Axial Deformation (δ = PL/AE)

Chain σ = P/A, ε = δ/L and E = σ/ε together and everything collapses into one line: δ = PL/AE. The product AE is the axial stiffness of the member, and dividing it by L gives the spring constant of a rod: a structural member really is just a very stiff spring. A 3 m steel hanger rod of 1000 mm² carrying 100 kN stretches δ = (100 000 × 3) ÷ (0.001 × 200 × 10⁹) = 0.0015 m, one and a half millimetres.

Two practical consequences. First, length is linear, so the elevator ropes at the bottom of a 400 m shaft stretch dramatically more than the same ropes near the top: the reason high-rise lifts need compensating ropes and re-levelling. Second, in a run of pipe supported by rods of different lengths, the long rods stretch more under the same load and quietly shed their share onto the short ones; in a redundant hanger array the load distributes by stiffness, not by fairness. If several segments are in series with different A, E or P, compute δ for each and add them.