A steel block 200 mm * 20 mm* 20 mm is subjected to a tensile force of 40 KN in the direction of its length. Determine the change in volume, if E is 205 KN/mm² poissions ratio = 0.3
To determine the change in volume of the steel block, we need to consider the concept of volumetric strain. Volumetric strain is defined as the change in volume divided by the original volume.
To calculate the change in volume, we need to find the original volume of the steel block. The original volume can be determined by multiplying the three dimensions of the block (length, width, and height).
Given:
Length (l) = 200 mm = 200/1000 m = 0.2 m
Width (b) = 20 mm = 20/1000 m = 0.02 m
Height (h) = 20 mm = 20/1000 m = 0.02 m
Original Volume (V) = l * b * h
Substituting the given values, we have:
V = 0.2 m * 0.02 m * 0.02 m
Now we need to calculate the change in volume. The change in volume (ΔV) can be calculated using Hooke's Law of Linear Elasticity and the strain formula.
Hooke's Law states that stress (σ) is proportional to strain (ε) within the elastic limit. In the case of volumetric strain, it is given by:
ε = (ΔV / V)
From the given data, we can calculate stress (σ) using the formula:
Stress (σ) = Force (F) / Area (A)
Given:
Force (F) = 40 kN = 40,000 N
Area (A) = b * h (since the force acts in the direction of the length)
Substituting the given values, we have:
Area (A) = 0.02 m * 0.02 m
Next, we can calculate the stress (σ) using the formula:
Stress (σ) = 40,000 N / (0.02 m * 0.02 m)
Now, we can use Hooke's Law to calculate strain (ε). Rearranging the formula, we have:
Strain (ε) = stress (σ) / Young's Modulus (E)
Given:
Young's Modulus (E) = 205 kN/mm² = 205,000 N/mm²
Substituting the given values, we have:
Strain (ε) = σ / E
Now we can calculate the strain (ε) by substituting the values of stress (σ) and Young's Modulus (E) into the equation.
Finally, we can calculate the change in volume (ΔV) using the formula:
ΔV = ε * V
Substituting the calculated values of strain (ε) and original volume (V), we can determine the change in volume of the steel block.