Composite sections under axial loading

Composite Members:

If two or more members of different materials are connected together and subjected to loads, then this is called as "Composite Members" or "Composite Sections".

Consider a composite bar of length L made up of two different materials (1) and (2). They are rigidly connected together in parallel and carrying compressive load P as shown in fig.

Let,
P = Total load applied on material (1) and (2),
P₁ = load taken by material (1),
P₂ = load taken by material (2).
Now,
P = P₁ + P₂
P = σ₁A₁ + σ₂A₂
If, δL = decrease in length,
this decrease in length is same for both bar, hence strain in both bar is same.
∴ e₁ = e₂
∴ σ₁/E₁ = σ₂/E₂
σ₁ = (^E₁/_E2).σ₂
σ₁ = (m).σ₂
where,
m = ^E₁/_E2 = modular ratio

Modular Ratio:

It is defined as the ratio of modulus of elasticity of two differents materials.
It is denoted by "m" (small letter m).
m = ^E₁/_E2
Where,
E₁ = Modulus of elasticity of material (1)
E₂ = Modulus of elasticity of material (2)