Six-story Frame Research Articles

Optimization of structures subjected to earthquake excitation using two-point adaptive approximation with trust region strategy

This study presents a gradient-based method, TPAA-TR, for optimizing structures under earthquake excitation. The method develops an efficient algorithm that can converge quickly to the optimal solution under time history loading. It uses two-point exponential approximation with consistent intermediate variables to construct explicit linear sub-problems, and applies filter method and trust region strategy to solve them. Merit functions and filters are used to balance the trade-off between reducing objectives and satisfying constraints, and promote convergence. The method performs nonlinear response history analysis for seismic analysis to account for the nonlinear behavior of structures. The effectiveness of the proposed method is demonstrated by three numerical examples: a three-story shear frame, a six-story frame installed with nonlinear devices and a nine-story three-dimensional (3D) reinforced concrete (RC) nonlinear building. The results show that the proposed method can achieve optimal solutions with less computational time and fewer function evaluations than existing methods.

Fusing physics-based and machine learning models for rapid ground-motion-adaptative probabilistic seismic fragility assessment

Performance-based earthquake engineering (PBEE) has asserted probabilistic seismic fragility assessment (PSFA) as the main research content in light of its irreplaceable significance for seismic decision-making in recent decades. Among the multiple approaches of PSFA implementation, the classical linear regression method (LRM) dominates over practice regarded as one of the most widely-used. However, the general LRM adopts quantile regression method (QRM) on the group of fragility curves to approximate a deterministic probability density distribution (PSD) of structural fragility against certain intensity measure (IM) of potentially confronting earthquake. Consequently, the QRM-derived fragility representation might not be credible enough while evaluating a newly-occurred seismic event owing to its neglect of specificity of stochastic ground motion. To address this issue, a fusing physics-based and machine learning models towards rapid ground-motion-adaptative probabilistic seismic fragility assessment (GmaPSFA) is proposed in present study. With sophisticated framework design and novel fragility hyperparameters estimation, the involved design philosophy and mechanism translating are both elaborated. To validate the method, both the LRM and GmaPSFA were conducted on a six-story frame structure, where a novel fully-automatic batch processing approach fusing APDL and coding languages was propounded for structural analysis. The comprehensive validating cases confirmed the powerful capability and significant superiority of proposed GmaPSFA in realizing rapid ground-motion-adaptative probabilistic seismic fragility assessment catering for modern PBEE.

Introducing a multi-layer pendulum isolator and investigating its effect on structures' responses during some earthquakes

To protect structures from earthquakes, various systems called base isolation are used, which reduce the force applied to the structure during ground movement by reducing the lateral stiffness of the structure. This makes the structure follow the movement of the earth, but softly and with a delay in response. In this research, an isolator with a new shape is proposed without having permanent displacement, similar to a pendulum, and can be used as an isolation system in structures. This system is called a multi-layer pendulum isolator. The system has the same period as a tall pendulum but is much smaller in size. The equations of the isolator were derived and solved by MATLAB software. Examples of frames were modeled in Abaqus under several earthquakes, and the responses of the system were obtained. Results showed that the proposed isolator reduced acceleration, drift, and base shear very effectively. For example, by using a multi-layer pendulum isolator in a six-story frame, it was found that the base shear and drift created in the first floor were reduced by more than sixty percent. The multi-layer pendulum isolator introduced showed that it was an efficient isolator system capable of reducing the destructive effects of an earthquake. The results of the system responses showed that the system reduced the maximum acceleration of the earthquake by more than seventy percent. The results of the FFT analysis showed that by using a suitable damper with a damping coefficient of more than ten percent, no resonance would occur in the system. Two different heights of the multi-layer isolators were compared. It was shown that for the isolator with a height of eighty centimeters, about twice as much material was used as for the isolator with a height of forty centimeters, but no significant improvement was observed in the results.

Earthquake Economic Loss Assessment of Reinforced Concrete Structures Using Multiple Response Variables

For buildings that meet the requirements of current seismic design codes, damage to nonstructural components and the internal objects of buildings often become the main source of the seismic economic losses of these buildings. However, the current specifications only consider the safety of ‘no collapse under strong earthquake’ and do not consider ‘functional recoverability’. In this paper, a six-story frame building was taken as an example. Four joint performance limit states were proposed, as per FEMA 273, to establish a two-dimensional probabilistic seismic demand model that considers parameter correlations. The limit state function was established, and the two-dimensional seismic vulnerability curve was calculated. The seismic intensity–economic loss curve and the annual average economic loss established by one-dimensional and two-dimensional seismic vulnerability curves were compared. The results showed that the seismic performance of the structure was lower than expected when using only a one-dimensional seismic vulnerability curve. However, the situation was more serious under high-intensity earthquake and high-performance levels.

Time Domain Damage Identification Approach of the Newly Hollow Floor Structure with TRMD

A tuned rolling mass damper system (TRMD) is newly combined with structural hollow slabs to act as an ensemble passive damping device to mitigate structural responses. The main advantage of this controlled configuration lies in its capacity to maintain architectural integrity. To investigate damage identification of this controlled structure with TRMD, a time domain identification approach with sensitivity-based model updating is studied in this paper. The simplified model and motion equation of a controlled structure with TRMD are derived considering the interaction force between the main structure and the damper. Furthermore, the dynamic response and dynamic response derivatives with respect to elemental variations in the controlled structure are analyzed to identify damage by minimizing the response difference between the intact state and the damaged state in the sensitivity-based updating procedure. A numerical example for a six-story frame structure with a TRMD on the top is employed to verify that not only the structural dynamic responses are controlled effectively by the rolling ball damper subjected to the earthquake excitation, but also damage location and extent can be identified accurately by the proposed method even with measurement noise considered. The shaking table test of a single-story frame equipped with TRMD is additionally carried out to validate the accuracy of the proposed structural damage identification method in the laboratory.

Structural Vibration Control with the Implementation of a Tuned Mass Rocking Wall System

A tuned mass rocking wall (TMRW)-frame structure system is proposed to improve the energy dissipation ability of the traditional rocking wall-frame system. Based on the energy dissipation principle of the traditional tuned mass damper (TMD), a TMRW is designed with proper mass and stiffness according to the dynamic characteristic of the host structure. Firstly, considering the presence of inherent structural damping, the dynamic amplification factor of the main mass was derived from the dynamic equations of the TMRW mechanism. A practical design table was then obtained after parameter study. Secondly, by taking a six-story frame structure as an example, the dynamic time-history analysis was conducted to study TMRW’s seismic performance. The inter-story drift ratios of the TMRW-frame, the traditional rocking wall-frame, and the frame structures were compared, and the seismic responses of the controlled and uncontrolled structures were also compared. The results demonstrate that the TMRW can effectively reduce the inter-story displacement of the host structure, and the lateral deformation mode of the host structure tends to be more uniform. However, compared with the traditional rocking wall-frame system, the proposed TMRW has less ability on coordinating deformation.

Weighted Transmissibility Assurance Criterion for Structural Damage Detection

Transmissibility function (TF) is a useful damage indicator for effective structural damage detection (SDD) under unknown external excitations. However, TF is not sensitive enough to structural damage under measurement noise. To improve the sensitivity of this indicator, a common model reduction technique, that is, the system equivalent reduction expansion process (SEREP) was first adopted to obtain reduced element stiffness matrices in the initial analytical finite-element model of a structure; this was used to weight the TFs in this study. Then, inspired by the cosine similarity measure, a novel damage indicator, called the weighted transmissibility assurance criterion (WTAC), was proposed for evaluating structural states. The effectiveness of the proposed damage indicator, WTAC, was first studied by a six-story frame in numerical simulations. The results showed that the TF weighted by the reduced element stiffness matrices improved the signal-to-noise ratio of the TF, and the proposed WTAC detected changes in structural states under noise. Moreover, further experimental studies on an aluminum alloy frame were conducted in order to assess the proposed WTAC. The results indicated that the proposed WTAC may provide a potential tool for effective SDD with strong robustness and stability for long-term monitoring on site.

Improving the nonlinear seismic performance of steel moment-resisting frames with minimizing the ductility damage index

In this paper, the parameters optimization of a tuned mass damper (TMD) is presented to enhance the seismic performance of a six-story steel structure based on the ductility damage index. Herein, the six-story frame is modeled nonlinearly in the OpenSees software by a concentrated plasticity model. Finally, the most suitable algorithm is selected among several optimization algorithms based on the convergence rate and the objective function's values. In this process, the water cycle algorithm has shown the best results. Therefore, the optimal parameters of the TMD are calculated by this algorithm in such a way that the ductility damage index is minimized in the six-story structure under earthquake loads. For this purpose, the nonlinear dynamic analysis of the structure is performed under earthquakes loads using the OpenSees software. Also, the optimum parameters of the TMD are computed to minimize the ductility damage index under the earthquake loads by linking the OpenSees and Matlab software. The results show that the optimum parameters of the TMD system obtained by the water cycle algorithm could appropriately decrease the ductility damage index. It can simultaneously increase the structure's seismic performance to reduce the displacement, stories damage, and drift ratio.

Progressive collapse of 2D reinforced concrete structures under sudden column removal

Once a column in building is removed due to gas explosion, vehicle impact, terrorist attack, earthquake or any natural disaster, the loading supported by removed column transfers to neighboring structural elements. If these elements are unable to resist the supplementary loading, they continue to fail, which leads to progressive collapse of building. In this paper, an efficient strategy to model and simulate the progressive collapse of multi-story reinforced concrete structure under sudden column removal is presented. The strategy is subdivided into several connected steps including failure mechanism creation, MBS dynamic analysis and dynamic contact simulation, the latter is solved by using conserving/decaying scheme to handle the stiff nonlinear dynamic equations. The effect of gravity loads, structure-ground contact, and structure-structure contact are accounted for as well. The main novelty in this study consists in the introduction of failure function, and the proper manner to control the mechanism creation of a frame until its total failure. Moreover, this contribution pertains to a very thorough investigation of progressive collapse of the structure under sudden column removal. The proposed methodology is applied to a six-story frame, and many different progressive collapse scenarios are investigated. The results illustrate the efficiency of the proposed strategy.

ANN based on forgetting factor for online model updating in substructure pseudo-dynamic hybrid simulation

Substructure pseudo-dynamic hybrid simulation (SPDHS) combining the advantages of physical experiments and numerical simulation has become an important testing method for evaluating the dynamic responses of structures. Various parameter identification methods have been proposed for online model updating. However, if there is large model gap between the assumed numerical models and the real models, the parameter identification methods will cause large prediction errors. This study presents an ANN (artificial neural network) method based on forgetting factor. During the SPDHS of model updating, a dynamic sample window is formed in each loading step with forgetting factor to keep balance between the new samples and historical ones. The effectiveness and anti-noise ability of this method are evaluated by numerical analysis of a six-story frame structure with BRBs (Buckling Restrained Brace). One BRB is simulated in OpenFresco as the experimental substructure, while the rest is modeled in MATLAB. The results show that ANN is able to present more hysteresis behaviors that do not exist in the initial assumed numerical models. It is demonstrated that the proposed method has good adaptability and prediction accuracy of restoring force even under different loading histories.

A new form of steel base isolation system for seismic high-rise building

The higher story of a building then it will be more vulnerable to its earthquake or seismic responses. The use of seismic devices will reduce earthquake force. In this study, the steel base isolation material has been proposed. This paper aims to design a new steel base isolation system that have good resistance in both of seismic vibration and axial pull out. The building data are 3D mini three-story, six-story, nine-story steel frame structures. The shaking table is used to test with two types of vibration, medium and maximum. FEM analysis was implemented to find the seismic responses. From the calculation results, a reduced response was obtained in conditions of moderate damage to a three-story frame with an average acceleration of 88% reduction, a maximum acceleration of 22% reduction and a six-story frame in heavy damage with an average acceleration of 73%, the maximum acceleration is reduced into 43%.

Feasibility study on model-based damage detection in shear frames using pseudo modal strain energy

This paper proposes a model-based approach for structural damage identification and quantification. Using pseudo modal strain energy and mode shape vectors, a damage-sensitive objective function is introduced which is suitable for damage estimation and quantification in shear frames. Whale optimization algorithm (WOA) is used to solve the problem and report the optimal solution as damage detection results. To illustrate the capability of the proposed method, a numerical example of a shear frame under different damage patterns is studied in both ideal and noisy cases. Furthermore, the performance of the WOA is compared with particle swarm optimization algorithm, as one the widely-used optimization techniques. The applicability of the method is also experimentally investigated by studying a six-story shear frame tested on a shake table. Based on the obtained results, the proposed method is able to assess the health of the shear building structures with high level of accuracy.

Optimization of shape memory alloy braces for concentrically braced steel braced frames

Abstract Expanding the use of smart braced frames to govern the seismic response of structures by providing ductility and elasticity has been hampered and delayed by cost indexes. The braces in frames comprise two segments of expensive shape memory alloys (SMAs) and high-strength steel with high stiffness. These smart materials can reduce seismic damage by providing stiffness, yielding, and phase shifting. In this study, the length of the SMA segments in three- and six-story frames (applied either at all floors or as part of a dual system) was increased to determine the optimal length at a constant period. Performance levels and fragility curves were obtained to evaluate the seismic behavior of the optimized frame. The response modification factor determined based on the static pushover, incremental nonlinear dynamic analysis, and linear dynamic analysis suggests the ductility and over-strength of the optimized frame. The probability of being in or exceeding each damage state was determined with a Monte Carlo analysis and was acceptable and in accordance with previous deterministic analysis results.

Uniform damping ratio-based design method for seismic retrofitting of elastoplastic RC structures using viscoelastic dampers

A simple design procedure is proposed for seismic retrofitting of existing structures using viscoelastic dampers (VEDs) based on the uniform damping ratio (UDR) concept to make full use of each damper. The UDR concept states that the equivalent damping ratios, which represent the energy dissipation capacities of the dampers, are the same for each installed VED. The stiffness and damping characteristic parameters of the damped structure can be formally decoupled using UDR-based derivations, which simplify the determination of the VEDs’ parameters. The generalized single-degree-of-freedom method and pushover analysis are adopted for a fast estimation of the seismic response of the damped elastoplastic structure. Taking the response reduction ratio as the design target, a seismic retrofit design procedure is proposed based on the UDR concept to meet the performance demand. Finally, a six-story frame is adopted to illustrate the proposed design method. The dynamic analysis results show that the seismic responses of the structure are well-controlled, as expected, and that the installed VEDs are used effectively. The conclusion can be drawn that the UDR-based design method for retrofitting an existing structure using VEDs is rational and effective.

Serviceability assessment of subway induced vibration of a frame structure using FEM

It is necessary to predict subway induced vibration if a new subway is to be built. To obtain the vibration response reliably, a three-dimensional (3D) FEM model, consisting of the tunnel, the soil, the subway load and the building above, is established in MIDAS GTS NX. For this study, it is a six-story frame structure built above line 3 of Guangzhou metro. The entire modeling process is described in detail, including the simplification of the carriage load and the determination of model parameters. Vibration measurements have been performed on the site of the building and the model is verified with the collected data. The predicted and measured vibration response are used together to assess vibration level due to the subway traffic in the building. The No.1 building can meet work and residence comfort requirement. This study demonstrates the applicability of the numerical train-tunnel-soil-structure model for the serviceability assessment of subway induced vibration and aims to provide practical references for engineering applications.

On the Nonlinear Transient Analysis of Planar Steel Frames with Semi-Rigid Connections: From Fundamentals to Algorithms and Numerical Studies

Abstract This paper presents the fundamentals for prediction of a more realistic behavior of planar steel frames with semi-rigid connections under dynamic loading. The majority of the research in this area concentrates on the nonlinear static analysis of frames with semi-rigid connections. Indeed, few studies have contributed to the nonlinear dynamic and vibration analyses of frames. Therefore, this article first describes the frames’ semi-rigid connection behavior under monotonic and cyclic loads, and presents the independent hardening technique adopted to simulate the joint behavior under cyclic excitation. In a finite element context, this paper presents an efficient numerical methodology that is proposed in algorithmic form to obtain the nonlinear transient response of the structural system. The paper also presents, in algorithmic form, a complete description of the adopted connection hysteretic model. Satisfying the equilibrium and compatibility conditions, and assuming only the connection’s rotational deformation due to bending as variable, this work obtains the tangent stiffness and mass matrices of the beam-column element with semi-rigid connections at the ends. The study concludes by verifying and validating the proposed numerical approach using four structural steel systems: a L-frame, a two-story frame, a six-story frame, and a four-bay five-story frame. The analyses show that the hysteresis of the semi-rigid connection has a strong effect on the frames’ responses and is an important source of damping during the structural vibration.

Spectrum-to-spectrum methods for the generation of elastic floor acceleration spectra

In seismic codes, the acceleration demand of nonstructural components is commonly expressed in terms of floor response spectra and estimated by means of simple predictive equations. By using the latter, response-history analysis of the structure is not required, being floor spectra calculated directly from the peak ground acceleration expected at the site. The price for this simplicity in the method used for the estimation of floor spectra is the generally poor approximation of the obtained predictions. Codes’ equations, in fact, do not explicitly account for important factors influencing floor spectra, such as the contribution of the higher modes of vibration of the structure and the actual value of the nonstructural components’ damping ratio. Alternative spectrum-to-spectrum methods for direct generation of floor spectra have been proposed, which include these factors and improve the accuracy of the predictions. Different approaches have been used and several methods developed. Despite large research effort, however, a comparative evaluation of the currently available proposals is still lacking. The objective of this paper is to fill this gap, by reviewing selected proposals representative of practice-oriented spectrum-to-spectrum methods. A case study consisting in a six-story frame is analyzed and predictions obtained with the investigated methods are compared with exact floor spectra derived from time-history analyses of the structure, as well as spectra calculated using the Eurocode 8 equation.

Damage identification using structural modes based on substructure virtual distortion method

A damage identification approach is presented using substructure virtual distortion method which takes the advantage of the fast structural reanalysis technique of virtual distortion method. The formulas of substructure virtual distortion method are deduced in frequency domain, and then the frequency response function of the damaged structure is constructed quickly via the superposition of the frequency response function of the intact structure and the frequency responses caused by the damage-coupling virtual distortions of the substructures. The structural damage extents are identified using the measured modal parameters. Two steps are adopted to increase the efficiency of optimization: the modals of finite element model are estimated quickly from the fast constructed frequency response function during the optimization and the primary distortions of the substructures are extracted by contribution analysis to further reduce the computational work. A six-story frame numerical model and an experiment of a cantilever beam are carried out, respectively, to verify the efficiency and accuracy of the proposed method.

Nonlinear dynamic collapse analysis of semi-rigid steel frames based on the finite particle method

This paper presents a numerical procedure based on the finite particle method (FPM) for the nonlinear dynamic collapse analysis of plane steel frames with semi-rigid connections. The FPM can be used to model the plane frame with finite separated particles; in particular, geometric nonlinearity and dynamic fracture. Fictitious motion was used to consider the geometrical nonlinearity, and the explicit time integration method was used for solving the dynamic equilibrium equations. In the FPM, particles are free to separate from each other, which is advantageous in the simulation of member fracture. To simulate member fracture, the fracture criterion and fracture model of the FPM were developed. Furthermore, to simulate the rigidity of a steel beam–column connection, an independent zero-length element was adopted, which can consider the influence of nonlinear and hysteretic connection stiffness. The nonlinear response results were compared with those of existing studies to verify the accuracy of the proposed numerical procedure. Additionally, the collapse analysis of a Vogel six-story frame showed that frames with semi-rigid connections have greater anti-collapse capacity than those with rigid connections do.

Analysis on Dynamic Response of Reinforced Concrete Frame for Resisting Progressive Collapse

In order to investigate the dynamic response of reinforced concrete spatial frames caused by initial damages, a six-story frame model is analyzed by employing the nonlinear dynamic methodology in accordance with the alternate path method issued by General Services Administration. In this paper, the fiber model and force-based beam-column element are utilized in OpenSees. Four various scenarios are separately analyzed with incremental dynamic analysis. It is shown that the model does not collapse and the internal force redistribution mainly appears in the components adjacent to the failure column. The model has the worst capacity to resist progressive collapse in the inner column demolition scenario. It is observed that the plastic hinges mainly concentrate on the beam ends of the failure bay at the beginning of the demolition of columns. Several plastic hinges emerge at the top-floor beam ends of some other bays in latter period. The number of plastic hinges in columns is much less than that in beams, which corresponds to the design principle ‘strong column and weak beam’.