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{
"metadata": {
"name": "",
"signature": "sha256:1983ff28cbb6fa2f27736543d13290cc4b84b616fb5e9a5a775ca4d190cec891"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter2-Principal planes and principal stress"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex1-pg37"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#calculate Normal stress intensity and Tangential stress intensity and Resultant stress intensity and angle\n",
"p_1 = 5.;##principal stress in tons/in^2\n",
"p_2 = 5./2.;##principal stress in tons/in^2\n",
"theta = 50*math.pi/180;##angle in degrees\n",
"p_n = p_1*math.cos(theta)**2+p_2*math.sin(theta)**2;##normal stress intensity\n",
"p_t = (p_1-p_2)*math.sin(theta)*math.cos(theta);##tangential stress intensity\n",
"p = math.sqrt((p_1*math.cos(theta))**2+(p_2*math.sin(theta))**2);##resultant intensity of stress\n",
"alpha = math.atan((p_2*math.sin(theta))/(p_1*math.cos(theta)));##in radians\n",
"alpha = alpha*180/math.pi;##in degrees\n",
"print'%s %.2f %s'%('Normal stress intensity p_n = ',p_n,' tons/in^2');\n",
"print'%s %.2f %s'%('h Tangential stress intensity p_t = ',p_t,' tons/in^2');\n",
"print'%s %.2f %s'%(' Resultant stress intensity p = ',p,'tons/in^2');\n",
"print'%s %.2f %s'%(' angle alpha p_n = ',alpha,' degrees');\n",
"\n",
"##there is an error in the answer given in text book\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Normal stress intensity p_n = 3.53 tons/in^2\n",
"h Tangential stress intensity p_t = 1.23 tons/in^2\n",
" Resultant stress intensity p = 3.74 tons/in^2\n",
" angle alpha p_n = 30.79 degrees\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex3-pg47"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#calculate The inclination of principal planes to the axis of the bolt and p_2 and Maximum shear stress is p_max and stress which acting alone will produce the same maximum strain \n",
"d = 3./4. ;##inches\n",
"P = 2.;##tons\n",
"Q = 0.5;##tons\n",
"m = 4.;\n",
"A = 0.25*math.pi*d**2;##in^2\n",
"p = P/A ;##tons/in^2\n",
"q = Q/A;##tons/in^2\n",
"theta = 0.5*math.atan(2.*q/p);##radians\n",
"theta1 = theta*180/math.pi;##degrees\n",
"theta2 = theta1+90;##degrees\n",
"print'%s %.2f %s'%('The inclination of principal planes to the axis of the bolt will be',theta1,'degres') \n",
"print'%s %.2f %s'%('The inclination of principal planes to the axis of the bolt will be',180-theta2,'degrees') \n",
"print'%s %.2f %s'%('The inclination of maximum shear planes to the axis of the bolt will be',theta1+45,'degress')\n",
"print'%s %.2f %s'%('The inclination of principal planes to the axis of the bolt will be',180-theta2-45,'degrees')\n",
"\n",
"p_1 = 0.5*p+math.sqrt(0.25*p**2+q**2);##tons/in^2\n",
"p_2 = 0.5*p-math.sqrt(0.25*p**2+q**2);##tons/in^2\n",
"p_max = 0.5*(p_1-p_2);##tons/in^2\n",
"p_s = p_1-(p_2/m);##tons/in^2 \n",
"print'%s %.2f %s'%('The principal stresse are given by p_1 =',p_1,'tons/in^2.,tensile')\n",
"print'%s %.2f %s'%('p_2 =',p_2,'tons/in^2.,compressive')\n",
"print'%s %.2f %s'%('p_2 =',p_2,'tons/in^2 .,compressive');\n",
"print'%s %.2f %s'%('Maximum shear stress is p_max =',p_max,'tons/in^2');\n",
"print'%s %.2f %s'%('The stress which acting alone will produce the same maximum strain is given by,',p_s,'tons/in^2');\n",
"\n",
"##there is an error in the answer given in text book"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The inclination of principal planes to the axis of the bolt will be 13.28 degres\n",
"The inclination of principal planes to the axis of the bolt will be 76.72 degrees\n",
"The inclination of maximum shear planes to the axis of the bolt will be 58.28 degress\n",
"The inclination of principal planes to the axis of the bolt will be 31.72 degrees\n",
"The principal stresse are given by p_1 = 4.79 tons/in^2.,tensile\n",
"p_2 = -0.27 tons/in^2.,compressive\n",
"p_2 = -0.27 tons/in^2 .,compressive\n",
"Maximum shear stress is p_max = 2.53 tons/in^2\n",
"The stress which acting alone will produce the same maximum strain is given by, 4.86 tons/in^2\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex4-pg51"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#calculate The principal stresses and The maximum shear stress and the planes offering it being inclined and the normal stress intensity \n",
"q = 2.;##tons/in^2\n",
"p = 5.;##tons/in^2\n",
"p_dash = 2.;##tons/in^2\n",
"theta = 0.5*math.atan(2*q/(p-p_dash));##radians\n",
"theta1 = theta*180/math.pi;##degrees\n",
"theta2 = theta1+90;##degrees\n",
"p_1 = 0.5*(p+p_dash)+math.sqrt(q**2 + 0.25*(p-p_dash)**2);##tons/in^2\n",
"p_2 = 0.5*(p+p_dash)-math.sqrt(q**2 + 0.25*(p-p_dash)**2);##tons/in^2\n",
"q_max = 0.5*(p_1-p_2);##tons/in^2\n",
"print'%s %.2f %s'%('The principal stresses are p_1 =',p_1,'tons/in^2 .,tensile')\n",
"print'%s %.2f %s'%('The principal stresses arep_2 =',p_2,'tons/in^2., tensile');\n",
"print'%s %.1f %s'%('The maximum shear stress is',q_max,'tons/in^2.,') \n",
"print'%s %.2f %s'%('the planes offering it being inclined at',theta1+45,'degrees') \n",
"print'%s %.2f %s'%('the planes offering it being inclined at',theta2+45,'degrees')\n",
"print'%s %.2f %s'%('to the plane having the normal stress intensity of',p,'tons/in^2.')\n",
"##there is an error in the answer given in text book\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The principal stresses are p_1 = 6.00 tons/in^2 .,tensile\n",
"The principal stresses arep_2 = 1.00 tons/in^2., tensile\n",
"The maximum shear stress is 2.5 tons/in^2.,\n",
"the planes offering it being inclined at 71.57 degrees\n",
"the planes offering it being inclined at 161.57 degrees\n",
"to the plane having the normal stress intensity of 5.00 tons/in^2.\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex5-pg51"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#calculate theta1 and theta2 and P_1 and P_2 and maximum shear intensity\n",
"p_res = 6.;##tons/in^2\n",
"p_dash = 4.;##tons/in^2\n",
"theta = 30.*math.pi/180.;##degrees\n",
"p_n = 4.;##tons/in^2\n",
"p = p_res*math.cos(theta);##tons/in^2\n",
"q = p_res*math.sin(theta);##tons/in^2\n",
"L = 2*q/(p-p_dash);\n",
"theta = 0.5*math.atan(2*q/(p-p_dash));\n",
"theta1 = theta*180/math.pi;##degrees\n",
"theta2 = theta1+90;##degrees\n",
"p_1 = 0.5*(p+p_dash)+math.sqrt(q**2 + 0.25*(p-p_dash)**2);##tons/in^2\n",
"p_2 = 0.5*(p+p_dash)-math.sqrt(q**2 + 0.25*(p-p_dash)**2);##tons/in^2\n",
"p_max = 0.5*(p_1-p_2);##tons/in^2\n",
"print'%s %.2f %s'%('Theta1 =',theta1,'degrees') \n",
"print'%s %.2f %s'%('Theta2 =',theta2,'degrees')\n",
"print'%s %.2f %s'%('p_1 =',p_1,'tons/in^2.,tensile')\n",
"print'%s %.2f %s'%('p_2 =',p_2,'tons/in^2.,tensile')\n",
"print'%s %.2f %s'%('The maximum shear intensity will be',p_max,'tons/in^2 across the planes of maximum shear.');\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Theta1 = 39.36 degrees\n",
"Theta2 = 129.36 degrees\n",
"p_1 = 7.66 tons/in^2.,tensile\n",
"p_2 = 1.54 tons/in^2.,tensile\n",
"The maximum shear intensity will be 3.06 tons/in^2 across the planes of maximum shear.\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex6-pg52"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#calculate tensiles and compressive \n",
"p_1 = 7.;##tons/in^2\n",
"p_2 = 4.;##tons/in^2\n",
"p_3 = 3.;##tons/in^2\n",
"m = 4.;\n",
"E = 13000.;##tons/in^2\n",
"e_1 = (p_1/E)+(p_2/(m*E))-(p_3/(m*E));\n",
"e_2 = (p_2/E)+(p_1/(m*E))+(p_3/(m*E));\n",
"e_3 = (p_3/E)-(p_1/(m*E))+(p_2/(m*E));\n",
"print'%s %.4f %s'%('e_1 =',e_1,'tensile')\n",
"print'%s %.4f %s'%('e_2 =',e_2,'compressive')\n",
"print'%s %.4f %s'%('e_3 =',e_3,'tensile')\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"e_1 = 0.0006 tensile\n",
"e_2 = 0.0005 compressive\n",
"e_3 = 0.0002 tensile\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex7-pg53"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#calculate the contraction in the length \n",
"a = 2.;##inches\n",
"l = 6.;##inches\n",
"E = 13000.;##tons/In^2\n",
"m = 1./0.3;\n",
"P = 20.;##tons\n",
"p_1 = P/a**2;##tons/in^2\n",
"p_2 = p_1/(2.*(m-1));##tons/in^2\n",
"e_1 = (5.-0.6*p_2)/E;##tons/in^2\n",
"del_l = e_1*l;##inches\n",
"print'%s %.4f %s'%('The contraction in the length del_l =',del_l,'inches');\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The contraction in the length del_l = 0.0020 inches\n"
]
}
],
"prompt_number": 3
}
],
"metadata": {}
}
]
}
|
