1. DEPARTMENT OF MECHANICAL AND MANUFACTURING ENGINEERING
UNIVERSITY OF NAIROBI
DEPARTMENT OF MECHANICAL AND MANUFACTURING ENGINEERING
ENGINEERING DESIGN II
FME 461
PART 6
GO NYANGASI
November 2008

2. BI-AXIAL STRESS AND MSS THEORY
FAILURE BOUNDARIES

3. MAXIMUM SHEAR STRESS Statement of the theory
When Yielding occurs in any material
The maximum shear stress at the point of failure
Equals or Exceeds
The maximum shear stress when yielding occurs
In the tension test specimen.

4. PLANE STRESS SITUATION
Three stresses exists on one plane and stresses on the third dimension are zero

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

6. PRINCIPAL STRESSES IN BIAXIAL STRESS SITUATION
ORDER OF MAGNITUDE
The principal stresses shown in the previous slide can represent two alternatives, which determine the order of magnitude of principal stresses
Principal stresses in the plane are of opposite sign
Principal stresses in the plane are of same sign

7. TRI-AXIAL STRESS SITUATION
Maximum shear stress at a location
Extreme values of shear stresses in each of the three principal planes are then given by the expressions below

8. BIAXIAL STRESS SITUATION
For plane (bi-axial) stress situation
Third principal stress is zero
The extreme values of shear stress are then expressed as:

9. UNI-AXIAL STRESS SITUATION
Simple tension is an example
When yielding occurs in tension test specimen

10. MOHR’S CIRCLE DIAGRAMS

11. BI-AXIAL STRESS
PRINCIPAL STRESSES: of OPPOSITE sign

12. MAXIMUM SHEAR STRESS THEORY IN BI-AXIAL STRESS
Principal stresses: of OPPOSITE sign

13. PRINCIPAL STRESSES: of OPPOSITE sign

14. BI-AXIAL STRESS PRINCIPAL STRESSES: of SAME sign
Expression for Maximum shear stress shown below- Illustrated in the next Slide
Expression for Failure boundaries

15. MAXIMUM SHEAR STRESS THEORY IN BI-AXIAL STRESS
Principal stresses: of SAME sign

16. PRINCIPAL STRESSES: of SAME sign
Expression for Failure boundaries

17. MAXIMUM SHEAR STRESS THEORY IN BI-AXIAL STRESS
Failure boundaries in bi-axial stress