Final answer:
To maintain a 0.500 m length difference between a steel and an aluminum beam, calculate their expansion using the linear expansion formula with their coefficients of linear expansion and set the difference equal to 0.500 m. Specific coefficients and the temperature range are needed for precise calculations.
Step-by-step explanation:
An engineer is tasked with designing a structure where a steel beam and an aluminum beam maintain a constant difference in length of 0.500 meters across various temperatures. To accomplish this, we need to consider the coefficients of linear expansion for both materials. The coefficient of linear expansion is a material property that describes how its length changes with temperature.
The linear expansion for a material can be calculated using the formula ΔL = αL₀ΔT, where ΔL is the change in length, α is the coefficient of linear expansion, L₀ is the initial length, and ΔT is the change in temperature. The goal is to ensure that the expansions and contractions due to temperature changes do not alter the 0.500 m length difference between the two beams.
To solve for the required lengths, set up an equation where the change in length of the steel beam minus the change in length of the aluminum beam equals 0.500 m, factoring in their respective coefficients of linear expansion and initial lengths. With the proper initial lengths and considering a temperature range, this difference in length can be maintained. To obtain the exact values, you would need the specific coefficients for steel and aluminum, and perform the calculations as per the temperature range dictated by 'ordinary temperatures'