Force-Based Beam-Column Element

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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 File:IntegrationTypes.pdf for more details on the available numerical integration options.

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

$eleTag	unique element object tag
$iNode $jNode	end nodes
$transfTag	identifier for previously-defined coordinate-transformation (CrdTransf) object
IntegrationType arg1 arg2 ...	specifies locations and weights of integration points and their associated section force-deformation models (see File:IntegrationTypes.pdf)
$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)

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)

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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

NOTE:

1. 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.
2. 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
3. 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 9 Lobatto 8 5; # 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

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 maintained by: Michael H. Scott, Oregon State University