Revised list of TBCs

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diff --git a/Engineering_Mechanics,_Schaum_Series_by_McLean/chapter10_2.ipynb b/Engineering_Mechanics,_Schaum_Series_by_McLean/chapter10_2.ipynb
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@@ -1,426 +0,0 @@
-{

- "metadata": {

-  "name": "chapter10.ipynb"

- },

- "nbformat": 3,

- "nbformat_minor": 0,

- "worksheets": [

-  {

-   "cells": [

-    {

-     "cell_type": "heading",

-     "level": 1,

-     "metadata": {},

-     "source": [

-      "Chapter 10: First Moments and Centroids"

-     ]

-    },

-    {

-     "cell_type": "heading",

-     "level": 2,

-     "metadata": {},

-     "source": [

-      "Example 10.10-5, Page no 160"

-     ]

-    },

-    {

-     "cell_type": "code",

-     "collapsed": false,

-     "input": [

-      "import math\n",

-      "import numpy as np\n",

-      "\n",

-      "#Initilization of variables\n",

-      "r=50 #mm\n",

-      "L1=75 #mm\n",

-      "L2=pi*r #mm\n",

-      "L3=61.2 #mm\n",

-      "# as theta1=45 degrees & theta2=60 degrees\n",

-      "sintheta1=sqrt(2)**-1\n",

-      "costheta1=sqrt(2)**-1\n",

-      "sintheta2=sqrt(3)*2**-1\n",

-      "costheta2=2**-1\n",

-      "\n",

-      "#Calculations\n",

-      "x_bar=np.array([(L1/2)*costheta1,L1*costheta1+r,L1*costheta1+100+(L3/2)*costheta2]) #mm\n",

-      "y_bar=np.array([(L1/2)*sintheta1,L1*sintheta1+(2*r)/pi,(L3/2)*sintheta2]) #mm\n",

-      "#Centroid Calculations\n",

-      "x=(L1*x_bar[0]+L2*x_bar[1]+L3*x_bar[2])/(L1+L2+L3) #mm\n",

-      "y=(L1*y_bar[0]+L2*y_bar[1]+L3*y_bar[2])/(L1+L2+L3) #mm\n",

-      "\n",

-      "#Result\n",

-      "print'The centroid is as follows:'\n",

-      "print'x=',round(x,1),\"mm\"\n",

-      "print'y=',round(y,1),\"mm\"\n",

-      "\n",

-      "# The answer may wary due to decimal point descrepancy"

-     ],

-     "language": "python",

-     "metadata": {},

-     "outputs": [

-      {

-       "output_type": "stream",

-       "stream": "stdout",

-       "text": [

-        "The centroid is as follows:\n",

-        "x= 97.0 mm\n",

-        "y= 57.7 mm\n"

-       ]

-      }

-     ],

-     "prompt_number": 4

-    },

-    {

-     "cell_type": "heading",

-     "level": 2,

-     "metadata": {},

-     "source": [

-      "Example 10.10-6, Page no 160"

-     ]

-    },

-    {

-     "cell_type": "code",

-     "collapsed": false,

-     "input": [

-      "import math\n",

-      "\n",

-      "#Initilization of variables\n",

-      "theta=75 #degrees\n",

-      "theta1=30 #degrees\n",

-      "sintheta=0.96\n",

-      "costheta=0.25\n",

-      "sintheta1=2**-1\n",

-      "costheta1=sqrt(3)*2**-1\n",

-      "alpha=(150*pi)/180 #rad\n",

-      "r=1\n",

-      "lhor=14 #in\n",

-      "\n",

-      "#calculations\n",

-      "a=((2*r)/alpha)*sintheta #in\n",

-      "p=90-theta\n",

-      "sinp=0.259\n",

-      "y=-a*sinp #in\n",

-      "#Length of arc\n",

-      "l=r*alpha #in\n",

-      "#Slope length calculations\n",

-      "DF=7 #in\n",

-      "AB=DF #in\n",

-      "BC=1 #in\n",

-      "BF=BC*costheta1 #in\n",

-      "FC=BC*sintheta1 #in\n",

-      "DC=DF+FC #in\n",

-      "EC=DC/costheta1 #in\n",

-      "#Centroid of EC is at G\n",

-      "yslope=0.5*EC*sintheta1+BF #in\n",

-      "#Y of composite figure\n",

-      "Y=((2*l*y)+14*-1+(2*EC*yslope))/(2*l+lhor+2*EC) #in\n",

-      "\n",

-      "#Result\n",

-      "print'The centroid is at Y=',round(Y,2),\"in\"\n"

-     ],

-     "language": "python",

-     "metadata": {},

-     "outputs": [

-      {

-       "output_type": "stream",

-       "stream": "stdout",

-       "text": [

-        "The centroid is at Y= 1.03 in\n"

-       ]

-      }

-     ],

-     "prompt_number": 13

-    },

-    {

-     "cell_type": "heading",

-     "level": 2,

-     "metadata": {},

-     "source": [

-      "Example 10.10-11, Page no 163"

-     ]

-    },

-    {

-     "cell_type": "code",

-     "collapsed": false,

-     "input": [

-      "import math\n",

-      "\n",

-      "#Initilization of variables\n",

-      "a=100 #mm\n",

-      "b=150 #mm\n",

-      "A1=2*10**4 #mm**2\n",

-      "A2=5*10**3 #mm**2\n",

-      "A3=(pi*(a/2)**2)/2 #mm**2\n",

-      "\n",

-      "#Calculations\n",

-      "x=(A1*a+A2*(133.3)-A3*b)/(A1+A2-A3) #mm\n",

-      "y=(A1*a*0.5+A2*(116.66)-A3*((4*a*0.5)/(3*pi)))/(A1+A2-A3) #mm\n",

-      "\n",

-      "#Result\n",

-      "print'The centroidal distances are'\n",

-      "print'x=',round(x,1),\"mm\"\n",

-      "print'y=',round(y,1),\"mm\"\n"

-     ],

-     "language": "python",

-     "metadata": {},

-     "outputs": [

-      {

-       "output_type": "stream",

-       "stream": "stdout",

-       "text": [

-        "The centroidal distances are\n",

-        "x= 98.6 mm\n",

-        "y= 71.2 mm\n"

-       ]

-      }

-     ],

-     "prompt_number": 14

-    },

-    {

-     "cell_type": "heading",

-     "level": 2,

-     "metadata": {},

-     "source": [

-      "Example 10.10-16, Page no 166"

-     ]

-    },

-    {

-     "cell_type": "code",

-     "collapsed": false,

-     "input": [

-      "import math\n",

-      "\n",

-      "#Initilization of variables\n",

-      "V=np.array([1728*10**3,432*10**3,7.54*10**3])\n",

-      "x_bar=np.array([60,140,60]) #mm\n",

-      "y_bar=np.array([30,20,30]) #mm\n",

-      "\n",

-      "#Calculations\n",

-      "x=(V[0]*x_bar[0]+V[1]*x_bar[1]+V[2]*x_bar[2])/(V[0]+V[1]+V[2]) #mm\n",

-      "y=(V[0]*y_bar[0]+V[1]*y_bar[1]+V[2]*y_bar[2])/(V[0]+V[1]+V[2]) #mm\n",

-      "z=120 #mm from symmetry\n",

-      "\n",

-      "#Result\n",

-      "print'The centroid is at'\n",

-      "print'x=',round(x,1),\"mm\"\n",

-      "print'y=',round(y,1),\"mm\"\n",

-      "print'z=',round(z,1),\"mm\"\n",

-      "\n",

-      "#Decimal accuracy causes discrepancy in answers\n"

-     ],

-     "language": "python",

-     "metadata": {},

-     "outputs": [

-      {

-       "output_type": "stream",

-       "stream": "stdout",

-       "text": [

-        "The centroid is at\n",

-        "x= 75.9 mm\n",

-        "y= 28.0 mm\n",

-        "z= 120.0 mm\n"

-       ]

-      }

-     ],

-     "prompt_number": 17

-    },

-    {

-     "cell_type": "heading",

-     "level": 2,

-     "metadata": {},

-     "source": [

-      "Example 10.10-17, Page no 166"

-     ]

-    },

-    {

-     "cell_type": "code",

-     "collapsed": false,

-     "input": [

-      "import math\n",

-      "\n",

-      "#Initilization of variables\n",

-      "# Here tx=30 degrees,ty=45 degrees& tz=60 degrees,, thus\n",

-      "sintx=2**-1\n",

-      "costx=sqrt(3)*2**-1\n",

-      "sinty=sqrt(2)**-1\n",

-      "costy=sqrt(2)**-1\n",

-      "sintz=sqrt(3)*2**-1\n",

-      "costz=2**-1\n",

-      "\n",

-      "#Calculations\n",

-      "V=np.array([10,15,25]) #in**3\n",

-      "x_bar=np.array([4,12,24]) #in\n",

-      "y_bar=np.array([4*costx,-6*costy,-4*costz])\n",

-      "z_bar=np.array([-4*sintx,6*sinty,-4*sintz])\n",

-      "#Centroid calculations\n",

-      "x=(V[0]*x_bar[0]+V[1]*x_bar[1]+V[2]*x_bar[2])/(V[0]+V[1]+V[2]) #in\n",

-      "y=(V[0]*y_bar[0]+V[1]*y_bar[1]+V[2]*y_bar[2])/(V[0]+V[1]+V[2]) #in\n",

-      "z=(V[0]*z_bar[0]+V[1]*z_bar[1]+V[2]*z_bar[2])/(V[0]+V[1]+V[2]) #in\n",

-      "\n",

-      "#Result\n",

-      "print'The centroid of three volumes is at'\n",

-      "print'x=',round(x,1),\"in\"\n",

-      "print'y=',round(y,2),\"in\"\n",

-      "print'z=',round(z,2),\"in\"\n",

-      "\n",

-      "# The ans for x is off by 0.4 in"

-     ],

-     "language": "python",

-     "metadata": {},

-     "outputs": [

-      {

-       "output_type": "stream",

-       "stream": "stdout",

-       "text": [

-        "The centroid of three volumes is at\n",

-        "x= 16.0 in\n",

-        "y= -1.58 in\n",

-        "z= -0.86 in\n"

-       ]

-      }

-     ],

-     "prompt_number": 22

-    },

-    {

-     "cell_type": "heading",

-     "level": 2,

-     "metadata": {},

-     "source": [

-      "Example 10.10-26, Page no 171"

-     ]

-    },

-    {

-     "cell_type": "code",

-     "collapsed": false,

-     "input": [

-      "# Part a\n",

-      "# Pefer textbook for part a.\n",

-      "\n",

-      "# Part b\n",

-      "\n",

-      "# Initilization of variables\n",

-      "w=150 #lb/ft**2\n",

-      "h=2 #ft height of the load\n",

-      "s=8 #ft span\n",

-      "b=2 #ft\n",

-      "\n",

-      "import math\n",

-      "from scipy.integrate import quad\n",

-      "def integrand(x, a, b):\n",

-      "    return x*(150*(x/4)*2)\n",

-      "a=1\n",

-      "b=1\n",

-      "M=quad(integrand, 0, s, args=(a,b))\n",

-      "Rr=M[0]/(2*s) #lb\n",

-      "\n",

-      "# Results\n",

-      "print'The value of M is',round(M[0]),\"lb-ft\"\n",

-      "print'The value of Rr is',round(Rr),\"lb\"\n",

-      "\n"

-     ],

-     "language": "python",

-     "metadata": {},

-     "outputs": [

-      {

-       "output_type": "stream",

-       "stream": "stdout",

-       "text": [

-        "The value of M is 12800.0 lb-ft\n",

-        "The value of Rr is 800.0 lb\n"

-       ]

-      }

-     ],

-     "prompt_number": 2

-    },

-    {

-     "cell_type": "heading",

-     "level": 2,

-     "metadata": {},

-     "source": [

-      "Example 10.10-27, Page no 172"

-     ]

-    },

-    {

-     "cell_type": "code",

-     "collapsed": false,

-     "input": [

-      "# Initilization of variables\n",

-      "\n",

-      "rho_m=1000 # kg/m**3\n",

-      "h=0.3 # m height of hole\n",

-      "b=0.6 # m width of hole\n",

-      "\n",

-      "import math\n",

-      "from scipy.integrate import quad\n",

-      "def integrand(y, a, b):\n",

-      "    return y*9.8*rho_m*(1.2-y)*(0.6)\n",

-      "a=1\n",

-      "b=1\n",

-      "I=quad(integrand, 0, h, args=(a,b))\n",

-      "B=I[0]/(2*(0.3))\n",

-      "\n",

-      "# Results\n",

-      "print'The value of B is',round(B),\"N\"\n"

-     ],

-     "language": "python",

-     "metadata": {},

-     "outputs": [

-      {

-       "output_type": "stream",

-       "stream": "stdout",

-       "text": [

-        "The value of B is 441.0 N\n"

-       ]

-      }

-     ],

-     "prompt_number": 5

-    },

-    {

-     "cell_type": "heading",

-     "level": 2,

-     "metadata": {},

-     "source": [

-      "Example 10.10-28, Page no 172"

-     ]

-    },

-    {

-     "cell_type": "code",

-     "collapsed": false,

-     "input": [

-      "import math\n",

-      "\n",

-      "#Initilization of variables\n",

-      "l=62.4 #lb/ft**3\n",

-      "h=12 #ft\n",

-      "f=105 #lb/ft**3\n",

-      "\n",

-      "#Calculations\n",

-      "p1=l*h #lb/ft**2\n",

-      "#Total force on left side\n",

-      "#Simplfying the equation we get a three degree equation in d\n",

-      "#solving for d\n",

-      "p=np.array([3**-1,0,-144,467])\n",

-      "r=roots(p)\n",

-      "d=r[2] #ft\n",

-      "\n",

-      "#Result\n",

-      "print'The value of d is',round(d,2),\"feet\"\n"

-     ],

-     "language": "python",

-     "metadata": {},

-     "outputs": [

-      {

-       "output_type": "stream",

-       "stream": "stdout",

-       "text": [

-        "The value of d is 3.33 feet\n"

-       ]

-      }

-     ],

-     "prompt_number": 24

-    }

-   ],

-   "metadata": {}

-  }

- ]

-}
\ No newline at end of file