Triple Friction Pendulum Element

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This command is used to construct a Triple Friction Pendulum Bearing element object. The element is a 3-dimensional triple friction pendulum bearing (TPB) (Figure 1) element with variable friction coefficient model [1] [2]. The element accounts for the vertical-horizontal coupling and the bidirectional coupling in horizontal behavior. The friction coefficient model is a general model that accounts for the variation of friction coefficient on velocity and vertical force. Other simplified friction coefficient models such as vertical-force-independent friction coefficient, velocity-independent friction coefficient and constant friction coefficient can also be defined. The element can also be used for modeling single friction pendulum bearings or double friction pendulum bearings by simplifying the general backbone curve of the TPB.

The horizontal normalized behavior of the element is an extension of the unidirectional behavior proposed by Fenz and Constantinou [3] and Morgan and Mahin [4]. The envelope normalized backbone curve for unidirectional behavior is in Figure 2 where effective radii are calculated from L_i=R_i- h_i, based on the bearing geometry in Figure 1. Displacements u_i^* and normalized forces f_i^* are evaluated according to [2], [3] or [4].

element TripleFrictionPendulum $eleTag $iNode $jNode

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$eleTag	unique element object tag
$iNode $jNode	end nodes

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EXAMPLE:

element TripleFrictionPendulum 1 1 2 ;

REFERENCES:

1) Dao ND, Ryan KL, Sato E, Sasaki T. Verification of a Three-dimensional Triple Pendulum Bearing Element with General Friction Model Using Full Scale Test Data. Submitted to Earthquake Engineering and Structural Dynamics, 2012.

2) Dao ND. Experimental and Analytical Studies of the Seismic Response of a Full-scale 5- story Steel Moment Frame Building Isolated by Triple Pendulum Bearings. Dissertation, University of Nevada – Reno, 2012

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Code Developed by: Nhan D. Dao, University of Nevada - Reno.

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Download these 3 ground motion files and change the extension ".tcl" to ".ATH" for EXAMPLES 2 to 7: Media:TCU065-E.tcl, Media:TCU065-N.tcl, Media:TCU065-V.tcl

EXAMPLE 1:

Unidirectional static pushover of a TPB element with constant friction coefficients.

Tcl code: Media:CheckingTripleFrictionPendulum_StaticCyclicPushover.tcl

Results:

EXAMPLE 2:

Unidirectional dynamic seismic analysis of a single mass supported by a TPB element with constant friction coefficients.

Tcl code: Media:CheckingTripleFrictionPendulum_1DDynamics_ConstFriction.tcl

Results:

EXAMPLE 3:

Unidirectional dynamic seismic analysis of a single mass supported by a TPB element with variable friction coefficients.

Tcl code: Media:CheckingTripleFrictionPendulum_1DDynamics_VariableFriction.tcl

Results:

EXAMPLE 4:

Two-dimensional dynamic seismic analysis of a single mass supported by a TPB element with constant friction coefficients.

Tcl code: Media:CheckingTripleFrictionPendulum_2DDynamic_ConstFriction.tcl

Results:

EXAMPLE 5:

Two-dimensional dynamic seismic analysis of a single mass supported by a TPB element with variable friction coefficients.

Tcl code: Media:CheckingTripleFrictionPendulum_2DDynamic_VariableFriction.tcl

Results:

EXAMPLE 6:

Three-dimensional dynamic seismic analysis of a single mass supported by a TPB element with constant friction coefficients.

Tcl code: Media:CheckingTripleFrictionPendulum_3DDynamic_ConstFriction.tcl

Results:

EXAMPLE 7:

Three-dimensional dynamic seismic analysis of a single mass supported by a TPB element with variable friction coefficients.

Tcl code: Media:CheckingTripleFrictionPendulum_3DDynamic_VariableFriction.tcl

Results: