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For direct-integration time-history analysis, improper viscous-proportional damping may lead to unrealistic axial response. As explained in the CSI Analysis Reference Manual (Material Properties > Material Damping > Viscous Proportional Damping), a damping matrix is computed as follows:
Here, c M and c K are the mass- and stiffness-proportional damping coefficients, M j is the mass matrix, and K j is the initial stiffness matrix. Dynamic equilibrium is then computed as the sum of stiffness forces, damping forces, inertial forces, and applied loading.
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