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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.
If the thickness of the wall of the cylindrical vessel is less than 1/15 to 1/20 of its internal diameter,the cylindrical vessel is known as Thin Cylinder. 

Tangential Stress (Circumferential Stress) or Hoop stress

Consider the tank shown being subjected to an internal pressure p. The length of the tank is L and the wall thickness is t . Considering the right half of the tank: 
The forces acting on this right half of the vessel are the total pressures F caused by the internal pressure p, and the total tension T in the walls.
The projected area subjected to internal pressure = A = DL
F = pxA = p.DL
The tangential stress in the walls = st
T =  st Awall = st . tL
But F = 2T
 p.DL = 2(st . tL) 
The tangential stress st = pD/2t
If there exist an external pressure po and an internal pressure pi, the the Tangential stress may be expressed as: 
st = (po - pi ) 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 the thickness wall t is so small compared to diameter of vessel D 
The area of the wall  Awall = pDt
the total longitudinal stress on the wall 
PL = sLpDt
The total internal force acting at the rear of the tank = F
F = p. Area of the end = p ( pD2/4)
There fore PL = F
sLpDt = p ( pD2/4)
The longitudinal stress sL = pD/4t
If there exist an external pressure and an internal pressure , the formula may be expressed as: 
sL = (po - pi ) D/4t
Note:
It can be observed that the tangential stress/hoop stress is twice that of the longitudinal stress. 

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
= 4tpD
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  1. Unknown17 January 2015 at 04:00

    Nice information, many thanks to the author. It is incomprehensible to me now, but in general, the usefulness and significance is overwhelming. Thanks again and good luck ! Reaction Kettles || Process Piping || Site Fabrication

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