diff options
| author | hardythe1 | 2015-06-11 17:31:11 +0530 |
|---|---|---|
| committer | hardythe1 | 2015-06-11 17:31:11 +0530 |
| commit | 251a07c4cbed1a5a960f5ed416ce6ac13c8152b7 (patch) | |
| tree | cb7f084fad6d7ee6ae89e586fad0e909b5408319 /Solid_Mechanics_by_S._M._A._Kazimi/Chapter2.ipynb | |
| parent | 47d7279a724246ef7aa0f5359cf417992ed04449 (diff) | |
| download | Python-Textbook-Companions-251a07c4cbed1a5a960f5ed416ce6ac13c8152b7.tar.gz Python-Textbook-Companions-251a07c4cbed1a5a960f5ed416ce6ac13c8152b7.tar.bz2 Python-Textbook-Companions-251a07c4cbed1a5a960f5ed416ce6ac13c8152b7.zip | |
add books
Diffstat (limited to 'Solid_Mechanics_by_S._M._A._Kazimi/Chapter2.ipynb')
| -rwxr-xr-x | Solid_Mechanics_by_S._M._A._Kazimi/Chapter2.ipynb | 389 |
1 files changed, 389 insertions, 0 deletions
diff --git a/Solid_Mechanics_by_S._M._A._Kazimi/Chapter2.ipynb b/Solid_Mechanics_by_S._M._A._Kazimi/Chapter2.ipynb new file mode 100755 index 00000000..656a8597 --- /dev/null +++ b/Solid_Mechanics_by_S._M._A._Kazimi/Chapter2.ipynb @@ -0,0 +1,389 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:7ce3350f5dcc3b0641adb55040e49ecdbd34a727a892086466c616c0ec4732d8"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter2-Analysis of Stress(Equlibrium) "
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex4-pg54"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#find the new stress tensor tau\n",
+ "import numpy\n",
+ "from numpy import linalg\n",
+ "## initialization of variables\n",
+ "\n",
+ "tau=([[200, 100, 0],\n",
+ " [100, 0, 0],\n",
+ " [0 ,0, 500]]) ## some units\n",
+ "theta=60. ## degrees\n",
+ "##calculations\n",
+ "theta1=theta/57.3\n",
+ "a=([[math.cos(theta1), math.sin(theta1), 0],\n",
+ " [-math.sin(theta1), math.cos(theta1), 0],\n",
+ " [0, 0, 1]])\n",
+ "b=numpy.transpose(a)\n",
+ "tau_new=numpy.dot(a,tau)\n",
+ "tau_new1=numpy.dot(tau_new,b)\n",
+ "## Results\n",
+ "print('The new stress tensor is')\n",
+ "print tau_new1"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The new stress tensor is\n",
+ "[[ 136.62361289 -136.59689227 0. ]\n",
+ " [-136.59689227 63.37638711 0. ]\n",
+ " [ 0. 0. 500. ]]"
+ ]
+ },
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex5-pg61"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "find the octahedral at this point\n",
+ "## initialization of variables\n",
+ "import math\n",
+ "sigma_1=100. ##kg*f/cm^2\n",
+ "sigma_2=100. ##kg*f/cm^2\n",
+ "sigma_3=-200. ##kg*f/cm^2\n",
+ "## calculations\n",
+ "tau_oct=1/3.*math.sqrt((sigma_1-sigma_2)**2+(sigma_2-sigma_3)**2+(sigma_3-sigma_1)**2)\n",
+ "## Results\n",
+ "print'%s %.2f %s '%('Octahedra shear stress at the point is=',tau_oct,' kgf/cm^2')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Octahedra shear stress at the point is= 141.42 kgf/cm^2 \n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex7-pg61"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "#check whether the invariants of stress sensor\n",
+ "import numpy\n",
+ "from numpy import linalg\n",
+ "## initialization of variable\n",
+ "tau=numpy.matrix([[200, 100, 0],\n",
+ " [100, 0, 0],\n",
+ " [0, 0, 500]]) ## some units\n",
+ "theta=60. ## degrees\n",
+ "##calculations\n",
+ "theta=theta*math.pi/180.\n",
+ "a=numpy.matrix([[math.cos(theta), math.sin(theta), 0],\n",
+ " [-math.sin(theta), math.cos(theta), 0],\n",
+ " [0, 0, 1]])\n",
+ "b=numpy.transpose(a)\n",
+ "tau_new=numpy.dot(a,tau)\n",
+ "tau_new1=numpy.dot(tau_new,b)\n",
+ "\n",
+ "## stress invariants :old \n",
+ "I1=tau[0,0]+tau[1,1]+tau[2,2]\n",
+ "I2=tau[0,0]*tau[1,1]+tau[1,1]*tau[2,2]+tau[2,2]*tau[0,0]-(tau[0,1]**2+tau[1,2]**2+tau[2,0]**2)\n",
+ "I3=tau[0,0]*tau[1,1]*tau[2,2]+2*tau[0,1]*tau[1,2]*tau[2,0]-(tau[0,0]*tau[1,2]**2+tau[1,1]*tau[2,0]**2+tau[2,2]*tau[0,1]**2)\n",
+ "\n",
+ "## stress invariants :new\n",
+ "I11=tau_new1[0,0]+tau_new1[0,0]+tau_new1[1,1]\n",
+ "I22=tau_new1[0,0]*tau_new1[1,1]+tau_new1[1,1]*tau_new1[2,2]+tau_new1[1,1]*tau_new1[0,0]-[tau_new1[0,1]**2+tau_new1[1,2]**2+tau_new1[1,0]**2]\n",
+ "I33=tau_new1[0,0]*tau_new1[1,1]*tau_new1[2,2]+2*tau_new1[0,1]*tau_new1[1,2]*tau_new1[2,0]-[tau_new1[0,0]*tau_new1[1,2]**2+tau_new1[1,1]*tau_new1[2,0]**2+tau_new1[2,2]*tau_new1[0,1]**2]\n",
+ "\n",
+ "## Results\n",
+ "print'%s %.2f %s %.2f %s %.2f %s %.2f %s %.2f %s %.2f' %('The invariants of old stress tensor are I1=',I1,' I2=',I2,' I3=',I3,' \\n and that of the new stress tensor are I1=',I11,' I2=',I22,' I3=',I33)\n",
+ "\n",
+ "print('\\n Hence the same stress tensor invariants')\n",
+ "\n",
+ "\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The invariants of old stress tensor are I1= 700.00 I2= 90000.00 I3= -5000000.00 \n",
+ " and that of the new stress tensor are I1= 336.60 I2= 11698.73 I3= -5000000.00\n",
+ "\n",
+ " Hence the same stress tensor invariants\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex8-pg67"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "## initialization of variables\n",
+ "#find the value of sigma 1 and sigma2 at biaxial yeilding and unaxial\n",
+ "sigma_3=0. ## kgf/cm**2\n",
+ "tau_oct=1500. ## kgf/cm**2\n",
+ "n=2 ## given that sigma_1=n*sigma_2\n",
+ "## calculations\n",
+ "sigma_2=1500.*3./(math.sqrt(2*n**2-2*n+2)) ## ## kgf/cm**2\n",
+ "sigma_1=n*sigma_2 ## kgf/cm**2 \n",
+ "sigma_0=4500./math.sqrt(2.) ## kgf/cm**2\n",
+ "## Results\n",
+ "print'%s %.2f %s %.2f %s %.2f %s '%('The necessary stresses sigma_1, sigma_2 for biaxial yielding are \\n ',sigma_2,' kgf/cm^2' '',sigma_1,' kgf/cm^2' and 'for uniaxial yielding sigma_0 ',sigma_0,'kgf/cm^2.')\n",
+ " \n",
+ "\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The necessary stresses sigma_1, sigma_2 for biaxial yielding are \n",
+ " 1837.12 kgf/cm^2 3674.23 for uniaxial yielding sigma_0 3181.98 kgf/cm^2. \n"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex9-pg68"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "##initialization of variables\n",
+ "#find the magnitude and direction of principal stress for the a b c\n",
+ "## part (a)\n",
+ "tau_xx=300 ## kgf/cm**2\n",
+ "tau_yy=0 ## kgf/cm**2\n",
+ "tau_xy=600 ## kgf/cm**2\n",
+ "##calculations\n",
+ "sigma_1=(tau_xx+tau_yy)/2.+math.sqrt((1./2.*(tau_xx-tau_yy))**2+tau_xy**2)\n",
+ "sigma_2=(tau_xx+tau_yy)/2-math.sqrt((1/2.*(tau_xx-tau_yy))**2+tau_xy**2)\n",
+ "Beta=math.atan(2*tau_xy/(tau_xx-tau_yy))\n",
+ "Beta=Beta*180/math.pi\n",
+ "##Results\n",
+ "print'%s %.2f%s %.2f %s %.2f %s'%('\\n Part (a) \\n The magnitude of principal stresses are',sigma_1,''and '',sigma_2,'kgf/cm^2' and' \\n the direction is given by 2*beta=',Beta,'')\n",
+ "\n",
+ "\n",
+ "##part (b)\n",
+ "tau_xx=1000 ## kgf/cm**2\n",
+ "tau_yy=150 ## kgf/cm**2\n",
+ "tau_xy=450 ## kgf/cm**2\n",
+ "## calculations\n",
+ "sigma_1=(tau_xx+tau_yy)/2+math.sqrt((1/2*(tau_xx-tau_yy))**2+tau_xy**2)\n",
+ "sigma_2=(tau_xx+tau_yy)/2-math.sqrt((1/2*(tau_xx-tau_yy))**2+tau_xy**2)\n",
+ "Beta=math.atan(2*tau_xy/(tau_xx-tau_yy))\n",
+ "Beta1=Beta*180./math.pi\n",
+ "## Results\n",
+ "print'%s %.2f %s %.2f %s %.2f %s '%('\\n Part (b) \\n The magnitude of principal stresses are',sigma_1,''and '',sigma_2,'kgf/cm^2' and' \\n the direction is given by 2*beta=',Beta1,'')\n",
+ "\n",
+ "## part (c)\n",
+ "tau_xx=-850 ## kgf/cm**2\n",
+ "tau_yy=350 ## kgf/cm**2\n",
+ "tau_xy=700 ## kgf/cm**2\n",
+ "## calculations\n",
+ "sigma_1=(tau_xx+tau_yy)/2+math.sqrt((1/2*(tau_xx-tau_yy))**2+tau_xy**2)\n",
+ "sigma_2=(tau_xx+tau_yy)/2-math.sqrt((1/2*(tau_xx-tau_yy))**2+tau_xy**2)\n",
+ "Beta=math.atan(2*tau_xy/(tau_xx-tau_yy))\n",
+ "Beta=Beta*57.3\n",
+ "## Results\n",
+ "print'%s %.2f %s %.2f %s %.2f %s '%('\\n Part (c) \\n The magnitude of principal stresses are',sigma_1,''and '',sigma_2,'kgf/cm^2' and' \\n the direction is given by 2*beta=',-Beta,'')\n",
+ " \n",
+ "\n",
+ "## wrong answers were given in textbook for part (b) (c)\n",
+ "\n",
+ "\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "\n",
+ " Part (a) \n",
+ " The magnitude of principal stresses are 768.47 -468.47 \n",
+ " the direction is given by 2*beta= 75.96 \n",
+ "\n",
+ " Part (b) \n",
+ " The magnitude of principal stresses are 1025.00 125.00 \n",
+ " the direction is given by 2*beta= 45.00 \n",
+ "\n",
+ " Part (c) \n",
+ " The magnitude of principal stresses are 450.00 -950.00 \n",
+ " the direction is given by 2*beta= 63.44 \n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex10-pg70"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "# initialization of variables\n",
+ "#find the intensity of diagonal tension\n",
+ "tau_xx= -1 # kgf/cm^2\n",
+ "tau_yy= 0 # kgf/cm^2\n",
+ "tau_xy= 7 # kgf/cm^2\n",
+ "# calculations \n",
+ "sigma_1=(tau_xx+tau_yy)/2.+math.sqrt((1/2.*(tau_xx-tau_yy))**2+tau_xy**2)\n",
+ "sigma_2=(tau_xx+tau_yy)/2.-math.sqrt((1/2.*(tau_xx-tau_yy))**2+tau_xy**2)\n",
+ "x=sigma_1 # positive one is tension\n",
+ "if(sigma_2>sigma_1):\n",
+ " x=sigma_2\n",
+ "\n",
+ "# Results\n",
+ "print'%s %.2f %s'%('The diagonal tension is ',x,' kgf/cm^2')\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The diagonal tension is 6.52 kgf/cm^2\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Ex11-pg70"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "import math\n",
+ "# initialization of variables\n",
+ "#find the state of stress at the joint\n",
+ "d=2 # m\n",
+ "l=10 # m\n",
+ "t=1 # cm\n",
+ "p=15 # kgf/cm^2\n",
+ "pitch= 2*math.pi #m\n",
+ "##calculations\n",
+ "w=2*math.pi*d/2. # m\n",
+ "theta=math.atan(w/(2*math.pi))\n",
+ "sigma_z=p*d*100./(4.*t)\n",
+ "sigma_th=p*d*100./(2.*t)\n",
+ "sigma_th_new=(sigma_th+sigma_z)/2.+(sigma_th-sigma_z)/2.*math.cos(2*theta)\n",
+ "tau_thz=(sigma_z-sigma_th)*math.sin(2.*theta)/2\n",
+ "# results\n",
+ "print'%s %.2f %s %.2f %s '%('At the junction, the normal and shear stresses are',sigma_th_new,'' and '',-tau_thz,' kgf/cm^2 \\n respectively, and the rivets must be designed for this')"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "At the junction, the normal and shear stresses are 1125.00 375.00 kgf/cm^2 \n",
+ " respectively, and the rivets must be designed for this \n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |