Stresses in Thin Cylinders

STRESSES IN THIN CYLINDERS

When the pressure inside the cylinder is developed, the cylinder walls are subjected to tensile stresses. There are two types of tensile stresses developed according to the direction in which they are acting.

(a) Circumferential or hoop stress

(b) Longitudinal stress

When these stresses exceed the permissible limit, the cylinder is likely to fail in the following two ways.

(i) It may split up into two semi circular halves along the cylinder axis as shown in Fig.5.1(i) and

(ii) It may split up into two cylinders as shown in Fig.5.1(ii).

(a) Circumferential or hoop stress

The stress in the circumferential direction due to tendency of bursting the cylinder along the longitudinal axis is called circumferential stress or hoop stress. Simply the stress acting along the circumference of the cylinder is called circumferential or hoop stress.

Consider a thin cylindrical pipe of diameter d and wall thickness t subjected to

an internal fluid pressure p.

We know that the circumferential stress is developed due to tendency of bursting along the longitudinal axis.

The bursting force along diameter of cylinder,

Since there are two thickness resisting the bursting force,

(b) Longitudinal stress

The stress in the longitudinal direction due to tendency of bursting the cylinder along the transverse plane is called longitudinal stress. Simply the stress acting along the length of the cylinder is known as longitudinal stress.

Consider a thin cylindrical shell of diameter d and wall thickness t and length / subjected to an internal pressure p.

Considering the axial bursting force tending to break the cylinder along the circumference,