Form: Joint Springs, Coupled 6 x 6 Springs
Springs are flexible connections to ground and are always linear elastic. Assigning a spring to a joint is only meaningful if structural objects are connected to the joint. Otherwise, the spring will support air, so to speak; that is, it will not support anything.
Important Note: It is possible to assign negative spring stiffness to a joint as long as the total stiffness at the joint remains positive (or zero). If some negative spring stiffness is to be assigned to a joint, do it with great care. Negative spring stiffness at a joint during the analysis causes the structure to be unstable. SAP2000 will attempt to solve an unstable structure. If a linear analysis is being performed, SAP2000 will issue several warnings. If a nonlinear analysis is being performed, no warnings will be issued, although the solution may have trouble converging. SAP2000 does not check for negative spring stiffness before running the analysis.
Tip: If a nonlinear spring to ground is needed, use a one-joint (grounded) link object. If springs are needed to connect between two points in the structure, use a two-joint (connecting) link object. Linear or nonlinear properties can be assigned to the link in either case.
Use the Assign menu > Joint > Springs command to open the Joint Springs form and assign to selected joints springs that are oriented in the global axes directions. Both translational and rotational springs can be assigned to a joint.
Select the joint(s) to be applied springs.
Click the Assign menu > Joint > Springs command to display the Joint Springs form.
Spring Direction and Coordinate System drop-down list. Select the Coordinate System within which the springs are being assigned.
Spring Stiffness. Type values for Spring Stiffness in the three Translation and three Rotation local directions. Specify the spring stiffness for one to all six of the degrees of freedom (three Translations and three Rotations) for the selected joint(s). Note that joint spring stiffnesses are always specified in the local coordinate system. No coupling of the six springs is specified here.
Options. Specify how the springs are to be applied:
Add to existing springs: Adds the specified spring stiffness to the joint. If one or more joint spring assignments have already been made, this option increases the existing spring stiffness, assuming that a positive spring stiffness is being assigned.
Replace existing springs: Replaces the currently specified spring stiffness, if any, with the new spring stiffness assignment. If no assignment exists, the new assignment is still made. This is the default option.
Delete existing springs: Deletes any and all joint spring assignments made to the selected joint(s). When this option is selected, the items in the Spring Stiffness area of the form are ignored when the OK button is clicked.
Advanced button. If required, specify the upper half of the Coupled 6X6 Spring matrix by clicking the Advanced button to display the Coupled 6 x 6 Springs form. That form provides edit boxes that can be used to specify joint springs that have coupled behavior, whereby the spring forces that act on a joint are related to the displacements of that joint by a 6x6 symmetric matrix of spring stiffness coefficients.
The above figure illustrates the 6x6 symmetric matrix of spring stiffness coefficients. When coupling is present, all 21 terms in the upper triangle of the matrix are specified. The other 15 terms are known by symmetry. For springs that do not couple the degrees of freedom, only the 6 diagonal terms are needed since the off-diagonal terms are all zero. The diagonal terms are specified for the spring stiffnesses when the Advanced button is not used.
Example: Use of this command is demonstrated in Problem J and Problem Y.
See Also