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

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

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

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

STRESS AT INNER SURFACE

STRESS ACROSS WALL Stress distribution across the wall

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

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

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

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

OPEN ENDED CYLINDER MAXIMUM NORMAL STRAIN IN THE TENSION TEST SPECIMEN

MAXIMUM NORMAL STRAIN Comparing maximum normal strains

DESIGN EQUATION Applying a factor of safety

DESIGN EQUATION Simplifying

DESIGN EQUATION Simplifying

DESIGN EQUATION Simplifying