Tuned mass damper (TMD) is a single‐terminal damper, while inerter is a two‐terminal one, which are effective control devices. So, a hybrid damper with a series‐parallel inerter system and a TMD (SPIS‐TMD) in series is proposed. The main work of the manuscript is as follows. Firstly, based on the mechanical diagram of SPIS‐TMD and its equipment on the roof of a high‐rise structure, the general form of seismic motion equation was derived using dynamic finite element technology. Secondly, based on the method of quadratic decomposition for power spectrum density function (QD‐PSDF), the concise analytic solutions for zero‐, first‐, and second‐order response spectral moments (ZFSO‐RSMs) of the general response of structure with SPIS‐TMD were deduced. Thirdly, in response to the numerous parameters that affect the safety of high‐rise structures and the varying difficulty for obtaining SPIS‐TMD’s parameters, an optimization analysis technique was proposed, which is constrained by dynamic reliability and SPIS‐TMD’s parameter weights. Finally, three examples were given and results show the following. (1) The proposed analytical solutions for ZFSO‐RSMs are correct and high efficiency and can be extended to analysis of stationary seismic responses of general linear structures. (2) Calculating results of ZFSO‐RSMs of general responses with the number of vibration modes corresponding to a participation weight of 100% is exactly the same as those with all vibration modes, and the calculating time of the case of the participation weight of 100% is less than 1/12 that of the case of all vibration modes. (3) The failure probabilities of the structure with SPIS‐TMD with optimal parameters using the proposed method (with a limit failure probability of 0.1587), the structure only equipped with TMD with the same TMD’s parameters as SPIS‐TMD, and the structure without dampers are 0.1570, 0.7060, and 0.9778, respectively. It indicates that under the same conditions, the hybrid damper SPIS‐TMD has a better damping effect than a single TMD.

The understanding of the effects of multidirectional loadings imposed on major load bearing elements such as reinforced concrete (RC) columns by seismic actions for collapse prevention is of utmost importance, and a few simplified models are available in the literature. In this study, the distinguishing features of two machine-learning (ML) methods, namely, multi expression programming (MEP) and adaptive neuro-fuzzy inference system (ANFIS) are exploited for the first time to develop eight novel prediction models (M1-to M4-MEP and M1-to M4-ANFIS) with different combinations of input parameters to predict the biaxial shear strength of RC columns (V). The performance of the developed models was assessed using various statistical indicators and by comparing them with the experimental values. Based on the statistical analysis of the developed models, M1-ANFIS and M1-MEP performed very well and exhibited the best overall efficiency of the studied ML methods. Simple mathematical formulations were also provided by the MEP algorithm for the prediction of V, using which the M1-MEP model was finalized based on its performance, accuracy, and generalization capability. A parametric analysis was also performed for the model to show that the mathematical formulation provided by MEP accurately represents the system under consideration and is imperative for prediction purposes. Based on its performance, the model can thus be recommended to update the current code provisions and engineering practices.