# Beam bending

1. Feb 2, 2017

### stressdave

I need to calculate the force or moment required to bend a thin strip into a circle

2. Feb 2, 2017

### Nidum

Depends on the material properties , the material cross section dimensions , the circle diameter , the means of forming the curvature and the amount of spring back that is acceptable .

Please tell me what you are actually trying to do .

3. Feb 3, 2017

### stressdave

Thanks for the reply. I have a 192 inch long steel strip of very low stiffness. We form it into a circle by hand and attach ends with fasteners. It is stowed by twisting it into a circle of 21 inches for stowage on the ISS. The question has been asked is what amount, if any, or creep, or set, will occur over 15 years. I don't think anything will change and the yield point is not reached. It is analogous to a windshield sun screen. Total spring back is required.

4. Feb 3, 2017

### Nidum

That's a hard problem to answer . I'll have to think about it .

What is the specific steel specification and the strip thickness ?

5. Feb 3, 2017

### Mech_Engineer

It sounds like you don't actually need the force, but instead need to calculate the maximum stress on the part in the stored configuration, and compare that force to a stress creep curve for the material it's made out of.

https://en.wikipedia.org/wiki/Creep_(deformation)

6. Feb 3, 2017

### malemdk

use strain gages to see whether the material is with in elastic limit.

7. Feb 4, 2017

### Nidum

Pro tem I can't see a way of deciding this matter theoretically .

Though the solution seems obvious common experience suggests that initially straight thin strip coiled up for a long time almost always shows some residual curvature when uncoiled again .

I know some of the mechanisms involved in this but putting the whole thing together to get numerical answers is likely to be problematic .

You certainly want to keep stress levels in the coiled strip very low ( ideally < 10% Yield Stress ) and if possible do an accelerated ageing test .

8. Feb 4, 2017

### Mech_Engineer

The method is to design the part to stay below the material's creep strength in the stored configuration. Creep strength commonly depends on temperature and a few other things, but it's possible to design for 99.9% spring back with the appropriate material.

9. Feb 7, 2017

### stressdave

It is spring steel per ASTM A313. The thickness is only .053 inch. The part is stowed in 70 deg F environment. I can't image creep will occur.

10. Feb 7, 2017

### Nidum

With your moderate temperatures and low stress levels I don't think that creep would be an active mechanism causing permanent curvature .

Permanent curvature could possibly be caused under these conditions by metallurgical changes and stress relaxation but best guess based on available information is that there is unlikely to be any significant problem . The strip could possibly have a slight permanent curvature but so little as to be unimportant .

Remember in any case that a thin strip can never be entirely straight under normal circumstances .

Last edited: Feb 7, 2017
11. Feb 7, 2017

### stressdave

Thanks again

12. Feb 9, 2017

### stressdave

Let me rephrase the question. How much force would it take to bend a strip of very stiffness 360 degrees around a 20 inch mandrel? The length of strip would be approximately 67 inches.

13. Feb 9, 2017

### Mech_Engineer

That's kind of a tough question actually, most typical beam bending equations assume small deflections and so won't apply to this situation. Have you done any testing up to this point?

14. Feb 9, 2017

### Nidum

You can use the limit state method to get an upper bound on the bending force .

15. Feb 10, 2017

### stressdave

I am not familiar with the limit state method. Let me ask a new question. What is the recommended coil wrap diameter of a .053 inch thick x .345 inch wide steel strip that will not yield the metal?

16. Feb 10, 2017

### stressdave

What would be the minimum coil wrap diameter of this strip stock?

17. Feb 10, 2017

### stressdave

Is there a minimum coil wrap diameter to avoid yield?

18. Feb 10, 2017

### Mech_Engineer

You have to keep the stress below the creep strength of the material, which will be lower than the yield strength. You need to first calculate the stress/strain for the ring in the "stored" state and see where you are. Do you have the stress calculation?