Formula for volumetric strain - Rectangular bar

Q.  When a rectangular bar is uniaxially loaded, the volumetric strain (ev) is given as ________
- Published on 21 Sep 15

a. σx / E(1- μ)
b. σx / E(1+ μ)
c. σx / E(1- 2μ)
d. σx / E(1+2μ)

ANSWER: σx / E(1- 2μ)

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    Discussion

  • Sravanthi   -Posted on 24 Nov 15
    Volumetric strain (δV/V) is given as

    (δV/V) = 1/E( σz+ σx +σy)

    here, E = Modulus of elasticity, σx = strain in X-direction, σy = strain in Y-direction, σz = strain in Z-direction


    - When a rectangular bar is uniaxially loaded, σz= σx= 0, therefore, the volumetric strain (ev) is given as (σx/ E)(1- 2μ)

    - When a rectangular bar is biaxially loaded σz=0, therefore the volumetric strain (ev) is given as (1/ E)(σx -σy) [1- 2μ]

    - When a rectangular bar is triaxially loaded, the volumetric strain (ev) is given as [(σz+ σx +σy)/E] [1 - 2μ]

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