Force-Based Beam-Column

This command is used to construct a forceBeamColumn element object, which is based on the iterative force-based formulation. A variety of numerical integration options can be used in the element state determination and encompass both distributed plasticity and plastic hinge integration. See image:IntegrationTypes.pdf for more details on the available numerical integration options.

Model.element(“forceBeamColumn”, name, nodes, geom, integration, cMass)

nodes [iNode,jNode],
iNode Ref(Node)
jNode Ref(Node)
geom Ref(geomTransf)
integration BeamInt
cMass = False bool Flag indicating whether to use consistent mass matrix.
mass = 0.0 float element mass per unit length

Original command that assumes Gauss-Lobatto integration with a copy of the same section force-deformation model at each integration point: 

element forceBeamColumn $eleTag $iNode $jNode
        $numIntgrPts $secTag $transfTag < -mass $massDens > < -iter
        $maxIters $tol > < -integration $intType >
eleTag

unique element object tag

numIntgrPts

number of Gauss-Lobatto integration points along the element.

secTag

identifier for previously-defined section object

Alternative command (kept for backward compatability): 

element nonlinearBeamColumn $eleTag $iNode $jNode
        $numIntgrPts $secTag $transfTag < -mass $massDens > 
        < -iter $maxIters $tol > < -integration $intType >
eleTag

unique element object tag

intType

numerical integration type, options are Lobatto, Legendre, Radau, NewtonCotes, Trapezoidal (optional, default= Lobatto)

NOTE:

The following three commands give the same element definition (with Gauss-Lobatto integration) despite some apparent permutations of the input arguments:

  1. element forceBeamColumn $eleTag $iNode $jNode $transfTag Lobatto $secTag $numIntgrPts
  2. element forceBeamColumn $eleTag $iNode $jNode $numIntgrPts $secTag $transfTag
  3. element nonlinearBeamColumn $eleTag $iNode $jNode $numIntgrPts $secTag $transfTag

Notes

  • The -iter switch enables the iterative form of the flexibility formulation. Note that the iterative form can improve the rate of global convergence at the expense of more local element computation.

  • The valid response elements that an element of this type will respond to are:

    • force or globalForce
    • localForce
    • basicForce
    • section $sectionNumber $arg1 $arg2 ... (note: sectionNumer is integer 1 through numIntegrPts)
    • basicDeformation
    • plasticDeformation
    • inflectionPoint
    • tangentDrift
    • integrationPoints
    • integrationWeights

  • Here is a link to the source code to obtain information about the location and weight of the Gauss-Lobatto integration points 1

Examples

force beam column element added with tag 1 between nodes 2 and 4 that has Gauss-Lobatto 5 integration points, each using section 8, and the element uses geometric transformation 9

element forceBeamColumn 1 2 4 9 Lobatto 8 5;

FURTHER DOCUMENTATION ON INTEGRATION OPTIONS:

image:IntegrationTypes.pdf

References

  • Neuenhofer, Ansgar, FC Filippou. Geometrically Nonlinear Flexibility-Based Frame Finite Element. ASCE Journal of Structural Engineering, Vol. 124, No. 6, June, 1998. ISSN 0733-9445/98/0006-0704-0711. Paper 16537. pp. 704-711.
  • Neuenhofer, Ansgar, FC Filippou. Evaluation of Nonlinear Frame Finite-Element Models. ASCE Journal of Structural Engineering, Vol. 123, No. 7, July, 1997. ISSN 0733-9445/97/0007-0958-0966. Paper No. 14157. pp. 958-966.
  • Neuenhofer, Ansgar, FC Filippou. ERRATA – Geometrically Nonlinear Flexibility-Based Frame Finite Element. ASCE Journal of Structural Engineering, Vol. 124, No. 6, June, 1998. ISSN 0733-9445/98/0006-0704-0711. Paper 16537. pp. 704-711.
  • Taucer, Fabio F, E Spacone, FC Filippou. A Fiber Beam-Column Element for Seismic Response Analysis of Reinforced Concrete Structures. Report No. UCB/EERC-91/17. Earthquake Engineering Research Center, College of Engineering, University of California, Berkeley. December 1991.
  • Spacone, Enrico, V Ciampi, FC Filippou. A Beam Element for Seismic Damage Analysis. Report No. UCB/EERC-92/07. Earthquake Engineering Research Center, College of Engineering, University of California, Berkeley. August 1992.

Code maintained by: Michael H. Scott, Oregon State University