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
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
|
{
"metadata": {
"name": "",
"signature": "sha256:d68e0c119bd3bfe882788d74028fcc8cbbdbb80bd702bb1bf7bdb0ffe972f8d9"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter8-Stability of Equlibrium-Columns"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex1-pg330"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate maximum axial load and for both ends and and fixed and one fix and one pinned\n",
"## initialization of variables\n",
"import math\n",
"L=5. ##m\n",
"D=20. ##cm\n",
"t=1. ##cm\n",
"E=2*10**6 ##kg/cm^2\n",
"I=2502. ##cm^4\n",
"L=5*100. ##cm\n",
"## calculations\n",
"P=E*I/(4.*L**2)\n",
"## results\n",
"print'%s %.2f %s'%('The maximal axial load taken is ',P/100,' Tonne')\n",
"print'%s %.2f %s'%('\\n for both ends pinned, P=',P*4/100,' Tonne',)\n",
"print'%s %.2f %s'%('\\n for both ends fixed, P=',P*16/100,' Tonne')\n",
"print'%s %.2f %s'%('\\n for one end fixed, one pinned, P=',P*4*2.13/100,' Tonne')\n",
"\n",
"## Evaluation of critical load (P) in the text is wrong\n",
"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The maximal axial load taken is 50.04 Tonne\n",
"\n",
" for both ends pinned, P= 200.16 Tonne\n",
"\n",
" for both ends fixed, P= 800.64 Tonne\n",
"\n",
" for one end fixed, one pinned, P= 426.34 Tonne\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex2-pg331"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate actual critical length ratio and critical length ratio \n",
"##initialization of variables\n",
"import math\n",
"E=2*10**6. ##kg/cm**2\n",
"sigma_y=2600. ##kg/cm**2\n",
"I=2502. ##cm**4\n",
"L=500. ##cm\n",
"A=59.7 ##cm**2\n",
"L_tcr=L/math.sqrt(I/A)\n",
"\n",
"print'%s %.2f %s'%('The actual critical length ratio is',L_tcr,'')\n",
"##case (b)\n",
"L_cr=math.sqrt(E*math.pi**2/sigma_y)\n",
"print('\\n case (b)')\n",
"print'%s %.2f %s'%('\\n The critical length ratio is ',L_cr,'')\n",
"\n",
"##case (a)\n",
"L_cr=math.sqrt(E*math.pi**2/(4.*sigma_y))\n",
"print('\\n case (a)')\n",
"print'%s %.2f %s'%('\\n The critical length ratio is ',L_cr,'')\n",
"\n",
"##case (c)\n",
"L_cr=math.sqrt(4.*E*math.pi**2./sigma_y)\n",
"print('\\n case (c)')\n",
"print'%s %.2f %s'%('\\n The critical length ratio is',L_cr,'')\n",
"\n",
"## case (d)\n",
"L_cr=math.sqrt(2.05*E*math.pi**2/sigma_y)\n",
"## Results\n",
"print('\\n case (d)')\n",
"print'%s %.2f %s'%('\\n The critical length ratio is ',L_cr,'')\n",
"print('\\n Only in case (a) actual ratio is more than critical ratio and material \\n remains elastic For cases (b), (c) and (d) critical length ratio is \\n much higher and hence the material yelds before crippling loads are reached')\n",
"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The actual critical length ratio is 77.23 \n",
"\n",
" case (b)\n",
"\n",
" The critical length ratio is 87.13 \n",
"\n",
" case (a)\n",
"\n",
" The critical length ratio is 43.57 \n",
"\n",
" case (c)\n",
"\n",
" The critical length ratio is 174.26 \n",
"\n",
" case (d)\n",
"\n",
" The critical length ratio is 124.75 \n",
"\n",
" Only in case (a) actual ratio is more than critical ratio and material \n",
" remains elastic For cases (b), (c) and (d) critical length ratio is \n",
" much higher and hence the material yelds before crippling loads are reached\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex3-pg336"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate crtical stress \n",
"##initialzation of variables\n",
"import math\n",
"h=3.5 ##m\n",
"A=22.4 ##cm**2\n",
"r=7.08 ##cm\n",
"E=2*10**6 ##kg/cm**2\n",
"Q=1/2.\n",
"## calculations\n",
"h=h*100.\n",
"Q1=(Q*h/r)**2\n",
"s_cr=E*math.pi**2/Q1\n",
"## results\n",
"print'%s %.2f %s'%('The critical stress is ',s_cr,' kg/cm**2')\n",
"print('\\n This is much higher than yield stress for the material, \\n so the column will fail by yielding')\n",
"\n",
"print('rounding off errors in the text')\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The critical stress is 32308.75 kg/cm**2\n",
"\n",
" This is much higher than yield stress for the material, \n",
" so the column will fail by yielding\n",
"rounding off errors in the text\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex4-pg337"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#find crippling load\n",
"##initialization of variables\n",
"import math\n",
"r_min=1.17 ##cm\n",
"A=17.21 ##cm^2\n",
"Q=1/2.\n",
"h=3.5 ##m\n",
"E=2*10**6 ##kg/cm^2\n",
"h=h*100.\n",
"## calculations\n",
"Q1=(Q*h/r_min)**2\n",
"s_cr=E*math.pi**2/Q1\n",
"P_cr=s_cr*A\n",
"## results\n",
"print'%s %.2f %s'%('The crippling load is ',P_cr,' kg')\n",
"\n",
"## wrong calculations given in the text\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The crippling load is 15184.70 kg\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex5-pg340"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"##initialization of variables\n",
"#find safe load\n",
"L=2.5 ##m\n",
"A=6.02 ##cm^2\n",
"Q1=105.\n",
"s=796.5 ##kg/cm^2\n",
"## calculations\n",
"P=2*A*s\n",
"print'%s %.2f %s'%('The safe load is ',P,' kg')\n",
"## Results\n",
"## wrong calculations in the text\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The safe load is 9589.86 kg\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex6-pg345"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate Permissible load by secent and rankine gordon and parabolic formula\n",
"##initialization of variables\n",
"import math\n",
"h=3.5 ##m\n",
"r_xx=7.08 ##cm\n",
"A=24.38 ##cm^2\n",
"Q=0.5\n",
"Q1=Q*h*100./r_xx\n",
"\n",
"##Permissible load by secent formula\n",
"P=1231.28*2*A\n",
"print'%s %.2f %s'%('Permissible load by secent formula: ',P,' kg')\n",
"\n",
"##Permissible load by Rankine-Gordon formula\n",
"P=1260./(1.+(24.75**2/18000.))*2*A\n",
"print'%s %.2f %s'%('\\n Permissible load by Rankine-Gordon formula: ',P,' kg')\n",
"\n",
"##Permissible load by parabolic formula\n",
"P=(1050-0.0233*Q1**2)*2*A\n",
"print'%s %.2f %s'%('\\n Permissible load by parabolic formula: ',P,' kg')\n",
"\n",
"##Permissible load by straight-line formula\n",
"P=(1120-Q1*4.8)*2*A\n",
"print'%s %.2f %s'%('\\n Permissible load by parabolic formula: ',P,' kg')\n",
"\n",
"print('Rounding off errors in the text')\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Permissible load by secent formula: 60037.21 kg\n",
"\n",
" Permissible load by Rankine-Gordon formula: 59415.61 kg\n",
"\n",
" Permissible load by parabolic formula: 50503.89 kg\n",
"\n",
" Permissible load by parabolic formula: 48826.12 kg\n",
"Rounding off errors in the text\n"
]
}
],
"prompt_number": 6
}
],
"metadata": {}
}
]
}
|
