In an axial-force member, the stresses and strains are uniformly distributed over the cross section. Typically examples of this type of member are shown in Fig. 3.20.
Since the stress is constant across the section, the equation of equilibrium may be written as
P = AÆ’
where P axial load
Æ’ tensile, compressive, or bearing stress
A cross-sectional area of the member
Similarly, if the strain is constant across the section, the strain corresponding to an axial tensile or compressive load is given by
The factor AE/L represents the stiffness of the member in resisting axial loads. It gives the magnitude of an axial load needed to produce a unit displacement.
Equations (3.50) to (3.51) hold for both tension and compression members. However, since compression members may buckle prematurely, these equations may apply only if the member is relatively short (Arts. 3.46 and 3.49).
