A material has linear strains along X, Y and Z directions as 0.05, 0.10 and 0.10, respectively. Hydrostatic stress acting at a point in the material is 25 N/mm². Calculate the bulk modulus.
- A500 N/mm²
- B100 N/mm²Correct
- C125 N/mm²
- D250 N/mm²
Solution
Concept
Bulk modulus is hydrostatic stress divided by volumetric strain.
Formula
ev = ex + ey + ez ; K = σ / ev
Step-by-step solution
1. Volumetric strain ev = ex + ey + ez = 0.05 + 0.10 + 0.10 = 0.25 2. Hydrostatic stress σ = 25 N/mm² 3. K = σ / ev = 25 / 0.25 = 100 N/mm²
Explanation
Under hydrostatic stress, volume change is measured by volumetric strain. Volumetric strain is the sum of the three linear strains. Bulk modulus = stress / volumetric strain = 25 / 0.25 = 100 N/mm².
Why the other options are wrong
A: 500 comes from using only one strain, 25/0.05. C: 125 does not match any correct relation. D: 250 comes from using 25/0.10, which is only one strain.
Shortcut
Add the three strains, then divide the stress by the sum.
Common mistake
Using only one linear strain instead of the sum of all three.
Correct answer: B) 100 N/mm²