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+{

+ "metadata": {

+  "name": ""

+ },

+ "nbformat": 3,

+ "nbformat_minor": 0,

+ "worksheets": [

+  {

+   "cells": [

+    {

+     "cell_type": "heading",

+     "level": 1,

+     "metadata": {},

+     "source": [

+      "Chapter 11:Design of Beams and Shafts"

+     ]

+    },

+    {

+     "cell_type": "heading",

+     "level": 3,

+     "metadata": {},

+     "source": [

+      "Example 11.1 Page No 544"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#Given\n",

+      "sigma_allow = 24    #ksi, stress\n",

+      "tou_allow = 14.5      #ksi, allowable stress\n",

+      "\n",

+      "#Shear and Moment Diagrams\n",

+      "V_max = 30         #kip, \n",

+      "M_max = 120         #kip, bending moment\n",

+      "\n",

+      "#Bending Stress\n",

+      "S_reqd = (M_max*(10**3))/sigma_allow\n",

+      "#Shear Stress\n",

+      "d = 17.9   #in\n",

+      "tw = 0.315  #inch\n",

+      "tou_avg = (V_max)/(d*tw)\n",

+      "\n",

+      "if tou_avg<14.5:\n",

+      "    print\"Use a W18*14\"\n"

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "Use a W18*14\n"

+       ]

+      }

+     ],

+     "prompt_number": 5

+    },

+    {

+     "cell_type": "heading",

+     "level": 3,

+     "metadata": {},

+     "source": [

+      "Example 11.2 Page No 545"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#Given\n",

+      "udl = 0.5         #kN/m\n",

+      "h_by_a = 1.5      \n",

+      "sigma_allow = 9 #MPa, allowable bending stress\n",

+      "tou_allow = 0.6 #MPa, allowable shear stress\n",

+      "\n",

+      "#calculation\n",

+      "#Shear and Moment Diagrams\n",

+      "import math\n",

+      "V_max =20         #kNm\n",

+      "M_max =10.67       #kNm\n",

+      "#Bending Stress\n",

+      "S_reqd = (M_max)/(sigma_allow*1000)\n",

+      "c = h_by_a/2.0\n",

+      "a_cube = (S_reqd*c*12)/(1.5**3) #S_reqd = I/c\n",

+      "a = a_cube**(1/3.0)\n",

+      "A = a*h_by_a*a\n",

+      "tou_max = (1.5*V_max)/(A*1000)\n",

+      "if tou_max>tou_allow:\n",

+      "    a_sqr = (3/2.0)*(V_max)/(h_by_a*tou_allow*1000)\n",

+      "    a =math.sqrt(a_sqr)\n",

+      "else:\n",

+      "    print\"not\"\n",

+      "\n",

+      "#Display\n",

+      "print\"The smallest width for the laminated wooden beam = \", round(a,2),\"m\"\n"

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "The smallest width for the laminated wooden beam =  0.18 m\n"

+       ]

+      }

+     ],

+     "prompt_number": 5

+    },

+    {

+     "cell_type": "heading",

+     "level": 3,

+     "metadata": {},

+     "source": [

+      "Example 11.3 Page No 546"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#Given\n",

+      "l = 200/1000.0       #m, length\n",

+      "t = 30/1000.0        #m\n",

+      "sigma_allow = 9     #MPa, shear stress\n",

+      "tou_allow = 0.6      #MPa, bending stress\n",

+      "V_nail = 1.50        #kN\n",

+      "l_bc = 2             #m\n",

+      "l_cd = 2            #m\n",

+      "\n",

+      "#Shear and Moment Diagrams\n",

+      "V_max = 20        #kN\n",

+      "M_max =10.67         #kNm\n",

+      "#Bending Stress\n",

+      "y1 = l/2.0\n",

+      "A1 = l*t\n",

+      "y2 = l+(t/2.0)\n",

+      "A2 = t*l\n",

+      "y_dash = (y1*A1 + y2*A2)/(A1 + A2)\n",

+      "\n",

+      "I1 = (t*l**3)/12.0 + (t*l*(y_dash - y1)**2)\n",

+      "I2 = (l*t**3)/12.0 + (t*l*(y2 - y_dash)**2)\n",

+      "I =I1 + I2\n",

+      "\n",

+      "c = y_dash\n",

+      "sigma = (M_max*c)/(I)\n",

+      "flag1 = 0\n",

+      "sigma_allow = sigma_allow*1000 #kPa\n",

+      "\n",

+      "if(sigma<sigma_allow):\n",

+      "    flag1 = 1\n",

+      "else:\n",

+      "    print\"otherwisw not\"\n",

+      "\n",

+      "#Shear Stress\n",

+      "y3 = y_dash/2.0\n",

+      "A3 = y_dash*t\n",

+      "Q = y3*A3\n",

+      "\n",

+      "tou = (V_max*Q)/(I*t)\n",

+      "tou_allow = tou_allow*1000 #kPa\n",

+      "flag2 =0\n",

+      "\n",

+      "if(tou<tou_allow):\n",

+      "    flag2 = 1\n",

+      "else:\n",

+      "    print\"flag2 is not equal to one\"\n",

+      "\n",

+      "#Nail Spacing\n",

+      "y4a = (l+t-y_dash)\n",

+      "y4 = y4a - (t/2.0)\n",

+      "A4 = l*t\n",

+      "Q4 = y4*A4\n",

+      "V_bc = 1.5 #kN\n",

+      "V_cd = 1 #kN\n",

+      "\n",

+      "q_bc = (V_bc*Q4)/I\n",

+      "q_cd = (V_cd*Q4)/I\n",

+      "\n",

+      "s_bc = (V_nail)/(q_bc)\n",

+      "s_cd = (V_nail)/(q_cd)\n",

+      "\n",

+      "chosen_bc = 150 #mm\n",

+      "chosen_cd = 250 #mm\n",

+      "\n",

+      "#Result\n",

+      "print'The design is safe in bending and shear.'\n",

+      "print'The calculated nail spacing BC ',round(s_bc,2),\"m\"\n",

+      "print'The calculated nail spacing CD ',round(s_cd,2),\"m\"\n",

+      "print'The chosen nail spacing BC     ',chosen_bc,\"mm\"\n",

+      "print'The chosen nail spacing CD     ',chosen_cd,\"mm\"\n",

+      "\n"

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "otherwisw not\n",

+        "flag2 is not equal to one\n",

+        "The design is safe in bending and shear.\n",

+        "The calculated nail spacing BC  0.17 m\n",

+        "The calculated nail spacing CD  0.26 m\n",

+        "The chosen nail spacing BC      150 mm\n",

+        "The chosen nail spacing CD      250 mm\n"

+       ]

+      }

+     ],

+     "prompt_number": 1

+    },

+    {

+     "cell_type": "heading",

+     "level": 3,

+     "metadata": {},

+     "source": [

+      "Example 11.6 Page No 560"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#Find smallest allowable diameter\n",

+      "\n",

+      "#Given\n",

+      "tou_allow = 50*10**6 #MPa, shear stress\n",

+      "T = 7.5              #Nm, torque\n",

+      "R_ah = 150           #N, horizontal force\n",

+      "R_av = 475           #N\n",

+      "l_ac = 0.25          #m\n",

+      "\n",

+      "#Calculation\n",

+      "import math\n",

+      "mc = R_ah*l_ac\n",

+      "m = R_av*l_ac\n",

+      "M_c = sqrt(m**2 + mc**2)\n",

+      "k = sqrt(M_c**2 + T**2)\n",

+      "c1 = (2*k)/(math.pi*tou_allow)\n",

+      "c = c1**(1/3.0)\n",

+      "d = 2*c*1000\n",

+      "\n",

+      "#Display\n",

+      "print\"The smallest allowable diameter of the shaft =\",round(d,1),\"mm\"\n"

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "The smallest allowable diameter of the shaft = 23.3 mm\n"

+       ]

+      }

+     ],

+     "prompt_number": 3

+    }

+   ],

+   "metadata": {}

+  }

+ ]

+}
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