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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 8: The Tension Test"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"### Example 8.1, Standard properties of the material, Page No. 281"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"Ultimate Tensile Strength = 92363.2 psi\n",
"0.2 percent offset yield strength = 74889.1 psi\n",
"Breaking Stress = 80880.2 psi\n",
"Elongation = 26.5 percent\n",
"Reduction of Area = 61.092 percent\n",
"\n",
"\n",
"Note: Slight Computational Errors in book\n"
]
}
],
"source": [
"\n",
"from math import pi\n",
"\n",
"#variable declaration\n",
"D=0.505;\n",
"Lo=2;\n",
"Lf=2.53;\n",
"Py=15000;\n",
"Pmax=18500;\n",
"Pf=16200;\n",
"D_f=0.315;\n",
"\n",
"#calculation\n",
"A0=pi*D**2/4;\n",
"Af=pi*D_f**2/4;\n",
"s_u=Pmax/A0;\n",
"s0=Py/A0;\n",
"s_f=Pf/A0;\n",
"e_f=(Lf-Lo)/Lo;\n",
"q=(A0-Af)/A0;\n",
"\n",
"#result\n",
"print('\\nUltimate Tensile Strength = %g psi\\n0.2 percent offset yield strength = %g psi\\nBreaking Stress = %g psi\\nElongation = %g percent\\nReduction of Area = %g percent\\n\\n\\nNote: Slight Computational Errors in book')%(s_u,s0,s_f,e_f*100,q*100);\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example 8.2, True Strain, Page No. 288"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"True Strain to fracture using changes in length = 0.405465\n",
"True Strain to fracture using changes in area = 0.405465\n",
"\n",
"\n",
"\n",
"For More ductile metals\n",
"True Strain to fracture using changes in length = 0.729961\n",
"True Strain to fracture using changes in diameter = 0.940007\n"
]
}
],
"source": [
"\n",
"from math import log\n",
"\n",
"#case 1\n",
"#variable declaration\n",
"Af=100.0;\n",
"Lf1=60.0;\n",
"A0=150.0;\n",
"L01=40.0;\n",
"Lf=83.0;\n",
"L0=40.0;\n",
"Df=8.0;\n",
"D0=12.8;\n",
"\n",
"#calculation\n",
"L1=float (Lf1/L01);\n",
"A1=float (A0/Af);\n",
"ef11=log(L1);\n",
"ef21=log(A1);\n",
"L2=(Lf/L0);\n",
"D2=D0/Df;5\n",
"ef12=log(L2);\n",
"ef22=2*log(D2);\n",
"\n",
"#result\n",
"print('\\nTrue Strain to fracture using changes in length = %g\\nTrue Strain to fracture using changes in area = %g')%(ef11,ef21);\n",
"print('\\n\\n\\nFor More ductile metals\\nTrue Strain to fracture using changes in length = %g\\nTrue Strain to fracture using changes in diameter = %g')%(ef12,ef22);\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example 8.3, Ultimate Tensile Strength, Page No. 290"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Ultimate Tensile Strength = 99729.2 psi\n"
]
}
],
"source": [
"\n",
"\n",
"from math import exp\n",
"\n",
"#variable declaration\n",
"def sigma(e):\n",
" return 200000*e**0.33;\n",
"E_u=0.33;\n",
"\n",
"#calculation\n",
"sigma_u=sigma(E_u);\n",
"s_u=sigma_u/exp(E_u);\n",
"\n",
"#result\n",
"print('Ultimate Tensile Strength = %g psi')%(s_u);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Example 8.4, Effect of Strain Rate, Page No. 298"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"At 70deg F\n",
"\n",
"sigma_a = 10.2 ksi\n",
"sigma_b = 13.8229 ksi\n",
"sigma_b/sigma_a = 1.35519\n",
"\n",
"\n",
"\n",
"At 825deg F\n",
"\n",
"sigma_a = 2.1 ksi\n",
"sigma_b = 5.54906 ksi\n",
"sigma_b/sigma_a = 2.64241\n",
"\n"
]
}
],
"source": [
"\n",
"\n",
"#variable declaration\n",
"C_70=10.2;\n",
"C_825=2.1;\n",
"m_70=0.066;\n",
"m_825=0.211;\n",
"e1=1;\n",
"e2=100;\n",
"\n",
"#calculation 1\n",
"print('\\nAt 70deg F\\n');\n",
"sigma_a=C_70*e1**m_70;\n",
"sigma_b=C_70*e2**m_70;\n",
"\n",
"#result 1\n",
"print('sigma_a = %g ksi\\nsigma_b = %g ksi\\nsigma_b/sigma_a = %g\\n')%(sigma_a,sigma_b,sigma_b/sigma_a);\n",
"\n",
"\n",
"#calculation 2\n",
"print('\\n\\nAt 825deg F\\n');\n",
"sigma_a=C_825*e1**m_825;\n",
"sigma_b=C_825*e2**m_825;\n",
"\n",
"#result 2\n",
"print('sigma_a = %g ksi\\nsigma_b = %g ksi\\nsigma_b/sigma_a = %g\\n')%(sigma_a,sigma_b,sigma_b/sigma_a);\n"
]
}
],
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"file_extension": ".py",
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|
