Pressure Vessel Thickness Calculation


In this article:
– we will talk about how to derive the formulas of stresses for thin-walled pressure vessels
– We will also look at the formulas for thick-walled pressure vessels
– Afterwards, we will compare with the formulas in ASME VIII Div 1.


Thin-Walled Pressure Vessels

In thermodynamics, we learned that pressure equals force per unit area.

P = F/A

We will use this concept in deriving the formulas of stresses.

Note that a pressure vessel is considered thin-walled when the radius to thickness ratio is greater than 10.
Thus, r/t > 10.



Tangential Stress (Circumferential Stress or Hoop Stress)

From the illustration, F and image 1T are in equilibrium where F is the force exerted by pressure while T is the tangential force exerted by the vessel. Calculating the forces using F = P*A based on the illustration, where σt is the tangential stress.

Note that σt has the same units of measurement as pressure.

F = P*D*L

T = σt*2*t*L

Equating the two, we come up with the formula for σt.

PDL = σt2tL

PD = σt2t

σt = PD/2t

Note that this formula can also be used for pipes.

pressure vessel, calculation

Longitudinal Stress

We calculate following the same concept as above, where L is the longitudinal force and σl is the longitudinal stress.
The area of a circle is πD2/4 while the circumference is πD.

image 3

Equating the two, we come up with the formula for σl .

image 4

Note that this formula is used for cylindrical and spherical vessels. From the two formulas, we can say that the tangential stress is twice as much as longitudinal stress.


Thick-Walled Pressure Vessels

There is a third type of stress which is the radial stress, sr. This stress is acting radially toward the axis. Note that we did not consider sr in thin-walled pressure vessels since this is negligible compared to tangential stress.

image 5

The formulas for stresses in thick-walled pressure vessels at any given radius are as follows:

image 6

The maximum shear stress is:

image 7

If the pressure vessel is closed, the longitudinal stress is:

image 8



Thickness of Shells Under Internal Pressure

where: E = joint efficiency

S = maximum allowable stress

R = inside radius

P = internal design pressure

t = minimum required thickness of shell

image 9


Photo credit to Supakitmod3 of


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  • aldwin - August 22, 2015 reply


    admin - August 22, 2015 reply

    Magandang araw sa iyo Kabayan!

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