Bars of Varying Cross Section

Now Let us consider a few cases of a little more difficulty. To give you a feeling of solid reality all solids have as far been represented by pictorial views. Given figure represents the projected view of a bar whose cross sectional area differs in different segments. Taking the elastic modulus of the material as 60 kN/mm², let us evaluate the entire elongation of the bar.

Though the bar contains no uniform cross-section, it contains segments of uniform cross section. Therefore, the total elongation of the bar might be determined as a total of the elongations of individual segments.

Thus,   δ = Σδ_i =   (P₁ L₁/ A₁E₁)

   + (P₂ L₂/ A₂ E₂) + ... + (P _i L_i / A_i E_i) + ... +

In the numerical instance under consideration

 δ = (750 × 300)/ ((π/4) × 200 ² × 60) + (750 × 400) / ((π/4) × 135² × 60) + (750 × 200)/ ((π/4) × 60 ² × 60) + (750 × 500)/ ((π /4) × 100 ² × 60)

= (750/ ((π/4) × 60) ((300/200²) + (400/135²) + (200/60²) + (500/100²)

= 2.14865 mm

In the bar, illustrated in Figure, the axial pull is applied at the ends and therefore the axial force in all of the members is similar.