Elastic Timoshenko Beam Column Element: Difference between revisions

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(Created page with '{{CommandManualMenu}} This command is used to construct an ElasticTimoshenkoBeam element object. A Timoshenko beam is a frame member that accounts for shear deformations. The ar...')
 
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{|  
{|  
| style="background:lime; color:black; width:800px" | ''' element ElasticTimoshenkoBeam $eleTag $iNode $jNode $E $G $A $Iz $Avy $transfTag'''
| style="background:lime; color:black; width:800px" | ''' element ElasticTimoshenkoBeam $eleTag $iNode $jNode $E $G $A $Iz $Avy $transfTag <-mass $massDens> <-cMass>'''
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{|  
{|  
| style="background:lime; color:black; width:800px" | ''' element ElasticTimoshenkoBeam $eleTag $iNode $jNode $E $G $A $Jx $Iy $Iz $Avy $Avz $transfTag'''
| style="background:lime; color:black; width:800px" | ''' element ElasticTimoshenkoBeam $eleTag $iNode $jNode $E $G $A $Jx $Iy $Iz $Avy $Avz $transfTag <-mass $massDens> <-cMass>'''
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|  style="width:150px" | '''$eleTag''' || unique element object tag
|  style="width:150px" | '''$eleTag''' || unique element object tag
|-
|-
|'''$iNode $jNode''' ||end nodes
| '''$iNode $jNode''' ||end nodes
|-
|-
| '''$E''' || Young's Modulus
| '''$E''' || Young's Modulus
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| '''$G''' || Shear Modulus
| '''$G''' || Shear Modulus
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|-
|'''$A''' || cross-sectional area of element
| '''$A''' || cross-sectional area of element
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|-
| '''$Jx''' || torsional moment of inertia of cross section
| '''$Jx''' || torsional moment of inertia of cross section
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|-
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| '''$transfTag''' || identifier for previously-defined coordinate-transformation (CrdTransf) object
| '''$transfTag''' || identifier for previously-defined coordinate-transformation (CrdTransf) object
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| '''$massDens''' || element mass per unit length (optional, default = 0.0)
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| '''-cMass''' || to form consistent mass matrix (optional, default = lumped mass matrix)
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The valid queries to an elastic Timoshenko beam element when creating an ElementRecorder object are 'force'.
The valid queries to an elastic Timoshenko beam element when creating an ElementRecorder object are 'force'.


For solid rectangular sections, shear area is often assumed to be 5/6 of the gross area. For I-shapes, the shear area can be approximated as Aweb.
For solid rectangular sections, the shear area is 5/6 of the gross area. For solid circular sections, the shear area is 9/10 of the gross area. For I-shapes, the shear area can be approximated as Aweb.




Latest revision as of 21:48, 25 March 2018



This command is used to construct an ElasticTimoshenkoBeam element object. A Timoshenko beam is a frame member that accounts for shear deformations. The arguments for the construction of an elastic Timoshenko beam element depend on the dimension of the problem, ndm:

For a two-dimensional problem:

element ElasticTimoshenkoBeam $eleTag $iNode $jNode $E $G $A $Iz $Avy $transfTag <-mass $massDens> <-cMass>

For a three-dimensional problem:

element ElasticTimoshenkoBeam $eleTag $iNode $jNode $E $G $A $Jx $Iy $Iz $Avy $Avz $transfTag <-mass $massDens> <-cMass>


$eleTag unique element object tag
$iNode $jNode end nodes
$E Young's Modulus
$G Shear Modulus
$A cross-sectional area of element
$Jx torsional moment of inertia of cross section
$Iy second moment of area about the local y-axis
$Iz second moment of area about the local z-axis
$Avy Shear area for the local y-axis
$Avz Shear area for the local z-axis
$transfTag identifier for previously-defined coordinate-transformation (CrdTransf) object
$massDens element mass per unit length (optional, default = 0.0)
-cMass to form consistent mass matrix (optional, default = lumped mass matrix)


NOTES:

The valid queries to an elastic Timoshenko beam element when creating an ElementRecorder object are 'force'.

For solid rectangular sections, the shear area is 5/6 of the gross area. For solid circular sections, the shear area is 9/10 of the gross area. For I-shapes, the shear area can be approximated as Aweb.


EXAMPLE:

element ElasticTimoshenkoBeam 1 2 4 100.0 45.0 6.0 4.5 5.0 9; # elastic Timoshenko element with tag 1 between nodes 2 and 4 with E=100, G=45, A=6.0, I=4.5 and Av=5.0 which uses transformation 9

Code Developed by: Andreas Schellenberg

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