Poisson’s ratio
It is the ratio of lateral strain to longitudinal strain and it is constant with in the elastic limit of the material.Poisson's Ratio is generally denoted by 'μ ' or u
The ratio is named after the French mathematician and physicist Siméon Poisson.
Note:
The tensile longitudinal stress produces compressive lateral strains or the compressive longitudinal stress produces tensile lateral strains.
(+ve Longitudinal strains produce -ve lateral strains or vice versa)
Let us consider a rectangular bar of cross section (bxd) and length l and it is subjected to a axial load acts in the direction of length of the bar.
The longitudinal tensile strain in the bar
e longitudinal = δl / l
Lateral compressive strains in the directions of breadth b and depth d of bar
elateral = δb/ b and
elateral = δd /d
where δl = Change in length
δb = Change in width =b' - b
δd = Change in depth = d' - d
The poisson's Ratio
m = elateral / e longitudinal
Lateral strain ,elateral = m.elongitudinalNote:
Perfectly incompressible isotropic material deformed elastically at small strains would have a Poisson's ratio of exactly 0.5.
Example: Rubber has a Poisson ratio of nearly 0.5. and Cork's Poisson ratio is close to zero. Most of the metals it is in between 0.25 to 0.33
Examples:
1.A metal rod 20 mm diameter and 2 m long is subjected to a tensile force of 60 kN, it showed and elongation of 2 mm and reduction of diameter by 0.006 mm. Calculate the Poisson's ratio.
Solution:
The longitudinal strain = e longitudinal = δl / l
= 2mm/ 2000 = 0.001
The Lateral Strain = elateral = δd /d
= 0.006mm/20mm =0.0003
The poisson's Ratio = m = elateral / e longitudinal
= 0.0003/0.001 = 0.3 Ans.
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