An engineer wants to design a structure in which the difference in length between a steel beam and an aluminum beam remains at 0.550 m regardless of temperature, for ordinary temperatures. What must the length of the steel beam be?

The  length of the steel beam  is 1.058 m

Explanation:

coefficient of linear expansivity of Aluminum, = 25 x 10⁻⁶ ⁰C⁻¹

coefficient of linear expansivity of steel, =  12 x 10⁻⁶ ⁰C⁻¹

Change in length of aluminum; ΔL = **ΔT

Change in length of steel; ΔL = **ΔT

difference in length of Aluminum and steel;

- = 0.55 m, for this difference to remain constant, then ΔL = ΔL

From the equation above,     = 0.55 +

Since,  ΔL = ΔL, then  **ΔT = **ΔT

At constant temperature, the equation becomes;

* = *

Recall;

To calculate the length of the steel beam;

Therefore, the  length of the steel beam  is 1.058 m

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