Ideal Gas in Structural Analysis

Technical Article on the Topic Structural Analysis Using Dlubal Software

  • Knowledge Base

Technical Article

In theory, an ideal gas consists of freely moving mass particles without extension in a volume space. In this space, each particle moves at a speed in one direction. The collision of one particle with another particle or the volume limitations leads to a deflection and a change in the speed of the particles.

The state of an enclosed gas can be described by the presumptions of the thermodynamic equilibrium. This results in the following general gas equation:
p ∙ V = n ∙ R ∙ T
where the state variables
p is the pressure
V is the volume
n is the is the amount of substance
R is the universal gas constant
T is the temperature

Ideal Gas Properties

When keeping certain state variables constant in the general gas equation, special properties of the ideal gas arise. It is useful to know these properties for using ideal gases in the structural analysis, and it helps to simulate certain load conditions accordingly.

Isothermal Change of State (Boyle-Mariotte)
If variables T and n are constant and acting pressure p is increased, volume V of the considered gas unit is reduced.

The following applies:

Formula 1

p  1Vp · V = constp1p2 = V2V1

Isobaric Process (Gay-Lussac)
If variables p and n are constant and acting temperature T is increased, volume V of the considered gas unit increases.

The following applies:

Formula 2

V  TVT = constV1V2 = T1T2

Isochoric Process (Amotons)
If variables V and n are constant and acting temperature T is increased, pressure p of the considered gas unit increases.

The following applies:

Formula 3

p  TpT = constp1p2 = T1T2

Application in Structural Analysis

In structural analysis, encased gases are usually used to transfer the external forces. In this case, it is required that the force acting locally on a certain location on the volume casing is transported by the enclosed gas to all other sides of the volume casing.

This property is used, for example, in insulated glass panes or inflated membrane cushions. In both cases, the volume casing is described by the load-bearing elements and filled with a gas. The volume limitations consist of rigid shell elements in the case of insulated glass panes, and flexible membrane elements in the case of membrane cushions. However, to use one example, wind or snow load acts on one side of the volume limitation in both cases, and is transferred by the enclosed gas to the adjacent volume limitations.

Since the temperature does not change suddenly in the load situations considered in structural analysis, the ideal gas with isothermal properties is usually simulated in the volume casing.

Implementation in RFEM

Solids can be defined in RFEM. These solids are described by the surrounding surfaces. In this type of volume cell of the surrounding shell and solid components, the solid definition can be inscribed with the gas type. This resulting gas volume requires describing the enclosed gas and determining the atmospheric state variables. The atmospheric state variables have no impact on the enclosed volume and only describe the initial situation for the simulation.

Image 01 - Gas behavior in gas volume

In the assigned load cases, the corresponding solid load can be applied for each gas solid. To simulate open or closed solids, it is possible to specify the resulting pressures/volumes or the pressure/volume changes.

Reference

[1] Wikipedia: Ideal gas
[2] Wikipedia: Ideal gas law
[3] Wagner, R.: Bauen mit Seilen und Membranen. Berlin: Beuth, 2016

Author

Dipl.-Ing. (BA) Andreas Niemeier, M.Eng.

Dipl.-Ing. (BA) Andreas Niemeier, M.Eng.

Mr. Niemeier is responsible for the development of RFEM, RSTAB, and the add-on modules for tensile membrane structures. Also, he is responsible for quality assurance and customer support.

Keywords

Gas volume PV Space between panes Climate Cushion Isothermal Space between glass panes

Downloads

Links

Write Comment...

Write Comment...

  • Views 1509x
  • Updated 11/04/2021

Contact Us

Contact Dlubal

Do you have further questions or need advice? Contact us via phone, email, chat, or forum, or find suggested solutions and useful tips on our FAQ page, available 24/7.

(267) 702-2815

[email protected]

Tensile Membrane Structure Design in RFEM 6

Tensile Membrane Structure Design in RFEM 6

Webinar 03/17/2022 2:00 PM - 3:00 PM EDT

Online Training | English

Eurocode 5 | Timber structures according to DIN EN 1995-1-1

Online Training 09/23/2021 8:30 AM - 12:30 PM CEST

Online Training | English

Eurocode 3 | Steel structures according to DIN EN 1993-1-1

Online Training 08/25/2021 8:30 AM - 12:30 PM CEST

Online Training | English

RFEM for Students | USA

Online Training 08/11/2021 1:00 PM - 4:00 PM EDT

Online Training | English

RFEM | Structural dynamics and earthquake design according to EC 8

Online Training 08/11/2021 8:30 AM - 12:30 PM CEST

Online Training | English

Eurocode 2 | Concrete structures according to DIN EN 1992-1-1

Online Training 07/29/2021 8:30 AM - 12:30 PM CEST

Online Training | English

RFEM | Basics

Online Training 07/13/2021 9:00 AM - 1:00 PM CEST

Online Training | English

RFEM | Basics | USA

Online Training 06/17/2021 9:00 AM - 1:00 PM EDT

Online Training | English

RFEM for Students | Part 3

Online Training 06/15/2021 2:00 PM - 4:30 PM CEST

Glass Design with Dlubal Software

Glass Design with Dlubal Software

Webinar 06/08/2021 2:00 PM - 2:45 PM CEST

Online Training | English

RFEM | Structural dynamics and earthquake design according to EC 8

Online Training 06/02/2021 8:30 AM - 12:30 PM CEST

Online Training | English

Eurocode 5 | Timber structures according to DIN EN 1995-1-1

Online Training 05/20/2021 8:30 AM - 12:30 PM CEST

Online Training | English

RFEM for Students | Part 2

Online Training 05/17/2021 2:00 PM - 4:30 PM CEST

Blast Time History Analysis in RFEM

Blast Time History Analysis in RFEM

Webinar 05/13/2021 2:00 PM - 3:00 PM EDT

Online Training | English

Eurocode 2 | Concrete structures according to DIN EN 1992-1-1

Online Training 05/12/2021 8:30 AM - 12:30 PM CEST

Timber Structures | Part 2: Design

Timber Beam and Surface Structures | Part 2: Design

Webinar 05/11/2021 2:00 PM - 3:00 PM CEST

Online Training | English

Eurocode 3 | Steel structures according to DIN EN 1993-1-1

Online Training 05/06/2021 8:30 AM - 12:30 PM CEST

Online Training | English

RFEM | Basics

Online Training 04/23/2021 8:30 AM - 12:30 PM CEST

RFEM 5
RFEM

Main Program

Structural engineering software for finite element analysis (FEA) of planar and spatial structural systems consisting of plates, walls, shells, members (beams), solids and contact elements

Price of First License
3,540.00 USD