Mechanical Engineering Chapter 4 Combined Stresses And Stress Transformations Notes Concerning The Solutions Presented Part 1

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:

3. It would be helpful to review Example Problems 4-1 and 4-2 that demonstrate these

procedures.

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

b. Then the 2D Mohr’s circle is generated manually using the same input data. The three

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:

a. The software operates only with U.S. units. SI values are converted to U.S. units.

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20

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psi

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53

1. 3D Mohr’s Circle Solution

3D Principal Stresses:

V

1

24142 ps

i

psi

54

ʹǤ

psi

ߪ௔௩௚ ߬௠௔௫

55

V

1

V

2

V

3

2. 3D Mohr’s Circle Solution

3D Principal Stresses:

V

1 46827 ps

i

psi

56

͵Ǥ

57

X-Axis

V

1

V

2

V

3

3. 3D Mohr’s Circle Solution

3D Principal Stresses:

V

1

50000 ps

i

V

2

0 psi

V

3

50000 psi

58

X-Axis

psi psi

psi

ͶǤ

59

V

1

V

2

V

3

X-Axis

4. 3D Mohr’s Circle Solution

3D Principal Stresses:

V

1

47082 ps

i

V

2

0 psi

V

3

87082 psi

60

psi

X-Axis

psi

ͷǤ

61

psi

V

1

V

2

V

3

5. 3D Mohr’s Circle Solution

3D Principal Stresses:

V

1

42462 ps

i

3

62

psi

psi psi

X-Axis

͸Ǥ

63

psi psi

X-Axis

V

1

V

2

V

3

6, 3D Mohr’s Circle Solution

3D Principal Stresses:

V

1

42462 ps

i

3

64

psi

psi psi

X-Axis

͹Ǥ

7. 3D Mohr’s Circle Solution

3D Principal Stresses:

V

1

71033

p

s

i

X-Axis

66

psi

X-Axis

ͺǤ

67

8. 3D Mohr’s Circle Solution

3D Principal Stresses:

V

1

168062

p

s

i

V

2

0 psi

V

88062 psi

V

1

V

2

V

3

ͻǤ

69

psi

9. 3D Mohr’s Circle Solution

3D Principal Stresses:

V

1

44.34 MP

a

V

2

0 MPa

V

3

144.34 MPa

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