This study explores the application of machine learning (ML) models, including Random Forest (RF), Extreme Gradient Boosting (XGB), and Artificial Neural Network (ANN), for predicting the mechanical properties of viscoelastic dampers (VED), specifically the storage and loss modulus. VEDs play a crucial role in structural engineering for mitigating dynamic responses to seismic and wind forces. Despite their effectiveness, predicting the mechanical properties of VEDs remains a challenge due to their sensitivity to various factors such as loading amplitude, frequency, and temperature. Leveraging ML models and Explainable AI (XAI) techniques, this research aims to enhance understanding of VED behavior under cyclic loading and provide valuable insights for utilizing ML models for prediction of VED mechanical properties. The study conducts experiments within a temperature chamber, subjecting VEDs to cyclic loading in different conditions to discern the effects of these features on storage and loss modulus. The features such as loading amplitude, frequency, temperature, and loading cycle are then utilized to train ML models. XAI techniques are applied to provide insights into the predictive mechanisms of these models, ensuring the accuracy and reliability of predictions. The results indicate that all three ML models exhibit commendable prediction capabilities, with the ANN demonstrating superior performance compared to RF and XGB. According to SHAP (Shapley Additive Explanations) analysis reveals that loading amplitude exhibits the highest impact, followed by working temperature, loading cycle, and loading frequency.

Past earthquakes have shown that steel storage rack structures are significantly vulnerable due to their specific structural characteristics, which is primarily governed by hook-type beam-to-upright joints. As adding devices or structural elements can obstruct storage bays and limit access, seismic retrofit of these structures is challenging. This study proposes a damping device which consists of a steel plate with two fuse notches and can be attached to beam-to-upright connections without affecting the structure's functionality. In addition to enhancing structural integrity and stiffness, this plate-type fuse dissipates seismic energy through controlled in-plane yielding when subjected to joint rotations. The mechanical behavior of the fuse is theoretically derived and verified using finite element analyses. To this end, an experimental rack subassembly test under cyclic loads is modeled and validated in both Ansys and OpenSees. Subsequently, it is retrofitted with the proposed fuse and its hysteretic behavior and the accuracy of the derived theoretical formulations are evaluated in a comprehensive parametric study. To further investigate the effectiveness of the developed damping device, a benchmark three-story four-bay rack structure is modeled and retrofitted in OpenSees. The seismic performance of this structure is evaluated and compared before and after retrofit using nonlinear time history analysis under a suite of ground motion records and pushover analysis. The results show that the original structure experiences global failure and dynamic instability under the Maximum Considered Earthquake hazard level, whereas the retrofitted structure meets the Collapse Prevention performance objective as designed using the established theoretical formulations.

The seismic performance of rack storage structures is mainly governed by the beam-to-upright connections, which are highly flexible and show considerable stiffness and strength degradation, along with pinching behavior. To address these vulnerabilities, a steel hysteretic damper is proposed which can be installed at these joints to improve seismic performance and energy dissipation. The damper consists of an L-shaped steel plate with a tapered section which acts as a fuse, yielding under rotational deformation at the joint. The mechanical behavior of the damper is theoretically formulated for the design purpose and it incorporates the derivation of slope-deflection equations for tapered members. The accuracy of the formulation is verified by comparing its prediction with a detailed finite element model in Ansys and OpenSees. The effects of geometric imperfections and buckling is also investigated using a probabilistic approach and finite element simulations. To further investigate the effectiveness of the proposed device, an experimental test on a beam-to-upright connection from a rack subassembly subjected to cyclic loading is simulated and validated in OpenSees. The damper's model is then applied to the validated system, and the cyclic behavior before and after retrofit is compared in terms of hysteretic response and energy dissipation. Results show that the proposed energy dissipation device can enhance stiffness, capacity and energy dissipation capability of the joints. The theoretical formulation, analysis modeling approach and simulations presented in this study provide a detailed insight into seismic behavior of steel rack storage structures.

In this research, a new steel hysteretic damper for seismic retrofit of structures is proposed and its performance is evaluated. The damper consists of a circular hollow column section and bidirectional flexural fuse at each end, made of steel with reduced section, which can be installed beside existing columns of the structure to minimize interference with architectural functions. The bidirectional fuses act as flexural hinges to dissipate the seismic energy. The theoretical formulation and the design procedure based on plastic analysis are provided for the proposed damper, and the results are compared with a finite element analysis (FEA) model. To validate the applicability of the proposed damper in structural analysis, a macromodel of the damper is also developed and calibrated by the derived theoretical formulas. The results are compared with the FEA, and the effectiveness of the damper is further investigated by the seismic retrofit of a reinforced concrete structure. An optimization technique based on slime mould is used to find the optimal number of dampers and their location. The performance of the structure is evaluated in terms of interstory drift ratios, residual displacements, and dissipation of seismic energy. The results show that the drift ratios decreased by 39.5%, residual displacements by 56 %, and energy dissipation by the columns from 17% to 2%. The results suggest that the proposed damper can be used to effectively protect structures from seismic loads.

Although there have been various research works on linear elastic analysis of structures with tapered, axially non-uniform, and composite members, less attention has been paid to a generalized linear elastic formulation for arbitrary heterogeneous members within the classical structural analysis framework. In this research, the slope-deflection equations are derived based on the Euler-Bernoulli kinematic assumptions in such a way that they can account for spatial variability in both geometry and material properties of structural members while retaining the exact classical form. By including axial deformations and deriving fixed-end forces, a generalized stiffness formulation for heterogeneous elements is obtained next, which is easy to understand and can be further implemented in classical matrix analysis and displacement methods. The application of the proposed formulations is shown using two benchmark problems, namely a heterogeneous beam, and a frame structure with axially non-uniform members. Reactions, internal forces, displacement and stress fields are obtained and explained elaborately, and their accuracies are verified by comparing with detailed finite element models established in the open-source software OpenSees. The results show that the developed structural analysis tools can be efficiently used for different types of structures and are highly accurate.

Viscoelastic damper is widely applied in structural energy dissipation and vibration control, as it is critical for ensuring the structural stability and enhancing energy dissipation. This study designs two novel viscoelastic dampers with patterned metasurface structure to improve the performance of dampers. The dynamic behaviors of novel dampers are investigated through dynamic loading experiments under different frequencies, temperatures, and displacement amplitudes. An equivalent fractional-order dual-branch model is proposed to consider the effect of temperature and frequency for viscoelastic constitutive model. Based on this model, the interfacial failure behavior between viscoelastic layer and rigid substrate is investigated, and the effects of temperature and frequency on the critical displacement and energy release rate is analyzed. The mechanical behavior of interfacial failure between the viscoelastic layer and steel plate under different patterned metasurface structures (palm-shaped and fingerprint-shaped) is investigated. A theoretical analysis is conducted on the effects of metasurface geometric parameters on interfacial bonding strength. Experiments and theories indicate that temperature, frequency, and the patterned metasurface interfacial design significantly influence interfacial bonding strength and energy dissipation of dampers. The present work demonstrates that effective metasurface structural design enhances interfacial bonding strength and fracture toughness, thereby improving energy dissipation capacity of the damper.

This study presents and studies the application of normalized Modified Bouc-Wen model to capture the nonlinear hysteretic behavior of viscoelastic dampers under cyclic loading. Six different tests were conducted on viscoelastic dampers with different frequencies and amplitudes to evaluate their energy dissipation performance. The model considers strength and stiffness degradation effects using a normalized form to capture nonlinear hysteretic behavior based on applied loading and energy dissipation. Since identifying Modified Bouc-Wen parameters from the experimental results is a challenging task due to the complexity and interdependence of the parameters in the model formulation, the Particle Swarm Optimization (PSO) algorithm was applied. The first stage involved exploring a wide range of parameter values to identify reasonable value ranges, and the second stage applied refined bounds to improve accuracy. The calibrated model was validated by comparing its results with experimental hysteresis curves, confirming good agreement in both stress-strain response and energy dissipation. Furthermore, various machine learning regression models were trained using measurable input parameters. The output variables were the remaining Modified Bouc-Wen parameters derived from PSO-based optimization. Among the tested machine learning models, Gradient Boosting achieved the best performance, effectively estimating the Bouc-Wen parameters and reliably predicting the overall hysteretic behavior. SHAP analysis was conducted to interpret the model, indicating that stiffness and amplitude were the most influential features in estimating the Modified Bouc-Wen parameters.

This study investigates the feasibility and applicability of spring-friction dampers for seismic retrofit of structures. Finite element analysis of the device was carried out to verify the relationship between the bolt pretension force and the friction yield force. Parametric study of the device was conducted to investigate the effect of the recovery force provided by the coil spring. The developed damper was applied to a five-story reinforced concrete (RC) framed building to assess its efficacy for seismic retrofit. The seismic performance of the device was thoroughly evaluated, focusing on its ability to reduce inter-story and residual displacements by dissipating seismic energy and providing stiffness and recovery force. The particle swarm optimization algorithm was applied to find out the optimum number of dampers and their optimum locations. The results demonstrate that the proposed damper and the optimum design scheme can be effectively utilized to protect structures against seismic loads.

One of the ways to design structures following damage avoidance design (DAD) philosophy is to decouple the seismic and gravity load resisting systems. During an earthquake, structural elements in the gravity load resisting system remain intact while the lateral load resisting system properly dissipates the energy using sacrificial or zero-damage seismic devices. In this research, a design procedure based on the iterative Newton-Raphson method is proposed which can be used in conjunction with the DAD philosophy to design structures to meet a given performance objective using seismic devices. This approach utilizes nonlinear time history analysis directly for seismic design, whereas conventional methods rely on static methods and use only nonlinear time history analysis to control the performance. The application of the developed method is shown by designing three various example structures with different levels of complexity with buckling-restrained braces (BRBs) and proves highly accurate. For instance, a three-dimensional asymmetric 4-story steel frame is designed using the developed method. The mean maximum interstory drift ratios of the preliminary design ranged from 2.50 % to 2.97 %. By using the proposed method, the target of 2.0 % at all stories was achieved within five iterations, with an error margin of less than 0.5 % (i.e. 2.0 % +/- 0.01 %).

In the field of structural engineering, optimizing retrofitting strategies for bolstering seismic resilience stands as a pressing challenge. Existing methods are often limited by the time-intensive nature of nonlinear time history (NLTH) analysis and the lack of transparency in machine learning (ML) techniques. This study presents an innovative framework for optimizing retrofitting strategies in structural engineering to enhance seismic resilience. The framework integrates eXtreme Gradient Boosting (XGBoost) and the Spring-Rotational Friction Damper (SRFD) retrofit system, known for its ability to dissipate seismic energy and incorporate self-centering mechanisms. The approach improves transparency in machine learning processes and streamlines design optimization. It uses eXplainable Artificial Intelligence (XAI) methods, such as SHapley Additive exPlanations (SHAP) and Local Interpretable Model-agnostic Explanations (LIME), to provide insights into model predictions and ensure clear decision-making processes. The framework uses data-driven optimization to tailor design parameters to specific seismic hazards, enhancing seismic resilience. Its accuracy was validated through a comprehensive analysis, showing low residual errors, favorable learning curves, and a mean squared error (MSE) of 0.00142. The research evaluates the framework using 2D and 3D case study structures, comparing metrics like maximum displacement, residual drift, maximum inter-story drift (MIDR), and energy dissipation. The seismic performance evaluation confirmed the effectiveness of the design procedure for determining optimal retrofit system parameters estimated by the eXplainable Machine Learning (XML) framework. This represents a significant advancement in seismic assessment methodologies, enabling engineers to make informed decisions about building safety and promoting the adoption of ML-based approaches in earthquake engineering.

The present research provides a theoretical and analytical assessment of a new bidirectional viscoelastic column damper for dissipation of seismic energy. This device includes a steel column with two orthogonally placed viscoelastic hinges at each end, which can dissipate the seismic energy under two concurrent horizontal seismic actions. Another advantage over conventional dampers and bracing systems is its vertical installation scheme, which maintains open bays and provides architectural flexibility. A theoretical model for the mechanical behavior of the damper is developed and contrasted with a detailed analytical and finite element models. The adaptive capability of the damper to exhibit varying stiffness and energy dissipation behavior is emphasized. The effectiveness of the proposed device is shown using the seismic retrofitting of a five-story steel frame structure. The seismic performance of the structure is evaluated using nonlinear time history analysis under a suite of earthquake ground motions. To meet a target interstory drift ratio, the Modified Cuckoo Search optimization algorithm is used and the optimum number and placement of dampers in the structure are determined. The performance of the structure is compared before and after retrofit in terms of maximum interstory drift ratio, residual displacement, and energy dissipation. The results show the efficiency and capability of the developed damper and applied retrofit design method using optimization.

This study investigates the feasibility and effectiveness of a friction damper made of brake pads, high-strength bolts, and a heavy-duty coil spring. It is positioned in the middle of a steel bracing to dissipate earthquake energy. To evaluate the effectiveness of the proposed damper, its mechanical behavior is evaluated through finite element analysis, and an analytical model is established for structural analysis and design. The analytical model of the damper is developed using SAP2000 software and is compared with the FE model generated in Ansys Mechanical software. Bayesian optimization technique with Gaussian process is employed to determine the minimum number and optimum locations of the dampers to satisfy a given limit state with minimum cost. The analytical model and the optimum design technique are applied to a 5-story reinforced concrete (RC) structure to assess its performance before and after retrofit for the maximum considered earthquake (MCE) conditions. The seismic performance is thoroughly evaluated regarding maximum interstory drift, residual displacement, and energy dissipation capability. Overall, the results demonstrate the efficiency of the proposed friction damper and optimum design technique in safeguarding structures against seismic loads.

Scissor-jack-damper (SJD), an advanced variant of the toggle-brace-damper, has encountered some small-to-medium applications in several practical projects. The application of large SJD is rather limited because it suffers out-of-plane instabilities, which is due to the SJD's planar configuration tagged by a low out-of-plane stiffness. To fix up this problem and to further explore the advantage of the SJD mechanism, the authors of this paper utilize an asymmetric 3D arrangement of rods and dampers to generate a triangular pyramid "3 dampers-6 rods" layout. The novel structuring scheme exhibits not only an enhanced robustness with better global stability but also an elevated efficiency. In this study, the displacement amplification factor, force amplification factor, and the equivalent damping coefficient of the proposed SJD are derived, wherein the force equilibrium (or energy conservation in a substitutive process) and the geometrical compatibility are accounted for. Taylor's series expansion and a simplified truncation are adopted to process the nonlinearity of the spatial SJD. The accuracy of the theoretical expression is proved against numerical modelling. It is shown that the equivalent damping coefficient of the dampers integrated in the novel SJD can be amplified by more than 10 times via a reasonable design configuration. The included angle theta between the rods plays the most important role in adjusting the amplification factor eta of the SJD, e.g, the value of eta drops from 14.01 to 7.13 as theta increases from 15 degrees to 25 degrees in a typical design scheme. An illustrative applicational example of the proposed SJD is provided. Compared with the conventional damper installation configuration, the 4-story demonstrative frame equipped with the proposed SJD shows a 52 % and a 26 % reduction in the peak roof displacement and the peak base shear, respectively.

In this paper a new seismic retrofit system composed of a steel frame with viscoelastic hinges is proposed and its applicability and efficiency are evaluated in a theoretical framework. First, the mechanical behavior of viscoelastic hinges and the system are studied and the related formulas are derived. The analytical model of the proposed seismic damper is established first, and the damper is subjected to cyclic loads to compare its hysteretic behavior with the one from the formulation. In order to further evaluate the efficiency of this system, the validated analytical model is used in seismic retrofit of a case study structure to reach the collapse prevention performance under the maximum considered earthquake hazard level. The seismic performance of the analysis model is compared before and after retrofit in terms of maximum interstory drift ratio, residual displacement, and energy dissipation of structural members and dampers. The results show that the proposed damper can be used to reach the stipulated drift limit state. Furthermore, the inelastic energy dissipated by the structural members is reduced drastically and the structure can be effectively protected against irreversible damages due to inelastic deformations.

In this research, the efficiency of a metallic energy dissipation device for seismic retrofit of an existing structure is evaluated by cyclic loading test. The proposed device, which is called multi -slit damper, is made of weak and strong slit dampers connected in series. Its energy dissipation mechanism consists of two stages: (i) yielding of the weak -slit damper under minor earthquakes; (ii) restraint of further deformations of the weak slit damper and activation of the strong slit damper under major earthquakes using a gap mechanism. A reinforced concrete (RC) frame with characteristics similar to soft -first -story structures is tested under cyclic loading before and after retrofit using the proposed device. The details of the experimental study are described and the test is simulated in an available commercial software to validate the analytical model of the damper. To further verify the applicability of the damper, it is applied to an analysis model of a 4 -story structure with soft first story and its seismic performance is evaluated before and after retrofit. The experimental and analysis results show that the multi -slit damper is effective in controlling seismic response of structures.

This paper presents an experimental and analytical study on a steel slit damper designed as an energy dissipative device for earthquake protection of structures considering soil-structure interaction. The steel slit damper is made of a steel plate with a number of slits cut out of it. The slit damper has an advantage as a seismic energy dissipation device in that the stiffness and the yield force of the damper can be easily controlled by changing the number and size of the vertical strips. Cyclic loading tests of the slit damper are carried out to verify its energy dissipation capability, and an analytical model is developed validated based on the test results. The seismic performance of a case study building is then assessed using nonlinear dynamic analysis with and without soil-structure interaction. The soil-structure system turns out to show larger seismic responses and thus seismic retrofit is required to satisfy a predefined performance limit state. The developed slit dampers are employed as a seismic energy dissipation device for retrofitting the case study structure taking into account the soil-structure interaction. The seismic performance evaluation of the model structure shows that the device works stably and dissipates significant amount of seismic energy during earthquake excitations, and is effective in lowering the seismic response of structures standing on soft soil.

In this research, a seismic retrofit device was proposed and its performance was tested under cyclic loading. The developed damper is composed of a steel frame with friction hinges and springs at corners to provide stiffness and restoring force. Theoretical formulas for its mechanical behavior and its analytical model were developed and verified by comparing them with the results of an experimental test. To further evaluate the applicability of this retrofit system, it was applied to the seismic retrofit of a case study structure designed without considering seismic load. The structure was retrofitted to satisfy a given performance objective and its seismic behavior was compared using nonlinear time history analysis before and after retrofit. The seismic performance of the structure was assessed in terms of maximum interstory drift ratio, residual displacement, and energy dissipation. It was observed that the installed retrofit frames could properly dissipate the seismic energy and reduce both inter-story drifts and residual displacements of the case study structure.

This study investigates a new seismic retrofit system that utilizes rotational friction dampers and axial springs. The retrofit system involves a steel frame with rotational friction dampers (RFD) at beam-column joints and linear springs at the corners, providing energy dissipation and self-centering capabilities to existing structures. The axial spring acts as a selfcentering mechanism that eliminates residual deformations, while the friction damper mitigates seismic damage. To evaluate the seismic performance of the proposed retrofit system, a series of cyclic loading tests were carried out on a steel beam-column subassembly equipped with the proposed devices. An analytical model was then developed to validate the experimental results. A performance point ratio (PPR) was presented to optimize the design parameters of the retrofit system, and a performancebased seismic design strategy was developed based on the PPR. The retrofit system's effectiveness and the presented performance-based design approach were evaluated through case study models, and the analysis results demonstrated that the developed retrofit system and the performance-based design procedure were effective in retrofitting structures for multi-level design objectives.

This research proposed a particle swarm optimization (PSO) based seismic retrofit design of moment frame structures using a steel frame assembly. Two full scale specimens of the steel frame assembly with different corner details were attached to one-story RC frames for seismic retrofit, and the lateral load resisting capacities of the retrofitted frames subjected to cyclic loads were compared with those of a bare RC frame. The open source software framework Opensees was used to develop an analytical model for validating the experimental results. The developed analytical model and the optimization scheme were applied to a case study structure for economic seismic retrofit design, and its seismic performance was assessed before and after the retrofit. The results show that the developed steel frame assembly was effective in increasing seismic load resisting capability of the structure, and the PSO algorithm could be applied as convenient optimization tool for seismic retrofit design of structures.