Calculate initial diameter from longitudinal strain and final diameter

In summary, to calculate the initial diameter of a wire that has been longitudinally strained by 30% and whose final diameter is 0.1cm, you can use the equation pi r1^2 L1 = pi r2^2 L2 and rearrange it to find the initial diameter. Assuming there is no volume change, the lateral strain would be 15% and the answer should be 0.114cm.
  • #1
Snoopdork
4
0
"Calculate the initial diameter of a wire that has been longitudinally strained by 30% and whose final diameter is 0.1cm. Assume no volume change."

Now I know that if there is no volume change, v=poisson's ratio= 0.5. Thus the lateral strain would equal 30%*0.5= 15%. But when I plug it into the strain equation and use a diameter of 0.1cm as the initial length, I get 0.1176. The answer is supposed to be 0.114cm.

Any thoughts?
 
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  • #2
If there is no volume change you don't have to know about wires or poisson ratio.
It's just a simple geometry excercise
pi r1^2 L1 = pi r2^2 L2 and L2 = 1.3 L1 just rearrange in terms of r1
 
  • #3
Wow I way over thought that one, thanks.
 

What is the formula for calculating initial diameter from longitudinal strain and final diameter?

The formula for calculating initial diameter from longitudinal strain and final diameter is:
Initial Diameter = Final Diameter / (1 + Longitudinal Strain)

Can this formula be used for any type of material?

Yes, this formula can be used for any type of material as long as the material behaves linearly and elastically under the applied strain.

How accurate is this calculation method?

The accuracy of this calculation method depends on the accuracy of the measurements of longitudinal strain and final diameter. If these measurements are precise, then the calculated initial diameter will also be precise. However, there may be some minor errors due to factors such as imperfections in the material or experimental conditions.

Are there any limitations to using this formula?

Yes, this formula assumes that the longitudinal strain is small, meaning that the material is only slightly stretched or compressed. If the strain is too large, the material may not behave linearly and the calculated initial diameter may not be accurate.

Can this formula be used for other types of strains?

No, this formula is specifically for calculating initial diameter from longitudinal strain and final diameter. It cannot be used for other types of strains, such as shear strain or volumetric strain.

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