At present, dampers are widely used in the field of energy dissipation in engineering structures. However, when the displacement and velocity output of dampers are not significant under small and medium-sized earthquakes, it is difficult for a damper to fully exert its energy dissipation capacity. The use of toggle-brace mechanisms in the structure is an effective method to solve the above problems, and the effect of toggle-brace-viscous dampers (referred to as TBVDs) in the structure can be reflected by a magnification factor (referred to as M_f). Therefore, it is particularly important to study the calculation method for the M_f of TBVD. Domestic and foreign scholars have achieved certain results in the study of the calculation method for the M_f of TBVD, and the corresponding calculation formula for the M_f has been proposed. Given the existing research results, this article conducts the following work: analyzing the shortcomings of existing methods for calculating the M_f of TBVD, proposing an improved method for calculating the M_f of viscous dampers, comparing the accuracy of existing and improved algorithms, and analyzing the calculation results to provide practical suggestions for engineering applications.

This study numerically investigated free vibration characteristics of functionally graded material (FGM) beams on Winkler–Pasternak three-parameter elastic foundations using the modified generalized differential quadrature (MGDQ) method. To compare the effects of different beam theories on the predicted frequency responses, an nth order generalized beam theory was employed to establish the governing equations of the system’s dynamic model within the Hamilton framework. As a pioneering effort, a MATLAB (version 2021a) computational program implementing the MGDQ method was developed to obtain the free vibration responses of foundation-supported FGM beams. Parametric analyses were conducted through numerical simulations to systematically examine the influences of various factors, including beam theories, damping coefficients, foundation stiffness parameters, boundary conditions, gradient indices, and span-to-thickness ratios, on the natural frequencies and damping ratios of FGM beams. The findings provide an essential theoretical foundation for dynamic characteristic analysis and functional design of foundation-supported FGM beam structures.

The research work herein presented is aimed at investigating the effects of different influencing factors on the in-plane failure mode of unreinforced masonry (URM) structures. Firstly, the in-plane stress failure criterion cited in this paper was introduced, and the corresponding judgment procedure was demonstrated. Then, various finite element models considering different influencing factors were established, which included the aspect ratio of pier (η), stiffness ratio of pier to spandrel (ρ) and vertical load (σ). Furthermore, the in-plane stress failure criterion that we introduced was used to evaluate the failure modes of each model. The main findings of the simulations were as follows: under the condition of (η ≤ 1.0), three failure modes emerged in all models, which included pier, mixed and spandrel failure modes, with the gradual increase in ρ. Once the value of η exceeded 1.0, all models exhibited the pier failure mode regardless of whether the value of ρ increased or decreased. Moreover, under the identical aspect ratio (η = 1.0), the failure modes of the models altered regularly with the increase in the value of σ (from 0.3 MPa to 0.6 MPa), which transferred from pier failure to mixed failure, and from mixed failure to spandrel failure. The research results not only provide theoretical reference for the design of new masonry buildings, but also provide technical guidance for the judgement and prediction of failure modes of existing masonry buildings.

Reinforced concrete (RC) frame structures in high-seismicity regions often exhibit vulnerability under strong earthquakes, necessitating effective retrofitting solutions. This study evaluates viscous fluid dampers (VFDs) as a solution for seismic retrofitting of an existing four-story RC school building in China’s high-seismicity zone. Nonlinear time-history analyses were conducted using ETABS under frequent earthquakes (FEs) and the maximum considered earthquake (MCE), comparing structural responses before and after retrofitting. The results demonstrate that VFDs reduced inter-story drift ratios by 10–40% (FEs) and 33–37% (MCE), ensuring compliance with code limits (1/50 under MCE). Base shear decreased by 34.6% (X-direction) and 32.3% (Y-direction), while dampers contributed 66.7% (X) and 40% (Y) of total energy dissipation under FEs, increasing to 74% (X) and 47% (Y) under the MCE. Additional damping ratios reached 3.3–3.7% (X) and 2.0–2.4% (Y), significantly mitigating plastic hinge formation. This study validates VFDs as a high-performance retrofitting solution for RC frames, offering superior energy dissipation compared to traditional methods.

Traditional anti-seismic methods are constrained by high construction costs and the potential for severe structural damage under earthquakes. Energy dissipation technology provides an effective solution for structural earthquake resistance by incorporating energy-dissipating devices within structures to actively absorb seismic energy. However, existing research lacks in-depth analysis of the influence of energy dissipation devices’ placement on structural dynamic response. Therefore, this study investigates the seismic mitigation effectiveness of viscous dampers in multi-storey frame structures and their optimal placement strategies. A comprehensive parametric investigation was conducted using a representative three-storey steel-frame kindergarten facility in Shandong Province as the prototype structure. Advanced finite element modeling was implemented through ETABS software to establish a high-fidelity structural analysis framework. Based on the supplemental virtual damping ratio seismic design method, damping schemes were designed, and the influence patterns of different viscous damper arrangement schemes on the seismic mitigation effectiveness of multi-storey frame structures were systematically investigated. Through rigorous comparative assessment of dynamic response characteristics and energy dissipation mechanisms inherent to three distinct energy dissipation device deployment strategies (perimeter distribution, central concentration, and upper-storey localization), this investigation delineates the governing principles underlying spatial positioning effects on structural seismic mitigation performance. This comprehensive investigation elucidates several pivotal findings: damping schemes developed through the supplemental virtual damping ratio-based design methodology demonstrate excellent applicability and predictive accuracy. All three spatial configurations effectively attenuate structural seismic response, achieving storey shear reductions of 15–30% and inter-storey drift reductions of 19–28%. Damper spatial positioning critically influences mitigation performance, with perimeter distribution outperforming central concentration, while upper-storey localization exhibits optimal overall effectiveness. These findings validate the engineering viability and structural reliability of viscous dampers in multi-storey frame applications, establishing a robust scientific foundation for energy dissipation technology implementation in seismic design practice.