Final answer:
The statement that a positive deformation implies an axial member becoming shorter is false; positive deformation indicates elongation. Deformation in axial members can occur through tension or compression, and its sign indicates the direction of the deformation.
Step-by-step explanation:
In the context of material deformation, the term epsilon represents the strain, which is the ratio of deformation to the original length (L). A positive value of deformation indicates that the material has been elongated, not shortened. Therefore, if epsilon = deformation / L, a positive value of deformation represents an axial member becoming shorter is false. The deformation can be either positive or negative, indicating tension (elongation) or compression (shortening), respectively.
When a force is applied to a wire or rod, it can lead to a change in length, known as axial deformation, which comes in two forms: tension (positive change in length) and compression (negative change in length). Mathematically, this is represented as ΔL, where ΔL is the change in length experienced by the material. The relationship between force (F), area (A), original length (L0), and Young's modulus (Y), is given by F / (A * ΔL) = Y / L0, which defines the elastic behavior of materials under small deformations.