A rectangular steel bar of size 100 mm × 25 mm × 20 mm has strains in x, y and z directions, 0.0065, 0.0025 and 0.002 respectively. The change in volume due to these strains is

Concept:

Volumetric strain:

It is defined as the ratio of change in volume to the initial volume of the body. It is equal to the sum of strain in all directions.

ϵv = ϵx + ϵy + ϵz  

It is also known as the ratio of change of volume to original volume.

\(\epsilon_v=\frac{\Delta V}{V}\)

Calculation:

Given:

Volume = 100 mm × 25 mm × 20 mm, 

ϵ_x = 0.0065, ϵ_y = 0.0025, ϵ_z = 0.002

ϵv = ϵx + ϵy + ϵz  

ϵv = 0.0065 + 0.0025 + 0.002 = 0.011

\(\epsilon_v=\frac{\Delta V}{V}\)

\({\Delta V}=\epsilon_v{V}\)

\({\Delta V}=0.011\times{100\times25\times20}=550\;mm^3\)