Extension and Compression

Extension and Compression 

in strength of materials, related types of deformation of a rod under the action of forces whose resultant is normal to the cross section of the rod and passes through its center of gravity. The linear (uniaxial) state of stress—one of the main types of stressed states of a parallelepiped—is a type of tension or compression. Extension and compression may be caused either by forces applied to the ends of the rod or by forces distributed throughout its volume, such as the weight of the rod itself or the forces of inertia. In addition to uniaxial tension and compression, biaxial and triaxial tension and compression also exist.

If a rod is in a uniform uniaxial state of stress, then the stress along the axis is σ₁ = N/F, where N is the tensile or compressive force and F is the area of the cross section, and the relation between the stress and relative strain in the region of elasticity is determined by Hooke’s law. The relation between the longitudinal (∊₁) and lateral (∊₂)) relative stresses of a rod in the region of elasticity under tension or compression has the form ∊₂ =μ∊₁, where μ is Poisson’s ratio. The dependence of relative strain on stress in the region of plasticity is described by complex (nonlinear) empirical laws. Tension causes elongation of the rod, and compression, shortening. On compression of a flexible rod, the phenomenon of loss of stability may also occur.

REFERENCES

Rabotnov, Iu. N. Soprotivlenie materialov. Moscow, 1962.
Soprolivlenie materialov, 2nd ed. Moscow, 1969.

A. A. BAT’