Change of Shape of an Element in Tension | 2018 | mdf, steel, plastic | 48 x 34 x 30 cm
"Change of Shape of an Element in Tension."
Because the dimensions of a bar in tension or compression are changed when a load is applied, the volume of the bar changes too. The change in volume can be calculated from the axial and lateral strains. Let us take a small element of isotropic material cut from a bar in tension.
The original shape of the element is a cube having sides of lengths a, b, and c in the x, y, and z directions, respectively. The x axis is taken in the longitudinal direction of the bar, which is the direction of the normal stresses σ produced by the axial forces. The elongation of the element in the direction of loading is a∈, where ∈ is the axial strain. Because the lateral strains are - v∈, the lateral dimensions decrease by bv∈ and cv∈ in the y and z directions, respectively. Thus the final dimensions of the element are a(1 + ∈), b(1 - v∈), and c(1 - v∈), and the final volume is Vē = abc(1 + ∈) (1 - v∈) (1 - v∈)
* Gere, J.M. en Timoshenko, S. P. (1991) Mechanics of materials (3e SI ed.)