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diff --git a/Testing_the_interface/chapter8_3.ipynb b/Testing_the_interface/chapter8_3.ipynb deleted file mode 100755 index 2e7289e4..00000000 --- a/Testing_the_interface/chapter8_3.ipynb +++ /dev/null @@ -1,524 +0,0 @@ -{ - "metadata": { - "name": "" - }, - "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", - "finding max. permissible pressures at various conditions\n", - "\"\"\"\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", - "calculating various quantities for cylindrical part of vessel\n", - "\"\"\"\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", - "principal stresses and maximum shear stresses at cross section\n", - "\"\"\"\n", - "\n", - "%pylab 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" - ] - }, - { - "output_type": "stream", - "stream": "stderr", - "text": [ - "WARNING: pylab import has clobbered these variables: ['power', 'random', 'fft', 'load', 'save', 'linalg', 'info']\n", - "`%pylab --no-import-all` prevents importing * from pylab and numpy\n" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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vXMmiMWPq7US/Z88AQkKm0qzZ0Fq/NzUulZjkmDodt7AQ2rXT3uEaHV2nXQgX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\nBY21q1yFr1zJojFjzF59Srg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- "text": [ - "<matplotlib.figure.Figure at 0x4171710>" - ] - } - ], - "prompt_number": 26 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example 8.4, page no. 570" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "\"\"\"\n", - "maximum tensile stress, maximum compressive stress, and maximum shear stress in the shaft.\n", - "\"\"\"\n", - "\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", - "calculate maximum allowable internal pressure\n", - "\"\"\"\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", - "principal stresses and maximum shear stresses\n", - "\"\"\"\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", - "principal stresses and maximum shear stresses at points & at the base of the post\n", - "\"\"\"\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": {} - } - ] -}
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