Question

an engineer wants to design a structure in which the difference in length between a steel beam and an aluminum beam remains at 0.500 m regardless of temperature, for ordinary temperatures. what must the lengths of the beams be?

Answer 1

the length will be 1.058

Step-by-step 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