A 50-foot steel beam will elongate by how many inches when heated from room temperature to about 1000 degrees Fahrenheit?

A 50-foot steel beam will elongate by how many inches when heated from room temperature to about 1000 degrees Fahrenheit?

• A. 3 inches at 500°F
• B. 9 inches at 1000°F
• C. 12 inches at 800°F
• D. 6 inches at 1200°F

Answer: (B)

Thermal expansion along a length is proportional to the original length, the temperature change, and the material’s linear expansion coefficient: ΔL = α L0 ΔT. For a 50-foot beam, L0 is 600 inches. Heating from room temperature to about 1000°F gives a ΔT of roughly 1000°F. Steel’s expansion coefficient at elevated temperatures is typically around 12–15 × 10^-6 per °F, so the elongation would be ΔL ≈ α × 600 × 1000 inches. With α ≈ 12×10^-6, you’d get about 7.2 inches; with α ≈ 15×10^-6, about 9 inches. Therefore, the option stating about 9 inches is consistent with a higher-end steel coefficient at that temperature, illustrating how a longer length and higher ΔT combine to produce a noticeable increase in length.

Thermal expansion along a length is proportional to the original length, the temperature change, and the material’s linear expansion coefficient: ΔL = α L0 ΔT. For a 50-foot beam, L0 is 600 inches. Heating from room temperature to about 1000°F gives a ΔT of roughly 1000°F. Steel’s expansion coefficient at elevated temperatures is typically around 12–15 × 10^-6 per °F, so the elongation would be ΔL ≈ α × 600 × 1000 inches. With α ≈ 12×10^-6, you’d get about 7.2 inches; with α ≈ 15×10^-6, about 9 inches. Therefore, the option stating about 9 inches is consistent with a higher-end steel coefficient at that temperature, illustrating how a longer length and higher ΔT combine to produce a noticeable increase in length.