Force-Based Beam-Column Element: Difference between revisions

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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.
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.


{|  
{|  
| style="background:yellow; color:black; width:800px" | '''element forceBeamColumn $eleTag $iNode $jNode $numIntgrPts $secTag $transfTag <-mass $massDens> <-iter $maxIters $tol> <-integration $intType>'''
| style="background:yellow; color:black; width:800px" | '''element forceBeamColumn $eleTag $iNode $jNode $transfTag "IntegrationType arg1 arg2 ..." <-mass $massDens> <-iter $maxIters $tol>'''
|}
 
{|
|  style="width:150px" | '''$eleTag''' || unique element object tag
|-
|'''$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 [[image: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)
|}
|}


To change the sections along the element length, the following form of command may be used:
 
Original command that assumes Gauss-Lobatto integration with a copy of the same section force-deformation model at each integration point:


{|  
{|  
| style="background:yellow; color:black; width:800px" | '''element forceBeamColumn $eleTag $iNode $jNode $numIntgrPts -sections $secTag1 $secTag2 ... $transfTag <-mass $massDens> <-iter $maxIters $tol> <-integration $intType>'''
| style="background:yellow; color:black; width:800px" | '''element forceBeamColumn $eleTag $iNode $jNode $numIntgrPts $secTag $transfTag <-mass $massDens> <-iter $maxIters $tol> <-integration $intType>'''
|}
 
{|
|  style="width:150px" | '''$eleTag''' || unique element object tag
|-
| '''$numIntgrPts''' || number of Gauss-Lobatto integration points along the element.
|-
| '''$secTag''' || identifier for previously-defined section object
|}
|}




Alternative command (kept for backward compatability) is:
Alternative command (kept for backward compatability):


{|  
{|  
| style="background:yellow; color:black; width:800px" | '''element nonlinearBeamColumn $eleTag $iNode $jNode $numIntgrPts $secTag $transfTag <-mass $massDens> <-iter $maxIters $tol> <-integration $intType>'''
| style="background:yellow; color:black; width:800px" | '''element nonlinearBeamColumn $eleTag $iNode $jNode $numIntgrPts $secTag $transfTag <-mass $massDens> <-iter $maxIters $tol> <-integration $intType>'''
|}
{|
|  style="width:150px" | '''$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:
# element forceBeamColumn $eleTag $iNode $jNode $transfTag Lobatto $secTag $numIntgrPts
# element forceBeamColumn $eleTag $iNode $jNode $numIntgrPts $secTag $transfTag
# element nonlinearBeamColumn $eleTag $iNode $jNode $numIntgrPts $secTag $transfTag


{|
|  style="width:150px" | '''$eleTag''' || unique element object tag
|-
|'''$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 Lobotto, Legendre, Radau, NewtonCotes, Trapezoidal (optional, default= Lobotto)
|}




NOTE:
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 -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:
#The valid response elements that an element of this type will respond to are:
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## localForce
## localForce
## basicForce
## basicForce
## section $sectionTag $arg1 $arg2 ...
## section $sectionNumber $arg1 $arg2 ...   (note: $sectionNumer is integer 1 through $numIntegrPts)
## basicDeformation
## basicDeformation
## plasticDeformation
## plasticDeformation
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EXAMPLE:
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
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




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Code Developed by: <span style="color:blue"> Micheal H. Scott, Oregon State University </span>
Code maintained by: [http://web.engr.oregonstate.edu/~mhscott Michael H. Scott, Oregon State University]

Latest revision as of 01:31, 11 April 2016



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)


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.



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

Retrieved from "https://opensees.ist.berkeley.edu/wiki/index.php?title=Force-Based_Beam-Column_Element&oldid=12226"