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Relation between modulus of elasticity (E), modulus of rigidity (G) and bulk modulus(K)

Relation between modulus of rigidity (G) and modulus of elasticity (E):

E= 2G (1 + μ)
where E= modulus of elasticity
μ= Poisson's ratio
G= modulus of rigidity

∴ E = 2G(1 + μ)

Relation between modulus of elasticity(E) and bulk modulus(K):

We known that when body is subjected to a tri-axial stress system, its volumetric strain is given by
eV = δV/V= ((σX + σY + σZ )/E)(1 - 2μ)
Here σX = σY = σZ = σ
∴ eV = (3σ/E)(1 - 2μ)
but K = σ / eV = σ / (3σ/E)(1 - 2μ)
∴ K = E / 3(1 - 2μ)

∴ E = 3K(1 - 2μ)

Relation between modulus of elasticity (E), modulus of rigidity (G) and bulk modulus(K):

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17 comments

  1. Atul goswamiDecember 4, 2017 at 10:26 AM

    Mst hai bhai good chaha gaye yara

    ReplyDelete
  2. UnknownDecember 7, 2017 at 6:09 AM

    Useful for mechanical engineers too ;) Cheers !

    ReplyDelete
  3. UnknownJanuary 9, 2018 at 5:51 AM

    good one useful for instrumentation engineers too!!!!! thanks man

    ReplyDelete
  4. Er. Ibrahim khanMarch 7, 2018 at 10:05 AM

    Thank-you for its relation but same problems updates on bases this formulas ok

    ReplyDelete
  5. UnknownOctober 28, 2018 at 9:20 AM

    Thanks

    ReplyDelete
  6. UnknownNovember 9, 2018 at 7:09 AM

    Thanks

    ReplyDelete
  7. smartestDecember 6, 2018 at 1:49 AM

    Mujhe ye bhut acchha lga.

    Lekin aur bhi bhut si equations hoti h jo mathematicaly proff krni hoti h .

    So please ese aur bhi equations ko proff kiya jaye

    Jisse sbhi ko aasani ho

    ReplyDelete
  8. SURYAFebruary 10, 2019 at 12:04 AM

    It's correct..

    ReplyDelete
  9. UnknownMarch 3, 2019 at 7:12 PM

    Thankyou!!!

    ReplyDelete
  10. UnknownJune 4, 2019 at 4:51 PM

    Derive all Elastic constant relationship please sent my gmail. Address

    ReplyDelete
  11. UnknownAugust 16, 2019 at 11:19 AM

    Superb!!!
    Thanks for posting 😊👍

    ReplyDelete
  12. UnknownAugust 28, 2019 at 9:15 AM

    Thankyou

    ReplyDelete
  13. ManojpasagadugulaNovember 6, 2019 at 8:13 PM

    I think derivation for this helps everyone.can you please provide a derivation....

    ReplyDelete
  14. UnknownJune 7, 2021 at 12:57 AM

    Very good

    ReplyDelete
  15. SelvamNovember 4, 2021 at 7:53 PM

    Informative and useful

    ReplyDelete
  16. Kamal DwivediMay 13, 2022 at 2:38 AM

    Very nice explanation can explain is there any difference between varignon's theorem and princeple of moments or both are same.

    ReplyDelete

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