Triple Friction Pendulum Bearing Element

This command is used to construct a Triple Friction Pendulum Bearing element object, which is defined by two nodes. The element can have zero length or the appropriate bearing height. The bearing has unidirectional (2D) or coupled (3D) friction properties (with post-yield stiffening due to the concave sliding surface) for the shear deformations, and force-deformation behaviors defined by UniaxialMaterials in the remaining two (2D) or four (3D) directions. To capture the uplift behavior of the bearing, the user-specified UniaxialMaterial in the axial direction is modified for no-tension behavior. P-Delta moments are entirely transferred to the concave sliding surface (iNode). It is important to note that rotations of the concave sliding surface (rotations at the iNode) affect the shear behavior of the bearing. If the element has non-zero length, the local x-axis is determined from the nodal geometry unless the optional x-axis vector is specified in which case the nodal geometry is ignored and the user-defined orientation is utilized.

TFP_backbone.gif
element TFP $eleTag $iNode $jNode $R1 $R2 $R3 $R4 $D1 $D2
        $D3 $D4 $d1 $d2 $d3 $d4 $mu1 $mu2 $mu3 $mu4 $h1 $h2 $h3 $h4 $H0 $colLoad
        <$K>

eleTag

unique element object tag

iNode jNode

end nodes

R1

Radius of inner bottom sliding surface

R2

Radius of inner top sliding surface

R3

Radius of outer bottom sliding surface

R4

Radius of outer top sliding surface

D1

Diameter of inner bottom sliding surface

D2

Diameter of inner top sliding surface

D3

Diameter of outer bottom sliding surface

D4

Diameter of outer top sliding surface

d1

diameter of inner slider

d2

diameter of inner slider

d3

diameter of outer bottom slider

d4

diameter of outer top slider

mu1

friction coefficient of inner bottom sliding surface

mu2

friction coefficient of inner top sliding surface

mu3

friction coefficient of outer bottom sliding surface

mu4

friction coefficient of outer top sliding surface

h1

height from inner bottom sliding surface to center of bearing

h2

height from inner top sliding surface to center of bearing

h3

height from outer bottom sliding surface to center of bearing

h4

height from inner top sliding surface to center of bearing

H0

total height of bearing

colLoad

initial axial load on bearing (only used for first time step then load come from model)

K

optional, stiffness of spring in vertical dirn (dof 2 if ndm= 2, dof 3 if ndm = 3) (default=1.0e15)

TFPwH0.gif
TFP_displaced.gif

NOTE:

  1. If the element has zero length and optional orientation vectors are not specified, the local element axes coincide with the global axes. Otherwise the local z-axis is defined by the cross product between the x- and y-vectors specified on the command line.
  2. The valid queries to a triple friction pendulum bearing element when creating an ElementRecorder object are ‘force,’ ‘localForce,’ ‘basicForce,’ ‘localDisplacement,’ ‘basicDisplacement’, ‘relativeDisp’, ‘plasticDisp’, and ‘material $matNum matArg1 matArg2 …’ Where $matNum is the number associated with the material whose data is to be output.
    1. relativeDisp returns relative displacements between the sliding components in the bearing. Relative displacements is the rotation (as shown in the figure above) multiplied by the respective radii. For each time step it returns 8 values; 4 for each horizontal direction.
    2. plasticDisp returns plastic displacements associated with relativeDisp

Examples

element TFP 1 1 2 12.0 12.0 88.0 88.0 12.0 12.0 44.0 44.0 8.0 8.0 12.5 12.5 0.02 0.02 0.09 0.12 3.0 3.0 4.5 4.5 12.5 45.0;

REFERENCE:

Becker, TC, Mahin, SA. “Experimental and analytical study of the bi-directional behavior of the triple friction pendulum isolator,” Earthquake Engineering and Structural Dynamics. (accepted for publication 03/11)read the paper


Code Developed by: Tracy Becker, University of California, Berkeley.

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