S11-1 NAS120, Section 11, May 2006 Copyright 2006 MSC.Software Corporation Section 11 Units

S11-2 NAS120, Section 11, May 2006 Copyright 2006 MSC.Software Corporation

S11-3 NAS120, Section 11, May 2006 Copyright 2006 MSC.Software Corporation n MSC.Nastran does not know what units you are using n It is up to the you to use a system of consistent units in the finite element model n This means that you must input all model quantities such as grid point locations, elastic modulus, applied loads, etc. using a consistent system of units n You must also interpret the model output quantities such as displacements and stresses in the same consistent system of units Units in MSC.Nastran

S11-4 NAS120, Section 11, May 2006 Copyright 2006 MSC.Software Corporation Newtons Second Law n A consistent set of units must satisfy Newtons Second Law of Motion: n In other words, one unit of force applied to one unit of mass must result in one unit of acceleration: n Whenever you are in doubt about a system of modeling units, use the equation above to check them. 1 unit force = 1 unit mass x 1 unit acceleration F = M. a

S11-5 NAS120, Section 11, May 2006 Copyright 2006 MSC.Software Corporation Base and Derived Units n Newtons Second Law of Motion contains the units of force, mass, length, and time. n We can choose any three of the four units as our base units. The fourth unit is then derived from these three base units. F = M. a Force Mass

S11-6 NAS120, Section 11, May 2006 Copyright 2006 MSC.Software Corporation Commonly Used Systems of Units n The two major systems of units used by engineers and scientists are the International System of Units (SI) and the U. S. Customary System (USCS). u The SI system is the modern version of the metric system. The base units include the meter (m), the kilogram mass (kg), and the second (sec). u The USCS is based on the British Imperial System. It is also known as the English System. The USCS includes two systems of units: l The foot-pound-second (fps) system - the base units include the foot (ft), the pound force (lb f ), and the second (sec). l The inch-pound-second (ips) system - the base units include the inch (in), the pound force (lb f ), and the second (sec).

S11-7 NAS120, Section 11, May 2006 Copyright 2006 MSC.Software Corporation SI Units n In the SI system of units, the base units are the meter, the kilogram mass, and the second. n The fourth unit, the unit of force, is derived from Newtons Second Law and is called the newton (N). n Lets check this system of units using Newtons Second Law: N = kg. m/sec 2 1 unit force 1 unit mass x 1 unit acceleration 1 N 1 kg x 1 m/sec 2 ?=?= ?=?=

S11-8 NAS120, Section 11, May 2006 Copyright 2006 MSC.Software Corporation SI-mm Units n A popular variation of the SI system of units uses the millimeter as the unit of length. The unit of force is the newton and the unit of time is the second. n In order to satisfy Newtons Second Law, the unit of mass must be the megagram (Mg), the metric ton (t), or the tonne (T e ). n Lets check this system of units using Newtons Second Law: Mg = t = T e = 1000 kg 1 unit force 1 unit mass x 1 unit acceleration 1 N 1 Mg x 1 mm/sec 2 ?=?= ?=?=

S11-9 NAS120, Section 11, May 2006 Copyright 2006 MSC.Software Corporation U. S. Customary fps System n In the U. S. Customary foot-pound-second system, the base units are the foot, the pound force, and the second. n The fourth unit, the unit of mass, is derived from Newtons Second Law and is called the slug. n Lets check this system of units using Newtons Second Law: slug = lb f. sec 2 /ft 1 unit force 1 unit mass x 1 unit acceleration 1 lb f 1 slug x 1 ft/sec 2 ?=?= ?=?=

S11-10 NAS120, Section 11, May 2006 Copyright 2006 MSC.Software Corporation U. S. Customary ips System n In the U. S. Customary inch-pound-second system, the base units are the inch, the pound force, and the second. n The fourth unit, the unit of mass, is derived from Newtons Second Law and has no official name. This unit is unofficially called the snail or the slinch. n Lets check this system of units using Newtons Second Law: snail = slinch = lb f. sec 2 /in 1 unit force 1 unit mass x 1 unit acceleration 1 lb f 1 lb f. sec 2 /in x 1 in/sec 2 ?=?= ?=?=

S11-11 NAS120, Section 11, May 2006 Copyright 2006 MSC.Software Corporation Weight Units vs. Mass Units n MSC.Nastran expects your mass input (MATi, CONMi, etc.) to be in consistent mass units. n However, mass property data for the U. S. Customary System are typically reported in the units of weight. There are two methods to handle the weight units: 1. Convert the weight units into the correct mass units before entering them into the finite element model. 2. Input the weight units into the finite element model. Then use the MSC.Nastran WTMASS parameter to convert weight units to mass units.

S11-12 NAS120, Section 11, May 2006 Copyright 2006 MSC.Software Corporation WTMASS Parameter Example n For example, you are modeling a steel structure in the U. S. Customary inch-pound-second system. The material density obtained from a handbook is show below: Method 1 Use Newtons Second Law to convert weight to mass: W = M x g M = W x 1/g = W x 1/386.1 = W x Mass Density = x = 7.33 x lb f. sec 2 /in 4 Weight Density = lb f /in 3 MAT1129.E E-4 Method 2 Enter the weight density directly into MSC.Nastran. Use the WTMASS parameter to convert weight units to mass units. MAT1129.E PARAMWTMASS

S11-13 NAS120, Section 11, May 2006 Copyright 2006 MSC.Software Corporation WTMASS Parameter Example (cont.) The WTMASS parameter is defined in MSC.Patran as shown on the right. The default value for this parameter is 1.0

S11-14 NAS120, Section 11, May 2006 Copyright 2006 MSC.Software Corporation Examples of Consistent Systems of Units System of Units InputOutput LengthForceElastic Modulus MassMass Density WTMASS Parameter 1 GDispForceStress 1mNPakgkg/m m/sec 2 mNPa 2mmNMPat or Mgt/mm 3 or Mg/mm mm/sec 2 mmNMPa 3ftlb f psfslugslug/ft ft/sec 2 ftlb f psf 4inlb f psilb f. sec 2 /inlb f. sec 2 /in in/sec 2 inlb f psi 5inlb f psilb f lb f /in x in/sec 2 inlb f psi n Following table contains some of the most commonly used consistent systems of units.