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+{
+ "metadata": {
+  "name": "",
+  "signature": "sha256:d708156611ec89eae1db1c06f5ba02ec9d179b4f495d97ecac600c0bd4aa5921"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+  {
+   "cells": [
+    {
+     "cell_type": "heading",
+     "level": 1,
+     "metadata": {},
+     "source": [
+      "Chapter 16 : Columns"
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 16.1 Page No : 417"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "\t\t\t\n",
+      "# Variables\n",
+      "E = 10.*10**6 \t\t\t#psi\n",
+      "ys = 6000. \t\t\t#psi\n",
+      "\t\t\t\n",
+      "# Calculations\n",
+      "lbyr = math.sqrt(math.pi**2*E/ys)\n",
+      "\t\t\t\n",
+      "# Results\n",
+      "print  'Slenderness Ratio = %.f '%(lbyr)\n",
+      "\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Slenderness Ratio = 128 \n"
+       ]
+      }
+     ],
+     "prompt_number": 1
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 16.2 Page No : 417"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "\t\t\t\n",
+      "# Variables\n",
+      "fs = 3.\n",
+      "W = 50. \t\t\t#kips\n",
+      "l = 20. \t\t\t#ft\n",
+      "E = 30.*10**6 \t\t\t#psi\n",
+      "\t\t\t\n",
+      "# Calculations\n",
+      "Pcr = fs*W\n",
+      "I = Pcr*10**3*(l*12)**2/(math.pi**2*E)\n",
+      "r = 2.01\n",
+      "lbyr = l*12/r\n",
+      "\t\t\t\n",
+      "# Results\n",
+      "print  'Required I  = %.1f in**4'%(I)\n",
+      "print  'slenderness ratio =%.f '%(lbyr)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Required I  = 29.2 in**4\n",
+        "slenderness ratio =119 \n"
+       ]
+      }
+     ],
+     "prompt_number": 3
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 16.3 Page No : 418"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "\n",
+      "\t\t\t\n",
+      "# Variables\n",
+      "L1 = 18. \t\t\t#ft\n",
+      "L2 = 9. \t\t\t#ft\n",
+      "I1 = 12.1 \t\t\t#in**4\n",
+      "I2 = 1.2 \t\t\t#in**4\n",
+      "E = 30.*10**6 \t\t\t#psi\n",
+      "\t\t\t\n",
+      "# Calculations\n",
+      "r1 = 2.05\n",
+      "lbyr = L1*12/r1\n",
+      "r2 = 0.65\n",
+      "lbyr2 = L2*12/r2\n",
+      "Pcr1 = math.pi**2*E*I1/(L1*12)**2\n",
+      "Pcr2 = math.pi**2*E*I2/(L2*12)**2\n",
+      "P = Pcr1/2.5\n",
+      "P2 = Pcr2/2.5\n",
+      "\t\t\t\n",
+      "# Results\n",
+      "print  'Design load of 1 = %.2f lb'%(round(P,-2))\n",
+      "print  'Design load of 2 =%.2f lb'%(round(P2,-2))\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Design load of 1 = 30700.00 lb\n",
+        "Design load of 2 =12200.00 lb\n"
+       ]
+      }
+     ],
+     "prompt_number": 5
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 16.4 Page No : 419"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "\t\t\t\n",
+      "# Variables\n",
+      "E = 30.*10**6\n",
+      "syp = 30000. \t\t\t#psi\n",
+      "I = 143.5 \t\t\t#in**4\n",
+      "A = 7.32 \t\t\t#in\n",
+      "\t\t\t\n",
+      "# Calculations\n",
+      "I1 = 2*I\n",
+      "A1 = 2*A\n",
+      "L = math.sqrt(2*math.pi**2*E*I1/(syp*A1))\n",
+      "\t\t\t\n",
+      "# Results\n",
+      "print  'Critical length of the column = %.0f in'%(L)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Critical length of the column = 622 in\n"
+       ]
+      }
+     ],
+     "prompt_number": 1
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 16.5 Page No : 421"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "\t\t\t\n",
+      "# Variables\n",
+      "x = 30. \t\t\t#in\n",
+      "x1 = 10. \t\t\t#in\n",
+      "E = 30.*10**6\n",
+      "d = 0.5 \t\t\t#in\n",
+      "syp = 60000. \t\t\t#psi\n",
+      "y1 = 8. \t\t\t#in\n",
+      "y2 = 2. \t\t\t#in\n",
+      "\t\t\t\n",
+      "# Calculations\n",
+      "ratio = 0.8\n",
+      "l = x+x1\n",
+      "lr = ratio*l\n",
+      "I = (math.pi*(d)**4)/64\n",
+      "Pcr = math.pi**2*E*I/lr**2\n",
+      "scr = Pcr/(math.pi*(d/2)**2)\n",
+      "F = Pcr*y2/(y1+y2)\n",
+      "\t\t\t\n",
+      "# Results\n",
+      "print  'Stress in the critical load = %.0f psi'%(round(scr,-1))\n",
+      "print  'Critical force F =%.0f lb'%(F)\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Stress in the critical load = 4520 psi\n",
+        "Critical force F =177 lb\n"
+       ]
+      }
+     ],
+     "prompt_number": 6
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 16.6 Page No : 423"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "\t\t\t\n",
+      "# Variables\n",
+      "l = 10. \t\t\t#ft\n",
+      "Ys = 33000. \t\t\t#psi\n",
+      "E = 30.*10**6\n",
+      "A = 13.24 \t\t\t#in**4\n",
+      "\t\t\t\n",
+      "# Calculations\n",
+      "r = 2.\n",
+      "lbyr = l*12/r\n",
+      "Cc = math.sqrt(2*math.pi**2*E/Ys)\n",
+      "fs = 5./3+3*(lbyr)/(8*Cc)+(lbyr)**3/(5*Cc**3)\n",
+      "Sa =((1-((lbyr)**2/(2*Cc**2)))*(Ys))/fs\n",
+      "Pa = Sa*A\n",
+      "\n",
+      "\t\t\t\n",
+      "# Results\n",
+      "print  'Premissible load = %.f kips'%(Pa/1000)\n",
+      "\n",
+      "# note : rounding off error."
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Premissible load = 212 kips\n"
+       ]
+      }
+     ],
+     "prompt_number": 10
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 16.7 Page No : 425"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math \n",
+      "from sympy import Symbol,solve\n",
+      "\t\t\t\n",
+      "# Variables\n",
+      "L = 12. \t\t\t#ft\n",
+      "Po = 100. \t\t\t#kips\n",
+      "e = 2. \t\t\t#ft\n",
+      "ys = 42000. \t\t\t#psi\n",
+      "A = 11.77 \t\t\t#in**2\n",
+      "rmin = 195. \t\t\t#in\n",
+      "Zmin = 11.0 \t\t\t#in**3\n",
+      "lbyr = 74.2\n",
+      "stress = 18. \t\t\t#ksi\n",
+      "\t\t\t\n",
+      "# Calculations\n",
+      "#P = (stress-(Po/A)/((1/A)+((e*12)/Zmin)))\n",
+      "P = Symbol(\"P\")\n",
+      "eq = (((Po+P)/A) + (P*(e*L)/11))/stress - 1\n",
+      "P = solve(eq,P)[0]\n",
+      "\t\t\t\n",
+      "# Results\n",
+      "print  'Additional Load = %.2f kips '%(P)\n",
+      "\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Additional Load = 4.19 kips \n"
+       ]
+      }
+     ],
+     "prompt_number": 1
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 16.8 Page No : 425"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "\t\t\t\n",
+      "# Variables\n",
+      "l = 15. \t\t\t#ft\n",
+      "Al = 80. \t\t\t#kips\n",
+      "El = 60. \t\t\t#kips\n",
+      "Ys = 33. \t\t\t#ksi\n",
+      "e = 4. \t\t\t#in\n",
+      "\t\t\t\n",
+      "# Calculations\n",
+      "A = 14.4\n",
+      "rmin = 2.54\n",
+      "Zxx = 54.6\n",
+      "lbyr = l*12/rmin\n",
+      "Smax = ((Al+El)/A)+El*e/Zxx\n",
+      "\t\t\t\n",
+      "# Results\n",
+      "print  'Maximum stress %.1f ksi'%(Smax)\n",
+      "print (\"10 WF 49 is the suitable one\")\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Maximum stress 14.1 ksi\n",
+        "10 WF 49 is the suitable one\n"
+       ]
+      }
+     ],
+     "prompt_number": 12
+    }
+   ],
+   "metadata": {}
+  }
+ ]
+}
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