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+{
+ "metadata": {
+  "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+  {
+   "cells": [
+    {
+     "cell_type": "heading",
+     "level": 1,
+     "metadata": {},
+     "source": [
+      "Chapter 7: Analysis of Stress and Strain"
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 7.1, page no. 472"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "\"\"\"\n",
+      "calculate stresses acting on an element inclined at 45\u00b0\n",
+      "\"\"\"\n",
+      "\n",
+      "import math \n",
+      "\n",
+      "#initialisation\n",
+      "# Let x1, y1 be the transformed direction inclined at 45 deegree to the original\n",
+      "sx = 16000                          # Direct stress in x-direction in psi\n",
+      "sy = 6000                           # Direct stress in y-direction \"\"\n",
+      "txy = 4000                          # Shear stress in y-direction \"\"\n",
+      "tyx = txy                           # Shear stress in x-direction \"\"\n",
+      "t = 45                              # Inclination pf plane in degree \n",
+      "\n",
+      "#calculation\n",
+      "sx1 = (sx+sy)/2 + ((sx-sy)*(math.cos(math.radians(2*t))/2.0)) + txy*math.sin(math.radians(2*t))       # Direct stress in x1-direction in psi\n",
+      "sy1 = (sx+sy)/2 - ((sx-sy)*(math.cos(math.radians(2*t))/2.0)) - txy*math.sin(math.radians(2*t))       # Direct stress in y1-direction in psi\n",
+      "tx1y1 =  - ((sx-sy)*(math.sin(math.radians(2*t))/2.0)) + txy*math.cos(math.radians(2*t))    # Shear stress in psi\n",
+      "\n",
+      "print \"The direct stress on the element in x1-direction is\", sx1, \"psi\"\n",
+      "print \"The direct stress on the element in y1-direction is\", sy1, \"psi\"\n",
+      "print \"The shear stress on the element\", tx1y1, \"psi\""
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The direct stress on the element in x1-direction is 15000.0 psi\n",
+        "The direct stress on the element in y1-direction is 7000.0 psi\n",
+        "The shear stress on the element -5000.0 psi\n"
+       ]
+      }
+     ],
+     "prompt_number": 1
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 7.2, page no. 473"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "\"\"\"\n",
+      "stresses acting on an element that is oriented at a clockwise 15\u00b0 \n",
+      "\"\"\"\n",
+      "\n",
+      "import math \n",
+      "\n",
+      "#initialisation\n",
+      "# Let x1, y1 be the transformed direction inclined at 15 deegree to the original\n",
+      "sx = -46e06                     # Direct stress in x-direction in Pa\n",
+      "sy = 12e06                      # Direct stress in y-direction \"\"\n",
+      "txy = -19e06                    # Shear stress in y-direction \"\"\n",
+      "t = -15                         # Inclination of plane in degree \n",
+      "\n",
+      "#calculation\n",
+      "sx1 = (sx+sy)/2.0 + ((sx-sy)*(math.cos(math.radians(2*t))/2.0)) + txy*math.sin(math.radians(2*t))   # Direct stress in x1-direction in Pa\n",
+      "sy1 = (sx+sy)/2.0 - ((sx-sy)*(math.cos(math.radians(2*t))/2.0)) - txy*math.sin(math.radians(2*t))   # Direct stress in y1-direction in Pa\n",
+      "tx1y1 = -((sx-sy)*(math.sin(math.radians(2*t))/2.0)) + txy*math.cos(math.radians(2*t))             # Shear stress in Pa\n",
+      "\n",
+      "\n",
+      "print \"The direct stress on the element in x1-direction is\", sx1, \"Pa\"\n",
+      "print \"The direct stress on the element in y1-direction is\", sy1, \"Pa\"\n",
+      "print \"The shear stress on the element\", tx1y1, \"Pa\""
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The direct stress on the element in x1-direction is -32614736.7097 Pa\n",
+        "The direct stress on the element in y1-direction is -1385263.29025 Pa\n",
+        "The shear stress on the element -30954482.6719 Pa\n"
+       ]
+      }
+     ],
+     "prompt_number": 2
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "example 7.3, page no. 481"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "\"\"\"\n",
+      "Calculate shear stress and principal stress\n",
+      "\"\"\"\n",
+      "\n",
+      "import math\n",
+      "\n",
+      "ax = 12300.0\n",
+      "ay = -4200.0\n",
+      "txy = -4700.0\n",
+      "\n",
+      "tan_2p = round((2*txy)/(ax-ay), 4)\n",
+      "\n",
+      "theta_p1 = 150.3\n",
+      "theta_p2 = 330.3\n",
+      "\n",
+      "stress1 = (ax+ay)/2.0\n",
+      "stress2 = (ax-ay)/2.0\n",
+      "a1 = stress1 + math.sqrt((stress2**2.0)+(txy**2.0))\n",
+      "a2 = stress1 - math.sqrt((stress2**2.0)+(txy**2.0))\n",
+      "\n",
+      "#python calculations differ a bit. hence, differences in the answer\n",
+      "print \"Principal stesses are \", round(a1), \"psi and \", round(a2), \" psi\"\n",
+      "\n",
+      "tmax = math.sqrt((stress2**2.0)+(txy**2.0))\n",
+      "print \"Maximum shear stress is \", round(tmax), \" psi\"\n",
+      "\n",
+      "a_aver = (ax+ay)/2.0\n",
+      "\n",
+      "print \"Normal stress acting at maximum shear stress = \", round(a_aver), \"psi\""
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Principal stesses are  13545.0 psi and  -5445.0  psi\n",
+        "Maximum shear stress is  9495.0  psi\n",
+        "Normal stress acting at maximum shear stress =  4050.0 psi\n"
+       ]
+      }
+     ],
+     "prompt_number": 53
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 7.4, page no. 492"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "\"\"\"\n",
+      "stresses acting on an element inclined at 30\u00b0 \n",
+      "\"\"\"\n",
+      "\n",
+      "import math \n",
+      "\n",
+      "#initialisation\n",
+      "sx = 90e06                      # Direct stress in x-direction in Pa\n",
+      "sy = 20e06                      # Direct stress in y-direction in Pa\n",
+      "t = 30                          # Inclination of element in degree\n",
+      "\n",
+      "#calculation\n",
+      "savg = (sx+sy)/2.0                                  # Average in-plane direct stress\n",
+      "txy = 0 \n",
+      "R = math.sqrt(((sx-sy)/2)**2+(txy)**2)              # Radius of mohr circle\n",
+      "\n",
+      "# Point D  at 2t = 60\n",
+      "sx1 = savg + R*math.cos(math.radians(2*t))          # Direct stress at point D \n",
+      "tx1y1 = -R*math.sin(math.radians(2*t))              # shear stress at point D\n",
+      "print \"The direct stress at point D is\", sx1, \"Pa\"\n",
+      "print \"The shear stress at point D is\", tx1y1, \"Pa\"\n",
+      "\n",
+      "# Point D  at 2t = 240\n",
+      "sx2 = savg + R*math.cos(math.radians(90 + t))       # Direct stress at point D \n",
+      "tx2y2 = R*math.sin(math.radians(90 + t))            # shear stress at point D\n",
+      "print \"The direct stress at point D_desh is\", sx2, \"Pa\"\n",
+      "print \"The shear stress at point D_desh is\", tx2y2, \"Pa\""
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The direct stress at point D is 72500000.0 Pa\n",
+        "The shear stress at point D is -30310889.1325 Pa\n",
+        "The direct stress at point D_desh is 37500000.0 Pa\n",
+        "The shear stress at point D_desh is 30310889.1325 Pa\n"
+       ]
+      }
+     ],
+     "prompt_number": 3
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 7.5, page no. 494"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "\"\"\"\n",
+      "stresses acting on an element, principal stress, max. shear stress\n",
+      "\"\"\"\n",
+      "\n",
+      "import math\n",
+      "import numpy\n",
+      "\n",
+      "#initialisation \n",
+      "sx = 15000                              # Direct stress in x-direction in psi\n",
+      "sy = 5000                               # Direct stress in y-direction \"\"\n",
+      "txy = 4000                              # Shear stress in y-direction \"\"\n",
+      "savg = (sx+sy)/2.0                        # Average in-plane direct stress\n",
+      "sx1 = 15000                             # Stress acting on face at theta = 0 degree\n",
+      "tx1y1 = 4000                            # Stress acting on face at theta = 0 degree\n",
+      "sx1_ = 5000                             \n",
+      "tx1y1_ = -4000                          \n",
+      "\n",
+      "#calculation\n",
+      "R = math.sqrt(((sx-sy)/2)**2+(txy)**2)              # Radius of mohr circle\n",
+      "\n",
+      "# Part (a)\n",
+      "t = 40                                              # Inclination of the plane in degree\n",
+      "f1 = numpy.degrees(numpy.arctan((4000.0/5000.0)))     # Angle between line CD and x1-axis\n",
+      "f2 = 80 - f1                                        # Angle between line CA and x1-axis\n",
+      "\n",
+      "# Point D  \n",
+      "sx1 = savg + R*math.cos(math.radians(f2))       # Direct stress at point D \n",
+      "tx1y1 = -R*math.sin(math.radians(f2))           # shear stress at point D\n",
+      "print \"The shear stress at point D\", round(tx1y1), \"psi\"\n",
+      "\n",
+      "# Point D'  \n",
+      "sx2 = savg - R*math.cos(math.radians(f2))       # Direct stress at point D' \n",
+      "tx2y2 = R*math.sin(math.radians(f2))            # shear stress at point D'\n",
+      "print \"The direct stres at point D_desh\", round(sx2), \"psi\"\n",
+      "\n",
+      "#Part (b)\n",
+      "sp1 = savg + R                                      # Maximum direct stress in mohe circle (at point P1)\n",
+      "tp1 = f1/2                                          # Inclination of plane of maximum direct stress\n",
+      "print \"with angle\",round(tp1,2) , \"degree The maximum direct stress at P1 is \",sp1 , \"psi\"\n",
+      "sp2 =  savg - R  # Minimum direct stress in mohe circle (at point P2)\n",
+      "tp2 = (f1+180)/2  # Inclination of plane of minimum direct stress\n",
+      "print \"with angle\", round(tp2,2), \"degree The maximum direct stress at P2 is \",sp2 , \"psi\"\n",
+      "\n",
+      "# Part (c)\n",
+      "tmax = R                                            # Maximum shear stress in mohe circle\n",
+      "ts1 = -(90 - f1)/2.0                                # Inclination of plane of maximum shear stress\n",
+      "print \"with plane incilation of\", tmax, \"psi The Maximum shear stress is \", round(ts1,2), \"deegree\""
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The shear stress at point D -4229.0 psi\n",
+        "The direct stres at point D_desh 5193.0 psi\n",
+        "with angle 19.33 degree The maximum direct stress at P1 is  16403.1242374 psi\n",
+        "with angle 109.33 degree The maximum direct stress at P2 is  3596.87576257 psi\n",
+        "with plane incilation of 6403.12423743 psi The Maximum shear stress is  -25.67 deegree\n"
+       ]
+      }
+     ],
+     "prompt_number": 1
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 7.6, Page number 497"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "\"\"\"\n",
+      "use Mohr\u2019s circle, to calculate various quantities\n",
+      "\"\"\"\n",
+      "\n",
+      "import math \n",
+      "import numpy\n",
+      "\n",
+      "\n",
+      "sx = -50e06                                 # Direct stress in x-direction in psi\n",
+      "sy = 10e06                                  # Direct stress in y-direction \"\"\n",
+      "txy = -40e06                                # Shear stress in y-direction \"\"\n",
+      "savg = (sx+sy)/2                            # Average in-plane direct stress\n",
+      "sx1 = -50e06\n",
+      "tx1y1 = -40e06                              # Stress acting on face at theta = 0 degree\n",
+      "sx1_ = 10e06\n",
+      "tx1y1_ = 40e06                              # Stress acting on face at theta = 0 degree\n",
+      "\n",
+      "#calculation\n",
+      "R = math.sqrt(((sx-sy)/2)**2+(txy)**2)      # Radius of mohr circle\n",
+      "\n",
+      "# Part (a)\n",
+      "t = 45                                                  # Inclination of the plane in degree\n",
+      "f1 = numpy.degrees(numpy.arctan((40e06/30e06)))       # Angle between line CD and x1-axis\n",
+      "f2 = 90 - f1  # Angle between line CA and x1-axis\n",
+      "\n",
+      "# Point D  \n",
+      "sx1 = savg - R*math.cos(math.radians(f2))           # Direct stress at point D \n",
+      "tx1y1 = R*math.sin(math.radians(f2))                # shear stress at point D\n",
+      "print \"The direct stres at point D\", sx1, \"Pa\"\n",
+      "print \"The shear stress at point D\", tx1y1, \"Pa\"\n",
+      "\n",
+      "# Point D'  \n",
+      "sx2 = savg + R*math.cos(math.radians(f2))           # Direct stress at point D' \n",
+      "tx2y2 = -R*math.sin(math.radians(f2))               # shear stress at point D'\n",
+      "print \"The direct stres at point D_desh\", sx2, \"Pa\"\n",
+      "print \"The shear stress at point D_desh\", tx2y2, \"Pa\"\n",
+      "\n",
+      "#Part (b)\n",
+      "sp1 =  savg + R                                         # Maximum direct stress in mohe circle (at point P1)\n",
+      "tp1 =(f1+180)/2                                         # Inclination of plane of maximum direct stress\n",
+      "print \"with angle\", round(tp1,2), \"degree\", \"The maximum direct stress at P1 is \",  sp1, \"Pa\" \n",
+      "sp2 =  savg - R                                         # Minimum direct stress in mohe circle (at point P2)\n",
+      "tp2 = f1/2                                              # Inclination of plane of minimum direct stress\n",
+      "print \"with angle\", round(tp2,2), \"degree\", \"The maximum direct stress at P2 is \", sp2, \"Pa\"\n",
+      "\n",
+      "# Part (c)\n",
+      "tmax = R                                                # Maximum shear stress in mohe circle\n",
+      "ts1 = (90 + f1)/2                                       # Inclination of plane of maximum shear stress\n",
+      "print \"with plane incilation of\", round(ts1,2), \"degree\", \"The Maximum shear stress is \", tmax, \"Pa\""
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The direct stres at point D -60000000.0 Pa\n",
+        "The shear stress at point D 30000000.0 Pa\n",
+        "The direct stres at point D_desh 20000000.0 Pa\n",
+        "The shear stress at point D_desh -30000000.0 Pa\n",
+        "with angle 116.57 degree The maximum direct stress at P1 is  30000000.0 Pa\n",
+        "with angle 26.57 degree The maximum direct stress at P2 is  -70000000.0 Pa\n",
+        "with plane incilation of 71.57 degree The Maximum shear stress is  50000000.0 Pa\n"
+       ]
+      }
+     ],
+     "prompt_number": 11
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 7.7, page no. 520"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "\"\"\"\n",
+      "calculate various quantities\n",
+      "\"\"\"\n",
+      "\n",
+      "import math\n",
+      "import numpy\n",
+      "\n",
+      "#initialisation\n",
+      "\n",
+      "ex = 340e-06                            # Strain in x-direction\n",
+      "ey = 110e-06                            # Strain in y-direction\n",
+      "txy = 180e-06                           # shear strain\n",
+      "\n",
+      "\n",
+      "# Part (a)\n",
+      "t = 30                                      # Inclination of the element in degree\n",
+      "ex1 = (ex+ey)/2.0 + ((ex-ey)/2.0)*math.cos(math.radians(2*t)) + (txy/2.0)*(math.sin(math.radians(2*t)))         # Strain in x1 direction (located at 30 degree)\n",
+      "tx1y1 = 2*(-((ex-ey)/2.0)*math.sin(math.radians(2*t)) + (txy/2.0)*(math.cos(math.radians(2*t))))                # Shear starin\n",
+      "ey1 = ex+ey-ex1                             # Strain in y1 direction (located at 30 degree)\n",
+      "print \"Strain in x1 direction (located at 30 degree) is\", round((ex1/1E-6),2),\"* 10^-6\"\n",
+      "print \"shear strain is\", round((tx1y1/1E-6),2),\"* 10^-6\"\n",
+      "print \"Strain in y1 direction (located at 30 degree) is\", ey1\n",
+      "\n",
+      "# Part (b)\n",
+      "e1 = (ex+ey)/2.0 + math.sqrt(((ex-ey)/2.0)**2 + (txy/2.0)**2) # Principle stress\n",
+      "e2 = (ex+ey)/2.0 - math.sqrt(((ex-ey)/2.0)**2 + (txy/2.0)**2) # Principle stress\n",
+      "tp1 = (0.5)*numpy.degrees(numpy.arctan((txy/(ex-ey)))) # Angle to principle stress direction\n",
+      "tp2 = 90 + tp1  # Angle to principle stress direction\n",
+      "e1 = (ex+ey)/2.0 + ((ex-ey)/2.0)*math.cos(math.radians(2*tp1)) + (txy/2.0)*(math.sin(math.radians(2*tp1)))      # Principle stress via another method\n",
+      "e2 = (ex+ey)/2.0 + ((ex-ey)/2.0)*math.cos(math.radians(2*tp2)) + (txy/2.0)*(math.sin(math.radians(2*tp2)))      # Principle stress via another method\n",
+      "print \"with angle\", round(tp1,2), \"degree\",\"The Principle stress is \", round(e1,4)\n",
+      "print \"with angle\",round(tp2,2), \"degree\",\"The Principle stress is \",round(e2,4)\n",
+      "\n",
+      "# Part (c)\n",
+      "tmax = 2*math.sqrt(((ex-ey)/2.0)**2 + (txy/2.0)**2)         # Maxmum shear strain\n",
+      "ts = tp1 + 45                                               # Orientation of element having maximum shear stress \n",
+      "tx1y1_ =  2*( -((ex-ey)/2)*math.sin(math.radians(2*ts)) + (txy/2)*(math.cos(math.radians(2*ts))))  # Shear starin assosiated with ts direction\n",
+      "print \"with angle\",round(ts,2), \"degree\",\"The Maximum shear strain is \",round(tx1y1_,4)\n",
+      "eavg = (e1+e2)/2.0                                          # Average atrain\n",
+      "print \"The average strain is\", eavg"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Strain in x1 direction (located at 30 degree) is 360.44 * 10^-6\n",
+        "shear strain is -109.19 * 10^-6\n",
+        "Strain in y1 direction (located at 30 degree) is 8.95577136594e-05\n",
+        "with angle 19.02 degree The Principle stress is  0.0004\n",
+        "with angle 109.02 degree The Principle stress is  0.0001\n",
+        "with angle 64.02 degree The Maximum shear strain is  -0.0003\n",
+        "The average strain is 0.000225\n"
+       ]
+      }
+     ],
+     "prompt_number": 5
+    }
+   ],
+   "metadata": {}
+  }
+ ]
+}
\ No newline at end of file