1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
|
{
"metadata": {
"name": "",
"signature": "sha256:688a5ddb04d5076a46d59fbb5d6dc8d907dec2ec735786354cef92d935d1ccd0"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 9: Deflections of beams"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.17, Page number 654"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"#Variable declaration\n",
"P = 5 #load(k)\n",
"L = 8*12 #beam length(in)\n",
"E = 30*10**6 #modulus of elasticity(psi)\n",
"I = 75.0 #moment of inertia(in^4)\n",
"q = 1.5*(1./12.)#load intensity(k/in)\n",
"\n",
"#Calculations\n",
"Sc = ((P*L**3)/(48*E*I))+((5.*q*L**4)/(384.*E*I))\n",
"\n",
"#Result\n",
"print \"The download deflection is\",Sc,\"in(Calculation mistake in textbook)\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The download deflection is 0.0001024 in(Calculation mistake in textbook)\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.23, Page number 682"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#Variable declaration\n",
"E = 30*10**6*144 #modulus of elasticity(lb/ft^2)\n",
"I = 25.92/12 #moment of inertia(ft^4)\n",
"x = 12 #ft\n",
"\n",
"#Calculations\n",
"'''The equivalent load q(x) for the beam is given by the following equation\n",
"q(x) = -700(x)^-1+800(x-6)^0 - 800(x-12)^0 - 5600(x-12)^-1 + 1500(x-16)^-1\n",
"Since the equation equals zero at all points except where x=16, we omit the last term\n",
"Taking 4th order integration, we obtain the following expression,'''\n",
"C1 = (-((350*x**3)/3)+((100*(x-6)**4)/3)-((100*(x-12)**4)/3)+((2800*(x-12)**3)/3))/12\n",
"print \"C1 =\",C1\n",
"\n",
"#For Deflection at point C\n",
"x = 6\n",
"Elv = ((350*x**3)/3)-(100*((x-6)**4)/3)+(100*((x-12)**4)/3)+(2800*((x-12)**3)/3)+(C1*x)\n",
"Sc = Elv/(E*I) #ft\n",
"\n",
"#For deflection at point D\n",
"x = 16\n",
"Elv_16 = ((350*x**3)/3)-(100*((x-6)**4)/3)+(100*((x-12)**4)/3)+(2800*((x-12)**3)/3)+(C1*x)\n",
"Sd = Elv_16/(E*I)\n",
"\n",
"#Results\n",
"print \"Deflection at point C is\",round((-Sc*12),8),\"in\"\n",
"print \"Deflection at point D is\",round((Sd*12),8),\"in\"\n",
"\n",
"print \"\\n Please note that there is a calculation mistake in textbook while calculating Elv. Hence, the difference in solution\"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"C1 = -13200\n",
"Deflection at point C is 0.00027315 in\n",
"Deflection at point D is 2.06e-06 in\n",
"\n",
" Please note that there is a calculation mistake in textbook while calculating Elv. Hence, the difference in solution\n"
]
}
],
"prompt_number": 19
}
],
"metadata": {}
}
]
}
|
