25-05-2012, 04:54 PM
Thin and thick cylinders
Thin and thick cylinders.pdf (Size: 151.54 KB / Downloads: 113)
Stresses in thin cylinders
If the wall thickness is less than about 7% of the inner diameter then the cylinder may be treated as a thin one. Thin walled cylinders are used as boiler shells, pressure tanks, pipes and in other low pressure processing equipments. In general three types of stresses are developed in pressure cylinders viz. circumferential or hoop stress, longitudinal stress in closed end cylinders and radial stresses. These stresses are demonstrated in figure-9.1.1.1.
In a thin walled cylinder the circumferential stresses may be assumed to be constant over the wall thickness and stress in the radial direction may be neglected for the analysis. Considering the equilibrium of a cut out section the circumferential stress σθ and longitudinal stress σz can be found. Consider a section of thin cylinder of radius r, wall thickness t and length L and subjected to an internal pressure p as shown in figure-9.1.1.2(a). Consider now an element of included angle dθ at an angle of θ from vertical. For equilibrium we may write
Design Principles
Pressure vessels are generally manufactured from curved sheets joined by welding. Mostly V– butt welded joints are used. The riveted joints may also be used but since the plates are weakened at the joint due to the rivet holes the plate thickness should be enhanced by taking into account the joint efficiency. It is probably more instructive to follow the design procedure of a pressure vessel. We consider a mild steel vessel of 1m diameter comprising a 2.5 m long cylindrical section with hemispherical ends to sustain an internal pressure of ( say) 2MPa.
Summary of this Lesson
Stresses developed in thin cylinders are first discussed in general and then the circumferential (θσ) and longitudinal stresses (zσ) are expressed in terms of internal pressure, radius and the shell thickness. Stresses in a spherical shell are also discussed. Basic design principle of thin cylinders are considered. Design of both welded and riveted joints for the shells are discussed.
Version