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diff --git a/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter9.ipynb b/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter9.ipynb new file mode 100644 index 00000000..64ddecc8 --- /dev/null +++ b/Engineering_Mechanics_of_Solids_by_Popov_E_P/chapter9.ipynb @@ -0,0 +1,246 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:cfde82eb2eac726301e92e1b27c27d3628db6f9b0e8b5d7b0cd15017ca0006f7"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 9:Elastic stress analysis and design"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.4 pagenumber 465"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Given \n",
+ "b = 40.0 #mm - The width of the beam crossection\n",
+ "h = 300.0 #mm - The length of the beam crossection \n",
+ "V = 40.0 #KN - The shear stress in teh crossection\n",
+ "M = 10.0 #KN-m - The bending moment on K----K crossection \n",
+ "c = h/2 #mm -The position at which maximum stress occurs on the crossection\n",
+ "I = b*(h**3)/12 #mmm4 - the moment of inertia \n",
+ "#Caliculations \n",
+ "\n",
+ "stress_max_1 = M*c*(10**6)/I #The maximum stress occurs at the end\n",
+ "stress_max_2 = -M*c*(10**6)/I #The maximum stress occurs at the end\n",
+ "y = 140 #mm The point of interest, the distance of element from com\n",
+ "n = y/(c) # The ratio of the distances from nuetral axis to the elements\n",
+ "stress_L_1 = n*stress_max_1 #The normal stress on elements L--L\n",
+ "stress_L_2 = -n*stress_max_1 #The normal stress on elements L--L\n",
+ "x = 10 #mm The length of the element\n",
+ "A = b*x #mm3 The area of the element \n",
+ "y_1 = y+x/2 # the com of element from com of whole system\n",
+ "stress_xy = V*A*y_1*(10**3)/(I*b) #Mpa - The shear stress on the element \n",
+ "#stresses acting in plane 30 degrees \n",
+ "o = 60 #degrees - the plane angle\n",
+ "stress_theta = stress_L_1/2 + stress_L_1*(math.cos(math.radians(o)))/2 - stress_xy*(math.sin(math.radians(o))) #Mpa by direct application of equations\n",
+ "stress_shear = -stress_L_1*(math.sin(math.radians(o)))/2 - stress_xy*(math.cos(math.radians(o))) #Mpa Shear stress\n",
+ " \n",
+ "print \"a)The principle stresses are \",round(stress_max_1,2),\"MPa,\",round(stress_max_2,2),\"Mpa\"\n",
+ "print \"b)The stresses on inclines plane \",round(stress_theta,2),\"Mpa noraml, \",round(stress_shear,2),\"Mpa shear \""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "a)The principle stresses are 16.67 MPa, -16.67 Mpa\n",
+ "b)The stresses on inclines plane 11.11 Mpa noraml, -7.06 Mpa shear \n"
+ ]
+ }
+ ],
+ "prompt_number": 20
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.5 page number 476"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Given\n",
+ "M = 10 #KN-m moment\n",
+ "v = 8.0 #KN - shear Stress \n",
+ "stress_allow = 8 #MPa - The maximum allowable stress\n",
+ "shear_allow_per = 1.4 #Mpa - The allowable stress perpendicular to grain\n",
+ "stress_allow_shear = 0.7 #MPa - The maximum allowable shear stress\n",
+ "#Caliculations \n",
+ "\n",
+ "S = M*(10**6)/stress_allow #mm3 \n",
+ "#lets arbitarly assume h = 2b\n",
+ "#S = b*(h**2)/6\n",
+ "h = pow(12*S,0.333) #The depth of the beam\n",
+ "b = h/2 #mm The width of the beam\n",
+ "A = h*b #mm2 The area of the crossection , assumption\n",
+ "stress_shear = 3*v*(10**3)/(2*A) #Mpa The strear stress \n",
+ "if stress_shear<stress_allow_shear:\n",
+ " print \"The stress developed \",round(stress_shear,2),\" is in allowable ranges for \",round(A,2),\"mm2 area\"\n",
+ "else:\n",
+ " print \"The stress developed\",stress_shear,\" is in non allowable ranges\",A,\"area\"\n",
+ "Area_allow = v*(10**3)/shear_allow_per #mm - the allowable area\n",
+ "print \"The minimum area is \",Area_allow ,\"mm2\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The stress developed 0.4 is in allowable ranges for 30077.85 mm2 area\n",
+ "The minimum area is 5714.28571429 mm2\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "pyout",
+ "prompt_number": 36,
+ "text": [
+ "8.0"
+ ]
+ }
+ ],
+ "prompt_number": 36
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.6 page number 478"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Given\n",
+ "stress_allow = 24 #ksi - The maximum allowable stress\n",
+ "stress_allow_shear = 14.5 #ksi- The maximum allowable shear stress\n",
+ "M_max = 36 #k-ft The maximum moment\n",
+ "l = 16 #in-The length of the rod\n",
+ "w = 2 #k/ft - The force distribution on the rod\n",
+ "R_A = 6.4 #k - The reaction at A\n",
+ "R_B = 25.6 #k - the reaction at B\n",
+ "v_max = R_B-l*w #kips the maximum stress, from diagram\n",
+ "#W8x24 is used from the appendix table 3 and 4 \n",
+ "l =0.245 #in - W8x24 crossesction length\n",
+ "#Caliculations \n",
+ "\n",
+ "stress_xy = v_max/A #ksi the approximate shear stress \n",
+ "if stress_xy < stress_allow_shear:\n",
+ " print \"W8x24 gives the allowable ranges of shear stress\"\n",
+ "else:\n",
+ " print \"W8x24 doesnot gives the allowable ranges of shear stress\"\n",
+ "k = 7.0/8 #in the distance from the outer face of the flange to the webfillet\n",
+ "#at+kt should not exceed 0.75 of yeild stress\n",
+ "#a1t+2kt should not exceed 0.75 of yeild stress\n",
+ "Stress_yp = 36 #Ksi - The yeild stress\n",
+ "t = 0.245 #in thickness of the web\n",
+ "#support a \n",
+ "a = R_A/(0.75*Stress_yp*t)-k #in lengths of the bearings\n",
+ "#support b\n",
+ "a_1 = R_B/(0.75*Stress_yp*t)-2*k #in lengths of the bearings\n",
+ "print \"lengths of the bearing at A \",round(a,3),\"in\"\n",
+ "print \"lengths of the bearing at B\",round(a_1,3),\"in\"\n",
+ " \n",
+ "\n",
+ "\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "W8x24 gives the allowable ranges of shear stress\n",
+ "lengths of the bearing at A 0.092 in\n",
+ "lengths of the bearing at B 2.12 in\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "pyout",
+ "prompt_number": 44,
+ "text": [
+ "0.875"
+ ]
+ }
+ ],
+ "prompt_number": 44
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 9.8 page number 483"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#given \n",
+ "hp = 63000 #horse power\n",
+ "T = hp*20*(10**-3)/63 #k-in the torsion implies due to horse power\n",
+ "stress_allow_shear = 6 #ksi- The maximum allowable shear stress\n",
+ "M_ver = 6.72/2 #k-in the vertical component of the moment \n",
+ "M_hor = 9.10 #k-in the horizantal component of the moment \n",
+ "#Caliculations \n",
+ "\n",
+ "M = pow(((M_ver**2)+(M_hor**2)),0.5) #K-in The resultant \n",
+ "d = pow((16*(((M**2)+(T**2))**0.5)/(stress_allow_shear*3.14)),0.333) #in, The suggested diameter from derivation\n",
+ "print \"The suggested diameter is\",round(d,2),\"in\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The suggested diameter is 2.66 in\n"
+ ]
+ }
+ ],
+ "prompt_number": 49
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
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