# Tension on the ring

1. Jan 29, 2010

### dE_logics

Imagine a ring; the image below shows the top cross section of the ring -

The arrows represent forces which is acting towards the inner side of the ring cause of a pressure which applies towards it's inner side.

Assuming the ring to be made up of a material having a plastic property, I want an expression for the tension produced in the ring.

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2. Jan 29, 2010

### minger

Do you own a copy of Roark? This looks like a ring under internal pressure. Actually, the load case you probably want is a simple shell of revolution under internal pressure. In my version its Chapter 13 load case 1b.
Hoop stress:
$$\sigma = \frac{qR}{t}$$

3. Jan 29, 2010

### FredGarvin

That is pretty much the definition of the hoop stress.

4. Jan 29, 2010

### dE_logics

5. Jan 29, 2010

### dE_logics

I did some calculations and found that the stress should be ~63.7% of 1/4th of the total force applied by the pressure.

6. Jan 29, 2010

### minger

??????

7. Jan 29, 2010

### FredGarvin

I understood 1/4th of 63.7% of that post. Care to rephrase this or tell us what you are getting at?

8. Jan 29, 2010

### dr dodge

is this a good book for the "techno savy" non engineer?

I would like to find a good formula book that was not a novel in "techno-ese" just formulas
(especially pressure and temp related)

dr

9. Jan 29, 2010

### CFDFEAGURU

Roark's book is pretty good. If you are crafty enough with mathematics you can derive some of the formulas in Roark with the help of Timoshenko's book "Plates and Shells" but you better be good.

Roark's book is good for the non-engineer. The hard part is knowing that you have the right boundary conditions specified.

Here is a link to it.

http://www.roarksformulas.com/

Be cautious of the online calculator.

Thanks
Matt

10. Jan 29, 2010

### FredGarvin

It is but you do have to have a basic understanding to fully understand it. The beginning sections of each chapter cover theory. However, it is, essentially, a book divided into different tables covering load/support scenarios with associated equations covering that scenario. I attached a typical page so you can see it.

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11. Jan 29, 2010

### dE_logics

aaa...just forget the 63.7% part...I'll work on it later.

Point is hooks stress is no different from normal stress right?...I mean if hook's stress comes as 500 mega pascals, then the stress in the material is 500 mega pascals right?

12. Jan 29, 2010

### Brian_C

The hoop stress is very easy to derive for this type of setup. There is no need for any fancy elasticity theory.

Last edited: Jan 29, 2010
13. Jan 30, 2010

### nvn

dE_logics: That is correct. Hoop stress is normal stress. Very good.

14. Jan 30, 2010

### dE_logics

Sounds sarcastic.

Is there a conversion or something?

Last edited: Jan 30, 2010
15. Jan 30, 2010

### FredGarvin

No. He was being serious. The hoop stress is the same thing as the normal stress because of the direction on an element that is perpendicular to a line around the circumference at some radius.

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16. Jan 30, 2010

### dE_logics

Oh...ok, thanks a lot people.

Need it urgently.

17. Feb 1, 2010

### dr dodge

thanks for the book review
I'll add it to my "wish list" when I go to the used book store
if not, it looks like it is worth the \$70 anyway

dr