[Solved] A rectangular steel bar of size 100 mm × 25 mm ×

When examining rectangular steel bars, particularly one of 100 mm × 25 mm dimensions, it’s essential to understand some core concepts related to volumetric strain. Volumetric strain is defined as the ratio of change in volume to the initial volume of a body, and it encompasses the cumulative strain experienced in all directional aspects.

Understanding Volumetric Strain

This strain can be mathematically represented as:

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

Where \( \Delta V \) signifies the change in volume while \( V \) represents the original volume.

Calculation Approach

For our specific case with the steel bar, the following dimensions are applicable:

Given Details

Volume Calculation:

Volume = 100 mm × 25 mm × 20 mm

Assuming the initial strains are defined as:

\( \epsilon_x = 0, \quad \epsilon_y = 0, \quad \epsilon_z = 0.002 \)

Strain Calculation

The overall volumetric strain is calculated as follows:

\( \epsilon_v = \epsilon_x + \epsilon_y + \epsilon_z = 0 + 0 + 0.002 = 0.002 \)

Final Volume Change

Now, substituting into the volume change formula:

\( \Delta V = \epsilon_v \times V = 0.002 \times (100 \times 25 \times 20) = 550 \; mm^3 \)

Further Information

For those seeking more detailed insights, further exploration can be found at the following:

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