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This article presents a Lyapunov precise integral-based analysis method for seismic structures with added viscous fluid dampers. This study uses the full stress algorithm as the optimization method, considering the mean square of interstory drifts as the optimization objective, the position of the damper as the optimization object, and the random vibration analysis method as the calculation method to optimize seismic frame structures with viscous dampers. A precise integral solution is derived for the Lyapunov equation based on the general expression of the Lyapunov differential equation for the damping system under the excitation of a nonstationary stochastic process using two types of modulation functions: g(t)=1 and g(t)=t. Finally, the optimal damping arrangement is achieved using this method with a six-layer non-eccentric planar frame. In addition, the optimization results of this study are verified with those in the literature using time-history analysis, which verifies the feasibility and effectiveness of the proposed method. This study provides a method for the optimal configuration of dampers for seismic response of structures, which is beneficial for engineering applications and the protection of seismic structures.

The accurate prediction of nonlinear structural behaviors under different seismic intensities is an important basis for seismic resilience assessments of building structures. The moment–rotation relationship is often used to characterize the seismic performance of connections, and is widely used in high-efficiency nonlinear structural analysis. In this paper, a method of calculating the curve using a four-linear equivalent model is presented, aiming to quantify the characteristic point parameters of the moment–rotation curves of monolithic precast beam–column (MPBC) connections for engineering design purposes. The method considered the contribution of the elastic flexure of beams and columns, the relative slip of beam longitudinal bars in the core zone, and the formation of plastic hinges at beam ends to the total deflection. Due to the presence of local complex configurations in MPBC connections, the fine fiber section method was used for moment–curvature analysis of critical beam sections. The determination of the sectional analysis processes was controlled by the strain of steel bars or concrete or their coupling effect. In addition, a two-step method was proposed to construct the moment–rotation relationship of cruciform beam–column connections for solving the deformation compatibility of beams on both sides of the column caused by asymmetric reinforcement and the strength difference between new and old concrete. To reflect the current manufacturing level of MPBC connections, 58 representative specimens reported in recent years were analyzed and classified as type 1–5. All types of MPBC connections and their 18 cast-in situ counterparts were calculated using the proposed method for both verification and quantification. The verification showed that the proposed method had good applicability to both cast-in situ and precast beam–column connections. The quantification showed that the characteristic point parameters were slightly different between these two connections. Accordingly, modification coefficients were suggested for MPBC connections to facilitate design.