lengths of steel and rod bars

Question

. A composite rod is made by joining two rods of different materials but with the same cross-sectional area as shown below. Design such a composite rod using steel (α = 11 x 10-6 / C°) and brass (α = 19 x 10-6 / C°) whose total length is 52.4 cm and whose effective coefficients of linear expansion is 13 x 10-6 / C°. Compute the lengths of the steel and brass rods that must be used. Neglect changes in cross-sectional area of the rods.

Answer 1

If the proportion of steel is a and that of brass is (1-a) then the composite coefficient of expansion is

11a+19(1-a) =13

The reason I chose the values is that a is a fraction between zero and 1 and we can multiply directly with the given composite length of the bar. All you need to do is solve the equation for a and determine the lengths of each component.