7.1 Bar under Axial Tension (or Compression); Common Case

The bar is straight, of any uniform cross section, of homogeneous material, and (if under compression) short or constrained against lateral buckling. The loads are applied at the ends, centrally, and in such a manner as to avoid nonuniform stress distribution at any section of the part under consideration. The stress does not exceed the proportional limit.

Behavior Parallel to the load the bar elongates (under tension) or shortens (under compression), the unit longitudinal strain being ? and the total longitudinal deflection in the length l being ?. At right angles to the load the bar contracts (under tension) or expands (under compression); the unit lateral strain ? ? is the same in all transverse directions, and the total lateral deflection ? ? in any direction is proportional to the lateral dimension d measured in that direction. Both longitudinal and lateral strains are proportional to the applied load. On any right section there is a uniform tensile (or compressive) stress ?; on any oblique section there is a uniform tensile (or compressive) normal stress ? _? and a uniform shear stress ? _?. The deformed bar under tension is represented in Fig. 7.1(a), and the stresses in Fig. 7.1(b).

Figure 7.1

Formulas. Let

P =...