Final answer:
To estimate the decrease in length of the steel column, we calculate the stress (σ), use Young's modulus (Y) for steel to find strain (ε), and then apply strain to determine the change in length (ΔL). By comparing ΔL to the original length, we assess the compression of the column.
Step-by-step explanation:
The structural steel column in question is experiencing compressive stress due to the force applied to it. To estimate by how much the column's length decreases under this stress, we use the formula for strain (ε) where ε = ΔL/L0. The stress (σ) is given by σ = F/A, where F is the force and A is the cross-sectional area. We also need Young's modulus (Y) for steel, which can typically be found in a table of physical constants. From these equations, we can solve for ΔL, the change in length, which is then compared to the original length to gauge the extent of the compression.
First, we calculate the cross-sectional area (A) of the column: A = 10 cm × 10 cm = 100 cm² = 0.01 m² since 1 cm² = 10⁻⁴ m². Next, we calculate the stress: σ = 6 × 10⁵ N / 0.01 m² = 6 × 10⁷ Pa. Now, using Young's modulus for steel Y ≈ 2 × 10¹¹ Pa, we can determine the strain: ε = σ / Y = (6 × 10⁷ Pa) / (2 × 10¹¹ Pa). The strain is a dimensionless quantity, and this ratio tells us how much the column shortens per unit length. Finally, we can find ΔL by multiplying ε by the original length: ΔL = ε × L0. After calculations, we compare ΔL to the original length to see the relative change.
It is important to note that this calculation is an idealization and actual conditions might cause deviations. For example, the effects of buckling or the material's yielding past its elastic limit are not considered here.