Consistent Unit Systems in FEA

Symbol Quantity Dimension N‐m SI N‐mm SI in‐lb System ft‐lb System
\(l\) length \(L\) meter(\(\text{m}\)) millimeter(\(\text{mm}\)) inch(\(\text{in}\)) foot(\(\text{ft}\))
\(m\) mass \(M\) kilogram(\(\text{kg}\)) tonne(\(\text{t}\), \(10^3\text{kg}\)) snail = 386.2 “lb mass” slug = 32.19 “lb mass”
\(F\) force \(MLT^{-2}\) Newton(\(\text{N}\)) Newton(\(\text{N}\)) pound-force(\(\text{lbf}\)) pound-force(\(\text{lbf}\))
\(v\) velocity \(LT^{-1}\) \(\text{m/s}\) \(\text{mm/s}\) \(\text{in/s}\) \(\text{ft/s}\)
\(a\) acceleration \(LT^{-2}\) \(\text{m/s}^2\) \(\text{mm/s}^2\) \(\text{in/s}^2\) \(\text{ft/s}^2\)
\(g\) gravity \(LT^{-2}\) \(9.8\text{m/s}^2\) \(9.8\times10^3\text{mm/s}^2\) \(386.2\text{in/s}^2\) \(32.19\text{ft/s}^2\)
\(\sigma/p\) stress/pressure \(ML^{-1}T^{-2}\) Pascal(\(\text{Pa}\), \(\text{N/m^2}\)) MegaPascal(\(\text{MPa}\), \(\text{N/mm^2}\)) \(\text{psi}\), \(\text{lbf/in}^2\) \(\text{lbf/ft}^2\)
\(\rho\) density \(ML^{-3}\) \(\text{kg/m}^3\) \(\text{t/mm}^3\) \(\text{snails/in}^3\) \(\text{slugs/ft}^3\)
\(E/W/M\) energy/work/moment \(ML^2T^{-2}\) Joule(\(\text{J}\), \(\text{N}\cdot\text{m}\)) milliJoule(\(\text{mJ}(10^{-3}\text{J})\), \(\text{N}\cdot\text{mm}\)) \(\text{lbf}\cdot\text{in}\) \(\text{lbf}\cdot\text{ft}\)

Discuss on Imperial Units

It is critical to note that a pound is not a unit of mass for engineers and should not be used as a unit of mass. That is to say:

A pound is a unit of force.

Not so obvious is that mass is now in units of “12 x slugs”. Although some have named this mass unit the “slinch” or “blob”, we prefer the colloquially applied name, the “snail”.

Further reading