1. DEPARTMENT OF MECHANICAL AND MANUFACTURING ENGINEERING
UNIVERSITY OF NAIROBI
DEPARTMENT OF MECHANICAL AND MANUFACTURING ENGINEERING
ENGINEERING DESIGN II
FME 461
PART 10
GO NYANGASI
January 2007

2. DISTORTION ENERGY THEORY IN BIAXIAL (PLANE) STRESS SITUATION

3. PRINCIPAL STRESSES IN BIAXIAL STRESS SITUATION
In plane stress situation, the principal stresses are given by the expression

4. EQUIVALENT STRESS
With plane stress, EQUIVALENT stress is

5. EQUIVALENT STRESS
Equivalent stress then becomes

6. PRINCIPAL STRESS IN TERMS OF PLANE STRESS ELEMENTS
Becomes

7. EQUIVALENT STRESS IN TERMS OF PLANE STRESS ELEMENTS
Consequently

8. EQUIVALENT STRESS-BI-AXIAL STRESS
IN TERMS OF STRESS ELEMENTS

9. EQUIVALENT STRESS
IN TERMS OF STRESS ELEMENTS

10. EQUIVALENT STRESS-BI-AXIAL STRESS
IN TERMS OF STRESS ELEMENTS

11. DISTORTION ENERGY THEORY
When Yielding occurs in any material,
The distortion strain energy per unit volume
At the point of failure
Equals or exceeds
When yielding occurs in the tension test specimen.

12. DISTORTION ENERGY THEORY PLANE STRESS SITUATION
Design equation becomes

13. PLANE STRESS SITUATION WITH ONE NORMAL STRESS
This situation of plane stress
With one normal stress only
Arises in the loading of shafts with combined torsion, bending,
Shafts with combined torsion and axial loads.