Displacement-based Seismic Design Research Articles

Displacement-based seismic design of SMA cable-restrained sliding lead rubber bearing for isolated continuous girder bridges

The sliding of isolation bearings in a bridge structure can reduce bridge pier damage, but bearing sliding under the strong earthquake may cause excessive displacement of the girders or even falling girders. This study proposes an innovative shape memory alloy (SMA) cable-restrained sliding lead rubber bearing (SMA-SLRB), which can maximise the sliding advantages of the bearing whilst combining the displacement-limiting capacity and self-centering capacity of the SMA cable. The working mechanism of the SMA-SLRB is firstly revealed, and the mechanical model of the SMA-SLRB is verified by tests. Then, the multilevel fortification performance target of isolated continuous girder bridges with SMA-SLRB is proposed. A displacement-based seismic design (DBSD) method for the SMA-SLRB isolated continuous girder bridge is established. Next, with the single pier model of a five-span isolated continuous girder bridge taken as an example, the displacement-based design is implemented, and the seismic performance of the bridge is evaluated. Finally, the seismic responses of bridges with SMA-SLRB and SLRB under extremely rare earthquakes are compared. Results show that the energy dissipation capacity and stiffness of SMA-SLRB are improved to varying degrees compared with SLRB. The bridge basically achieves the design target displacement and meets the requirements of multilevel fortification performance, which confirms the effectiveness of the DBSD method. Under extremely rare earthquakes, the SMA-SLRB can effectively reduce the maximum displacement and residual displacement of the girder compared with the SLRB.

Seismic performance of self-centering braced rocking frame with novel self-centering friction dampers characterized by low-secondary stiffness

Research has demonstrated that self-centering energy dissipation dampers (SCEDs) are effective devices for reducing the residual deformation of structures after a strong earthquake. However, the equivalent damping ratio of SCEDs is relatively lower than that of conventional dampers such as viscous dampers, BRBs, or friction dampers. According to displacement spectrums, the lower damping ratio could result in a lower natural period and higher equivalent stiffness of structures for a given displacement target, and thus the structures could attract more earthquake action to the structures. To alleviate the problem, a novel self-centering damper composed of elastic post-buckling plates and adjustable friction devices (PBSCFD) was proposed and used as the self-centering braces for a self-centering braced rocking frame (SBRF) structure for example. First, the theoretical force-displacement relationship of the PBSCFD was derived based on its configuration and work principle, and then a scaled PBSCFD was manufactured and tested to investigate its mechanical properties and verify the theoretical constitutive model. Subsequently, the SBRF structure with PBSCFDs was designed by the direct displacement-based seismic design method (DDBD), and its seismic performance was examined by elastic–plastic time-history analysis. Finally, the effects of the secondary stiffness ratio of the self-centering braces on seismic mitigation of the SBRF structure were investigated. The results show that PBSCFDs is characterized by classic self-centering behavior with low secondary stiffness, which can be designed to obtain significant control effects on the base/interstorey shear and interstorey drift ratio of the SBRF structure under rare and extremely rare earthquake compared to the conventional SCEDs with significant secondary stiffness.

A novel self-centering friction damper with elastic post-buckling plates to retrofit bridge bents

The self-centering energy dissipation dampers (SCEDs) have been demonstrated in mitigating the residual deformation of structures under strong ground motions. However, existing researches show that the damping force demand of SCEDs is higher than conventional dampers such as viscous dampers, BRBs or friction dampers for same design displacement of self-centering retrofitted structures, which could lead to higher base shear and acceleration responses of structures. In order to alleviate the problem, a novel self-centering damper composed of elastic post-buckling plates and adjustable friction devices (PBSCFD) was proposed. Compared with conventional SCEDs, the proposed PBSCFD has low secondary stiffness and adjustable energy dissipation capacity, which is beneficial to control the additional internal force of members adjacent to the damper in self-centering retrofitted structures. Based on the configuration and working principle of the PBSCFD, the theoretical force-displacement relationship of the damper was derived. Subsequently, a scaled PBSCFD was manufactured and tested under quasi-static loading to investigate its mechanical properties and to verify the theoretical constitutive model. In order to demonstrate the seismic performance of PBSCFDs, the double-column bridge bent retrofitted with PBSCFDs was designed by direct displacement-based seismic design method (DDBD), and its seismic performance was examined by elastic-plastic time-history analysis. Finally, effects of secondary stiffness ratio of self-centering dampers on seismic mitigation of self-centering retrofitted bridge bent were investigated. The results show that PBSCFDs have certain advantages in controlling the base shear and acceleration of the retrofitted bridge bent compared to conventional SCEDs with significant secondary stiffness.

Probabilistic seismic performance assessment of low-damage self-recovering prefabricated concrete frame subjected to near-field pulse-like earthquakes

The low-damage self-recovering prefabricated concrete (SRPC) frame using modular mild steel dampers is illustrated. Six low-cyclic repeated loading tests adopted 5 types of modular mild steel dampers were performed on the same fabricate joint specimen in turn. Based on the field test results and the displacement-based seismic design (DBSD) approach, a new SRPC deficient frame with four sizes of mild steel dampers are established, and elastoplastic time history analysis are conducted on four scenarios under near-field earthquakes respectively. To evaluate the collapse resistance of the new structure moduli designed in accordance with current design codes without considering the near-field earthquakes in the earthquake-prone regions, the probabilistic seismic performance assessments (i.e., hazard, fragility, risk) are conducted at the DBE and MCE earthquake levels under near-field ground motions. Annual and 50-year probability of exceedance (POE) results reflect that the new framework relieves the failed progression with a lower POE and meets the performance safety criteria under the near-field earthquakes. Furthermore, setting appropriate dimensions of mild steel dampers at the beam-column joints can effectively enhance the collapse resistance and whole safety of the new SRPC frame. This research will further promote the establishment of a reliable earthquake design method for new low-damage SRPC structures under near-field earthquakes.

Seismic design and performance evaluation of steel braced frames with assembled self-centering buckling-restrained braces

In this study, an assembled self-centering buckling-restrained brace (ASC-BRB) is developed for seismic resilience of structures. The self-centering system of the brace mainly consists of a group of disc springs and two sets of steel strands in series to enhance the deformability and achieve the post-hardening behavior for limiting the rapid displacement development of structures under extreme earthquakes. The theoretical restoring force model is first derived according to the working principle of ASC-BRB and successfully validated by experiments. An empirical ductility demand spectral model of ASC-BRB frames is developed according to the parametric analysis on the seismic responses of the corresponding nonlinear single-degree-of-freedom (SDOF) system. The spectral model considers the influences of all independent hysteretic parameters of ASC-BRB, and the physical parameters of the brace can be determined directly from the complete hysteretic parameters. Then a displacement-based seismic design procedure for designing ASC-BRB frames is proposed. The design results indicate that the designed frames generally need at most one iterative design to meet the target performance. Although the ASC-BRBs are designed with partial self-centering behavior, the frames can still exhibit approving post-earthquake recoverability with negligible residual displacements under strong earthquakes when the values of brace hysteretic parameters are chosen reasonably. When designing ASC-BRB frames, a strength ratio β of 0.25 and a strength ratio of steel strands η2 of 0.2 is recommended for improving the seismic performance and post-earthquake resilience of structures. Compared with the existing SC-BRBs with much higher initial stiffness, the proposed ASC-BRB can control the structural peak floor acceleration more effectively, which is beneficial for non-structural components.

Seismic design and shaking table test of continuous girder bridges with winding rope fluid viscous dampers

In order to decrease the seismic response of continuous girder bridges, a winding rope fluid viscous damper (WRFVD) was proposed, which is installed on sliding piers, and connected to the deck by winding ropes. In this paper, the mechanical properties of WRFVD were derived and verified by the dynamic performance test. The direct displacement-based seismic design (DDBD) method of WRFVD was developed. Then, a scaled three-span continuous girder bridge was designed for the shaking table test to investigate the seismic performance of WRFVD and validate the seismic design method. The test results showed that WRFVD can effectively reduce the internal force of the fixed pier and the deck displacement. Additionally, the corresponding numerical simulations were carried out to compare with the test results, which are in good agreement with experimental data with acceptable difference. Then a series of nonlinear time history analyses based on the test model was conducted to evaluate the effectiveness of the DDBD method of WRFVD. The test and numerical results reveal that the DDBD method of WRFVD can effectively calculate the seismic response of continuous girder bridges with WRFVD.

Lateral displacement mode of column-supported modular steel structures with semi-rigid connections

The lateral displacement of a column-supported modular steel structure with semi-rigid connections (CSMSS-SRC) owing to lateral loading was investigated to determine the corresponding lateral displacement mode and establish a foundation for a direct displacement-based seismic design method. Theoretical equations for the lateral displacement caused by the bending deformation of beams and columns, axial deformation of columns, and shear deformation of the vertical inter-module connections were theoretically derived using slope–deflection equations, unit-load method, and shear deformation definition, respectively. Two simplified single frame finite element models were then established to verify the theoretical equations and study the effects of the rotational and horizontal shear stiffnesses of the vertical inter-module connections on the lateral displacement of the CSMSS-SRC. The results showed that the proposed lateral displacement equations are highly accurate. Furthermore, although the rotational stiffness of the vertical inter-module connection did not exert an appreciable effect on the lateral displacement of the CSMSS-SRC, its horizontal shear stiffness did. These results are expected to provide a reference for the engineering design of CSMSS-SRC.

Optimization Analysis of Hysteretic Dampers Design Parameters on Seismic Performance of a Novel Self-Centering Prefabricated Concrete Frame

ABSTRACT To study the effect of the design parameters of dampers on seismic behaviors of the novel self-centering prefabricated concrete (SCPC) frame joint, eight pseudo-static loading tests with five sizes of dampers were conducted. Furthermore, three sizes parameters of dampers are applied on the seven-story prefabricated frames which are designed by the displacement-based method. Elastoplastic time-history analyses of three buildings are conducted at the DBE and MCE levels, respectively. Finally, the displacement-based seismic design method of the novel frame is implied to be effective, and the optimal design parameters of the proposed hysteretic damper for the novel SCPC frame are obtained.

Direct Displacement-based Seismic Design of Glulam Frames with Buckling Restrained Braces

ABSTRACT This paper presents a direct displacement-based design (DDBD) approach for the buckling restrained braces (BRBs) braced glue-laminated timber (glulam) frame (BRBGF) structures. First, the critical design parameters of the DDBD approach were derived for BRBGFs. Then, using experimentally verified numerical models, pushover analyses and nonlinear time-history analyses (NLTHAs) were conducted on a series of one-storey BRBGFs to calibrate the stiffness adjustment factor λ for BRB-timber connections and the spectral displacement reduction factor η. Finally, the DDBD approach was verified as a prospective approach for the seismic design of multi-storey BRBGF buildings by NLTHAs of the case study buildings.

A Simplified Displacement Spectrum Model Based on Recent Digital Strong-Motion Data

ABSTRACT Displacement spectrum is an essential aspect in displacement-based seismic design (DBSD) philosophy that, comparing to force-based, describes in a more explicit way the structural response and the damage. To better apply DBSD, the displacement spectrum model in period ranging up to 15 s is rephrased using recent high-quality digital strong motion data worldwide, particularly from China territory. After systematical analysis conducted of the influence factors as magnitude, distance, and site conditions on displacement spectrum, it is found that magnitude played a more predominant role in characterizing displacement spectrum that is normalized by peak ground-motion displacement than site conditions and distance. A simplified magnitude-scaled model consisting of four straight line segments constrained by three corner periods and their corresponding amplitudes is proposed to model the normalized displacement spectrum. Comparison with seismic data and the published models verifies the applicability of the proposed model especially for strong earthquakes. Residual analysis indicates the simplified model satisfactorily matches the records with respect to magnitude and distance but the variability of model prediction slightly tends to grow as magnitude and distance increase.

Study of bilinear elastic horizontal displacement spectrum models

To obtain elastic horizontal displacement spectra for different damping ratios for use in displacement-based seismic design, the influences of the moment magnitude, fault distance, and site class on the 5%-damped elastic horizontal displacement spectrum are first investigated using the ASK14 ground motion prediction equation (GMPE). Then, bilinear displacement spectrum models for different damping ratios are proposed based on the statistical characteristics of the displacement spectra of strong motion records with the principle of retaining the major influencing factors and neglecting the minor ones, and the models are used to describe uniform hazard displacement spectra for a point source site with a return period of 475 years. Finally, the method for implementing the proposed models in practical applications is discussed. The results of the study show the following. The moment magnitude is the main factor affecting the shape of the displacement spectrum. The proposed bilinear displacement spectrum models can reflect the influence of the moment magnitude, reflect the statistical characteristics of the displacement spectra of the actual strong motion records, and well describe the uniform hazard displacement spectra of the point source site with a return period of 475 years. The zoning map of the two spectral displacements and the corresponding site amplification factors and damping scaling factors of the bedrock site at each seismic hazard level are provided to enable the implementation of the proposed bilinear displacement spectrum models in practical applications.

Seismic design and performance of a steel frame-shear plate shear wall with self-centering energy dissipation braces structure

The steel plate shear wall with self-centering energy dissipation braces (SPSW-SCEDB) is a new seismic lateral resistant component. This paper outlines the performance requirements of the steel frame-shear plate shear wall with self-centering energy dissipation braces (SF-SCSPSW) structure and presents a direct displacement-based seismic design method for the structure. A combined strip model of the SPSW-SCEDB that considers the effect of the bolted connection on the wall plate is established. The comparison of the simulated and experimental results shows that the model can accurately predict the strength and hysteretic behavior under cyclic loading. The 8- and 15-story prototype buildings were designed using the presented method. The results of nonlinear dynamic analysis showed that larger inter-story deformations occurred on the lower floors, and the inter-story ratios gradually decreased with an increase in the number of floors. The maximum inter-story drift ratio (1.73%) of the 8-story structure under mega earthquakes and the maximum residual drift ratio (0.018%) of the 15-story structure under large earthquakes were less than the limit values (2% and 0.5%). Local yielding occurred between the brace connection and the column under mega earthquakes, but the columns remained in an elastic state. The seismic responses of the SPSW-SCEDBs in the two structures met the performance requirements of being elastic and suffering light and moderate and serious damage under frequent, medium, large, and mega earthquakes, respectively. The effectiveness of the proposed design method was verified.

Calibrated Equivalent Viscous Damping for Direct Displacement Based Seismic Design of Pallet-Type Steel Storage Racks

ABSTRACT Direct displacement-based seismic design has been proposed for pallet-type steel storage racks. Damping models are developed in this study for pallet-type steel storage racks in the down-aisle and cross-aisle directions for use in direct displacement-based seismic design. The damping models are developed using results from reversed cyclic tests at a component level or at a system level. Jacobsen’s approach is used to develop a first set of damping models. The damping models are then assessed using results from nonlinear time-history analyses. Finally, the damping models are calibrated using an iterative procedure based on results from nonlinear time-history analyses.

Direct displacement-based seismic design of buckling-restrained braced RC frames

Direct displacement-based seismic design of buckling-restrained braced RC frames

Displacement-based seismic design of buildings with thin reinforced concrete structural walls with a single curtain of welded wire mesh

Displacement-based seismic design of buildings with thin reinforced concrete structural walls with a single curtain of welded wire mesh

Calibrated Equivalent Viscous Damping for Direct Displacement-Based Seismic Design of Suspended Piping Trapeze Restraint Installations

ABSTRACT Direct displacement-based seismic design has been recently proposed for the seismic design of non-structural building elements. This paper deals with the development of damping models, relating equivalent viscous damping ratio to drift amplitude, for suspended piping trapeze restraint installations for direct displacement-based seismic design. The damping models are developed using reversed cyclic test data available in the literature. First, damping models are proposed using Jacobsen’s equal area approach. The damping models developed using Jacobsen’s approach are then assessed and calibrated using nonlinear time history analyses of single degree-of-freedom archetypes representing suspended piping trapeze restraint installations in buildings.

A Generalized Artificial Neural Network for Displacement-Based Seismic Design of Mass Timber Rocking Walls

ABSTRACT Displacement-based seismic design often requires nonlinear time history simulation of building responses which is computationally intensive. This technical note presents an artificial neural network (ANN) designed to generate max inter-story drift for buildings with post-tensioned mass timber (MT) rocking walls systems. This particular lateral system was selected because it is an innovative system with limited physical design parameters, making it an ideal candidate for ANN. The proposed model achieved significantly higher computational efficiency than time history simulation, while maintaining similar level of accuracy. The proposed method could potentially be used for automated design of MT rocking wall lateral systems.

Evaluation of nonlinear static and dynamic analysis of steel braced frame buildings subjected to near-field earthquakes using FBD and DBD

Near-field earthquake is one of the primary sources of ground motions that significantly affecting the structure's seismic response in its surrounding area containing pulse-long periods. The two popular and reliable approaches for the seismic investigation of structures are known as the force and displacement-based seismic design (FBD and DBD), extensively developed in the literature. In the present study, three types of steel buildings were defined for the seismic analysis, including five, eight, and fifteen-story steel buildings as the representatives of the multi-story, middle-rise, and small high-rise buildings, respectively. Steel structure designs and nonlinear analysis were done by implementing SAP2000 and Opensees software, respectively. The designed buildings were analyzed statistically and dynamically by performing the criteria determined in the FEMA-P750, Standard Code 2800, FEMA 356, and FEMA-P695, and then, FBD and DBD results were compared. The nonlinear static analysis results showed the acceptable displacements corresponding to the displacement criteria suggested by FEMA 356, showing the desirable performance of the designed structures. Also, the dynamic analysis results confirmed the reliability of the FEMA 356′s design criteria for the five and 8-story steel structures. However, the small high-rise building design has not met the regulations suggested by FEMA 356.

Seismic Design Method of Self-Centring-Segment Bridge Piers with Tensile-Type Viscoelastic Dampers

This paper aims to study the deformational behaviour of tensile-type viscoelastic dampers under different earthquake excitation directions. A method for calculating the corresponding equivalent additional stiffness and damping of a self-centring-segment bridge pier is derived. Using the displacement-based seismic design method, a design method for self-centring-segment bridge piers with tensile-type viscoelastic dampers is proposed. Using the proposed method, a self-centring-segment bridge pier is designed. Based on dynamic analysis of the finite element model by OpenSees, the effectiveness of the proposed seismic design method is validated.

RC walls in Australia: displacement-based seismic design in accordance with AS 1170.4 and AS 3600

ABSTRACT Displacement-based methods, such as a non-linear static pushover analysis (e.g. the capacity spectrum method), have many advantages compared to traditional force-based design methods. However, implementing a non-linear analysis and design method in accordance with the Australian Standard for concrete structures (AS 3600) introduces many difficult technical issues into the design, of which the standard provides little guidance. The aim of this study is to provide a framework and general guidance for designers who wish to perform non-linear displacement-based analysis methods for RC wall buildings. The paper will present how these methods can be used in accordance with the Australian Standard for earthquake actions (AS 1170.4) to assess seismic compliance and then provide recommendations for the requirements stipulated by AS 3600, which includes an experimentally validated tension stiffening model, nonlinear stress-strain material curves, mean material properties and material strain limits. The paper is concluded with a case study example of how a displacement-based seismic assessment can be performed using a typical case study building.