1. DEPARTMENT OF MECHANICAL AND MANUFACTURING ENGINEERING
UNIVERSITY OF NAIROBI
DEPARTMENT OF MECHANICAL AND MANUFACTURING ENGINEERING
ENGINEERING DESIGN II
FME 461
PART 16
GO NYANGASI
January 2007

2. LAME’S EQUATION MAXIMUM NORMAL STRESS THEORY
APLLIED TO
THICK WALLED CYLINDER OF BRITTLE MATERIAL

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

4. LOCATION OF EXTREME STRESSES AT INNER SURFACE
For close ended cylinder, extreme stresses occurring at inner surface are

5. STRESS AT INNER SURFACE

6. STRESS ACROSS WALL
Stress distribution across the wall

7. LOCATION OF EXTREME STRESSES AT INNER SURFACE
Extreme stresses occur at inner surface since

8. PRINCIPAL STRESSES AT THE EXPECTED POINT OF FAILURE
This is at inners surface with stresses

9. MAXIMUM NORMAL STRESS THEORY
CYLINDER FROM BRITTLE MATERIAL SUBJECT TO INTERNAL PRESSURE
For a brittle material such as cast iron, the maximum normal stress theory of failure is applied. This says:
When failure occurs in any material, the maximum normal stress at the point of failure equals or exceeds the maximum normal stress when failure occurs in the tension test specimen.

10. MAXIMUM NORMAL STRESS THEORY
MAXIMUM NORMAL STRESS IN THE TENSION TEST SPECIMEN

11. PRINCIPAL STRESSES AT THE POINT OF FAILURE
Stress condition is extreme at inside surface of cylinder where

12. MAXIMUM NORMAL STRESS
The maximum normal stress at the location is tensile while the minimum normal stress is compressive.
Failure could therefore be caused by either the maximum tensile stress, or the minimum compressive stress.
However, the cast iron material has a compressive strength which is many times higher than the tensile strength.
Failure will therefore be caused by the higher tensile stress acting on the lower tensile strength of the material.

13. APPLYING THE THEORY
When failure occurs maximum normal stress equals tensile strength

14. MAXIMUM NORMAL STRESS
Identifying a design or allowable stress

15. DESIGN EQUATION
Comparing stress and strength

16. DESIGN EQUATION
Comparing stress and strength

17. DESIGN EQUATION
Simplifying