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
|
NOTE: Sy=0 in all cases
Sn_max=(Sx/2)+sqrt(((Sx/2)^2)+(Txy^2))
Sn_min=(Sx/2)-sqrt(((Sx/2)^2)+(Txy^2))
T_max=[Sn_max+Sn_min]/2
(a) AXIAL LOAD ONLY
Sx=7.64 MN/m^2
Txy=0.00 MN/m^2
Maximum normal stress=7.64 MN/m^2
Minimum normal stress=0.00 MN/m^2
Maximum shear stress=3.82 MN/m^2
(b) BENDING ONLY
Section at which cantilever is fixed is critical
{Sx=(M*c)/I at topmost point of section at which cantilever is fixed}
At the topmost point of section at which cantilever is fixed,
Sx=61.12 MN/m^2
Txy=0.00 MN/m^2
Maximum normal stress=61.12 MN/m^2
Minimum normal stress=0.00 MN/m^2
Maximum shear stress=30.56 MN/m^2
{Sx=-(M*c)/I at topmost point of section at which cantilever is fixed}
At the bottom point of section at which cantilever is fixed,
Sx=-61.12 MN/m^2
Txy=0.00 MN/m^2
Maximum normal stress=0.00 MN/m^2
Minimum normal stress=-61.12 MN/m^2
Maximum shear stress=30.56 MN/m^2
(c) TORSION ONLY
Here, the critical points occur along the outer surface of the member
Sx=0.00 MN/m^2
Txy=40.74 MN/m^2
Maximum normal stress=40.74 MN/m^2
Minimum normal stress=-40.74 MN/m^2
Maximum shear stress=40.74 MN/m^2
(d) BENDING AND TORSION
Section at which cantilever is fixed is critical
At the topmost point of section at which cantilever is fixed,
Sx=61.12 MN/m^2
Txy=40.74 MN/m^2
Maximum normal stress=81.49 MN/m^2
Minimum normal stress=-20.37 MN/m^2
Maximum shear stress=50.93 MN/m^2
At the bottom point of section at which cantilever is fixed,
Sx=-61.12 MN/m^2
Txy=40.74 MN/m^2
Maximum normal stress=20.37 MN/m^2
Minimum normal stress=-81.49 MN/m^2
Maximum shear stress=50.93 MN/m^2
The magnitudes of stresses at the two points are same.
The different signs of normal stresses indicate that while topmost fibres are in
tension,the bottom fibres are in compression.
The different signs of shear stress are of no consequence.
(e) BENDING AND AXIAL LOAD
Section at which cantilever is fixed is critical
At the topmost point of section at which cantilever is fixed,
Sx=68.75 MN/m^2
Txy=0.00 MN/m^2
Maximum normal stress=68.75 MN/m^2
Minimum normal stress=0.00 MN/m^2
Maximum shear stress=34.38 MN/m^2
At the bottom point of section at which cantilever is fixed,
Sx=-53.48 MN/m^2
Txy=0.00 MN/m^2
Maximum normal stress=0.00 MN/m^2
Minimum normal stress=-53.48 MN/m^2
Maximum shear stress=26.74 MN/m^2
(f) TORSION AND AXIAL LOAD
Critical points are those on the outer surface of the cantilever
At the topmost point of section at which cantilever is fixed,
Sx=7.64 MN/m^2
Txy=40.74 MN/m^2
Maximum normal stress=44.74 MN/m^2
Minimum normal stress=-37.10 MN/m^2
Maximum shear stress=40.92 MN/m^2
(g) BENDING, TORSION AND AXIAL LOAD
Section at which cantilever is fixed is critical
At the topmost point of section at which cantilever is fixed,
Sx=68.75 MN/m^2
Txy=40.74 MN/m^2
Maximum normal stress=87.69 MN/m^2
Minimum normal stress=-18.93 MN/m^2
Maximum shear stress=53.31 MN/m^2
At the bottom point of section at which cantilever is fixed,
Sx=-53.48 MN/m^2
Txy=40.74 MN/m^2
Maximum normal stress=22.00 MN/m^2
Minimum normal stress=-75.47 MN/m^2
Maximum shear stress=48.73 MN/m^2
|
