Course subject(s) 2. Axial Loaded Members

### Summary of Key Equations

In this unit, we examined the development of a Force-Displacement relation for axial loaded members. For a generic axial loaded member where the internal axial force (P), material stiffness (E), and cross-sectional area (A) all vary with position x along the length of the beam (L), this relationship can be expressed as:

$\delta=\int_{L}\frac{P(x)}{E(x) A(x)}dx$

In many cases, we deal with axial loaded members with a uniform cross section, uniform material stffness, and uniform internal load. In this case, the above relationship reduces to:

$\delta=\frac{PL}{EA}$

Some axial loaded members, such as cables and springs, have complex geometries. In these cases, effective stiffnesses (k) or effective areas (Aeff) are determined experimentally to relate load and deformation:

$\delta_{spring}=\frac{P}{k}$

$\delta_{cable}=\frac{PL}{EA_{eff}}$