Determine the stress in composite bar:

How do you determine the stress in composite bar? What is Modular Ratio?
Sol.:
It becomes essential to have a compound tie or strut (column) where the two or more material elements are fastened together to prevent uneven straining. The salient features of such composite system are: System extends (or contracts) as one unit when it is subjected to tensile (or compressive) load. This implies that the deformation (extension or contraction) of every element is same.

Strain deformation per unit length of each element is same.

Total external load on system equals sum of loads carried out by different materials comprising the composite system.

Take a composite bar subjected to load P and fixed at the top as shown in the given figure. Total load is shared by two bars and as such
 ...(i)
Further elongation in 2 bars are same,  that is,  δL₁ = δL₂ = δL₃ ...(ii)

If strain in bar are equal e₁ =  e₂;  σ₁/E₁ = σ₂/E₂

or, σ₁/ σ₂ = E₁/E₂ (when the length is same)

This ratio E₁/E₂ is called as Modular ratio.

Modular Ratio: Modular ratio is ratio of moduli of elasticity of the two materials. It can be denoted by µ.