Multiaxial Deformations and Stress Analyses

When a structure is subjected to uniaxial tension, the transverse dimensions decrease (the structure undergoes lateral contractions) while simultaneously elongating in the direction of the applied load. This was illustrated in the previous chapter through the phenomenon called necking. For stresses within the proportionality limit, the results of uniaxial tension and compression experiments suggest that the ratio of deformations occurring in the axial and lateral directions is constant. For a given material, this constant is called the Poisson’s ratio and is commonly denoted by the symbol ν (nu): Consider the rectangular bar with dimensions a, b, and c shown in Figure 8.1. To be able to differentiate strains involved in different directions, a rectangular coordinate system is adopted. The bar is subjected to tensile forces of magnitude F _x in the x direction that induces a tensile stress a _x (Figure 8.2).