PDelta Transformation

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This command is used to construct the P-Delta Coordinate Transformation (PDeltaCrdTransf) object, which performs a linear geometric transformation of beam stiffness and resisting force from the basic system to the global coordinate system, considering second-order P-Delta effects. NOTE: P LARGE Delta effects do not include P small delta effects.

For a two-dimensional problem:

geomTransf PDelta $transfTag <-jntOffset $dXi $dYi $dXj $dYj>

For a three-dimensional problem:

geomTransf PDelta $transfTag $vecxzX $vecxzY $vecxzZ <-jntOffset $dXi $dYi $dZi $dXj $dYj $dZj>



$transfTag integer tag identifying transformation
$vecxzX $vecxzY $vecxzZ X, Y, and Z components of vecxz, the vector used to define the local x-z plane of the local-coordinate system. The local y-axis is defined by taking the cross product of the vecxz vector and the x-axis.

These components are specified in the global-coordinate system X,Y,Z and define a vector that is in a plane parallel to the x-z plane of the local-coordinate system.

These items need to be specified for the three-dimensional problem.

$dXi $dYi $dZi joint offset values -- offsets specified with respect to the global coordinate system for element-end node i (the number of arguments depends on the dimensions of the current model). The offset vector is oriented from node i to node j as shown in a figure below. (optional)
$dXj $dYj $dZj joint offset values -- offsets specified with respect to the global coordinate system for element-end node j (the number of arguments depends on the dimensions of the current model). The offset vector is oriented from node j to node i as shown in a figure below. (optional)


The element coordinate system is specified as follows:

The x-axis is the axis connecting the two element nodes; the y- and z-axes are then defined using a vector that lies on a plane parallel to the local x-z plane -- vecxz. The local y-axis is defined by taking the cross product of the vecxz vector and the x-axis. The z-axis by taking the cross-product of x and y vectors. The section is attached to the element such that the y-z coordinate system used to specify the section corresponds to the y-z axes of the element.


ElementOrentation.gif

RigidElementOffsets.gif


EXAMPLE:

ElementCrossSection.png

ElementOrientation.png

ElementVectors.png

  1. Element 1 : tag 1 : vecxZ = zaxis

geomTransf PDelta 1 0 0 -1

  1. Element 2 : tag 2 : vecxZ = y axis

geomTransf PDelta 2 0 1 0


Code Developed by: Remo Magalhaes de Souza

Images Developed by: Silvia Mazzoni