Question

How can I model tension-only members in response spectrum analysis?

Answer

Response spectrum analysis is a linear type of analysis for which effective stiffness and effective damping are used. Nonlinear properties (such as those defined for nonlinear links and other nonlinear elements like cables) are ignored for response spectrum analysis. The response spectrum analysis is based on the stiffness used for the related modal analysis case - it can be either stiffness for zero initial conditions or stiffness at the end of nonlinear case:

If you need to consider complete nonlinear behavior, it would be necessary to run nonlinear time history analysis.