Structural dynamic responses of building structures with non-viscous dampers under Kanai–Tajimi spectrum excitation

•Unified expressions of structural dynamic responses are given by decoupling the ground motion equation.•Explicit form of quadratic orthogonalized power spectral density function (QO-PSDF) of dynamic responses is obtained.•The concise close-form solutions of spectral moments and variances are proposed based on their explicit expression of QO-PSDF.•Three examples are examined and they prove the accuracy and applicability of the proposed method in both single- and multi-degree of freedom structures (SDOF and MDOF).