Formula for bending a rod in the elastic range

In summary, the conversation discusses the potential existence of a formula for calculating the minimum radius that a rod can be bent around while staying in the elastic range. The example given is a 1/4" diameter rod made of HDPE with a modulus of elasticity of 0.8 GPa and the goal is to determine the minimum radius for bending without causing deformation. It is noted that more information may be needed to fully answer the question.
  • #1
pistorinoj
5
0
Is there a formula to calculate the radius that a rod of a given radius can be bent around while staying in the elastic range?

For example, if I had a rod that was 1/4" in diameter and made of HDPE (which I think has a modulus of elasticity of 0.8 GPa), how would I calculate the minimum radius the rod could be bent around while still staying in the elastic range so that it could be unwound without deformation?
 
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  • #2
I think the answer to your question would need more information than just the modulus.

<Moderator's note: removed advice to post in ME after moving the thread to ME.>
 
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Related to Formula for bending a rod in the elastic range

1. What is the formula for bending a rod in the elastic range?

The formula for bending a rod in the elastic range is known as the Euler-Bernoulli beam theory, which states that the maximum stress in a beam is directly proportional to the bending moment and inversely proportional to the moment of inertia and the distance from the neutral axis.

2. How do you determine the maximum stress in a bent rod?

The maximum stress in a bent rod can be calculated using the formula: σ = (My/I), where σ is the stress, M is the bending moment, y is the distance from the neutral axis, and I is the moment of inertia.

3. What is the elastic range for a bent rod?

The elastic range for a bent rod is the range within which the rod can be bent without permanently deforming. This range is also known as the linear elastic range and is determined by the material properties of the rod.

4. Can the formula for bending a rod in the elastic range be applied to all materials?

The formula for bending a rod in the elastic range can be applied to most materials, as long as they exhibit linear elastic behavior. However, for some materials with non-linear behavior, more complex formulas may be required to accurately calculate the bending stress.

5. How does the moment of inertia affect the bending of a rod?

The moment of inertia is a measure of an object's resistance to bending. A larger moment of inertia means that the rod is stiffer and can withstand higher bending stresses, while a smaller moment of inertia means that the rod is more flexible and may deform more easily when bent.

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