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diff --git a/Testing_the_interface/chapter7_1.ipynb b/Testing_the_interface/chapter7_1.ipynb deleted file mode 100755 index 7c80c103..00000000 --- a/Testing_the_interface/chapter7_1.ipynb +++ /dev/null @@ -1,465 +0,0 @@ -{ - "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\", sp1, \"psi The maximum direct stress at P1 is \", round(tp1,2), \"degree\"\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\", sp2, \"psi The maximum direct stress at P2 is \", round(tp2,2), \"degree\"\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 16403.1242374 psi The maximum direct stress at P1 is 19.33 degree\n", - "with angle 3596.87576257 psi The maximum direct stress at P2 is 109.33 degree\n", - "with plane incilation of 6403.12423743 psi The Maximum shear stress is -25.67 deegree\n" - ] - } - ], - "prompt_number": 6 - }, - { - "cell_type": "heading", - "level": 2, - "metadata": {}, - "source": [ - "Example 7.6" - ] - }, - { - "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\", tp1, \"degree\",\"The Principle stress is \", e1\n", - "print \"with angle\",tp2, \"degree\",\"The Principle stress is \",e2\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 \",tx1y1_tx1y1_,\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 19.0235212659 degree The Principle stress is 0.000371030818665\n", - "with angle 109.023521266 degree The Principle stress is 7.89691813349e-05\n", - "with angle 64.02 degree The Maximum shear strain is -0.00029206163733\n", - "The average strain is 0.000225\n" - ] - } - ], - "prompt_number": 12 - } - ], - "metadata": {} - } - ] -}
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