Answer:
Step-by-step explanation:
To calculate the compressive stress and the amount of compression in the steel column, we can use the following formulas:
1. Compressive Stress:
Compressive stress (σ) is calculated by dividing the force (load) applied to the column by the cross-sectional area of the column.
σ = F / A
where:
σ = Compressive stress
F = Load applied to the column
A = Cross-sectional area of the column
2. Compression:
The amount of compression (∆L) can be calculated using Hooke's Law, which states that the deformation of a material is directly proportional to the applied force.
∆L = (F * L) / (A * E)
where:
∆L = Amount of compression
F = Load applied to the column
L = Original length of the column
A = Cross-sectional area of the column
E = Modulus of elasticity of the material
Given the following information:
- Load (F) = 50 MN (50 * 10^6 N)
- Length (L) = 3 m
- Diameter (d) = 0.4 m
- Modulus of elasticity (E) = 200 GPa (200 * 10^9 Pa)
First, let's calculate the cross-sectional area (A) of the column using the diameter:
A = π * (d/2)^2
= π * (0.4/2)^2
≈ 0.1257 m^2
Now, we can calculate the compressive stress (σ):
σ = F / A
= (50 * 10^6 N) / 0.1257 m^2
≈ 398.408 MPa
Finally, we can calculate the amount of compression (∆L):
∆L = (F * L) / (A * E)
= ((50 * 10^6 N) * 3 m) / (0.1257 m^2 * 200 * 10^9 Pa)
≈ 0.5962 m (or 596.2 mm)
Therefore, the compressive stress in the steel column is approximately 398.408 MPa, and the column is compressed by approximately 0.5962 m (or 596.2 mm).