{
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{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 13 : Deflection of Beams"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 13.1 Page No : 313"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\t\t\t\n",
"# Variables\n",
"E = 1.5*10**6\n",
"F1 = -100. \t\t\t#lb\n",
"F2 = -100. \t\t\t#lb\n",
"x1 = 6 \t\t\t#in\n",
"x2 = 6 \t\t\t#in\n",
"Ina = 64 \t\t\t#in**4\n",
"h1 = -600 \t\t\t#lb ft\n",
"h2 = -1200 \t\t\t#lb ft\n",
"xa1 = 10 \t\t\t# in\n",
"xa2 = 8 \t\t\t#in\n",
"\t\t\t\n",
"# Calculations\n",
"deltamax = ((1./2)*x1*xa1*h1+(1./2)*(x1+x2)*h2*xa2)*(1728)/(E*Ina)\n",
"\t\t\t\n",
"# Results\n",
"print 'maximum deflection = %.2f in'%(deltamax)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"maximum deflection = -1.36 in\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 13.2 Page No : 314"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\t\t\t\n",
"# Variables\n",
"E = 1.5*10**6\n",
"I = 50. \t \t\t#in**4\n",
"delta = -1. \t\t\t#in\n",
"l = 8. \t\t\t#ft\n",
"\t\t\t\n",
"# Calculations\n",
"w = -delta*8*E*I/(l**4*1728)\n",
"\t\t\t\n",
"# Results\n",
"print 'distributed weight = %.1f lb per ft'%(w)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"distributed weight = 84.8 lb per ft\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 13.3 Page No : 315"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\t\t\t\n",
"# Variables\n",
"W = 50. \t\t\t#lb/ft\n",
"x = 5. \t\t\t#ft\n",
"x1 = 2. \t\t\t#ft\n",
"\t\t\t\n",
"# Calculations\n",
"V = W*x\n",
"M = W*((x/2)+x1)*x\n",
"M1 = W*x*(x+x1)\n",
"M2 = -M\n",
"M3 = -W*x*x/2\n",
"EIdeltamax = ((1./2)*(x+x1)*M1*((x+x1)/3))+(x+x1)*M2*((x+x1)/2)+(1./3)*x*M3*(x/4)\n",
"\t\t\t\n",
"# Results\n",
"print 'maximum value of EIdeltax = %.1f lb ft**3'%(round(EIdeltamax,-2))\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"maximum value of EIdeltax = -14600.0 lb ft**3\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 13.5 Page No : 329"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\t\t\t\n",
"# Variables\n",
"w = 180. \t\t\t#lb/ft\n",
"l = 8. \t\t\t#ft\n",
"P = 1200. \t\t\t#lb\n",
"b = 6. \t\t\t#ft\n",
"E = 3*10.**6\n",
"I = 64. \t\t\t#in**4\n",
"\t\t\t\n",
"# Calculations\n",
"delta = ((w*l**4)/(8))+((P*b**2)*(3*l-b)/(6))\n",
"\t\t\t\n",
"# Results\n",
"print 'deflection of the free end = %.1fbyEI ft'%(round(delta,-3))\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"deflection of the free end = 222000.0byEI ft\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 13.6 Page No : 329"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\t\t\t\n",
"# Variables\n",
"P = 6. \t\t\t#kips\n",
"w = 3. \t \t\t#kips/ft\n",
"L1 = 8. \t\t\t#ft\n",
"L2 = 8. \t\t\t#ft\n",
"\t\t\t\n",
"# Calculations\n",
"delta = (P*(L1+L2)**3/192)+(w*(L1+L2)**4/768)\n",
"\t\t\t\n",
"# Results\n",
"print 'midspan value of deflection = %.1f kip ft**3'%(delta)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"midspan value of deflection = 384.0 kip ft**3\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 13.7 Page No : 331"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\t\t\t\n",
"# Variables\n",
"x1 = 3. \t\t\t#ft\n",
"x2 = 3. \t\t\t#ft\n",
"x3 = 3. \t\t\t#ft\n",
"x4 = 3. \t\t\t#ft\n",
"W1 = 4. \t\t\t#kips\n",
"W2 = 8. \t\t\t#kips\n",
"l = x1+x2+x3+x4\n",
"\t\t\t\n",
"# Calculations\n",
"b = x2+x3+x4\n",
"b1 = x4\n",
"a = x1\n",
"x = l/2\n",
"P = (((W1*b*(l/b*(x-a)**3+(l**2-b**2)*x-x**3))/(6*l))+((W2*b1*x*(l**2-x**2-b1**2))/(6*l)))*(48/l**3)\n",
"R1 = 3+2-(P/2)\n",
"R2 = P\n",
"R3 = 1+6-(P/2)\n",
"\t\t\t\n",
"# Results\n",
"print 'R1 = %.3f kips'%(R1)\n",
"print 'R2 =%.2f kips'%(R2)\n",
"print 'R3 =%.3f kips'%(R3)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"R1 = 0.875 kips\n",
"R2 =8.25 kips\n",
"R3 =2.875 kips\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 13.8 Page No : 333"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from numpy import linalg\n",
"\t\t\t\n",
"# Variables\n",
"P = 680. \t\t\t#lb\n",
"K = 1000. \t\t\t#lb/in\n",
"L = 6. \t\t\t#ft\n",
"E = 30.*10**6\n",
"Ina = 1.728 \t\t\t#in**4\n",
"\t\t\t\n",
"# Calculations\n",
"A = [[((L*12)**3/(3*E*Ina)),-(1/K)],[1,1]]\n",
"b = [0,P]\n",
"c = linalg.solve(A,b)\n",
"Pb = c[0]\n",
"Ps = c[1]\n",
"\t\t\t\n",
"# Results\n",
"print 'Force in the spring = %.2f psi'%(Ps)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Force in the spring = 480.00 psi\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 13.9 Page No : 334"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\t\t\t\n",
"# Variables\n",
"I = 1.5 \t\t\t#in**4\n",
"Da = 0.5 \t\t\t#in\n",
"E = 30.*10**6\n",
"l = 60. \t\t\t#in\n",
"\t\t\t\n",
"# Calculations\n",
"F = 6*Da*E*I/(l**3)\n",
"\t\t\t\n",
"# Results\n",
"print 'F = %.2f lb'%(F)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"F = 625.00 lb\n"
]
}
],
"prompt_number": 8
}
],
"metadata": {}
}
]
}