A composite bar of length L = L1+L2, is made up from a rod of material I and of length L1 attached to a rod of material 2 and of length L2 as shown. If α1 and α2 are their respeclive coefficients of linear expansion, then equivalent coefficient of linear expansion for the composite rod is:

When it has been given a temperature change ∆T, the new length of the composite bar is the sum of the individual final lengths (Let 'α' be required coefficient of linear expansion)L' = L'1+L'2L(1+α∆T) = L1(1+α1∆T)+L2(1+α2∆T)⇒L + Lα∆T = L1+L1α1∆T + L2+L2α2∆T⇒L+Lα∆T = L+L1α1∆T+L2α2∆T(∵ L1+L2 = L)⇒ Lα∆T = L1α1∆T + L2α2∆T⇒α = L1α1+L2α2L