What is Hoop stress (Circumferential stress) and longitudinal stress in pressure vessels?

 It all starts from fabrication of pressure vessel.

Let me explain you.

Consider a cylindrical pressure vessel which has been fabricated as per the your requirement. (see below figure)

• When you fabricate any vessel, you need some plates, pipes, etc. Not everything is ready made. 
• Post this, you need to weld plates and pipes na! 

There are many layers of sheets of stainless steel or metal.

When this vessel is subjected to internal pressure, stress observed at different places/ points.

Let us cut down this cylinder perpendicular to its axis. See following image.

“Circumferential (hoop) stress is due to longitudinal weld and Longitudinal stress is due to circumferential weld.”

If we need to calculate this stresses applied to cylinder, we need equation for this.

Let us see how we can create equation.

Hoop stress: This stress is due to longitudinal weld.

It proportional on internal pressure and internal diameter of vessel. When both increases, stress increases.

It inversely proportional to thickness. Twice the thickness to be exact as per figure shown. If thickness increases, stress decreases.

σh = Pi Di / (2 t)

Longitudinal stress: This stress is due to circumferential weld.

It proportional on internal pressure and internal diameter of vessel. When both increases, stress increases.

It inversely proportional to thickness. Four times the thickness to be exact as per figure shown. If thickness increases, stress decreases.

σl = Pi Di / (4 t)

 

Hope you got the exact idea…Thanks for reading.