How to find a value for poisson's ratio

In summary: Also, note that Poisson's ratio is defined as the negative of the ratio.In summary, the problem involves a rod with specific dimensions and an axial load. The question asks for the value of Poisson's ratio, which is calculated by finding the lateral strain and longitudinal strain. After some discussion and corrections, the final calculation for Poisson's ratio is -2.666.
  • #1
shortshanks
10
0

Homework Statement


The question is: A rod of 50mm in diameter and 0.8m in length is subjected to an axial load of 150kn. If the rod entends by 1.4mm and there is a decrease in diameter of 0.01mm, determine: The value of poissons ratio?


Homework Equations



v=lateral strain/longitudinal strain

e= change/original

The Attempt at a Solution



My attempt is: e(lat)=0.01/0.050
=0.2
e(long)= change in length/original length
= 0.014/0.8
= 1.75x 10-3
 
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  • #2
It appears that you didn't convert delta_d from 0.01mm to 0.00001m.
 
  • #3
And you converted 1.4 mm to meters incorrectly as well.
 
  • #4
how about: 1.4mm/800mm = 1.75x10-3 (0.00175) (longitudinal)
-0.1mm/0.50mm = -2x10-3 (0.002) (lateral)

lateral/longitudinal= -0.002/0.00175 = -1.1428
 
  • #5
Is the decrease in diameter 0.1 mm or 0.01 mm?
 
  • #6
oops! 0.01mm.
-0.01mm/0.050mm = -0.02mm (lateral)
1.4mm/800 = 1.75x10-3 (0.00175) (longitudinal)

lateral/longitudinal = -0.02/0.00175 = -11.428

Im not sure if this is right though as -11.428 does not tallie up with any ratio for any material for poissons ratio. What do you think?
 
  • #7
Can anyone let me know if I am heading in the right direction with my answer please?
 
  • #8
Check your lateral strain calculation again, particularly the units, and note that Poisson's ratio is defined as the negative of the ratio.
 
  • #9
0.001/0.050 = 0.02 (lateral)
1.4/800 = 1.75x10-3 (0.0075) (longitudinal)

0.02/0.0075 = 2.666
I think I finally have it, can someone confirm please?
If I do then thank you to everyone who helped!
 
  • #10
Check your lateral strain calculation again, particularly the units.
 

Related to How to find a value for poisson's ratio

1. What is Poisson's ratio and why is it important in materials science?

Poisson's ratio is a measure of the ratio of lateral strain to axial strain in a material. It is important in materials science because it helps us understand how a material will behave under stress and how it will deform when subjected to external forces.

2. How do I calculate Poisson's ratio?

Poisson's ratio can be calculated by dividing the lateral strain by the axial strain. It can also be determined experimentally by measuring the change in diameter and length of a material when it is under stress.

3. What is a typical range of values for Poisson's ratio?

The range of values for Poisson's ratio can vary depending on the material, but generally it falls between 0.0 and 0.5. Most metals have a Poisson's ratio between 0.25 and 0.35, while rubber and other polymers have a higher ratio of around 0.5.

4. How does Poisson's ratio affect the mechanical properties of a material?

Poisson's ratio is related to the stiffness and strength of a material. Materials with a low Poisson's ratio are generally stiffer and stronger, while those with a high Poisson's ratio tend to be more flexible and less strong.

5. Can Poisson's ratio change under different conditions?

Yes, Poisson's ratio can change under different conditions such as temperature, pressure, and strain rate. It can also vary depending on the direction in which the material is being strained.

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