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Radial stress in pressure vessels

by jayanth nivas
Tags: pressure, radial, stress, vessels
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jayanth nivas
Aug27-13, 12:27 AM
P: 15
Hi all,
I have started with my understanding of pressure vessels and i have some queries on the topic.

1) I understand the part of axial stresses.When a cylinder capped at both ends is subjected to internal pressure,it tends to increase the length of the shell,and therefore a resistance is offered by pressure vessel,which is measured by load (Internal pressure X circular area )/ the cross sectional area of Pressure vessel (One between I.D & O.D of the vessel)

2) To some extent,I understand the concept of hoop stress.The internal pressure inside the cylinder tries to displace the circumferential elements farther (Increasing the diameter of the cylinder).Therefore the hoop stress is measured by load (internal pressure X projected area )/ cross sectional area of pressure vessel (one which is the product of thickness and length considered)

3) My query now is,what is radial stress?.And what is the load for it and what is the area resisting it?.In what way it tries to deform the pressure vessel ?.And why do we
neglect it for thin walled pressure vessels and consider it for thick walled pressure vessels ?

4) Also are both hoop and radial stress a response to diametrical deformation ?

My understanding on this topic is elementary and I apologize if I have misstated something.

Thanks for going through the post.
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Aug27-13, 11:37 AM
P: 343
Circumferential (hoop) and radial stresses are responses to diametrical deformation. To state just for completeness, the hoop stress is stress in the direction along the circumference, and radial stress is a stress in the radial direction. For a internally pressurized cylinder, the hoop stress is generally a tensile stress along the circumference of the cylinder, while a radial stress is usually a compressive stress between the outer and inner surfaces of the cylinder. These radial and hoop stresses can be formulated as a function of internal and external pressure and the inner and outer radii, so no "area" calculations are necessary.

In thick-walled vessels, there is a distribution of tangential and radial stress across the thickness of the cylinder. Generally, the stresses are highest for both radial and tangential (hoop) stress at the inner surface of the cylinder. However, when the wall thickness of the cylinder is less than 1/20th the radius (according to Shigley), the distribution has a valid approximation of an average tangential stress. As well, the radial stress tends not to matter much because it's so small when compared to the hoop stress. That's also why we can use plane stresses when talking about thin-walled cylinders. The tangential stress then becomes your driving design factor for thin-walled vessels.
Aug28-13, 03:41 PM
Sci Advisor
P: 1,747
Have you noticed that for a uniform cylinder under pressure, the hoop stress is twice the axial stress. That explains why pipes split along their length when they burst.

Aug28-13, 05:54 PM
Sci Advisor
HW Helper
P: 6,948
Radial stress in pressure vessels

On the inside surface of the cylinder, the radial stress is the same as the internal pressure. On the outside, it is the same as the external pressure (often atmospheric pressure, 14 psi or 0.1 MPa). Through the thickness of the cylinder, it varies almost linearly between those values.

For a thin cylinder the radial stress of the order of P is negligible compared with the other stress components with are of the order of Pr/t or Pl/t, and for a thin cylinder r/t and l/t are big numbers.

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