Elastic modulii:

In the process of the above solution, we have introduced two terms, namely, m₂ and m₃ whose values are the ratios E₂/ E₁ and E₃/E₁ respectively. These ratios are the ratios of Elastic modulii of two different materials and, hence, are called Modular Ratios.

Let us now solve the problem of load sharing in the composite member shown in Figure. Here, we have

P = 60 kN

L = 400 mm

A₁ = π/4× 50² = 1963.5 mm²

A₂ = π/4 × (90² - 50²) = 4398.23 mm²

A₃ = π/4 × (120² - 90²) = 4948 mm²

Elastic moduli for the materials, namely aluminium, copper and steel may be taken as 80 kN/mm², 120 kN/mm² and 200 kN/mm² respectively.

m₁ =   E₂/E₁ = 120/80 = 1.5

m₂ = E₃/E₁ = 200/80 = 2.5

Substituting these values in Eq. (12),

P₁ = 60/(1+1.5× (4398.23/1963.5)+2.5 × 4948/1963.5)

= 5.62852 kN

Now, using Eq. (10),

P₂ =5.62852/1963.5 ×1.5×4398.23 = 18.912 kN

P₃ = 5.62852/1963.5 ×2.5×4948 =35.4595 kN