# Consistent System of Units

- Fundamental Units
One of the widely used standard system of units in the metric system is the International System of Units (SI). As defined by the SI system, there are seven fundamental units of measure. These fundamental units are not dependent on other units or to each other. All other units are derived from these seven fundamental units.

The seven fundamental units are units of seven fundamental quantities, which are: mass, length, time, temperature, electric current, light intensity, and amount of substance in matter. Of these seven quantities, the fundamental quantities of measure typically used in structural analysis are: mass, length, time, and temperature. The units of these four fundamental quantities are the main focus in this section.

- Base Units
The base units are defined as a set of fundamental units in any measurement system. This set of units is typically based on an agreed upon standard or natural process. Other units within the measurement system can be derived from these base units. The base units for the SI system are kilogram (mass), meter (length), second (time), and kelvin (temperature). The other 3 SI system base units are not listed for the purpose of brevity in this section.

- Derived Units
Quantities of measure derived from the fundamental quantities are termed as derived quantities. Derived units are units which are used to represent derived quantities. By definition, the derived units are dependent on the base units. For instance, in the SI unit system, the quantity force has a unit of newton (N) which is derived from the units of mass (kg), length (m), and time (s) and is represented as 1 N = 1 kg.m/s

^{2}. - Consistent Set of Units
A consistent set of units is defined as a set of base and derived units, wherein the derived units are consistent with the set of base units of the units system. If the set of derived units you are using do not exhibit consistency with the base units, you should convert the derived units into a consistent set of units prior to plugging in the data in the OptiStruct model.

Based on the fundamental quantities of measure, the table below illustrates a set of derived units consistent with the base units in different unit systems.

Quantity SI System (Metric) (kg, m, s)

Metric (tonne, mm, s)

English (lbf.s

^{2}/in, in, s)English (slug, ft, s)

Base units: Mass kg ton lbf.s ^{2}/inslug Length m mm in ft Time s s s s Derived units: Force N N lbf lbf Stress Pa MPa psi lbf/ft ^{2}Elastic Modulus Pa MPa psi lbf/ft ^{2}Density kg/m ^{3}tonne/mm ^{3}lbf.s ^{2}/in^{4}slug/ft ^{3}Acceleration m/s ^{2}mm/s ^{2}in/s ^{2}ft/s ^{2}Angular Acceleration rad/s ^{2}rad/s ^{2}rad/s ^{2}rad/s ^{2}Velocity m/s mm/s in/s ft/s Angular Velocity rad/s rad/s rad/s rad/s Energy J N.mm lbf.in lbf.ft Power W N.mm/s lbf.in/s lbf.ft/s Steel Properties: Density 7.83E+3 kg/m ^{3}7.83E-9 tonnes/mm ^{3}7.33E-4 lbf.s ^{2}/in^{4}1.52E+1 slug/ft ^{3}Young’s Modulus 2.07E+11 Pa 2.07E+5 MPa 3.00E+7 psi 4.32E+9 lbf/ft ^{2}Gravity; Acceleration due to gravity (g) 9.8 m/s ^{2}9.8E+3 mm/s ^{2}386.0 in/s ^{2}32.17 ft/s ^{2}Water (Thermal): Conductivity 0.598 W/m.K 0.598 mW/mm.K Density 1000 kg/m ^{3}1.0E-9 tonne/mm ^{3}Specify Heat Capacity 4183 J/kg.K 4.183E+9 mJ/tonne.K Water (Darcy): Permeability 1.0E-7 m ^{2}0.1 mm ^{2}Dynamic Viscosity 0.001 Pa.s 1.0E-9 MPa.s