A composite bar of length L = L1 + L2 is made up from a rod of material 1 and of length L1 attached to a rod of material 2 and of length L2 as shown .If α1 and α2 are their respective coefficients of linear expansion, then equivalent coefficient of linear expansion for the composite rod will be given by :

A composite bar. When it has been given a temperature change ΔT, the new length of the composite bar is the sum of the individual final lengths (Let " a " be required coefficient of linear expansion)L=L1+L2L(1+αΔT)=L11+α1ΔT+L21+α2ΔT⇒L+LαΔT=L1+L1α1ΔT+L2+L2α2ΔT⇒L+LαΔT=L+L1α1ΔT+L2α2ΔT ∗L1+L2=L⇒LαAT=L1α1ΔT+L2α2AT⇒a=L1α1+L2α2L