Bars of Varying Cross Section:

Let us now assume a few cases of a little more complexity. To provide you a feeling of solid reality all solids have so far been represented through pictorial views. Figure 16 represents the projected view of a bar whose cross sectional area differs in various segments. Taking the elastic modulus of the material as 60 kN/mm², let us elaborates the total elongation of the bar.

Figure

While the bar has no uniform cross-section, it consists of segments of uniform cross section. Therefore, the total elongation of the bar could be computed as a sum of the elongations of individual segments.

Thus,  δ = Σδ_i =   P₁L₁/A₁E₁ + P₂L₂/A₂ E₂ + ... + P_iL_i/A_i E_i + ...