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+{
+ "metadata": {
+  "name": "",
+  "signature": "sha256:0d2067363679e9ceade333ea9bc4385c2fb9b29e28a336c6f2561c38a5e262ab"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+  {
+   "cells": [
+    {
+     "cell_type": "heading",
+     "level": 1,
+     "metadata": {},
+     "source": [
+      "Chapter 8: Applications of Plane Stress Pressure Vessels Beams and Combined Loadings"
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 8.1, page no. 546"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "\n",
+      "\n",
+      "import math \n",
+      "\n",
+      "#initialisation\n",
+      "d = 18                                  # inner idameter of the hemisphere in inch\n",
+      "t = 1.0/4.0                                 # thickness of the hemisphere in inch\n",
+      "\n",
+      "\n",
+      "#calculation\n",
+      "# Part (a)\n",
+      "sa = 14000                                # Allowable tensile stress in Psi\n",
+      "Pa = (2*t*sa)/(d/2.0)                     # Maximum permissible air pressure in Psi\n",
+      "print \"Maximum permissible air pressure in the tank (Part(a)) is\", round(Pa,1), \"psi\"\n",
+      "\n",
+      "# Part (b)\n",
+      "sb = 6000                                  # Allowable shear stress in Psi\n",
+      "Pb = (4*t*sb)/(d/2.0)                      # Maximum permissible air pressure in Psi\n",
+      "print \"Maximum permissible air pressure in the tank (Part(b)) is\", round(Pb,1), \"psi\"\n",
+      "\n",
+      "# Part (c)\n",
+      "e = 0.0003                                # Allowable Strain in Outer sufrface of the hemisphere\n",
+      "E = 29e06                                 # Modulus of epasticity of the steel in Psi\n",
+      "v = 0.28                                  # Poissions's ratio of the steel\n",
+      "Pc = (2*t*E*e)/((d/2.0)*(1-v))            # Maximum permissible air pressure in Psi\n",
+      "print \"Maximum permissible air pressure in the tank (Part(c)) is\", round(Pc,1), \"psi\"\n",
+      "\n",
+      "# Part (d)\n",
+      "Tf = 8100                                 # failure tensile load in lb/in \n",
+      "n = 2.5                                   # Required factor of safetty against failure of the weld\n",
+      "Ta = Tf / n                               # Allowable load in ld/in \n",
+      "sd = (Ta*(1))/(t*(1))                     # Allowable tensile stress in Psi\n",
+      "Pd = (2*t*sd)/(d/2.0)                       # Maximum permissible air pressure in Psi\n",
+      "print \"Maximum permissible air pressure in the tank (Part(d)) is\", round(Pd,1), \"psi\"\n",
+      "\n",
+      "# Part (e)\n",
+      "Pallow = Pb  \n",
+      "print \"Maximum permissible air pressure in the tank (Part(e)) is\", round(Pb,1) ,\"psi\""
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Maximum permissible air pressure in the tank (Part(a)) is 777.8 psi\n",
+        "Maximum permissible air pressure in the tank (Part(b)) is 666.7 psi\n",
+        "Maximum permissible air pressure in the tank (Part(c)) is 671.3 psi\n",
+        "Maximum permissible air pressure in the tank (Part(d)) is 720.0 psi\n",
+        "Maximum permissible air pressure in the tank (Part(e)) is 666.7 psi\n"
+       ]
+      }
+     ],
+     "prompt_number": 2
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 8.2, page no. 552"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "\n",
+      "\n",
+      "import math \n",
+      "\n",
+      "#initialisation\n",
+      "a = 55                              # Angle made by helix with longitudinal axis in degree\n",
+      "r = 1.8                             # Inner radius of vessel in m\n",
+      "t = 0.02                            # thickness of vessel in m\n",
+      "E = 200e09                          # Modulus of ealsticity of steel in Pa\n",
+      "v = 0.3                             # Poission's ratio of steel \n",
+      "P = 800e03                          # Pressure inside the tank in Pa\n",
+      "\n",
+      "\n",
+      "#calculation\n",
+      "# Part (a)\n",
+      "s1 = (P*r)/t                        # Circumferential stress in Pa\n",
+      "s2 = (P*r)/(2*t)                    # Longitudinal stress in Pa\n",
+      "\n",
+      "print \"Circumferential stress is \", s1, \"Pa\"\n",
+      "print \"Longitudinal stress is \", s2, \"Pa\"\n",
+      "\n",
+      "# Part (b)\n",
+      "t_max_z = (s1-s2)/2.0               # Maximum inplane shear stress in Pa\n",
+      "t_max = s1/2.0                      # Maximum out of plane shear stress in Pa\n",
+      "\n",
+      "print \"Maximum inplane shear stress is \", t_max_z, \"Pa\"\n",
+      "print \"Maximum inplane shear stress is \", t_max, \"Pa\"\n",
+      "\n",
+      "# Part (c)\n",
+      "e1 = (s1/(2*E))*(2-v)               # Strain in circumferential direction \n",
+      "e2 = (s2/E)*(1-(2*v))               # Strain in longitudinal direction\n",
+      "\n",
+      "print \"Strain in circumferential direction is %e\"%(e1)\n",
+      "print \"Strain in longitudinal direction is \", e2\n",
+      "\n",
+      "# Part (d)\n",
+      "# x1 is the direction along the helix\n",
+      "theta = 90 - a  \n",
+      "sx1 = ((P*r)/(4*t))*(3-math.cos(math.radians(2*theta))) # Stress along x1 direction\n",
+      "tx1y1 = ((P*r)/(4*t))*(math.sin(math.radians(2*theta))) # Shear stress in x1y1 plane\n",
+      "sy1 = s1+s2-sx1  # Stress along y1 direction\n",
+      "\n",
+      "print \"Stress along y1 direction is \", sy1\n",
+      "\n",
+      "# Mohr Circle Method\n",
+      "savg = (s1+s2)/2.0                    # Average stress in Pa\n",
+      "R = (s1 - s2 )/2.0                    # Radius of Mohr's Circle in Pa\n",
+      "sx1_ = savg - R*math.cos(math.radians(2*theta))             # Stress along x1 direction\n",
+      "tx1y1_ = R*math.sin(math.radians(2*theta))                  # Shear stress in x1y1 plane\n",
+      "print \"Stress along x1 direction is \", sx1_, \"Pa\"\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Circumferential stress is  72000000.0 Pa\n",
+        "Longitudinal stress is  36000000.0 Pa\n",
+        "Maximum inplane shear stress is  18000000.0 Pa\n",
+        "Maximum inplane shear stress is  36000000.0 Pa\n",
+        "Strain in circumferential direction is 3.060000e-04\n",
+        "Strain in longitudinal direction is  7.2e-05\n",
+        "Stress along y1 direction is  60156362.5799\n",
+        "Stress along x1 direction is  47843637.4201 Pa\n"
+       ]
+      }
+     ],
+     "prompt_number": 13
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 8.3, page no. 562"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "\n",
+      "\n",
+      "%matplotlib inline\n",
+      "from matplotlib import *\n",
+      "from pylab import *\n",
+      "import numpy\n",
+      "\n",
+      "#initialisation\n",
+      "L = 6.0                               # Span of the beam in ft\n",
+      "P = 10800                             # Pressure acting in lb\n",
+      "c = 2.0                               # in ft\n",
+      "b = 2.0                               # Width of cross section of the beam in inch\n",
+      "h = 6.0                               # Height of the cross section of the beam in inch\n",
+      "x = 9.0                               # in inch\n",
+      "\n",
+      "#calculation\n",
+      "Ra = P/3.0                                          # Reaction at point at A\n",
+      "V = Ra                                              # Shear force at section mn \n",
+      "M = Ra*x                                            # Bending moment at the section mn\n",
+      "I = (b*h**3)/12.0                                   # Moment of inertia in in4\n",
+      "y = linspace(-3, 3, 61)\n",
+      "sx = -(M/I)*y                                       # Normal stress on  crossection  mn\n",
+      "Q = (b*(h/2-y))*(y+((((h/2.0)-y)/2.0)))               # First moment of recmath.tangular cross section\n",
+      "txy = (V*Q)/(I*b)                                   # Shear stress acting on x face of the stress element\n",
+      "s1 = (sx/2.0)+numpy.sqrt((sx/2.0)**2+(txy)**2)       # Principal Tesile stress on the cross section\n",
+      "s2 = (sx/2.0)-numpy.sqrt((sx/2.0)**2+(txy)**2)       # Principal Compressive stress on the cross section\n",
+      "tmax = numpy.sqrt((sx/2)**2+(txy)**2)                # Maximum shear stress on the cross section\n",
+      "plot(sx,y,'o',color='c')\n",
+      "plot(txy,y,'+',color='m')\n",
+      "plot(s1,y,'--',color='y')\n",
+      "plot(s2,y,'<',color='k')\n",
+      "plot(tmax,y,label=\"Maximum shear stress on cross section\")\n",
+      "legend()\n",
+      "show()\n",
+      "#print \"Principal Tesile stress on the cross section\", s1, \"psi\"\n",
+      "#print \"Principal Compressive stress on the cross section\", s2, \"psi\"\n",
+      "\n",
+      "# Conclusions \n",
+      "s1_max = 14400.0                            # Maximum tensile stress in Psi\n",
+      "txy_max = 900.0                             # Maximum shear stress in Psi\n",
+      "t_max = 14400.0/2.0                         # Largest shear stress at 45 degree plane"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Populating the interactive namespace from numpy and matplotlib\n"
+       ]
+      },
+      {
+       "metadata": {},
+       "output_type": "display_data",
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qtAvhQuQar6JGhhn9gw8+SM6JE1zYsUOf0QeeOUPz0lLJ6Svx97+Bixd/qNNj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\nAAAASUVORK5CYII=\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x263ff90>"
+       ]
+      }
+     ],
+     "prompt_number": 1
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 8.4, page no. 570"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "\n",
+      "import math \n",
+      "\n",
+      "#initialisation\n",
+      "d = 0.05                                # Diameter of shaft in m\n",
+      "T = 2400                                # Torque transmitted by the shaft in N-m\n",
+      "P = 125000                              # Tensile force\n",
+      "\n",
+      "#calculation\n",
+      "s0 = (4*P)/(math.pi*d**2)               # Tensile stress in\n",
+      "t0 = (16*T)/(math.pi*d**3)              # Shear force \n",
+      "# Stresses along x and y direction\n",
+      "sx = 0 \n",
+      "sy = s0 \n",
+      "txy = -t0  \n",
+      "s1 = (sx+sy)/2.0 + math.sqrt(((sx-sy)/2.0)**2 + (txy)**2)   # Maximum tensile stress \n",
+      "s2 = (sx+sy)/2.0 - math.sqrt(((sx-sy)/2.0)**2 + (txy)**2)   # Maximum compressive stress \n",
+      "tmax =  math.sqrt(((sx-sy)/2)**2 + (txy)**2)            # Maximum in plane shear stress \n",
+      "print \"Maximum tensile stress %e\" %s1, \"Pa\"\n",
+      "print \"Maximum compressive stress %e\" %s2, \"Pa\"\n",
+      "print \"Maximum in plane shear stress %e \" %tmax, \"Pa\""
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Maximum tensile stress 1.346662e+08 Pa\n",
+        "Maximum compressive stress -7.100421e+07 Pa\n",
+        "Maximum in plane shear stress 1.028352e+08  Pa\n"
+       ]
+      }
+     ],
+     "prompt_number": 5
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 8.5, page no. 573"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "\n",
+      "\n",
+      "import math \n",
+      "\n",
+      "\n",
+      "#initialisation\n",
+      "P = 12                              # Axial load in K\n",
+      "r = 2.1                             # Inner radius of the cylinder in inch\n",
+      "t = 0.15                            # Thickness of the cylinder in inch\n",
+      "ta = 6500                           # Allowable shear stress in Psi\n",
+      "\n",
+      "#calculation\n",
+      "p1 = (ta - 3032)/3.5                # allowable internal pressure\n",
+      "p2 = (ta + 3032)/3.5                # allowable internal pressure\n",
+      "p3 = 6500/7.0                       # allowable internal pressure\n",
+      "\n",
+      "prs_allowable = min(p1,p2,p3)              # Minimum pressure would govern the design\n",
+      "print \"Maximum allowable internal pressure \", round(prs_allowable), \"psi\""
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Maximum allowable internal pressure  929.0 psi\n"
+       ]
+      }
+     ],
+     "prompt_number": 3
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 8.6, page no. 574"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "\n",
+      "\n",
+      "import math \n",
+      "\n",
+      "#initialisation\n",
+      "d1 = 0.18                                   # Inner diameter of circular pole in m\n",
+      "d2 = 0.22                                   # Outer diameter of circular pole in m\n",
+      "P = 2000                                    # Pressure of wind in Pa\n",
+      "b = 1.5                                     # Distance between centre line of pole and board in m\n",
+      "h = 6.6                                     # Distance between centre line of board and bottom of the ploe in m\n",
+      "\n",
+      "#calculation\n",
+      "W = P*(2*1.2)                               # Force at the midpoint of sign \n",
+      "V = W                                       # Load\n",
+      "T = W*b                                     # Torque acting on the pole\n",
+      "M = W*h                                     # Moment at the bottom of the pole\n",
+      "I = (math.pi/64.0)*(d2**4-d1**4)            # Momet of inertia of cross section of the pole\n",
+      "sa = (M*d2)/(2*I)                           # Tensile stress at A \n",
+      "Ip = (math.pi/32.0)*(d2**4-d1**4)           # Polar momet of inertia of cross section of the pole\n",
+      "t1 = (T*d2)/(2*Ip)                          # Shear stress at A and B\n",
+      "r1 = d1/2.0                                 # Inner radius of circular pole in m\n",
+      "r2 = d2/2.0                                 # Outer radius of circular pole in m\n",
+      "A = math.pi*(r2**2-r1**2)                   # Area of the cross section\n",
+      "t2 = ((4*V)/(3*A))*((r2**2 + r1*r2 +r1**2)/(r2**2+r1**2))  # Shear stress at point B \n",
+      "\n",
+      "# Principle stresses \n",
+      "sxa = 0\n",
+      "sya = sa\n",
+      "txya = t1\n",
+      "sxb = 0\n",
+      "syb = 0\n",
+      "txyb = t1+t2 \n",
+      "\n",
+      "# Stresses at A\n",
+      "s1a = (sxa+sya)/2.0 + math.sqrt(((sxa-sya)/2)**2 + (txya)**2)                 # Maximum tensile stress \n",
+      "s2a = (sxa+sya)/2.0 - math.sqrt(((sxa-sya)/2)**2 + (txya)**2)                 # Maximum compressive stress \n",
+      "tmaxa =  math.sqrt(((sxa-sya)/2)**2 + (txya)**2)                            # Maximum in plane shear stress\n",
+      "\n",
+      "print \"Maximum tensile stress at point A is\", s1a, \"Pa\"\n",
+      "print \"Maximum compressive stress at point A is\", s2a, \"Pa\"\n",
+      "print \"Maximum in plane shear stress at point A is\", tmaxa, \"Pa\"\n",
+      "\n",
+      "# Stress at B \n",
+      "s1b = (sxb+syb)/2.0 + math.sqrt(((sxb-syb)/2)**2 + (txyb)**2)                 # Maximum tensile stress \n",
+      "s2b = (sxb+syb)/2.0 - math.sqrt(((sxb-syb)/2)**2 + (txyb)**2)                 # Maximum compressive stress \n",
+      "tmaxb =  math.sqrt(((sxb-syb)/2.0)**2 + (txyb)**2)                            # Maximum in plane shear stress \n",
+      "print \"Maximum tensile stress at point B is\", s1b, \"Pa\"\n",
+      "print \"Maximum compressive stress at point B is\", s2b, \"Pa\"\n",
+      "print \"Maximum in plane shear stress at point B is\", tmaxb, \"Pa\""
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Maximum tensile stress at point A is 55613361.197 Pa\n",
+        "Maximum compressive stress at point A is -700178.455718 Pa\n",
+        "Maximum in plane shear stress at point A is 28156769.8263 Pa\n",
+        "Maximum tensile stress at point B is 6999035.59641 Pa\n",
+        "Maximum compressive stress at point B is -6999035.59641 Pa\n",
+        "Maximum in plane shear stress at point B is 6999035.59641 Pa\n"
+       ]
+      }
+     ],
+     "prompt_number": 8
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 8.7, page no. 578"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "\n",
+      "\n",
+      "import math \n",
+      "\n",
+      "#initialisation\n",
+      "b = 6                           # Outer dimension of the pole in inch\n",
+      "t = 0.5                         # thickness of the pole\n",
+      "P1 = 20*(6.75*24)               # Load acting at the midpoint of the platform\n",
+      "d = 9                           # Distance between longitudinal axis of the post and midpoint of platform\n",
+      "P2 = 800                        # Load in lb\n",
+      "h = 52                          # Distance between base and point of action of P2\n",
+      "\n",
+      "#calculation\n",
+      "M1 = P1*d                       # Moment due to P1\n",
+      "M2 = P2*h                       # Moment due to P2\n",
+      "A = b**2 - (b-2*t)**2           # Area of the cross section\n",
+      "sp1 = P1/A                      # Comoressive stress due to P1 at A and B\n",
+      "I = (1.0/12.0)*(b**4 - (b-2*t)**4)  # Moment of inertia of the cross section\n",
+      "sm1 = (M1*b)/(2*I)              # Comoressive stress due to M1 at A and B\n",
+      "Aweb = (2*t)*(b-(2*t))          # Area of the web\n",
+      "tp2 = P2/Aweb                   # Shear stress at point B by lpad P2\n",
+      "sm2 = (M2*b)/(2*I)              # Comoressive stress due to M2 at A \n",
+      "sa = sp1+sm1+sm2                # Total Compressive stress at point A\n",
+      "sb = sp1+sm1                    # Total compressive at point B \n",
+      "tb = tp2                        # Shear stress at point B\n",
+      "\n",
+      "# Principle stresses \n",
+      "sxa = 0\n",
+      "sya = -sa\n",
+      "txya = 0\n",
+      "sxb = 0\n",
+      "syb = -sb\n",
+      "txyb = tp2 \n",
+      "\n",
+      "# Stresses at A\n",
+      "s1a = (sxa+sya)/2 + math.sqrt(((sxa-sya)/2)**2 + (txya)**2)             # Maximum tensile stress \n",
+      "s2a = (sxa+sya)/2 - math.sqrt(((sxa-sya)/2)**2 + (txya)**2)             # Maximum compressive stress \n",
+      "tmaxa =  math.sqrt(((sxa-sya)/2)**2 + (txya)**2)                        # Maximum in plane shear stress\n",
+      "print \"Maximum tensile stress at point A is\", s1a,\"Psi\"\n",
+      "print \"Maximum compressive stress at point A is\", round(s2a,2), \"Psi\"\n",
+      "print \"Maximum in plane shear stress at point A is\", round(tmaxa,2), \"Psi\"\n",
+      "\n",
+      "# Stress at B \n",
+      "s1b = (sxb+syb)/2 + math.sqrt(((sxb-syb)/2)**2 + (txyb)**2)             # Maximum tensile stress \n",
+      "s2b = (sxb+syb)/2 - math.sqrt(((sxb-syb)/2)**2 + (txyb)**2)             # Maximum compressive stress \n",
+      "tmaxb =  math.sqrt(((sxb-syb)/2)**2 + (txyb)**2)                        # Maximum in plane shear stress\n",
+      "print \"Maximum tensile stress at point B is\", round(s1b,2), \"Psi\"\n",
+      "print \"Maximum compressive stress at point B is\", round(s2b,2), \"Psi\"\n",
+      "print \"Maximum in plane shear stress at point B is\", round(tmaxb,2), \"Psi\""
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Maximum tensile stress at point A is 0.0 Psi\n",
+        "Maximum compressive stress at point A is -4090.91 Psi\n",
+        "Maximum in plane shear stress at point A is 2045.45 Psi\n",
+        "Maximum tensile stress at point B is 13.67 Psi\n",
+        "Maximum compressive stress at point B is -1872.69 Psi\n",
+        "Maximum in plane shear stress at point B is 943.18 Psi\n"
+       ]
+      }
+     ],
+     "prompt_number": 5
+    }
+   ],
+   "metadata": {}
+  }
+ ]
+}
\ No newline at end of file