Users:General FEM Analysis/Elements Reference/Truss1

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General Description

Element Type

  • This TRUSS1 element is a truss element with 3 translational degrees of freedom per node
  • The truss element neglects bending and torsional stiffness
  • The ratio of the cross-sectional dimensions and the length is much smaller than 1( a/L << 1 and b/L << 1), the truss is reduced to its center-line
  • The cross-sectional area is constant over the element
  • The truss element is also used as a cable, as which it can also account for prestress

Degrees of Freedom

The membrane element uses the 3 translatoric degrees of freedom, DISP_X, DISP_Y, DISP_Z.

Input Parameters

Parameter Description

Compulsory Parameters
Parameter Values, Default(*) Description
MAT EL-MAT int Number for the used Material

e.g. MAT=EL-MAT 1

AREA cross-section area of the cable
SIG11 Prestress of the cable.
Optional Parameters
Parameter Values, Default(*) Description
LAGRANGE TOTAL, UPDATED Definition of lagrange type. UPDATED for form finding and TOTAL for statics or dynamics. (e.g. LAGRANGE=UPDATED)

Example of a Complete Input Block

MAT= EL-MAT 1   AREA=1.0
PRESTRESS       SIG11=1.0

Element Loading

Being a line element not all general load cases are applicable.

Dead Load

  • implemented


The theory and finite element formulation is described in detail in [1] , [2] and [3].

For the correct use of the truss element and the interpretation of related results, the following aspects should be considered:

Material parameter

With the parameter MAT the material that is used in the calculation is defined. Being a line element with constant, fixed cross-sectional area, only linear elastic isotropic is foreseen for now.

Cross-section area parameter

The parameter AREA defines the cross-section area of the truss. The area is assumed constant over the element and throughout the computation.

Lagrange type

With the (optional) LARANGE parameter it is possible to switch between form finding and statical/dynamical analysis. For the value UPDATED the element is for form finding and for the value TOTAL the element is for statical/dynamical analysis. It is important that the LANGRANGE parameter match to the type of analysis.

Tests and Benchmarks

The element Truss1 has successfully been tested in 3D in various linear and geometrically non-linear static applications, as well as in dynamic analyses, be it as columns/trusses or as a (prestressed) cable.

Benchmark examples

  • cable under dead weight in a static geometrically non-linear analysis in a planar configuration: ..\examples\benchmark_examples\elements\truss1_dead_nln\cbm_trusss.dat
  • two-bar truss with arc-length path following: ..\examples\benchmark_examples\analyses\stanln_2bartruss_arclength_l\cbm_2bartruss_arclength_fixed.dat
  • dynamic eigenfrequency analysis of a prestressed string (modelled as a cable of trusses): ..\examples\benchmark_examples\analyses\eigenvalue_truss1_I\cbm_vib_row_50_elm.txt
  • form-finding of a four-point sail where the TRUSS1 is used as edge cable, column and retention cable: ..\examples\benchmark_examples\analyses\formfinding_membrane1_I\cbm_4_point_Fofi.txt
  • static geometrically non-linear analysis of a prestressed membrane under snow load: ..\examples\benchmark_examples\analyses\stanln_membrane1_I\cbm_4_point.txt


  1. Dieringer, F.: Implementierung eines geometrisch nichtlinearen Membranelements in einer objektorientierten Programmierumgebung, Master's Thesis, Lehrstuhl für Statik, Technische Universität München, 2009
  2. Linhard, J.: Numerisch-mechanische Betrachtung des Entwurfsprozesses von Membrantragwerken, Lehrstuhl für Statik, Technische Universität München, 2009
  3. Dieringer, F.: Numerical Methods for the Design and Analysis of Tensile Structures, Lehrstuhl für Statik, Technische Universität München, 2014

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