DEPARTMENT OF MECHANICAL AND MANUFACTURING ENGINEERING UNIVERSITY OF NAIROBI DEPARTMENT OF MECHANICAL AND MANUFACTURING ENGINEERING ENGINEERING DESIGN II FME 461 PART 13 GO NYANGASI January 2007

CYLINDERS SUBJECT TO INTERNAL PRESSURE THICK WALLED CYLINDERS

Application Examples Cylinders subject to internal pressure are members such as hydraulic cylinders, gun barrels, pipes carrying fluids at high pressure, etc. Such members are analysed as thick walled cylinders subject to internal and external pressure.

OPEN ENDED CYLINDERS DETERMINATION OF LOAD AND STRESSES When cylinder is open ended and Subjected to internal and external pressure The pressure load induces internal stresses in the wall thickness of the cylinder. Stresses induced occur in the tangential direction as well as the radial direction in the wall thickness.

CYLINDER WITH CLOSED ENDS DETERMINATION OF LOADS AND STRESSES When the ends of the cylinders are closed, an additional longitudinal stress is induced as a result of the internal pressure operating on the closed end of the cylinder. Designing the member involves choosing material for the cylinder, and the dimensions such as wall thickness Safety is achieved by ensuring that the stresses induced do not exceed the strength of the material The significant stress is identified and determined, and is then compared with the appropriate indicator of strength for the material used for the cylinder wall.

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

TANGENTIAL AND RADIAL STRESSES INDUCED Stresses induced in the cylinder walls are determined through several steps: Consider the requirements of static equilibrium for the elemental fibres in the cylinder wall Consider requirements for compatibility in the deformations of elemental fibres Apply the known boundary conditions of radial pressure at inside surface and at outside surface

RADIAL AND TANGENTIAL Internal and External Pressure Expressions for stress across cylinder wall

RADIAL AND TANGENTIAL Zero External Pressure Expressions for stress across cylinder wall

STRESS AT INNER SURFACE For cylinder subject to internal pressure

STRESS AT OUTER SURFACE For cylinder subject to internal pressure

LONGITUDINAL STRESS Stress assumed uniform across wall thickness

STRESS AT INNER SURFACE

STRESSES ACROSS WALL Internal Pressure only Stress distribution across cylinder wall