Is it possible to do this without Poission's ratio?

In summary, the given problem involves determining the force needed to cause a .003mm diameter reduction in a 20mm diameter steel alloy bar with a modulus of elasticity of 205 GPa. The bar experiences an elastic deformation when a force is applied along its axis. In order to solve the problem, you will need to know Poisson's ratio, which is not given by the professor.
  • #1
Nodnarb98
this is the problem as our professor gave it to us

"A steel alloy bar (modulus of elasticity of 205 GPa) is 20mm in diameter and experiances an
elastic deformation by applying a force along its axis (IE pulling it apart perpendicular to the
circular cross section). Determine the force needed to cause a .003mm diameter reduction."
is it even possible to do the problem without the ratio? if so where do I start?

2. Homework Equations I Know stress =f/a, and strain = Δl/l and hooke's law σ=Eεz. as you can see he didn't give us possion's ratio, used in εz=-εx/v.

The Attempt at a Solution


I've tried setting it up multiple ways, but each time i have more unknowns that equations. I emailed my instructor but he hasn't answered

Thanks!
 
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  • #2
In my judgment, you need to know Poisson's ratio. Assume 0.3
 
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  • #3
Thanks
 

1. What is Poisson's ratio?

Poisson's ratio is a material property that describes the ratio of transverse strain to axial strain when a material is stretched. It is named after French mathematician Siméon Denis Poisson.

2. Why would someone want to do something without Poisson's ratio?

There are a few reasons why someone might want to do something without Poisson's ratio. One reason could be that they are studying a material that does not exhibit this property, such as a liquid or gas. Another reason could be that they are trying to engineer a material with specific properties, and Poisson's ratio is not desirable for their application.

3. Is it possible to have a material without Poisson's ratio?

Yes, it is possible to have a material without Poisson's ratio. As mentioned before, liquids and gases do not have a Poisson's ratio. Additionally, certain materials can be engineered to have a near-zero or even negative Poisson's ratio, such as auxetic materials.

4. What are the implications of having a material without Poisson's ratio?

The implications of having a material without Poisson's ratio depend on the specific application. In some cases, it may be beneficial to have a material without this property, as it can lead to unique mechanical behaviors. However, in other cases, not having Poisson's ratio can make a material less stable and more prone to buckling or deformation.

5. Can we design structures without considering Poisson's ratio?

In most cases, Poisson's ratio should be considered when designing structures, as it is an important mechanical property that can affect the stability and behavior of a material. However, in certain applications, such as non-load-bearing structures or structures made from materials without Poisson's ratio, it may not be necessary to consider this property.

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