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stressdave

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

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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

- #1

stressdave

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

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Nidum

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Please tell me what you are actually trying to do .

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stressdave

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Nidum

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What is the specific steel specification and the strip thickness ?

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Mech_Engineer

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

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malemdk

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

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Nidum

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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 .

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Mech_Engineer

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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.

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stressdave

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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.Nidum said:

What is the specific steel specification and the strip thickness ?

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Nidum

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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 .

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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stressdave

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Thanks againNidum said:

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 .

- #12

stressdave

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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.Mech_Engineer said:

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

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Mech_Engineer

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Nidum

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

- #15

stressdave

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

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stressdave

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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.

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

- #17

stressdave

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

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 .

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Mech_Engineer

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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.

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).

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.

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.

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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