ߪ௔௩௚ ൌെͺͷǤͲͳͻͺǤ͵ͳ  ൌ ߬௠௔௫
psi
ͳͲǤ
71
ɐൌǦͺͷǤͲ ͳͻͺǤ͵ͳൌɒ
psi
10. 3D Mohr’s Circle Solution
3D Principal Stresses:
V
1
113.305 MP
a
V
2
0 MPa
V
3
283.305 MPa
72
െͳͷ ൌ ߪ௔௩௚ ͹͸Ǥ͵ʹ  ൌ ߬௠௔௫
͸ͳǤ͵ʹ ൌ ߪଵ
െͻͳǤ͵ʹ ൌ ߪଶ
X-Axis
psi
psi
psi
ͳͳǤ
11.
11. 3D Mohr’s Circle Solution
3D Principal Stresses:
V
1
61.322 MP
a
V
2
0 MPa
1
2
74
ͳͷ͸Ǥ͹͸ ൌ ߪଵ
ߪଶൌ െͺ͸Ǥ͹͸
ͳʹͳǤ͹͸  ൌ ߬௠௔௫
ߪ௔௩௚ ൌ͵ͷǤͲ
psi
psi
psi
X-Axis
ͳʹǤ
75
12. 3D Mohr’s Circle Solution
3D Principal Stresses:
V
1
156.758 MP
a
V
2
0 MPa
V
3
86.758 MPa
ͳͷ͸Ǥ͹͸ൌɐͳ
ɐʹൌǦͺ͸Ǥ͹͸
ͳʹͳǤ͹͸ൌɒ
ɐൌ͵ͷǤͲ
psi
X-Axis
76
ߪ௔௩௚ ൌെ͵ͷǤͲͳʹͳǤ͹͸  ൌ ߬௠௔௫
13.
77
X-Axis
13. 3D Mohr’s Circle Solution
3D Principal Stresses:
V
86.758 MPa
3
78
14.
ɒ
ൌ
ͶͲ 
ɐʹൌ
ͲͶͲ 
ɒൌ
ͶͲ
ɐͳൌͶͲ
Ͷͷι
ɐൌͲǡɐ
ൌͲǡɒ
ൌͶͲ
ɐʹൌǦͶͲ
ɐͳൌͶͲ
ሺͲǡͶͲሻ

ɐ
ʹԄɐൌͻͲι
79
ɐʹൌǦͶͲ
ɐͳൌͶͲ
ሺͲǡ ͶͲሻ
ɒ
ൌɒ
ɐ
ʹԄɐൌͻͲι
X-Axis
V
1
V
2
V
3
ɐൌͲǡɐ
ൌͲǡɒ
ൌͶͲ
14. 3D Mohr’s Circle Solution
3D Principal Stresses:
V
1
40 MP
a
V
0 MPa
3
80
ͺͷǤͲ  ൌ ߪ௔௩௚Ǣ ͳ͸ͷǤͲ  ൌ ߬௠௔௫
psi
psi psi
െͺͲǤͲ ൌ ߪଶʹͷͲ ൌ ߪଵ
15.
81
V
V
15. 3D Mohr’s Circle Solution
3D Principal Stresses:
V
1
250 MP
a
3
82
psi
psi
ߪ௔௩௚ ൌെͳͷǤͲ߬௠௔௫ ൌ͹ͳǤͷͻ
ߪଶൌെͺ͸Ǥͷͻߪଵൌ ͷ͸Ǥͷͻ
X-Axis
psi
psi psi
16.
െͳͷǤͲ ൌ ߪ௔௩௚
െͺ͸Ǥͷͻ  ൌ ߪଶ͹ͳǤͷͻ ൌ ߬௠௔௫
െͺͲ
െ͵Ͳ
ͷͲ
ͷ͸Ǥͷͻ
ߪଵ
psi
psi
psi
psi
psi
psi
83
16. 3D Mohr’s Circle Solution
3D Principal Stresses:
V
1
56.589
M
P
a
ɐʹൌǦͺ͸Ǥͷͻ ɐͳൌͷ͸Ǥͷͻ


V
1
V
2
V
3
84
psi
psi
psi
psi
psi psi
psi
ߪ௔௩௚ ൌͷͲǤͲͶͲ͵Ǥͳ  ൌ ߬௠௔௫
ߪଶൌ െ͵ͷ͵Ǥͳ Ͷͷ͵Ǥͳ ൌ ߪଵ
psi
psi
psi
X-Axis
17.
85
V
1
V
2
V
3
17. 3D Mohr’s Circle Solution
3D Principal Stresses:
V
1
453.113 MP
a
V
2
0 MPa
V
3
353.113 MPa
86
ͲͳͶͲ ʹͲͲ
ߪଶߪଵ
X-Axis
psi
psi psi
ͳ͹Ͳ 
ߪ
௔௩௚
ൌ͵Ͳ
psi
psi
psi
psi
18.
87
ɐൌ͵Ͳ
ɒൌͳ͹Ͳ
X-Axis
psi
18. 3D Mohr’s Circle Solution
3D Principal Stresses:
V
1
200 MP
a
3
88
psi
psi 47.17 MPa
19.
89


ɐʹ ɐͳ
V
1
V
2
V
3
19. 3D Mohr’s Circle Solution
3D Principal Stresses:
V
42.170
M
P
a
3