From d36fc3b8f88cc3108ffff6151e376b619b9abb01 Mon Sep 17 00:00:00 2001 From: kinitrupti Date: Fri, 12 May 2017 18:40:35 +0530 Subject: Revised list of TBCs --- .../chapter10_2.ipynb | 426 --------------------- 1 file changed, 426 deletions(-) delete mode 100755 Engineering_Mechanics,_Schaum_Series_by_McLean/chapter10_2.ipynb (limited to 'Engineering_Mechanics,_Schaum_Series_by_McLean/chapter10_2.ipynb') diff --git a/Engineering_Mechanics,_Schaum_Series_by_McLean/chapter10_2.ipynb b/Engineering_Mechanics,_Schaum_Series_by_McLean/chapter10_2.ipynb deleted file mode 100755 index 3ce0f857..00000000 --- a/Engineering_Mechanics,_Schaum_Series_by_McLean/chapter10_2.ipynb +++ /dev/null @@ -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 -- cgit