# Coefficient of linear thermal expansion of a composite bar

question: a composite bar of length L=L1+L2 is made from a bar of material 1 and length L1 attached to a bar of material 2 and length L2.

show that the effective coefficient of linear thermal expansion is :

alpha= (a1L1+a2L2)/L

[- alpha/a=coefficient of linear thermal expansion]

i have no idea how to derive that equation, the only thing i no/learned from reading the book is that the equation for the coefficient of linear thermal expansion for one material is alpha=(delta L)/Lo(delta T)

anyone who can show me/drop some hints would be greatly appreciated.

Hint: The expansion ($\Delta L$) of the composite bar is the sum of the expansions of each segment.