Equivalent Area of a Composite Section:

On reconsideration, we may rewrite Eq. (11) as follows:

P₁ =     PA₁ /[ A₁ + m₂ A₂ + m₃ A₃ + ...]

P₁/A₁ = P/[ A₁ + m₂ A₂ + m₃ A₃ + ...]

In Eq. (12), we recognize that P₁/A₁ is the stress induced in material 1 and hence,

σ₁ = P/ [A₁ + m₂ A₂ + m₃ A₃ + ...]

The denominator within Eq. (13) has Area unit and is known as the equivalent area of the composite bar, as if composite bar totally made of material 1 alone. Instead, if the composite bar in Figure is wholly made of aluminum, then the equivalent area is given as

A_eq = A₁ + m₂ A₂ + m₃ A₃

= 1963.5 + (1.5 × 4398.23) + (2.5 × 4948)

= 20930.86 mm²

That is, the composite bar, shown in Figure, is equivalent to an aluminium bar of cross sectional area 20930.86 mm², in resisting axial forces. (An aluminium bar of 163.25 mm diameter will give this area.)