The figure shows a vertical rod of length L pinned on top. A force F directed vertically downwards acts on the free end of the rod resulting in the elongation of the rod by a factor delta. The parameters of the rod are A and E.

For axial members, the relationship between the internal force in the member and the member's deformation can be expressed as:

δ=FLAE

where δ= deformation, F = internal force, L = length, A = area, and E = elastic modulus. This relationship is termed the force-deformation relationship.

When temperature change is a factor in the problem, another term is added to this relationship to account for thermal effects:

δ=FLAE+αTL

where α = coefficient of thermal expansion
and T = change in temperature.