3.1.10.18. Elastic Timoshenko Beam Column Element

This command constructs an elastic Timoshenko beam-column element that includes shear deformation. The command name in OpenSees is ElasticTimoshenkoBeam (aliases ElasticTimoshenkoBeam2d / ElasticTimoshenkoBeam3d). Section properties may be supplied directly or through a previously defined section object.

For a two-dimensional problem (ndm=2, ndf=3):

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

element ElasticTimoshenkoBeam $eleTag $iNode $jNode $secTag $transfTag <-mass $massDens> <-cMass> <-geomNonlinear>

For a three-dimensional problem (ndm=3, ndf=6):

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

Argument	Type	Description
$eleTag	integer	unique element tag
$iNode $jNode	integer	end node tags
$E	float	Young’s modulus
$G	float	shear modulus
$A	float	cross-sectional area
$J	float	torsional moment of inertia (3D)
$Iz $Iy	float	second moments of area
$Avy $Avz	float	shear areas for local y and z directions
$secTag	integer	tag of a section object (alternative to explicit properties)
$transfTag	integer	geometric transformation tag
$massDens	float	element mass per unit length (optional; default 0.0)
-cMass	string	form consistent mass matrix (optional)
-geomNonlinear	string	enable geometric nonlinearity flag (optional)

Note

1. The valid queries to an elastic Timoshenko beam element when creating an Element Recorder are force.

2. For solid rectangular sections, the shear area is typically 5/6 of the gross area; for solid circular sections, 9/10 of the gross area; for I-shapes, the shear area may be approximated as the web area.

Example

1. Tcl Code

element ElasticTimoshenkoBeam 1 2 4 100.0 45.0 6.0 4.5 5.0 9

2. Python Code

element('ElasticTimoshenkoBeam', 1, 2, 4, 100.0, 45.0, 6.0, 4.5, 5.0, 9)

Code developed by: Andreas Schellenberg