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what is the equation for poisson’s ratio ????????????

Charitha Gorrela , 7 Years ago
Grade 12th Pass
anser 1 Answers
Mayajyothi C J

Last Activity: 7 Years ago

It is the ratio between lateral strain and longitudinal strain.
Poison’s ratio,
\sigma = \frac{Lateral strain}{longitudinal strain}= \frac{\beta}{\alpha}= - \frac{(\Delta d/d)}{\Delta l/l}
 
                                                             l – length
                                                            d – diameter
  • The negative sign indicates that as length increases diameter decreases 
  • Theoretically the value of \sigma lies between  – 1 and + 0.5
  • Experimentally the value of \sigma  lies between 0 and +0.5
Relation between Y, K,n and \sigma
1.Y = 3K (1 – 2\sigma)                                                                              Y- Young’s modulus
                                                                                                        K- Bulk modulus
2.Y = 2n (1 + \sigma)​                                                                                n- Rigidity modulus
 
3.\sigma = \frac{3K - 2n}{2n + 6K}
 
 
4. \sigma = \frac{Y}{2n} - 1
 
Hope this was helpful. Please approve ^_^
 
 

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