50
CHAPTER 4
COMBINED STRESSES AND
STRESS TRANSFORMATIONS
NOTES CONCERNING THE SOLUTIONS PRESENTED FOR
MOHR’S CIRCLE PROBLEMS IN CHAPTER 4:
1. The objectives for all problems are to transform the given data for normal and shear
2. In general, the procedures follow:
a. The General Procedure for Computing Principal Stresses and Maximum Shear
4. Also, Example Problems 4-3 to 4-6 show completed Mohr’s circles for sets of given data
5. Problem 4-1 is shown in three forms;
a. The given data are processed using the equations in Section 4-3, particularly equations
are demonstrated in Example Problem 4-1.
6. The remaining problems are shown using software to perform the calculations and to
generate the Mohr’s circles for both 2D and 3D analysis. Note for these problems:
b. Each solution has tabulated results for principal stresses, maximum shear stress, and
52
53
1. 3D Mohr’s Circle Solution
3D Principal Stresses:
124142 ps
i
54
55
2. 3D Mohr’s Circle Solution
3D Principal Stresses:
1
46827 ps
i
X-Axis
56
57
3. 3D Mohr’s Circle Solution
3D Principal Stresses:
58
psi
59
4. 3D Mohr’s Circle Solution
3D Principal Stresses:
1
47082 ps
i
60
X-Axis
61
5. 3D Mohr’s Circle Solution
3D Principal Stresses:
62
X-Axis
63
6, 3D Mohr’s Circle Solution
3D Principal Stresses:
1
42462 ps
i
64
psi
65
7. 3D Mohr’s Circle Solution
3D Principal Stresses:
171033
p
s
i
66
X-Axis
67
8. 3D Mohr’s Circle Solution
3D Principal Stresses:
1168062
p
s
i
X-Axis
68
psi
psi
psi
69
psi
9. 3D Mohr’s Circle Solution
3D Principal Stresses:
3
144.34 MPa