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
|
{
"metadata": {
"name": "",
"signature": "sha256:9a486aadfd6b9085cbabcb01b6c4b7704df2013ab12ac6b342be3bf11e26b98d"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 7:Bending Stresses in Beams"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Problem 7.1,page no.298"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Given\n",
"#Variable declaration\n",
"b=120 #Width of plate in mm\n",
"t=20 #Thickness of plate in mm\n",
"R=10*10**3 #Radius of curvature in mm\n",
"E=2e5 #Young's modulus in N/sq.mm\n",
"\n",
"#Calculation\n",
"I=b*t**3/12 #Moment of inertia in mm^4\n",
"y_max=t/2 #Maximum distance in mm\n",
"sigma_max=int((E/R)*y_max) #Maximum stress in N/sq.mm\n",
"M=round((E/R*I)*(10**-6),1) #Bending moment in kNm\n",
"\n",
"#Result\n",
"print \"Maximum stress =\",sigma_max,\"N/mm^2\"\n",
"print \"Bending moment =\",M,\"kNm\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Maximum stress = 200 N/mm^2\n",
"Bending moment = 1.6 kNm\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Problem 7.8,page no.305"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"import math\n",
"\n",
"#Given\n",
"#Variable declaration\n",
"W=20*1000 #Total load in N\n",
"L=3.6 #Span in m\n",
"sigma_max=7 #Maximum stress in N/sq.mm\n",
"\n",
"#Calculation\n",
"M1=W*L/8*1e3 #Maximum Bending moment in Nmm\n",
"b1=round((M1*3/(sigma_max*2))**(1/3),1) #Breadth of the beam in mm\n",
"d1=int(round(2*b1,0)) #depth of the beam in mm\n",
"M2=W*L/4*1e3 #Maximum Bending moment in Nmm\n",
"b2=float(str(round((M2*3/(sigma_max*2))**(1/3),4))[:6]) #Breadth of the beam in mm\n",
"d2=2*b2 #depth of the beam in mm\n",
"\n",
"#Result\n",
"print \"Dimensions of the cross-section:\"\n",
"print \"Breadth of beam =\",b1,\"mm\"\n",
"print \"Depth of beam\",d1,\"mm\"\n",
"\n",
"print \"Dimensions of the cross-section when the beam carries a point load at the centre:\"\n",
"print \"Breadth of beam =\",b2,\"mm\"\n",
"print \"Depth of beam\",d2,\"mm\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Dimensions of the cross-section:\n",
"Breadth of beam = 124.5 mm\n",
"Depth of beam 249 mm\n",
"Dimensions of the cross-section when the beam carries a point load at the centre:\n",
"Breadth of beam = 156.82 mm\n",
"Depth of beam 313.64 mm\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
|
