Force-Based Beam-Column Element

This command is used to construct a force beam element object, which is based on the non-iterative (or 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>

---

$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=1)
$tol	tolerance for satisfaction of element compatibility (optional, default=10-16)
$intType	numerical integration type, options are Lobotto, Legendre, Radau, NewtonCotes, Trapezoidal (optional, default= Lobotto)

NOTE:

• The default integration along the element is based on Gauss-Lobatto quadrature rule (two integration points at the element ends).

• The default element is prismatic, i.e. the beam is represented by the section model identified by $secTag at each integration point.

• 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 queries to a nonlinear beam-column element when creating an ElementRecorder object are 'force,' 'stiffness,' and 'section $secNum secArg1 secArg2...' Where $secNum refers to the integration point whose data is to be output.

• 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

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

1. forces or globalForces
2. localForces
3. basicForces
4. section $sectionTag $arg1 $arg2 ...
5. basicDeformations
6. plasticDeformations
7. inflectionPoint
8. tangentDrift
9. integrationPoints
10. integrationWeights

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 Scott, Oregon State University