If heated to a temperature of 538°C (1000°F), how far can a 31-meter (100-foot) steel beam elongate?

To determine how far a 31-meter (100-foot) steel beam can elongate when heated to 538°C (1000°F), it is important to understand the properties of steel as it relates to thermal expansion. Steel expands when subjected to high temperatures, and the amount of expansion can be calculated using the linear expansion formula:

ΔL = L0 * α * ΔT

Where:

• ΔL is the change in length (elongation),
• L0 is the original length of the beam,
• α is the coefficient of linear expansion for steel (approximately 11 x 10^-6 per °C),
• ΔT is the change in temperature in °C.

For this scenario, the original length (L0) is 31 meters, the temperature has increased from room temperature (approximately 20°C) to 538°C, giving us a ΔT of approximately 518°C.

Calculating the elongation:

1. Convert the original length to millimeters: L0 = 31 meters * 1000 mm/m = 31,000 mm.

2. Calculate the change in length: ΔL = 31,000 mm * (11 x 10^-6 mm/mm/°C)