Which ratio is known as Poisson's ratio in unrestrained members?

Poisson's ratio is defined as the ratio of the lateral strain to the axial strain in unrestrained members when they are subjected to an axial load. This concept pertains to how materials deform under stress: when a material is stretched or compressed along one direction (axial direction), it typically experiences a simultaneous contraction or expansion in the perpendicular direction (lateral direction).

Mathematically, Poisson's ratio (ν) can be expressed as:

ν = - (lateral strain) / (axial strain)

This means that if you were to increase the length of a rod (axial strain), it will also change its diameter (lateral strain). The negative sign indicates that an increase in length leads to a decrease in diameter.

Understanding Poisson's ratio is crucial in material science and structural engineering, as it helps predict how a material will behave under various loading conditions, influencing design choices in engineering applications.