can you please explain poisson's ratio with formula and how it is actually to be applied?

Asked by devyani.gauri99 | 28th Dec, 2015, 09:40: PM

Expert Answer:

Poisson's ratio is given as 
begin mathsize 12px style straight sigma equals fraction numerator Lateral space strain space over denominator Longitudinal space strain end fraction end style
When a deforming force is applied at the free ends of a suspended wire of radius R and length l, then the radius of the wire decreases by dR and its length increases by dl. So, a single force produces two types of strains: 
begin mathsize 12px style Longitudinal space strain equals fraction numerator increment straight l over denominator straight l end fraction space and space Lateral space strain equals fraction numerator negative increment straight R over denominator straight R end fraction end style
Thus, begin mathsize 12px style straight sigma equals fraction numerator Lateral space strain space over denominator Longitudinal space strain end fraction equals fraction numerator negative increment straight R divided by straight R over denominator increment straight l divided by straight l end fraction end style 
The negative sign shows that if the length of the wire increases, then the radius decreases. 

Answered by Yashvanti Jain | 29th Dec, 2015, 11:14: AM