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
|
{
"metadata": {
"name": "",
"signature": "sha256:5150ceeff814b37f327edfa239de19ec011af3bd135e00c577336409efc3a800"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 16:Torsion of Shafts and Springs"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Problem 16.1,page no.675"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#Given\n",
"#Variable declaration\n",
"D=150 #Diameter of the shaft in mm\n",
"tau=45 #Maximum shear stress in N/sq.mm\n",
"\n",
"#Calculation\n",
"T=int(math.pi/16*tau*D**3)*1e-3 #Maximum torque transmitted by the shaft in N-m\n",
"\n",
"#Result\n",
"print \"Maximum torque =\",T,\"N-m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Maximum torque = 29820.586 N-m\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Problem 16.3,page no.677"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Given\n",
"#Variable declaration\n",
"Do=200 #Outer diameter in mm\n",
"Di=100 #Inner diameter in mm\n",
"tau=40 #Maximum shear stress in N/sq.mm\n",
"\n",
"#Calculation\n",
"T=int(round((math.pi)/16*tau*((Do**4-Di**4)/Do),-1))*1e-3 #Maximum torque transmitted by the shaft in Nm\n",
"\n",
"#Result\n",
"print \"Maximum torque transmitted by the shaft =\",T,\"Nm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Maximum torque transmitted by the shaft = 58904.86 Nm\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Problem 16.7,page no.682"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"\n",
"#Given\n",
"#Variable declaration\n",
"Do=120 #External diameter in mm\n",
"P=300*1000 #Power in W\n",
"N=200 #Speed in r.p.m\n",
"tau=60 #Maximum shear stress in N/sq.mm\n",
"\n",
"#Calculation\n",
"T=round((P*60)/(2*math.pi*N),1)*1e3 #Torque transmitted in Nmm \n",
"Di=round(((Do**4)-((T*16*Do)/(math.pi*tau)))**(1/4),1) #Maximum internal diameter in mm\n",
"\n",
"#Result\n",
"print \"Maximum Internal diameter =\",Di,\"mm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Maximum Internal diameter = 88.5 mm\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Problem 16.8,page no.683"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#Given\n",
"#Variable declaration\n",
"D=15*10 #Diameter of shaft in mm\n",
"P=150*1e3 #Power transmitted in W\n",
"N=180 #Speed of shaft in r.p.m\n",
"\n",
"#Calculation\n",
"T=(P*60)/(2*math.pi*N)*1e3 #Torque transmitted in Nmm\n",
"tau=int((16*T)/(math.pi*D**3)) #Maximum shear stress in N/sq.mm\n",
"\n",
"#Result\n",
"print \"Maximum shear stress =\",tau,\"N/mm^2\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Maximum shear stress = 12 N/mm^2\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Problem 16.9,page no.683"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"#Given\n",
"#Variable declaration\n",
"P=300*1000 #Power in W\n",
"N=100 #Speed in r.p.m\n",
"tau=80 #Maximum shear stress in N/sq.mm\n",
"\n",
"#Calculation\n",
"#case(a):\n",
"T=(P*60)/(2*math.pi*N)*1e3 #Torque transmitted in Nmm\n",
"D=round(((16*T)/(math.pi*tau))**(1/3),0) #Diameter of solid shaft in mm\n",
"#case(b):\n",
"Do=round(((T*16)/(math.pi*tau*(1-0.6**4)))**(1/3),0) #External diameter of hollow shaft in mm\n",
"Di=0.6*Do #Internal diameter of hollow shaft in mm\n",
"Per=(D**2-(Do**2-Di**2))/(D**2)*100 #Percentage saving in weight\n",
"\n",
"#Result\n",
"print \"Diameter of solid shaft =\",D,\"mm\"\n",
"print \"Percentage saving in weight = %.2f%%\"%Per"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Diameter of solid shaft = 122.0 mm\n",
"Percentage saving in weight = 29.55%\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Problem 16.10,page no.685"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#Given\n",
"#Variable declaration\n",
"P=75e3 #Power transmitted in W\n",
"N=200 #R.P.M of the shaft \n",
"tau=70 #Shear stress in N/sq.mm\n",
"\n",
"#Calculation\n",
"T=P*60/(math.pi*2*N)*1e3 #Mean Torque transmitted in Nmm\n",
"Tmax=1.3*T #Maximum Torque transmitted in Nmm\n",
"D=round((16*Tmax/(math.pi*tau))**(1/3),0) #Suitable diameter of the shaft in mm\n",
"\n",
"#Result\n",
"print \"Diameter of the shaft = %d mm\"%D"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Diameter of the shaft = 70 mm\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Problem 16.11,page no.685"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#Given\n",
"#Variable declaration\n",
"P=300e3 #Power transmitted in W\n",
"N=80 #speed of the shaft in r.p.m\n",
"tau=60 #Maximum shear stress in N/sq.mm\n",
"\n",
"#Calculation\n",
"T=P*60/(math.pi*2*N)*1e3 #Mean Torque transmitted in Nmm\n",
"Tmax=1.4*T #Maximum Torque transmitted in Nmm\n",
"D=round((16*Tmax/(math.pi*tau))**(1/3),0) #Suitable diameter of the shaft in mm\n",
"Do=round(((Tmax*16)/(math.pi*tau*(1-0.6**4)))**(1/3),0) #External diameter of hollow shaft in mm\n",
"Di=0.6*Do #Internal diameter of hollow shaft in mm\n",
"\n",
"#Result\n",
"print \"External diameter of hollow shaft = %d mm\"%Do\n",
"print \"Internal diameter of hollow shaft = %d mm\"%Di"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"External diameter of hollow shaft = 170 mm\n",
"Internal diameter of hollow shaft = 102 mm\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
|
