Axial Load Calculator

An axial load acts along the longitudinal axis of a member, and if it passes through the centroid of the section the resulting normal stress is uniform: sigma equals P over A. Elongation follows from Hooke's law integrated over the length, delta equals P times L divided by A times E, where E is the modulus of elasticity. Rearranged, A times E over L is the axial stiffness in pounds per inch, the effective spring constant of the member. Representative moduli are 29,000 ksi for structural steel, about 10,000 ksi for aluminum, and roughly 1,300 to 1,900 ksi for softwood parallel to grain, which is why a wood post of equal area and load shortens more than fifteen times as much as a steel one. Capacity is judged against yield. Common structural steels are ASTM A36 at 36 ksi and A992, the standard for hot-rolled wide-flange shapes, at a minimum 50 ksi. The yield force is Fy times A, and the ratio of that to the applied load is the factor of safety; allowable stress design for tension members corresponds to a value near 1.67. The critical limitation is that these equations describe stability-independent behavior only. A compression member with meaningful slenderness fails by buckling at a load given by the Euler and inelastic column curves, frequently far below yield. The deformation result also assumes elastic response, a constant cross section, concentric loading, and no local or connection effects.

The relationship underlying this calculation is Hooke's law. Robert Hooke published it in 1678 as the Latin phrase ut tensio sic vis, as the extension so the force, having first published it as an anagram in 1676 to secure priority while he continued working. Hooke stated proportionality for whole springs and wires rather than as a property of the material. Thomas Young, in his 1807 lectures on natural philosophy, introduced the modulus that bears his name and made stiffness independent of specimen size, and Augustin-Louis Cauchy in the 1820s formalized stress and strain as continuum quantities, completing the sigma equals E times epsilon form used today. Column behavior developed in parallel. Leonhard Euler derived the elastic buckling load of a slender strut in the eighteenth century, and nineteenth-century testing showed that stockier columns fail inelastically well below the Euler curve, which is why modern codes blend the two regimes. Codification followed the growth of steel construction. The American Institute of Steel Construction, formed in 1921, issued its first specification in the 1920s, and its allowable stress design provisions governed American steel practice for decades. Load and resistance factor design was introduced in the mid-1980s, and the two formats were merged into a single unified specification in 2005, so tension and compression members are now checked against the same nominal strengths under either approach.