The figure shows the deflection suffered by a vertical rod of length L. The parameters of the rod are A and E. The rod is pinned at its top end and a force F directed vertically downwards is applied on the free end at its bottom. This force causes elongation of the rod by delta units.

For axial members, the relationship between the internal force in the member and the member's deformaton 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.

The force-deformation relationships for bars (1) and (2) are:

δ1=F1L1A1E1               δ2=F2L2A2E2