1. 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

2. CYLINDERS SUBJECT TO INTERNAL PRESSURE
THICK WALLED CYLINDERS

3. 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.

4. 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.

5. 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.

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

7. 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

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

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

10. STRESS AT INNER SURFACE
For cylinder subject to internal pressure

11. STRESS AT OUTER SURFACE
For cylinder subject to internal pressure

12. LONGITUDINAL STRESS
Stress assumed uniform across wall thickness

13. STRESS AT INNER SURFACE

14. STRESSES ACROSS WALL Internal Pressure only
Stress distribution across cylinder wall