAYAAABFpK+YAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAASUVORK5CYII=\n", + "text": [ + "<matplotlib.figure.Figure at 0x10b5afad0>" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.4.3, Page No:108" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "\n", + "#Variable Decleration\n", + "L=12 #Length of the beam in ft\n", + "F=1000 #Force at the tip of the beam in lb\n", + "#w=30x Force per length on the beam in lb/ft\n", + "a=15 #Constant\n", + "\n", + "#Calculations\n", + "#Part(1)\n", + "#Here all the computation is in variable form\n", + "#Applying the sum of forces\n", + "#V=1000-15x^2\n", + "#Applying moment about C\n", + "#M=1000x-5x^3\n", + "\n", + "#Part(2)\n", + "#Max BM when shear force is zero\n", + "x=(F*a**-1)**0.5 #Length at which BM is max in ft\n", + "M_max=F*x-5*x**3 #Max BM in lb.ft\n", + "\n", + "#Result\n", + "b=np.linspace(0,L,20) #Array\n", + "c=np.linspace(0,0,20) #Zero array\n", + "V=F-(15*b**2) #Shear Force\n", + "M=F*b-5*b**3 #Bending Moment\n", + "\n", + "#Shear force plot\n", + "plt.plot(b,V,b,c)\n", + "plt.xlabel(\"Length in ft\")\n", + "plt.ylabel(\"Shear Force in lb\")\n", + "plt.show()\n", + "\n", + "#Bending Moment plot\n", + "plt.plot(b,M)\n", + "plt.xlabel(\"Length in ft\")\n", + "plt.ylabel(\"Bending Moment in lb.ft\")\n", + "plt.show()\n", + "\n", + "print \"The maximum BM is\",round(M_max),\"lb.ft\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": "iVBORw0KGgoAAAANSUhEUgAAAZUAAAEPCAYAAACKplkeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n", + "text": [ + "<matplotlib.figure.Figure at 0x10bc81f10>" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": "iVBORw0KGgoAAAANSUhEUgAAAY0AAAEPCAYAAAC+35gCAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n6iMAAAAASUVORK5CYII=\n", + "text": [ + "<matplotlib.figure.Figure at 0x10bd236d0>" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The maximum BM is 5443.0 lb.ft\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "\n", + "Example 4.4.4, Page no:117\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "#Variable Decleration\n", + "P=30 #Force in kN\n", + "M=40 #Moment in kN.m\n", + "L1=3 #Length in m\n", + "L2=4 #Length in m\n", + "Ra=14 #Reaction at A in kN\n", + "Re=16 #Reaction at E in kN\n", + "\n", + "#Calculations\n", + "#The plotting will done different from that done in the textbook\n", + "#Plot for Shear Force\n", + "x_shear=[0,0.000000001,L2,L2+0.000000001,L2+L1,L2+L1*2,L2+L1*2+0.00000001]\n", + "y_shear=[0,Ra,Ra,Ra-P,Ra-P,Ra-P,0]\n", + "#Plot for Bending Moment\n", + "x_bm=[0,L2,L2+L1,L2+L1+0.00000001,L2+L1+L1]\n", + "y_bm=[0,Ra*L2,Ra*(L2+L1)-P*L1,Ra*(L2+L1)-P*L1+M,0]\n", + "#Zero line\n", + "x1=[0,0,0,0,0,0,0]\n", + "\n", + "#Result\n", + "print \"The plots below are the answers\"\n", + "\n", + "plt.plot(x_shear,y_shear,x_shear,x1)\n", + "plt.xlabel(\"Distance from point A in m\")\n", + "plt.ylabel(\"Shear Force in kN\")\n", + "plt.show()\n", + "\n", + "plt.plot(x_bm,y_bm)\n", + "plt.xlabel(\"Distance from point A in m\")\n", + "plt.ylabel(\"Bending Moment in kN.m\")\n", + "plt.show()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The plots below are the answers\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": "iVBORw0KGgoAAAANSUhEUgAAAYgAAAEPCAYAAABY9lNGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nkwlCktTJBCFJ6vT/AXRCVK96moUqAAAAAElFTkSuQmCC\n", + "text": [ + "<matplotlib.figure.Figure at 0x10bd21990>" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": "iVBORw0KGgoAAAANSUhEUgAAAYEAAAEPCAYAAACk43iMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nEtMgICJSYhoERERKTIOAiEiJ/X/78ZG0r2MmbQAAAABJRU5ErkJggg==\n", + "text": [ + "<matplotlib.figure.Figure at 0x10bdcae90>" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.4.5, Page No:119" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "\n", + "#Variable Decleration\n", + "w1=400 #UDL in lb/ft\n", + "P=400 #Point load at C in lb\n", + "w2=200 #UDL in lb/ft\n", + "L1=2 #Length in ft\n", + "L2=1 #Length in ft\n", + "L3=4 #Length in ft\n", + "V_A=0 #Shear force at A in lb\n", + "Rb=-1520 #Reaction at B in lb\n", + "Rd=-880 #Reaction at D in lb\n", + "d=1.6 #Distance in ft\n", + "\n", + "#Calculations\n", + "#The plotting of the Shear force diagram and the Bending Moment Diagram \n", + "#Will be done different from that done in the textbook\n", + "\n", + "#Calculations for Shear Force\n", + "Area1=P*L1 #Area of w diagram from A to B\n", + "Area2=0 #Area of w diagram from B to C\n", + "Area3=w2*L3 #Area of w diagram from C to D\n", + "V_B_left=V_A-Area1 #Shear Force at left of B in lb\n", + "V_B_right=V_B_left-Rb #Shear force at right of B in lb\n", + "V_C_left=V_B_right-Area2 #Shear Force at left of C in lb\n", + "V_C_right=V_C_left-P #Shear Force at right of C in lb\n", + "V_D_left=V_C_right-Area3 #Shear Force at left of D in lb\n", + "V_D_right=V_D_left-Rd #Shear Force at right of D in lb\n", + "V_E=0 #Shear Force at E in lb\n", + "\n", + "#Calculations for Bending Moments\n", + "AreaV1=0.5*L1*V_B_left #Area of V diagram\n", + "AreaV2=V_C_left*L2 #Area of V diagram from B to C\n", + "AreaV3=V_D_left*(L3-d)*0.5 #Area of V diagram from F to D\n", + "M_A=0 #Moment at A in lb.ft\n", + "M_B=M_A+AreaV1 #Moment about B in lb.ft\n", + "M_C=M_B+AreaV2 #Moment about C in lb.ft\n", + "M_F=M_C+V_C_right*0.5*d #Moment about F in lb.ft\n", + "M_D=M_F+AreaV3 #Moment about D in lb.ft\n", + "M_E=0 #Moment about E in lb.ft\n", + "\n", + "#Result\n", + "print \"The following plots are the results\"\n", + "\n", + "#Plotting\n", + "\n", + "#Shear Force\n", + "x=[0,L1,L1+0.000001,L1+d,L1+d+0.000001,L1+L3,L1+L3+0.000001,L1+L3+L1]\n", + "V=[V_A,V_B_left,V_B_right,V_C_left,V_C_right,V_D_left,V_D_right,V_E]\n", + "zero=[0,0,0,0,0,0,0,0]\n", + "plt.plot(x,V,x,zero)\n", + "plt.xlabel(\"Length in ft\")\n", + "plt.ylabel(\"Shear Force in lb\")\n", + "plt.title(\"Shear Force Diagram\")\n", + "plt.show()\n", + "\n", + "#Bending Moment\n", + "x1=[0,L1,L1+L2,L1+L2+d,L1+L3,L1+L3+L1]\n", + "BM=[M_A,M_B,M_C,M_F,M_D,M_E]\n", + "zero1=[0,0,0,0,0,0]\n", + "plt.plot(x1,BM,x1,zero1)\n", + "plt.xlabel(\"Length in ft\")\n", + "plt.ylabel(\"Bending Moment in lb.ft\")\n", + "plt.title(\"Bending Moment Diagram\")\n", + "plt.show()\n", + "\n", + "#The Bending Moment Diagram differs from that in the textbook because of curve type" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The following plots are the results\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": "iVBORw0KGgoAAAANSUhEUgAAAYwAAAEZCAYAAACEkhK6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nccIwM7NC/j98YLpV4JrJ+QAAAABJRU5ErkJggg==\n", + "text": [ + "<matplotlib.figure.Figure at 0x10b6bd690>" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": "iVBORw0KGgoAAAANSUhEUgAAAYwAAAEZCAYAAACEkhK6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", + "text": [ + "<matplotlib.figure.Figure at 0x10bf2d310>" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 4.4.6, Page No:127" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Variable Decleration\n", + "P1=15 #Load in kN\n", + "P2=25 #Load in kN\n", + "P3=50 #Load in kN\n", + "R=90 #Load in kN\n", + "L1=3.5 #Length in m\n", + "L2=2 #Length in m\n", + "L3=3 #Length in m\n", + "L=12 #Total span in m\n", + "\n", + "#Calculation\n", + "#Part 1\n", + "#Maximum Bending Moment at A\n", + "R1=R*L1*L**-1 #Reaction 1 in kN\n", + "M_A=R1*L1 #Moment about A in kN.m\n", + "#Maximum Bending Moment at B\n", + "R1_2=R*(L1+(L3-L2))*L**-1 #reaction 1 in kN\n", + "M_B=R1_2*(L1+(L3-L2))-P1*L2 #Moment at B in kN.m\n", + "\n", + "#Maximum Moment at C\n", + "R2=(P2+P3)*(L2+L3)*L**-1 #Reaction 2 in kN\n", + "M_C=R2*(L2+L3) #Moment at C in kN.m\n", + "\n", + "M_max=max(M_A,M_B,M_C) #Maximum Bending Moment in kN.m\n", + "\n", + "#Part 2\n", + "R2_2=R*(L-L3)*L**-1 #Reaction 2 in kN\n", + "\n", + "V_max=max(R1,R2,R1_2,R2_2) #Maximum Shear Force in kN\n", + "\n", + "\n", + "#Result\n", + "print \"The maximum Shear force is\",V_max,\"kN and the Maximum Bending Moment is\",round(M_max,1),\"kN.m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The maximum Shear force is 67.5 kN and the Maximum Bending Moment is 156.3 kN.m\n" + ] + } + ], + "prompt_number": 22 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file |