Numerical - Change in volume, given - stresses in x, y and z direction

Q.  A rectangular bar has volume of 1.5 x 106 mm3. What is the change in volume, if stresses in x, y and z direction are 100 Mpa, 150 Mpa and 160 Mpa respectively. (Assume K = 2 x 105 N/mm2 & μ = 0.3)
- Published on 21 Sep 15

a. 1000 mm3
b. 1230 mm3
c. 1500 mm3
d. 2000 mm3

ANSWER: 1230 mm3

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    Discussion

  • ajay   -Posted on 10 Aug 23
    that is not K, it is E
  • Sravanthi   -Posted on 24 Nov 15
    Given: Volume = 1.5 x 106 mm3, Poisson's ratio (μ) = 0.3

    Formula: 1) ev = [σx / K + σy / K + σz / K ] x [1 - 2μ]

    ev is the volumetric strain, σx,

    2) Change in volume (δV) = ev x V


    Solution:

    1) ev = [(100 / 2 x 105) + (150 / 2 x 105) + (160 / 2 x 105)] x [1 - 2μ]

    = 2.05 x 10– 3 [1 – 2 (0.3)]

    = 8.2 x 10– 4

    2) Change in volume (δV) = ev x V

    Substituting the value of ev = 8.2 x 10-4 and V = 1.5 x 106 mm3

    = 8.2 x 10-4 x 1.5 x 106 mm3

    = 1230 mm3

    Change in volume = 1230 mm3

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