3.1.10.17. Elastic Beam Column Element with Stiffness Modifiers

This element models a prismatic elastic beam-column member using stiffness modifiers that account for the presence of end rotational springs. It is intended for dynamic analysis of frame structures with concentrated plasticity hinges, where numerical damping from standard elastic elements can be problematic.

The command names in OpenSees are ModElasticBeam2d and ModElasticBeam3d. Full formulation details, stiffness modifier definitions, and references are given in Modified Elastic Beam Column Element.

For ndm=2:

element ModElasticBeam2d $eleTag $iNode $jNode $A $E $Iz $K11 $K33 $K44 $transfTag <-mass $massDens> <-cMass>

For ndm=3:

element ModElasticBeam3d $eleTag $iNode $jNode $A $E $G $J $Iy $Iz $K11y $K33y $K44y $K11z $K33z $K44z $transfTag <-mass $massDens> <-cMass>

Argument	Type	Description
$eleTag	integer	unique element tag
$iNode $jNode	integer	end node tags
$A	float	cross-sectional area
$E	float	Young’s modulus
$G	float	shear modulus (3D only)
$J	float	torsional inertia (3D only)
$Iz $Iy	float	second moments of area
$K11 $K33 $K44	float	stiffness modifier coefficients (2D)
$K11y $K33y $K44y	float	stiffness modifiers for bending about local y (3D)
$K11z $K33z $K44z	float	stiffness modifiers for bending about local z (3D)
$transfTag	integer	geometric transformation tag
$massDens	float	element mass per unit length (optional; default 0.0)
-cMass	string	form consistent mass matrix (optional)

Example

1. Tcl Code

element ModElasticBeam2d 1 1 2 10.0 29000.0 100.0 1.0 1.0 1.0 1

2. Python Code

element('ModElasticBeam2d', 1, 1, 2, 10.0, 29000.0, 100.0, 1.0, 1.0, 1.0, 1)

Code developed by: fmk