### Stresses in thin cylinders

Date : 2016-06-23 12:24:21

Introduction:

The unbalanced force acting on the left wall is called the bursting force and the force due to internal stresses acting on the wall thickness of the cylinder is called the resisting force.

Description:

Consider a thin seamless cylindrical shell of nominal diameter d, and shell thickness which is containing some fluid at an internal pressure of p. The two ends of the cylinder are closed with walls perpendicular to the shell. We shall consider a vertical plane YY which cuts the cylinder anywhere along the length. We shall consider the left portion of the cylinder and see the nature and magnitude of the internal stresses acting on the section. • It can be seen that the internal stresses acts over the shaded annular portion of the cylinder, which is the wall area exposed due to the cutting the by plane Y-Y. The direction of these internal stresses will be clearly longitudinal as the exposed areas is in the vertical plane.
• In addition it can also be seen that these stresses develop owing to the unbalanced horizontal force acting on the left vertical wall of the cylinder, since the pressure acting on the curved walls balance each other.
• Thus the stresses will be tensile in nature so as to maintain equilibrium. The unbalanced force acting on the left wall is called the bursting force and the force due to internal stresses acting on the wall thickness of the cylinder is called the resisting force.

We can write the expressions for the bursting and resisting forces as below.

It can be clearly seen that the bursting force is caused due to the internal pressure acting on the vertical circular wall of nominal diameter d.

Hence, the bursting force The resisting force is generated by the longitudinal tensile stress σl acting on the vertical area exposed, of thickness t and diameter d.

Hence, the resisting force For equilibrium, the resisting force should be equal to the bursting force.
Thus, we get This internal stress is called longitudinal stress, indicating the direction in which it is acting and its nature will be tensile.