1. DEPARTMENT OF MECHANICAL AND MANUFACTURING ENGINEERING
UNIVERSITY OF NAIROBI
DEPARTMENT OF MECHANICAL AND MANUFACTURING ENGINEERING
ENGINEERING DESIGN II
FME 461
PART 14
GO NYANGASI
January 2007

2. BIRNIE’S EQUATION MAXIMUM NORMAL STRAIN THEORY
APLLIED TO
OPEN ENDED THICK WALLED CYLINDER OF DUCTILE MATERIAL

3. EXTERNAL LOAD AND DIMENSIONS OF MEMBER
Sketch shows a thick walled cylinder intended as a hydraulic cylinder.

4. LOCATION OF EXTREME STRESSES AT INNER SURFACE
Extreme stresses occur at inner surface
ZERO Longitudinal stress-OPEN ENDED

5. STRESS AT INNER SURFACE

6. STRESS ACROSS WALL
Stress distribution across the wall

7. PRINCIPAL STRESSES AT THE EXPECTED POINT OF FAILURE
This is at inner surface with stresses

8. MAXIMUM NORMAL STRAIN THREE DIMENSIONAL STRESS
Coincides with maximum normal stress and is given by the expression

9. OPEN ENDED CYLINDER AT INNER SURFACE OF CYLINDER
Maximum normal stresses at the inside surface of cylinder are given by

10. OPEN ENDED CYLINDER
Substituting the values of principal stresses to obtain maximum normal strain

11. OPEN ENDED CYLINDER
MAXIMUM NORMAL STRAIN IN THE TENSION TEST SPECIMEN

12. MAXIMUM NORMAL STRAIN
Comparing maximum normal strains

13. DESIGN EQUATION
Applying a factor of safety

14. DESIGN EQUATION
Simplifying

15. DESIGN EQUATION
Simplifying

16. DESIGN EQUATION
Simplifying