Stresses in Composite Bars and Load Carrying Capacity of Composite Bars:

You have understood how a total load applied on a composite bar is shared through various components of a composite. Though this is certainly enlightenment on the behaviour of composite bars, we required to learn more in order to apply the concept in practically more meaningful way. That is, we required to learn

(a)        What will be the total load that a composite bar can carry, and

(b)       To carry a given load, how should a composite bar be proportioned?

For this purpose, we should know the strength of every material and also we should be able to compute the stresses induced in the several components of a composite bar.

We have already learnt the compatibility condition in which the axial deformations undergone through all the components of a composite bar should be equal.

As the lengths of components are also equivalent, the strain in each component should also be equal. Taking the strain of the composite bar as ε, stress in any component might be expressed as

σ_i = E_i  × ε

or        σ_i = E_i/E₁ × E₁   × ε

or        = m_i    × E₁   × ε

Since, E₁ × ε = σ1, then we can write

σ_i = m_i  × σ₁

Eq. (15) expresses the relationship in which the stress induced in any component of a composite bar should be proportional to its elastic modulus or modular ratio. For instance, in the RCC column display in Figure, the stress in steel, σs, will be 18 times the stress in concrete. You could have seen this through yourself, if you had divided the load shared through each member by its area of cross section. Use of Eq. (15) saves a few computational effort.