Thin-walled Pressure Vessels

a Tank or pipe carrying a fluid or gas under a pressure is subjected to tensile forces, which resist bursting, developed across longitudinal and transverse sections.

TANGENTIAL STRESS, t (Hoop Stress)Consider the tank shown being subjected to an internal pressure . The length of the tank is and the wall thickness is . Isolating the right half of the tank:

The forces acting are the total pressures caused by the internal pressure and the total tension in the walls .F=PA=P*D*LT=ttL

h=PD/2tIf there exist an external pressure and an internal pressure , the formula may be expressed as:h=(Pi-Po)D/2t

LONGITUDINAL STRESS

Consider the free body diagram in the transverse section of the tank:

The total force acting at the rear of the tank must equal to the total longitudinal stress on the wall . Since is so small compared to , the area of the wall is close to PiDt

And Therefore t=PD/4tIf there exist an external pressure and an internal pressure , the formula may be expressed as:t=(Po-Pi)D/4t

From This it can be easily observed that the tangential stress ( Hoop ) is twice the longitudinal stress .h = 2 t

Spherical Shell :

If a spherical tank of diameter and thickness contains gas under a pressure of , the stress at the wall can be expressed as:

t=(D/Po-Pi)4t