# Calculating Force/Moment to Bend Strip into Circle

• stressdave
In summary: The rest is trade study and experience.In summary, the force or moment required to bend a thin strip into a circle depends on the material properties, cross section dimensions, circle diameter, means of forming the curvature, and acceptable amount of spring back. The specific steel specification and strip thickness also play a role in determining the force needed. Creep and stress relaxation can cause permanent curvature in the strip, but with moderate temperatures and low stress levels, it is unlikely to be a significant problem. The minimum coil wrap diameter to avoid yield depends on keeping stress levels below the creep strength of the material. The limit state method can be used to get an upper bound on the bending force, but the recommended coil
stressdave
I need to calculate the force or moment required to bend a thin strip into a circle

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 .

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.

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

What is the specific steel specification and the strip thickness ?

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)

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

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 .

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

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.

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

What is the specific steel specification and the strip thickness ?
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.

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 .

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Nidum said:
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 .
Thanks again

Mech_Engineer said:
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)
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.

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?

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

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

stressdave said:
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.
stressdave said:
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.
stressdave said:
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.
What would be the minimum coil wrap diameter of this strip stock?

Nidum said:
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 .
Is there a minimum coil wrap diameter to avoid yield?

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?

## 1. How do you calculate the force needed to bend a strip into a circle?

The force needed to bend a strip into a circle can be calculated using the formula F = YI/R, where F is the required force, Y is the Young's modulus of the material, I is the moment of inertia of the strip, and R is the radius of the circle. The moment of inertia can be calculated by multiplying the cross-sectional area of the strip by the square of its distance from the center of the circle.

## 2. What is the Young's modulus of the material?

The Young's modulus is a measure of the stiffness of a material and is defined as the ratio of stress to strain. It is typically represented by the letter Y and is measured in units of pressure, such as pounds per square inch (psi) or megapascals (MPa).

## 3. How does the thickness of the strip affect the force needed to bend it into a circle?

The thickness of the strip directly affects the moment of inertia, which in turn affects the required force. A thicker strip will have a higher moment of inertia, meaning it will require a greater force to bend it into a circle compared to a thinner strip.

## 4. Can you use this formula for any material?

The formula F = YI/R can be used for any material as long as its Young's modulus and moment of inertia are known. However, it is important to note that this formula assumes the material is elastic and does not take into account any plastic deformation that may occur during the bending process.

## 5. How can you calculate the moment needed to bend a strip into a circle?

To calculate the moment needed to bend a strip into a circle, you can use the formula M = FR, where M is the moment, F is the force calculated from the first formula, and R is the radius of the circle. This formula is based on the principle of torque, which states that the moment of a force is equal to the force multiplied by the distance from the pivot point.

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