# C. Consistent Units

This appendix describes common consistent sets of units. Maintaining a consistent set of units is crucial in using Sierra/SM when entering material properties and interpreting results. The only variables that have intrinsic units are rotations, which are in radians. All other variables depend on the consistent set of units that the user uses in inputting the material properties and dimensioning the geometry.

A consistent set of units is made by picking the base units. When using the International System (SI), these are length, mass, and time, while in the English unit systems, these base units are length, force, and time. All other units are then derived from these base units. Table 1 provides several examples of commonly used consistent sets of units. In general, the names of the unit systems in this table are taken from the names of the base units. For example, CGS stands for (centimeters, grams, seconds) and IPS stands for (inches, pounds, seconds).

Table 1 Consistent Unit Sets
| SI | CGS | IPS | FPS | MMTS
--- | --- | --- | --- | --- | ---
Mass | kg | g | \(\mathrm{lb} \cdot \mathrm{s}^2/\mathrm{in}\) | slug | tonne
Length | m | cm | in | ft | mm
Time | s | s | s | s | s
Density | \(\mathrm{kg}/\mathrm{m}^3\) | \(\mathrm{g}/\mathrm{cm}^3\) | \(\mathrm{lb}\cdot \mathrm{s}^2/\mathrm{in}^4\) | \(\mathrm{slug}/\mathrm{ft}^3\) | \(\mathrm{tonne}/\mathrm{mm}^3\)
Force | N | N | N | N | N
Pressure | Pa | \(\mathrm{dyn}/\mathrm{cm}^2\) | psi | psf | MPa
Moment | \(\mathrm{N}\cdot \mathrm{m}\) | \(\mathrm{dyn}\cdot \mathrm{cm}\) | \(\mathrm{lb}\cdot \mathrm{in}\) | \(\mathrm{ft}\cdot \mathrm{lb}\) | \(\mathrm{N}\cdot \mathrm{mm}\)
Temperature | K | K | \(^{\circ}\mathrm{R}\) | \(^{\circ}\mathrm{R}\) | K
Energy | J | erg | \(\mathrm{lb}\cdot \mathrm{in}\) | \(\mathrm{lb}\cdot \mathrm{ft}\) | mJ
Velocity | \(\mathrm{m}/\mathrm{s}\) | \(\mathrm{cm}/\mathrm{s}\) | \(\mathrm{in}/\mathrm{s}\) | \(\mathrm{ft}/\mathrm{s}\) | \(\mathrm{mm}/\mathrm{s}\)
Acceleration | \(\mathrm{m}/\mathrm{s}^2\) | \(\mathrm{cm}/\mathrm{s}^2\) | \(\mathrm{in}/\mathrm{s}^2\) | \(\mathrm{ft}/\mathrm{s}^2\) | \(\mathrm{mm}/\mathrm{s}^2\)

One of the most common mistakes related to consistent units comes in when entering density. For example, in the IPS system, a common error is to enter the density of stainless steel as \(0.289 \mathrm{lb}/\mathrm{in}^2\), when it should be entered as \(7.48\times 10^{-4} \mathrm{lb}\cdot \mathrm{s}^2/\mathrm{in}\). The weight per unit volume should be divided by the gravitational constant (386.4 \(\mathrm{in}/\mathrm{s}^2\) in this case) to obtain a mass per unit volume.