Dynamics

1st eigenvalue of a high-rise building
1st eigenvalue of a high-rise building

Sophisticated constructions require both static and dynamic structure analyses. These analyses can range from resonant frequency determination and time-step calculations to nonlinear cable dynamics.  The Dynamics program module lets you analyze 2D and 3D beam, cable, area and solid models.

Dynamic Analyses:

  • Calculation of beam, cable, area and solid models
  • Determination of eigenvalues and eigenvectors
  • Stiffnesses according to second-order theory
  • Distributed dead loads, point masses and masses from loads
  • Periodic and free load-time curves
  • Simultaneous variable exciters at any node
  • Free node accelerations
  • Lehr's damping, mass and stiffness-proportional damping, Rayleigh's system damping and single viscous dampers
  • Modal analyses and direct integration of motion equations
  • Time-step integration for all system reactions with selectable iteration steps
  • Stationary response
  • Evaluation of response spectra acc. to EC 8, DIN, OENORM and SIA
  • User-defined response spectra
  • Calculation and output of effective modal masses
  • Dynamic train crossing on any track
  • Collapse analysis e.g. component failure
  • Animation of all time-step calculations

Resonance Frequency Determination

Determining the eigenvalues and eigenvectors forms the basis for most dynamic analyses. The distribution of mass that these analyses take into account is the result of the system geometry, the additional point masses and the equivalent masses of the selected load cases.

Response Spectrum Method for Earthquake Checks

In this check, the soil acceleration and the calculation coefficients are specified according to the selected standard for any given beam or shell structure depending on the earthquake zone, the subsoil, the damping and the structure class.  The check then calculates the structure reactions associated with the resonant frequencies based on the response spectrum method and superposes them according to the SRSS or CQC method. The resulting internal forces are then available for further superposition with the static load cases and subsequent design. In order to evaluate the modes of vibration to be considered, the applied masses are contrasted with the effective modal masses. If necessary, you can define custom response spectrums.

Vibration Calculations

Time-step calculations are carried out for periodic and transient load-time curves and specified node accelerations. These calculations can factor in exciters of variable frequency at the same time. You can select the number and duration of the individual time steps. Mass and stiffness-proportional damping, the Lehr's damping measure, Rayleigh's system damping and/or single viscous dampers can be used depending on the calculation. At selected nodes the system response can be calculated using a fixed frequency range in the steady state (stationary response).

Dynamic Train Crossing

Dynamic train crossing is another interesting calculation option provided by the program. This option offers an easy way to analyze the dynamic stress for any beam and shell structure based on predefined trains such as the ICE or Thalys or user-defined trains.

The description of the tracks is carried out by entering any continuous line on the structure. Multiple tracks can be considered simultaneously, so that, for example, the effect trains traveling in opposite directions have on each other can be investigated.

The load model of the typical trains for high-speed lines are stored in the program. Additionally, user-defined train loads can be added. Further default parameters are the speed and the departure time for each train. Every train is assigned to one track. By varying the departure times, the intervals between the different trains can be defined.

The dynamic train crossing can be analyzed as part of a direct or modal time step integration. The amount and duration of the time steps can be entered by the user. The vibration behavior and the desired route of the train are considered here.

Result Display and Processing

Deformations, speeds, accelerations, internal forces and support reactions for each time step are provided as calculation results. These can be represented individually or as time-step diagrams. Additionally, the deformation can be dynamically animated in the System Viewer.
For further analyses, the results can superposed with reactions from static calculations and then designed.

References

Bathe, K. J.
Finite Elemente Methoden (Finite Element Methods).
Springer Verlag, Berlin 1986.

DIN 4149:1981
Bauten in deutschen Erdbebengebieten -
Lastannahmen, Bemessung und Ausführung üblicher Hochbauten
(Buildings in German Earthquake Areas - Design Loads, Analysis and Structural Design of Common Buildings).
Publisher: DIN Deutsches Institut für Normung e.V., Berlin
Beuth Verlag, Berlin 1981.

DIN 4149:2005-04
Bauten in deutschen Erdbebengebieten -
Lastannahmen, Bemessung und Ausführung üblicher Hochbauten
(Buildings in German Earthquake Areas - Design Loads, Analysis and Structural Design of Common Buildings).
Publisher: DIN Deutsches Institut für Normung e.V., Berlin
Beuth Verlag, Berlin 2005.

EN 1998-1:2010-12
Eurocode 8: Auslegung von Bauwerken gegen Erdbeben -
Teil 1: Grundlagen, Erdbebeneinwirkungen und Regeln für Hochbauten (Eurocde 8: Design of structures for earthquake resistance - Part 1: General rules, seismic actions and rules for buildings).
Publisher: DIN Deutsches Institut für Normung e.V., Berlin
Beuth Verlag, Berlin 2010.

Hughes, T. J .R.
The finite element method,
Prentice-Hall Int. Ed., New Jersey 1987.

Lecture Notes in Engineering
Finite Element Analysis for Engineering Design.
Springer Verlag, Berlin 1988.

Link, M.
Finite Elemente in der Statik und Dynamik (Finite Elements in Statics and Dynamics).
Teubner Verlag, Stuttgart 1984.

Meskouris, K.
Baudynamik (Structural Dynamics).
Verlag W. Ernst & Sohn, Berlin 1999.

Müller, F. P.
Baudynamik (Structural Dynamics), Betonkalender Teil II.
Verlag Ernst & Sohn, Berlin 1978.

OENORM B 4015:2007-02
Belastungsannahmen im Bauwesen - Außergewöhnliche Einwirkungen -
Erdbebeneinwirkungen - Grundlagen und Berechnungsverfahren, Ausgabe 2007-02-01
(Load Assumptions in Civil Engineering - Additional Actions - Fundamentals and Analysis Methods, Edition 2007-02-01).
Österreichisches Normungsinstitut (ON), Wien 2007.

Schwarz, H. R.
Methode der finiten Elemente (Methods of Finite Elements). Teubner Studienbücher.
Teubner Verlag, Stuttgart 1984.

SIA 261:2003 Bauwesen
Einwirkungen auf Tragwerke (Actions on Structures). Swiss standard SN 505 261,
Registered standard of the Swiss Association for Standardization SNV.
Schweizerischer Ingenieur- und Architektenverein, Zürich 2003.

Zienkiewicz, O. C.
Methode der finiten Elemente, Studienausgabe (Methods of Finite Elements, Study Edition).
Hanser Verlag, München 1984.