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{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 8 : Mechanical Testing"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 8.1 pageno : 195"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variables\n",
"b = 225.;\t\t\t#in mm\n",
"h = 10. \t\t\t#in mm\n",
"l = 1100.;\t\t\t#in mm\n",
"f1 = 250.;\t\t\t#in N\n",
"f2 = 350;\t\t\t#in N at which glass breaks\n",
"\n",
"# Calculations\n",
"m = f1*l/4.;\t\t\t#in N-mm\n",
"f = f1/2.; \t\t\t#in N\n",
"a = (6*m)/(b*h**2);\t\t\t#in N/mm**2\n",
"t = (3*f)/(2*b*h);\t\t\t#in N/sqmm\n",
"r = f2*l/4;\t\t\t #in N-mm\n",
"i = (b*h**3)/12;\t\t\t#in mm**4\n",
"y = h/2;\t \t\t#in mm\n",
"mr = r*y/i;\t\t \t#in n/sqmm\n",
"\n",
"# Results\n",
"print \"Flexural Strength (in N/sqmm) = %.2f N/mm**2\"%a\n",
"print \"Shear Strength (in N/sqmm) = %3f N/mm**2\"%t\n",
"print \"Modulous of Rupture (in N/sqmm) = %.2f N/mm**2\"%mr\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Flexural Strength (in N/sqmm) = 18.33 N/mm**2\n",
"Shear Strength (in N/sqmm) = 0.083333 N/mm**2\n",
"Modulous of Rupture (in N/sqmm) = 25.67 N/mm**2\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 8.2 pageno : 201"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math \n",
"\n",
"# Variables\n",
"d = 5.; \t\t\t#in mm\n",
"\n",
"# Calculations\n",
"id = 32.5/10;\t\t\t#indentation diameter in mm\n",
"p = 30*d**2;\t\t\t#load for steel specimen in kgf\n",
"bhn = p/((3.14*d/2)*(d-math.sqrt(d**2-id**2)));\t\t\t#in kgf/sqmm\n",
"\n",
"# Results\n",
"print \"Load P for steel specimen (in kgf) = %.f kgf\"%p\n",
"print \"BRINELL HARDNESS NUMBER of the steel specimen = %.1f\"%bhn\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Load P for steel specimen (in kgf) = 750 kgf\n",
"BRINELL HARDNESS NUMBER of the steel specimen = 79.6\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 8.3 pageno : 209"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math \n",
"\n",
"# Variables\n",
"l = 0.1;\t\t\t#frictinal and windage losses in kgf-m\n",
"dr = 5.9;\t\t\t#dial reading in kgf-m\n",
"w = 19.33;\t\t\t#weight of hammer in kgf-m\n",
"t = 10.;\t\t\t#in mm\n",
"ui = 30.;\t\t\t#in kgf-m\n",
"a = 160.;\t\t\t#angle in degrees\n",
"r = 0.8;\t\t\t#swing radius in m\n",
"\n",
"\n",
"# Calculations\n",
"u = dr-l;\t \t\t#in kgf-m\n",
"d = t/5;\t\t \t#depth of V-notch in mm\n",
"te = t-d;\t\t \t #effective thickness in mm\n",
"ve = 75.*10*te; \t\t\t#effective volume in cu. mm\n",
"vem = ve*10.**-9;\t\t\t#in cu. m\n",
"mr = u/vem;\t \t\t#in kgf/sqm\n",
"ae = t*te; \t\t\t#effective area of cross section in sqmm\n",
"aem = ae*10**-6;\t\t\t#in sqm\n",
"is_ = u/aem;\t\t \t#in kg/m\n",
"uf = ui-u;\t\t\t#in kgf-m\n",
"hf = uf/w;\t\t\t#in m\n",
"B = math.degrees(math.acos(1-(uf/(w*r))))\n",
"\n",
"# Results\n",
"print \"Rupture Energy (in kgf-m) = %.1f kgf-m\"%u\n",
"print \"Modulous Of Rupture (in kgf/sqm) = %.1e kgf/m**2\"%mr\n",
"print \"Notch Imapct Strength (in kg/m) = %.2e kgm\"%is_\n",
"print \"Height risen by Hammer (in m) = %.2f m\"%hf\n",
"print \"Angle after Breaking the specimen (in degress) = %.1f degrees\"%(B)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Rupture Energy (in kgf-m) = 5.8 kgf-m\n",
"Modulous Of Rupture (in kgf/sqm) = 9.7e+05 kgf/m**2\n",
"Notch Imapct Strength (in kg/m) = 7.25e+04 kgm\n",
"Height risen by Hammer (in m) = 1.25 m\n",
"Angle after Breaking the specimen (in degress) = 124.4 degrees\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 8.4 pageno : 211"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variables\n",
"a_m = 70.; \t \t\t#mean stress in Mpa\n",
"a_r = 210.;\t \t \t#stress amplitude in Mpa\n",
"\n",
"# Calculations\n",
"a_max = ((2*a_m)+a_r)/2;\t\t\t#maximum stress in MPa\n",
"a_min = 2*a_m-a_max;\t \t\t#Minimum stress in MPa\n",
"s = a_min/a_max;\t\t\t #stress ratio\n",
"sr = a_max-a_min; \t\t\t#stress range in MPa\n",
"\n",
"# Results\n",
"print \"Maximum Stress Level (in MPa) = \",a_max\n",
"print \"Minimum Stress Level (in MPa) = \",a_min\n",
"print \"Stress Ratio = \",s\n",
"print \"Stress Range (in MPa) = \",sr\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Maximum Stress Level (in MPa) = 175.0\n",
"Minimum Stress Level (in MPa) = -35.0\n",
"Stress Ratio = -0.2\n",
"Stress Range (in MPa) = 210.0\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 8.5 pageno : 212"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variables\n",
"p_min = 20.;\t\t\t#in kN\n",
"p_max = 50.;\t\t\t#in kN\n",
"l = 500.; \t\t\t#in mm\n",
"d = 60.;\t \t\t#in mm\n",
"a_u = 650.;\t\t \t#in MPa\n",
"a_y = 520.;\t\t #in MPa\n",
"fos = 1.8;\t\t\t #factor of safety\n",
"\n",
"# Calculations\n",
"m_max = p_max*l/4;\t\t\t#maximum bending moment in kN mm\n",
"m_min = p_min*l/4;\t\t\t#minimum bending moment in kN mm\n",
"m_m = (m_max+m_min)/2;\t\t\t#mean bending moment in kN mm\n",
"m_a = (m_max-m_min)/2;\t\t\t#alternating bending moment in kN mm\n",
"z = 3.14*d**3/32;\n",
"a_m = (m_m/z)*1000;\t\t\t#mean bending stress in MPa\n",
"a_a = (m_a/z)*1000;\t\t\t#alternating bending stress in MPa\n",
"a_e1 = a_a/((1/fos)-(a_m/a_u)**2*fos);\t\t\t#in MPa\n",
"a_e2 = a_a/((1/fos)-(a_m/a_u));\t\t\t#in MPa\n",
"a_e3 = a_a/((1/fos)-(a_m/a_y));\t\t\t#in MPa\n",
"\n",
"# Results\n",
"print \"ENDURANCE STRESS FROM Gerbers Parabolic Function (in MPa) = %.2f MPa\"%a_e1\n",
"print \"ENDURANCE STRESS FROM Goodman Straight Line Relation (in MPa) = %.2f MPa\"%a_e2\n",
"print \"ENDURANCE STRESS FROM Soderberg Straight Line Relation (in MPa) = %.2f MPa\"%a_e3\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"ENDURANCE STRESS FROM Gerbers Parabolic Function (in MPa) = 236.52 MPa\n",
"ENDURANCE STRESS FROM Goodman Straight Line Relation (in MPa) = 371.71 MPa\n",
"ENDURANCE STRESS FROM Soderberg Straight Line Relation (in MPa) = 557.78 MPa\n"
]
}
],
"prompt_number": 11
}
],
"metadata": {}
}
]
}