DEPARTMENT OF MECHANICAL AND MANUFACTURING ENGINEERING UNIVERSITY OF NAIROBI DEPARTMENT OF MECHANICAL AND MANUFACTURING ENGINEERING ENGINEERING DESIGN II FME 461 PART 15 GO NYANGASI January 2007

CLAVARINO’S EQUATION MAXIMUM NORMAL STRAIN THEORY APLLIED TO CLOSE ENDED THICK WALLED CYLINDER OF DUCTILE 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

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

MAXIMUM NORMAL STRAIN THREE DIMENSIONAL STRESS This is given by the expression

CLOSE ENDED CYLINDER LONGITUDINAL STRESS IS NOT ZERO Maximum normal stresses at the inside surface of cylinder are given by

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

CLOSE 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