Force-Based Beam-Column Element

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This command is used to construct a force beam element object, which is based on the iterative force formulation, and considers the spread of plasticity along the element.

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

To change the sections along the element length, the following form of command may be used:

element forceBeamColumn $eleTag $iNode $jNode $numIntgrPts -sections $secTag1 $secTag2 ... $transfTag <-mass $massDens> <-iter $maxIters $tol> <-integration $intType>

Alternative command (kept for backward compatability) is:

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

Alternative command using various numerical integration options (see File:IntegrationTypes.pdf):

element forceBeamColumn $eleTag $iNode $jNode $transfTag "IntegrationType arg1 arg2 ..." <-mass $massDens> <-iter $maxIters $tol>

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$eleTag	unique element object tag
$iNode $jNode	end nodes
$numIntgrPts	number of integration points along the element.
$secTag	identifier for previously-defined section object
$secTag1 $secTag2 ...	$numIntgrPts identifiers of previously-defined section object
$transfTag	identifier for previously-defined coordinate-transformation (CrdTransf) object
$massDens	element mass density (per unit length), from which a lumped-mass matrix is formed (optional, default=0.0)
$maxIters	maximum number of iterations to undertake to satisfy element compatibility (optional, default=10)
$tol	tolerance for satisfaction of element compatibility (optional, default=10-12)
$intType	numerical integration type, options are Lobatto, Legendre, Radau, NewtonCotes, Trapezoidal (optional, default= Lobatto)

NOTE:

1. The default integration along the element is based on Gauss-Lobatto quadrature rule (two integration points at the element ends).
2. The default element is prismatic, i.e. the beam is represented by the section model identified by $secTag at each integration point.
3. 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.
4. The valid response elements that an element of this type will respond to are:
   1. force or globalForce
   2. localForce
   3. basicForce
   4. section $sectionNumber $arg1 $arg2 ... (note: $sectionNumer is integer 1 through $numIntegrPts)
   5. basicDeformation
   6. plasticDeformation
   7. inflectionPoint
   8. tangentDrift
   9. integrationPoints
   10. integrationWeights
5. Here is a link to the source code to obtain information about the location and weight of the Gauss-Lobatto integration points [1]

EXAMPLE:

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

FURTHER DOCUMENTATION ON INTEGRATION OPTIONS:

File: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.

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Code Developed by: Micheal H. Scott, Oregon State University