Linear Transformation

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This command is used to construct a linear coordinate transformation (LinearCrdTransf) object, which performs a linear geometric transformation of beam stiffness and resisting force from the basic system to the global-coordinate system.

For a two-dimensional problem:

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

For a three-dimensional problem:

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

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$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 i to node j 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 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.

NOTE: When in 2D, local x and y axes are in the X-Y plane, where X and Y are global axes. Local x axis is the axis connecting the two element nodes, and local y and z axes follow the right-hand rule (e.g., if the element is aligned with the positive Y axis, the local y axis is aligned with the positive X axis, and if the element is aligned with the positive X axis, the local y axis is aligned with the positive Y axis). Orientation of local y and z axes is important for definition of the fiber section.

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EXAMPLE:

1. Element 1 : tag 1 : vecxZ = zaxis

geomTransf Linear 1 0 0 -1

1. Element 2 : tag 2 : vecxZ = y axis

geomTransf Linear 2 0 1 0

Code Developed by: Remo Magalhaes de Souza

Images Developed by: Silvia Mazzoni