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### Horizontal diametrical plane

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

Introduction:

Resultant vertical component is acting upwards, the internal stress on the horizontal strip of dimensions l and t will be acting downwards indicating that the nature of this stress is tensile.

Description:

• We shall consider the equilibrium of the top portion of the cylinder. The horizontal pressure acting on the two end walls will balance each other and hence, there will be no longitudinal stress in the wall of the cylinder.
• The pressure acting on the curved surface of the shell creates the bursting force for this free body diagram which should be balanced by the reacting force caused by the development of internal stresses along with wall thickness of the cylinder.
• Since the plane XX is horizontal, the cylinder’s wall exposed by the cutting, will also be horizontal and it will be in the form of two rectangular strips, along with longitudinal direction of length l and thickness t.
• Thus, the stress acting on this strip will be in the vertical direction.

Fig: 1

The pressure acting on the curved surface acts normal to the surface and hence, it will be acting in different direction at different points along the surface. The vertical component of the bursting force is obtained by considering an element at angle θ to the horizontal which is subtended by an angle dθ at the centre as shown in Figure 1. The length of this element may be the total length of the cylinder itself. The revolution of the elemental force in the vertical direction is shown in Figure 2.

Fig: 2

The radial force acting on the element,

Since this resultant vertical component is acting upwards, the internal stress on the horizontal strip of dimensions l and t will be acting downwards indicating that the nature of this stress is tensile.

Since the equilibrium is maintained by the action of bursting and resisting forces only, they must be equal.

This stress is called the hoop stress acting in the circumferential direction and it will be tensile in nature.