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

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

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

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

STRESS AT INNER SURFACE

STRESS ACROSS WALL Stress distribution across the wall

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

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

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.

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

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

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.

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

MAXIMUM NORMAL STRESS Identifying a design or allowable stress

DESIGN EQUATION Comparing stress and strength

DESIGN EQUATION Comparing stress and strength

DESIGN EQUATION Simplifying