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During nonlinear direct-integration time-history analysis, special consideration may be needed for modeling stiffness-proportional damping of stiff elements which experience inelastic softening. As explained in the CSI Analysis Reference Manual (Material Properties > Material Damping > Viscous Proportional Damping), the damping matrix for element j is computed as follows:
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During analysis, nonlinear elements may undergo significant softening due to yielding. This may generate significant damping forces in elements that are initially stiff if the softening results in significant deformational velocity. These damping forces, while properly in equilibrium with other forces at a joint connected to the stiff element, may cause a jump in stiffness forces between the softening element and connected elements. Such a condition may occur, for example, in a concrete column modeled with multiple elements containing hinges. When the initially-stiff column is subjected to cyclic bending, cracking and the ratcheting of yielding tensile rebar will soften element response. Axial velocity and excessive c K K j damping contribution may then generate large differences in the axial force between adjacent elements in the same column. While this jump is in axial force satisfies dynamic equilibrium, it may not be the desired behavior. Users may need to implement additional measures achieve the expected results.
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Additional details and descriptions may be found in the CSI Analysis Reference Manual (Nonlinear Time-History Analysis > Nonlinear Direct-Integration Time-History Analysis > Damping).