Sample 1, Original Length 250 mm and 10 mm Diameter, Length after testing 250.23 mm the force used for the test was 15KN
Calculate the Stress and Strain for each of the Samples and from this and, assuming the material has remained within the elastic limit, determine their modulus of elasticity.
To calculate the stress and strain for each sample, we'll use the formulas:
1. Stress (σ) = Force (F) / Cross-sectional Area (A)
2. Strain (ε) = Change in Length (ΔL) / Original Length (L₀)
First, let's calculate the cross-sectional area of the sample using its diameter:
1. Cross-sectional Area (A) = π * (Diameter/2)²
= π * (10 mm/2)²
= 78.54 mm²
For Sample 1:
- Original Length (L₀) = 250 mm
- Change in Length (ΔL) = 250.23 mm - 250 mm = 0.23 mm
- Force (F) = 15 kN = 15,000 N
Now we can calculate the stress and strain for Sample 1:
1. Stress (σ) = Force (F) / Cross-sectional Area (A)
= 15,000 N / 78.54 mm² ≈ 191.15 N/mm²
2. Strain (ε) = Change in Length (ΔL) / Original Length (L₀)
= 0.23 mm / 250 mm ≈ 0.00092 (dimensionless)
Now let's assume that the material has remained within the elastic limit. As a result, stress and strain will be proportional, allowing us to determine the modulus of elasticity (E).
3. Modulus of Elasticity (E) = Stress (σ) / Strain (ε)
= 191.15 N/mm² / 0.00092 ≈ 207,989.13 N/mm²
So, for Sample 1, the stress is approximately 191.15 N/mm², the strain is approximately 0.00092, and the modulus of elasticity is approximately 207,989.13 N/mm².
You can use the same calculations with the corresponding values for the other samples to determine their stress, strain, and modulus of elasticity.