Equivalent Area of a Composite Section:

On reconsideration, we might rewrite Eq. as follows :

P = PA₁       / [ A₁ + m₂ A₂ + m₃ A₃ + ...]                  .....(1)

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

In Eq. (1), we identify that P1/ A1 is the stress induced in material 1 and therefore,

σ₁  = P/[ A₁ + m₂ A₂ + m₃ A₃ + ...]

 The denominator in Equation (13) has Area unit and it is called the equivalent area of the composite bar, as if composite bar completely build of material 1 alone. In other terms, if the composite bar in given figure is completely 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 means, the composite bar is equivalent to an aluminium bar of cross sectional area 20930.86 mm², in the resisting axial forces. (An aluminium bar of 163.25 mm diameter shall give this area.)

One of the practical instances of composite bars is the RCC column. Here, a 400 mm × 400 mm square cross section of a RCC column is reinforced having 8 numbers of 32 mm diameter mild steel bars.