Elastic Timoshenko Beam Column Element

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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>

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$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

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Code Developed by: Andreas Schellenberg