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
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
|
{
"metadata": {
"name": "",
"signature": "sha256:8abe3316b17e7378affc20eb461733ec12ced2dbb39d65e4c948dd2ef8dc33e9"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 19: Combined open and closed section beams"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 19.1 Pg.No. 552"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from scipy import integrate\n",
"from sympy import *\n",
"import math\n",
"\n",
"l1=100 #lengths shown in Fig(mm)\n",
"l2=200\n",
"F=100*10**3 #force applied (N)\n",
"\n",
"y_bar=(2*l1*2*50+2*l2*2*l1+l2*2*l2)/(4*l1*2+4*l2*2)\n",
"Ixx=2*(2*l1**3/12+2*l1*25**2)+400*2*75**2+l2*2*125**2+2*(2*l2**3/12+2*l2*25**2)\n",
"\n",
"s1=Symbol('s1')\n",
"q12=-round(10**4*F/Ixx)/10**4*(integrate(-50+2*s1,s1))\n",
"print \"\\nq12 = %s\"%(q12)\n",
"\n",
"s2=Symbol('s2')\n",
"q23=-round(10**4*F/Ixx)/10**4*(integrate(2*75,s2))-34.5\n",
"print \"\\nq23 = %s\"%(q23)\n",
"\n",
"s3=Symbol('s3')\n",
"q03=-round(10**4*F/Ixx)/10**4*(integrate(2*75,s3))\n",
"print \"\\nq03 = %s\"%(q03)\n",
"\n",
"s4=Symbol('s4')\n",
"q34=-round(10**4*F/Ixx)/10**4*(integrate(2*(75-s4),s4))-242.5\n",
"print \"\\nq34 = %s\"%(q34)\n",
"\n",
"s5=Symbol('s5')\n",
"q94=-round(10**4*F/Ixx)/10**4*(integrate(-2*125,s5))\n",
"print \"\\nq94 = %s\\n\"%(q94)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"q12 = -0.0069*s1**2 + 0.345*s1\n",
"\n",
"q23 = -1.035*s2 - 34.5\n",
"\n",
"q03 = -1.035*s3\n",
"\n",
"q34 = 0.0069*s4**2 - 1.035*s4 - 242.5\n",
"\n",
"q94 = 1.725*s5\n",
"\n"
]
}
],
"prompt_number": 35
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 19.2 Pg.No.555"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from scipy import integrate\n",
"from sympy import symbols\n",
"import math\n",
"\n",
"A=20000 #nose cell area (mm^2)\n",
"L_w=900 #outer wall (mm)\n",
"L=300 #width of wall (mm)\n",
"length=600 #length of open section (mm)\n",
"G=25000 #shear modulus (N/mm^2)\n",
"T=10*10**6 #torque applied (kN.m)\n",
"t1=1.5 #thickness of closed section\n",
"t2=2 #thickness of open section\n",
"\n",
"GJ_cl=4*A**2*G/(L_w+L)*t1\n",
"\n",
"print \"torsoinal rigidity of closed section = %2.2e N.mm^2 \\n\"%(GJ_cl)\n",
"\n",
"GJ_op=G*(length+L)*t2**3/3\n",
"print \"torsional rigidity of open section = %2.1e N.mm^2 \\n\"%(GJ_op)\n",
"\n",
"GJ=GJ_cl+GJ_op\n",
"print \"total torsional rigidity = %5.3e N.mm^2\\n\"%(GJ)\n",
"\n",
"dO_by_dz=T/GJ\n",
"print \"angle of twist per unit length = %1.4f rad/mm\\n\"%(dO_by_dz)\n",
"\n",
"q_cl=GJ_cl/2/A*dO_by_dz\n",
"print \"maximum shear stress in the closed section = %3.1f N/mm^2\\n\"%(q_cl/1.5)\n",
"\n",
"#eqn 18.10 T_max=GtdO/dz\n",
"T_max=G*t2*dO_by_dz\n",
"print \"maximum shear stress in the open section = %2.0f N/mm^2\\n\"%(T_max)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"torsoinal rigidity of closed section = 5.00e+10 N.mm^2 \n",
"\n",
"torsional rigidity of open section = 6.0e+07 N.mm^2 \n",
"\n",
"total torsional rigidity = 5.006e+10 N.mm^2\n",
"\n",
"angle of twist per unit length = 0.0002 rad/mm\n",
"\n",
"maximum shear stress in the closed section = 166.5 N/mm^2\n",
"\n",
"maximum shear stress in the open section = 10 N/mm^2\n",
"\n"
]
}
],
"prompt_number": 31
}
],
"metadata": {}
}
]
}
|
