What is the NORMAL STRESS in a thin walled pressure vessel?

I am aware of only 2 types of stresses in thin walled pressure vessels: Longitudinal & Tangential.

Is any one of these 2 is considered as the NORMAL STRESS? If yes, which one and why?


2 Answers 2


Both Axial stress, (parallel to the axis of cylindrical symmetry) and Hoop Stress (in the tangential direction) are "Normal Stresses".

They are "Normal", because, if you consider an infinitesimal unit volume, the stresses can be considered to be entirely axial in the X and Y directions respectively. There is no stress in the Z direction because of the 'thin wall' assumption.

The other types of stress are Bending, and Shear, neither of which can be induced by the pressure of the gas, in a symmetrical vessel.

  • $\begingroup$ Is longitudinal stress not considered as Axial stress? $\endgroup$ Dec 8, 2017 at 8:33
  • $\begingroup$ Yes, it is. A normal stress is a stress that occurs when a member is loaded by an axial force. $\endgroup$ Dec 8, 2017 at 9:18

For thick wall assumption, the normal stress is also called the radial stress. The thick wall assumption has thick walls and adds a small internal "normal" radial stress:

$$\sigma_r = \frac{r_i^2P_i-r_o^2P_o}{r_o^2-r_i^2} - \frac{(P_i-P_o)r_i^2r_o^2}{(r_o^2-r_i^2)r^2}$$

Note this stress is much smaller compared to the tangential and axial stress, which is why it is normally ignored.


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