A steel block 200mm x 20mm x 20mm is subjected to tensile faro of Gone in the direction of its Length. Determine the change in volume if E is 20KN/mm2 and Poisson’s ratio = 0.3.
To determine the change in volume of the steel block subjected to tensile force, we can use the formula for volumetric strain.
Volumetric strain (ε) is given by:
ε = 2 * (1 + ν) * (σ / E)
where:
ν is the Poisson's ratio,
σ is the stress,
E is the elastic modulus (Young's modulus).
In this case, since the block is subjected to tensile force along its length, the stress (σ) can be calculated using Hooke's Law, which states that stress is equal to the applied force divided by the cross-sectional area.
The cross-sectional area (A) of the block can be calculated as the product of its width (20mm) and thickness (20mm):
A = 20mm * 20mm = 400mm²
The applied force (F) can be calculated using the stress equation:
F = σ * A
Given the values:
E = 20 KN/mm²
ν = 0.3
A = 400mm²
Now, we can calculate the applied force and the stress as follows:
σ = F / A
The change in volume (ΔV) can be calculated using the volumetric strain equation:
ΔV = V * ε
where V is the initial volume of the block.
To find the initial volume of the block, we can multiply its dimensions:
V = Length * Width * Thickness
Let's plug in the values and calculate step by step:
1. Calculation of applied force (F):
F = σ * A
2. Calculation of stress (σ):
σ = F / A
3. Calculation of initial volume (V):
V = Length * Width * Thickness
4. Calculation of volumetric strain (ε):
ε = 2 * (1 + ν) * (σ / E)
5. Calculation of change in volume (ΔV):
ΔV = V * ε
By following these calculations, you can determine the change in volume of the steel block when subjected to the given tensile force.