Elastic Beam Column Element with Stiffness Modifiers

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This command is used to construct a ModelasticBeam2d element object. The arguments for the construction of an elastic beam-column element with stiffness modifiers is applicable for 2-D problems. This element should be used for modelling of a structural element with an equivalent combination of one elastic element with stiffness-proportional damping, and two springs at its two ends with no stiffness proportional damping to represent a prismatic section. The modelling technique is based on a number of analytical studies discussed in Zareian and Medina (2010) [1] and Zareian and Krawinkler [3].

element ModelasticBeam2d $eleTag $iNode $jNode $A $E $Iz $K11 $K33 $K44 $transfTag

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$eleTag	unique element object tag
$iNode $jNode	end nodes
$A	cross-sectional area of element
$E	Young's Modulus
$Iz	second moment of area about the local z-axis
$K11	stiffness modifier for translation
$K33	stiffness modifier for translation
$K44	stiffness modifier for rotation
$transfTag	identifier for previously-defined coordinate-transformation (CrdTransf) object

NOTE:

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

EXAMPLE:

element ModelasticBeam2d 1 2 4 5.5 100.0 1e6 4.0 4.0 2.0 1; # elastic element tag 1 between nodes 2 and 4 with area 5.5, E 100 and IZ 1e6 with K11=K33=4.0, K44=2.0 which uses transformation 1

References:

[1]	Ibarra, L. F., and Krawinkler, H. (2005). “Global collapse of frame structures under seismic excitations,” Technical Report 152, The John A. Blume Earthquake Engineering Research Center, Department of Civil Engineering, Stanford University, Stanford, CA. [electronic version: https://blume.stanford.edu/tech_reports]
[2]	Zareian, F. and Medina, R. A. (2010). “A practical method for proper modeling of structural damping in inelastic plane structural systems,” Computers & Structures, Vol. 88, 1-2, pp. 45-53.
[3]	Zareian, F. and Krawinkler, H. (2009). "Simplified performance-based earthquake engineering" Technical Report 169, The John A. Blume Earthquake Engineering Research Center, Department of Civil Engineering, Stanford University, Stanford, CA. [electronic version: https://blume.stanford.edu/tech_reports]

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Code Developed by: by Dr. Dimitrios G. Lignos (McGill University)