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| author | Thomas Stephen Lee | 2015-08-28 16:53:23 +0530 |
|---|---|---|
| committer | Thomas Stephen Lee | 2015-08-28 16:53:23 +0530 |
| commit | db0855dbeb41ecb8a51dde8587d43e5d7e83620f (patch) | |
| tree | b95975d958cba9af36cb1680e3f77205354f6512 /Engineering_Mechanics_by_Tayal_A.K./appendix_8.ipynb | |
| parent | 5a86a20b9de487553d4ef88719fb0fd76a5dd6a7 (diff) | |
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diff --git a/Engineering_Mechanics_by_Tayal_A.K./appendix_8.ipynb b/Engineering_Mechanics_by_Tayal_A.K./appendix_8.ipynb new file mode 100755 index 00000000..cf97f900 --- /dev/null +++ b/Engineering_Mechanics_by_Tayal_A.K./appendix_8.ipynb @@ -0,0 +1,1002 @@ +{
+ "metadata": {
+ "name": "appendix.ipynb"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Appendix"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 26.26-1,Page No:638"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "#Initilization of variables\n",
+ "\n",
+ "P=[-5,2,14] #Point co-ordinates\n",
+ "\n",
+ "#Calculations\n",
+ "r=(P[0]**2+P[1]**2+P[2]**2)**0.5 #Magnitude of the poistion vector\n",
+ "\n",
+ "#Direction cosines\n",
+ "l=P[0]/r \n",
+ "m=P[1]/r\n",
+ "n=P[2]/r\n",
+ "\n",
+ "\n",
+ "#Unit Vector calculations\n",
+ "\n",
+ "r_unit=[l,m,n]\n",
+ "\n",
+ "#Results\n",
+ "\n",
+ "print\"The unit vector in the direction of r is \",round(r_unit[0],2),\"i +\",round(r_unit[1],3),\"j +\",round(r_unit[2],3),\"k\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The unit vector in the direction of r is -0.33 i + 0.133 j + 0.933 k\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 26.26-2,Page No:639"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilizatin of variable\n",
+ "F=10 #N\n",
+ "P_1=[2,4,3] \n",
+ "P_2=[1,-5,2]\n",
+ "\n",
+ "#Calculations\n",
+ "d_x=P_2[0]-P_1[0] \n",
+ "d_y=P_2[1]-P_1[1]\n",
+ "d_z=P_2[2]-P_1[2]\n",
+ "d=(d_x**2+d_y**2+d_z**2)**0.5\n",
+ "Fx=(F/d)*d_x #N\n",
+ "Fy=(F/d)*d_y #N\n",
+ "Fz=(F/d)*d_z #N\n",
+ "#Direction cosines\n",
+ "l=Fx/F\n",
+ "m=Fy/F\n",
+ "n=Fz/F\n",
+ "#Angles\n",
+ "theta_x=arccos(l)*(180/pi) #degrees\n",
+ "theta_y=arccos(m)*(180/pi) #degrees\n",
+ "theta_z=arccos(n)*(180/pi) #degrees\n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print\"The force in vector notation is \",round(Fx,1),\"i \",round(Fy,2),\"j \",round(Fz,1),\"k\"\n",
+ "print\"Thetax=\",round(theta_x,1),\" degrees\",\"\", \"Thetay=\",round(theta_y,2),\"degrees\",\"\", \"Thetaz=\",round(theta_z,1), \"degrees\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The force in vector notation is -1.1 i + -9.88 j + -1.1 k\n",
+ "Thetax= 96.3 degrees Thetay= 171.07 degrees Thetaz= 96.3 degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 26.26-3,Page No:640"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initiliation of variables\n",
+ "T=2500 #N\n",
+ "\n",
+ "#Co-ordinates\n",
+ "Q=[40,0,-30]\n",
+ "P=[0,80,0]\n",
+ "\n",
+ "#Calculations\n",
+ "mag_QP=sqrt((P[0]-Q[0])**2+(P[1]-Q[1])**2+(P[2]-Q[2])**2) #Magnitude\n",
+ "QP=[(P[0]-Q[0]),(P[1]-Q[1]),(P[2]-Q[2])] \n",
+ "F=(T*mag_QP**-1)*QP #N\n",
+ "thetax=arccos(F[0]/T)*(180/pi) #degrees\n",
+ "thetay=arccos(F[1]/T)*(180/pi) #degrees\n",
+ "thetaz=arccos(F[2]/T)*(180/pi) #degrees\n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print\"The force vector is \",round(F[0]),\"i +\",round(F[1]),\"j +\",round(F[2]),\"k\"\n",
+ "\n",
+ "#Answer in the textbook is printed as 1600 which is incorrect\n",
+ "print\"The angles are thetax=\",round(thetax,1),\"degrees\",\"\",\"thetay=\",round(thetay),\" degrees\",\"\",\" thetaz=\",round(thetaz,1),\" degrees\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The force vector is -40.0 i + 80.0 j + 30.0 k\n",
+ "The angles are thetax= 180.0 degrees thetay= 90.0 degrees thetaz= 90.0 degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 50
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 26.26-4,Page No:642"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initilization of variables\n",
+ "\n",
+ "A=[2,-1,1]\n",
+ "B=[1,1,2]\n",
+ "C=[3,-2,4]\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "R=[A[0]+B[0]+C[0],A[1]+B[1]+C[1],A[2]+B[2]+C[2]] #Resultant\n",
+ "R1=[R[0],R[1],R[2]]\n",
+ "mag=sqrt(R[0]**2+R[1]**2+R[2]**2)\n",
+ "\n",
+ "#Unit vector\n",
+ "U=R1/mag \n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print\"The unit vector is \",round(U[0],3),\"i\",round(U[1],3),\"j +\",round(U[2],2),\"k\"\n",
+ "#Answer for k part is incorrect in the textbook\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The unit vector is 0.636 i -0.212 j + 0.74 k\n"
+ ]
+ }
+ ],
+ "prompt_number": 47
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 26.26-5,Page No:642"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initilization of variables\n",
+ "A=[2,-6,-3]\n",
+ "B=[4,3,-1] \n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "AdotB=A[0]*B[0]+A[1]*B[1]+A[2]*B[2] \n",
+ "magA=sqrt(A[0]**2+A[1]**2+A[2]**2) \n",
+ "magB=sqrt(B[0]**2+B[1]**2+B[2]**2)\n",
+ "theta=arccos(AdotB/(magA*magB))*(180/pi) #degrees\n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print\"The product of both the vectors is \",round(AdotB)\n",
+ "print\"The angle between them is \",round(theta,1),\"degrees\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The product of both the vectors is -7.0\n",
+ "The angle between them is 101.3 degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 26.26-6,Page No:643"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initilization of variables\n",
+ "\n",
+ "A=[4,-3,1]\n",
+ "P=[2,3,-1]\n",
+ "Q=[-2,-4,3]\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "B=[Q[0]-P[0],Q[1]-P[1],Q[2]-P[2]]\n",
+ "AdotB=A[0]*B[0]+A[1]*B[1]+A[2]*B[2]\n",
+ "magB=sqrt(B[0]**2+B[1]**2+B[2]**2)\n",
+ "A_costheta=AdotB/magB\n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print\"The value of A_costheta is \",round(A_costheta)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ " The value of A_costheta is 1.0\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 26.26-7,Page No:643"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilization of variables\n",
+ "\n",
+ "F=[5,10,-15]\n",
+ "a=[1,0,3]\n",
+ "b=[3,-1,-6]\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "d=[b[0]-a[0],b[1]-a[1],b[2]-a[2]]\n",
+ "\n",
+ "Work_done=(F[0]*d[0])+(F[1]*d[1])+(F[2]*d[2])\n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print\"The work done is \",round(Work_done)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The work done is 135.0\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 26.26-8,Page No:644"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initilization of variables\n",
+ "A=[2,-6,-3]\n",
+ "B=[4,3,-1]\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "AcrossB=[(A[1]*B[2]-B[1]*A[2]),A[2]*B[0]-A[0]*B[2],A[0]*B[1]-A[1]*B[0]]\n",
+ "mag=sqrt(AcrossB[0]**2+AcrossB[1]**2+AcrossB[2]**2)\n",
+ "n=AcrossB/mag\n",
+ "magA=(A[0]**2+A[1]**2+A[2]**2)**0.5\n",
+ "magB=(B[0]**2+B[1]**2+B[2]**2)**0.5\n",
+ "theta=arcsin(mag/(magA*magB))*(180/pi)\n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print\"The cross prcoduct of the two vectors is \",AcrossB[0],\"i\",AcrossB[1],\"j\",AcrossB[2],\"k\"\n",
+ "print\"The angle between the two is \",round(theta,1),\"degrees\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The cross prcoduct of the two vectors is 15 i -10 j 30 k\n",
+ "The angle between the two is 78.7 degrees\n"
+ ]
+ }
+ ],
+ "prompt_number": 42
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 26.26-9,Page No:645"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#Initilizatin of variable\n",
+ "omega=2 # rad/second\n",
+ "A=[0,1,2] \n",
+ "B=[1,3,-2]\n",
+ "P=[3,6,4]\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "# Point co-ordinates of axis of rotation is \n",
+ "S=[1,2,-4]\n",
+ "R=sqrt(S[0]**2+S[1]**2+S[2]**2) # magnitude of position vector\n",
+ "# Unit vector calculations along axis of rotation\n",
+ "R_unit=S/R\n",
+ "w=omega*R_unit\n",
+ "# Position vector calculations\n",
+ "r=(P[0]-A[0])+(P[1]-A[1])+(P[2]-A[2])\n",
+ "v=w*r\n",
+ "# Magnitude of v \n",
+ "v_mag=sqrt(v[0]**2+v[1]**2+v[2]**2)\n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print\"The linear velocity of point P is \",round(v_mag)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The linear velocity of point P is 20.0\n"
+ ]
+ }
+ ],
+ "prompt_number": 51
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 26.26-10,Page No:647"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialization\n",
+ "\n",
+ "O=[-2,3,5]\n",
+ "F=[4,4,-1]\n",
+ "P=[1,-2,4]\n",
+ "Q=[5,2,3]\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "r1=[P[0]-O[0],P[1]-O[1],P[2]-O[2]]\n",
+ "\n",
+ "moment=[(r1[1]*F[2]-r1[2]*F[1]),(r1[2]*F[0]-r1[0]*F[2]),(r1[0]*F[1]-r1[1]*F[0])] #momentum\n",
+ "\n",
+ "r2=[Q[0]-O[0],Q[1]-O[1],Q[2]-O[2]]\n",
+ "\n",
+ "moment1=[(r2[1]*F[2]-r2[2]*F[1]),(r2[2]*F[0]-r2[0]*F[2]),(r2[0]*F[1]-r2[1]*F[0])]#momentum\n",
+ "\n",
+ "#result\n",
+ "\n",
+ "print\"The moment about point O is \",round(moment[0],3),\"i\",round(moment[1],3),\"j +\",round(moment[2],3),\"k\"\n",
+ "print\"The moment about point O is \",round(moment1[0],3),\"i\",round(moment1[1],3),\"j +\",round(moment1[2],3),\"k\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The moment about point O is 9.0 i -1.0 j + 32.0 k\n",
+ "The moment about point O is 9.0 i -1.0 j + 32.0 k\n"
+ ]
+ }
+ ],
+ "prompt_number": 62
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 26.26-11,Page No:647"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialization\n",
+ "\n",
+ "F=[3,2,-4]\n",
+ "P=[1,-1,2]\n",
+ "O=[2,-1,3]\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "r=[P[0]-O[0],P[1]-O[1],P[2]-O[2]]\n",
+ "\n",
+ "M=[(r[1]*F[2]-r[2]*F[1]),(r[2]*F[0]-r[0]*F[2]),(r[0]*F[1]-r[1]*F[0])]\n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print\"The moment of force about point O is \",round(M[0]),\"i\",round(M[1]),\"j +\",round(M[2]),\"k\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The moment of force about point O is 2.0 i -7.0 j + -2.0 k\n"
+ ]
+ }
+ ],
+ "prompt_number": 64
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 26.26-12,Page No:648"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initiaization\n",
+ "\n",
+ "A=[4,-1,7]\n",
+ "O=[1,-3,2]\n",
+ "V=[9,6,-2]\n",
+ "\n",
+ "#Clalculation\n",
+ "\n",
+ "mag_v=sqrt(V[0]**2+V[1]**2+V[2]**2)\n",
+ "\n",
+ "F=[(22/mag_v)*V[0],(22/mag_v)*V[1],(22/mag_v)*V[2]]\n",
+ "\n",
+ "r=[A[0]-O[0],A[1]-O[1],A[2]-O[2]]\n",
+ "\n",
+ "M=[r[1]*F[2]-F[1]*r[2],r[0]*F[2]-r[2]*F[0],r[0]*F[1]-r[1]*F[0]]\n",
+ "\n",
+ "#result\n",
+ "\n",
+ "print\"\",round(M[0]),\"i\",\"+\",round(M[1]),\"j\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ " -68.0 i + -102.0 j\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 26.26-13,Page No:648"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialization\n",
+ "\n",
+ "F=[50,-80,30]\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#unit vector in u direction\n",
+ "u=[cos(30*(pi/180)),cos(60*(pi/180)),cos(90*(pi/180))]\n",
+ "#unit vector in v direction\n",
+ "v=[1*cos(120*(pi/180)),1*cos(30*(pi/180)),1*cos(90*(pi/180))]\n",
+ "#unit vector in w direction\n",
+ "w=[1*cos(90*(pi/180)),1*cos(90*(pi/180)),1*cos(0*(pi/180))]\n",
+ "\n",
+ "#component of force F\n",
+ "\n",
+ "U=F[0]*u[0]+F[1]*u[1]+F[2]*u[2] #component force along u\n",
+ "V=F[0]*v[0]+F[1]*v[1]+F[2]*v[2] #component force along v\n",
+ "W=F[0]*w[0]+F[1]*w[1]+F[2]*w[2] #component force along w\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print\"the component force along u is \",round(U,1)\n",
+ "print\"the component force along v is \",round(V,2)\n",
+ "print\"the component force along w is \",round(W,1)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "the component force along u is 3.3\n",
+ "the component force along v is -94.28\n",
+ "the component force along w is 30.0\n"
+ ]
+ }
+ ],
+ "prompt_number": 90
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 26.26-14,Page No:649"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialization\n",
+ "\n",
+ "\n",
+ "F_v=100 #N\n",
+ "A=[0,0,0]\n",
+ "B=[0.5,0,0]\n",
+ "C=[0.5,0,1]\n",
+ "D=[0,0,1]\n",
+ "E=[0,0.5,0]\n",
+ "F=[0.5,0.5,0]\n",
+ "G=[0.5,0.5,1]\n",
+ "H=[0,0.5,1]\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "F_vec=F_v/sqrt((F[0]-C[0])**2+(F[1]-C[1])**2+(F[2]-C[2])**2)\n",
+ "F_x=(F[0]-C[0])*F_vec\n",
+ "F_y=(F[1]-C[1])*F_vec\n",
+ "F_z=(F[2]-C[2])*F_vec\n",
+ "\n",
+ "F=[F_x,F_y,F_z]\n",
+ "\n",
+ "#moment about point E\n",
+ "\n",
+ "#taking position vector r directed from E on force F\n",
+ "r_ec=[C[0]-E[0],C[1]-E[1],C[2]-E[2]]\n",
+ "\n",
+ "#M_e=r_ec*F\n",
+ "\n",
+ "M_e=[(r_ec[1]*F[2]-r_ec[2]*F[1]),(r_ec[0]*F[2]-r_ec[2]*F[0]),(r_ec[0]*F[1]-r_ec[1]*F[0])]\n",
+ "\n",
+ "#unit vector in direction AE is n_ae\n",
+ "\n",
+ "n_ae=[0,1,0]\n",
+ "\n",
+ "#moment about axis AE\n",
+ "#M_ae=M_e*n_ae\n",
+ "\n",
+ "M_ae=[M_e[0]*n_ae[0],M_e[1]*n_ae[1],M_e[2]*n_ae[2]] \n",
+ "\n",
+ "#result\n",
+ "\n",
+ "print\"moment of force about E is \",round(M_e[0]),\"i\",round(M_e[1]),\"j +\",round(M_e[2]),\"k\" #answer given in book is wrong \n",
+ "print\"moment of force about axis AE is \",round(M_ae[0]),\"i\",round(M_ae[1]),\"j +\",round(M_ae[2]),\"k\" #answer given in book is wrong "
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "moment of force about E is 0.0 i -45.0 j + 22.0 k\n",
+ "moment of force about axis AE is 0.0 i -45.0 j + 0.0 k\n"
+ ]
+ }
+ ],
+ "prompt_number": 103
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 26.26-15,Page No:652"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialization\n",
+ "F_1=5 #kN\n",
+ "F_2=7.5 #kN\n",
+ "F_3=10 #kN\n",
+ "A=[0,0,0]\n",
+ "E=[0,1,0]\n",
+ "D=[0,0,2]\n",
+ "F=[3,1,0]\n",
+ "G=[3,1,2]\n",
+ "H=[0,1,2]\n",
+ "#calculation\n",
+ "\n",
+ "F1=[F_1*3**-1*(F[0]-E[0]),F_1/3*(F[1]-E[1]),F_1/3*(F[2]-E[2])] #5/sqrt(9)=5/3\n",
+ "F2=[F_2*(H[0]),F_2*-H[1],F_2*0] #force is only acting in the y direction\n",
+ "F3=[F_3/3.6*(G[0]-E[0]),F_3/3.6*(G[1]-E[1]),F_3/3.6*(G[2]-E[2])] #10/sqrt(13)=10/3.6\n",
+ "\n",
+ "#resultant force R\n",
+ "\n",
+ "#R=F1+F2+F3\n",
+ "R=[F1[0]+F2[0]+F3[0],F1[1]+F2[1]+F3[1],F1[2]+F2[2]+F3[2]]\n",
+ "\n",
+ "#resultant force along axis AE\n",
+ "\n",
+ "r_ae=[E[0]-A[0],E[1]-A[1],E[2]-A[2]]\n",
+ "\n",
+ "r_ad=[D[0]-A[0],D[1]-A[1],D[2]-A[2]]\n",
+ "\n",
+ "#moments of force about A\n",
+ "\n",
+ "#M_ra=r_ae*F1+r_ae*F2+r_ae*F3\n",
+ "\n",
+ "M_ra1=[(r_ae[1]*F1[2]-r_ae[2]*F1[1]),(r_ae[0]*F1[2]-r_ae[2]*F1[0]),(r_ae[0]*F1[1]-r_ae[1]*F1[0])] #r_ae*F1\n",
+ "M_ra2=[(r_ad[1]*F2[2]-r_ad[2]*F2[1]),(r_ad[0]*F2[2]-r_ad[2]*F2[0]),(r_ad[0]*F2[1]-r_ad[1]*F2[0])] #r_ae*F2\n",
+ "M_ra3=[(r_ae[1]*F3[2]-r_ae[2]*F3[1]),(r_ae[0]*F3[2]-r_ae[2]*F3[0]),(r_ae[0]*F3[1]-r_ae[1]*F3[0])] #r_ae*F3\n",
+ "\n",
+ "M_ra=[M_ra1[0]+M_ra2[0]+M_ra3[0],M_ra1[1]+M_ra2[1]+M_ra3[1],M_ra1[2]+M_ra2[2]+M_ra3[2]]\n",
+ "\n",
+ "#Results\n",
+ "\n",
+ "print\"resultant force R\",round(R[0],2),\"i\",round(R[1],2),\"j +\",round(R[2],2),\"k\"\n",
+ "print\"moments of all forces about A\",round(M_ra[0],3),\"i +\",round(M_ra[1]),\"j\",round(M_ra[2],3),\"k\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "resultant force R 13.33 i -7.5 j + 5.56 k\n",
+ "moments of all forces about A 20.556 i + 0.0 j -13.333 k\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 26.26-16,Page No:654"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialization\n",
+ "\n",
+ "F=20 #kN\n",
+ "M_x=76 #kNm\n",
+ "M_y=82 #kNm\n",
+ "\n",
+ "#Calculation\n",
+ "\n",
+ "#Force shifted to P by distance x\n",
+ "x=M_x*F**-1\n",
+ "\n",
+ "#Force shifted to P by distance z\n",
+ "z=M_y*F**-1\n",
+ "\n",
+ "#result\n",
+ "\n",
+ "print\"the force shifted to P by distance x\",round(x,2),\"m\"\n",
+ "print\"the force shited to P by distance y\",round(z,2),\"m\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "the force shifted to P by distance x 3.8 m\n",
+ "the force shited to P by distance y 4.1 m\n"
+ ]
+ }
+ ],
+ "prompt_number": 109
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 26.26-17,Page No:655"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "#initialization\n",
+ "\n",
+ "A=[0,4.5,0]\n",
+ "B=[2.8,0,0]\n",
+ "C=[0,0,-2.4]\n",
+ "D=[-2.6,0,1.8]\n",
+ "\n",
+ "#calculations\n",
+ "\n",
+ "#tension in cable AB\n",
+ "x=(B[0]**2+A[1]**2)**0.5\n",
+ "T_ab=[(B[0]-A[0])/x,(B[1]-A[1])/x,(B[2]-A[2])/x]\n",
+ "\n",
+ "#tension in cable AC\n",
+ "y=(C[2]**2+A[1]**2)**0.5\n",
+ "T_ac=[(C[0]-A[0])/y,(C[1]-A[1])/y,(C[2]-A[2])/y]\n",
+ "\n",
+ "#tension in cable AD\n",
+ "z=(D[0]**2+D[2]**2+A[1]**2)**0.5\n",
+ "T_ad=[[(D[0]-A[0])/z,(D[1]-A[1])/z,(D[2]-A[2])/z]]\n",
+ "\n",
+ "#weight acting vertically downwards \n",
+ "W=[0*5000,1*5000,0*5000]\n",
+ "\n",
+ "#Solving using equations of equlibrium\n",
+ "import math\n",
+ "import numpy as np\n",
+ "A=np.array([[0.528,-0.473,0],[0,-0.327,0.47],[0.85,0.818,0.88]])\n",
+ "B=np.array([0,0,5000])\n",
+ "C=np.linalg.solve(A,B)\n",
+ "\n",
+ "#result\n",
+ "print \"T_AB =\",round(C[0],1),\"N\",\"T_AD =\",round(C[1]),\"N\",\"T_AC\",round(C[2],1),\"N\" \n",
+ "#answer varies due to decimal accuracy in python\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "T_AB = 2043.7 N T_AD = 2281.0 N T_AC 1587.2 N\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 26.26-18,Page No:656"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "\n",
+ "# Initilization of variables\n",
+ "P=5 # kN\n",
+ "Q=3 # kN\n",
+ "C=5 # kNm # couple\n",
+ "# ref fig.20 # Notations have been assumed\n",
+ "z1=1.5 # m\n",
+ "z2=0.625 # m\n",
+ "z3=0.5 # m\n",
+ "x1=3.5 # m\n",
+ "x2=0.625 # m\n",
+ "# Calculations\n",
+ "# sum M_x=0\n",
+ "R_A=((P*z2)+(Q*z3)+C)*z1**-1 # kN\n",
+ "# M_z=0\n",
+ "R_C=((Q*x1)+(P*x2))*x1**-1 # kN\n",
+ "# sum F_y=0\n",
+ "R_B=P+Q-R_A-R_C # kN\n",
+ "# Results\n",
+ "\n",
+ "print\"The reactions are: \",round(R_A,3),\"kN\",round(R_C,3),\"kN\",round(R_B,2),\"kN\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The reactions are: 6.417 kN 3.893 kN -2.31 kN\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 26.26-19,Page No:657"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "import numpy as np\n",
+ "\n",
+ "# Initilization of variables\n",
+ "F=2 # kN\n",
+ "W=1 # kN\n",
+ "# Co-ordinates as matrices\n",
+ "A=[0,0,0]\n",
+ "C=[0,0,1.2]\n",
+ "B=[0,0,2.5]\n",
+ "D=[-1,1,0]\n",
+ "E=[1,1,0]\n",
+ "F=[0,0,1]\n",
+ "G=[0,0,2]\n",
+ "# Force vector\n",
+ "f=[0,-2,0]\n",
+ "# Weight vector\n",
+ "w=[0,-1,0]\n",
+ "# Calculations\n",
+ "# we have 5 unknowns: A_x,A_y,A_z,T_FE & T_GD\n",
+ "# we define and solve eqn's 1,2,3,4&5 using matrix as,\n",
+ "P=np.array([[1,0,0,0.58,-0.41],[0,1,0,0.58,0.41],[0,0,1,-0.58,-0.82],[0,0,0,0.58,0.82],[0,0,0,0.58,-0.82]])\n",
+ "Q=np.array([0,3,0,6.25,0])\n",
+ "X=np.linalg.solve(P,Q)\n",
+ "\n",
+ "\n",
+ "# Results\n",
+ "\n",
+ "print\"The components of reaction at A are: A_x=\",round(X[0],2),\" kN \",\" A_y=\",round(X[1],2),\" kN \",\"and A_z=\",round(X[2],2),\" kN\"\n",
+ "print\"The tensions in the cable are: T_FE=\",round(X[3],2),\" kN \",\"and T_GD=\",round(X[4],1), \"kN \"\n",
+ "# The solution in the textbook is incorrect and yeilds singularity in matrix calculation.\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The components of reaction at A are: A_x= -1.56 kN A_y= -1.69 kN and A_z= 6.25 kN\n",
+ "The tensions in the cable are: T_FE= 5.39 kN and T_GD= 3.8 kN \n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
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