Displacement-based Seismic Design Method 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.

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.

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.

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.

A displacement-based seismic design method for building structures with nonlinear viscoelastic dampers

A displacement-based seismic design method for building structures with nonlinear viscoelastic dampers

Seismic response of multi-span continuous irregular bridges using displacement-based and conventional force-based methods

In the recent years, the displacement-based seismic design (DBD) method of structures has been recognized as the alternative design method to the conventional force-based seismic design (FBD) method. The problems inherited in the FBD method are mostly overcome by the DBD method as it better correlates the structural damage with displacement-based quantities. In this study, the seismic response of multi-span bridges with varying number of spans and unequal pier heights was evaluated using the DBD method and compared with the conventional FBD method. Two approaches were employed in the DBD method, such as the traditional direct displacement-based seismic design (DDBD) approach and the proposed approach in this study entitled as alternative-to-direct displacement-based seismic design (ADBD). For seismic evaluation of the bridge structures with the FBD method, acceleration response spectra as suggested in the Bangladesh National Building Code were used; while in the DBD method, displacement response spectra for different damping ratios were developed keeping consistency with the above-mentioned design acceleration spectra. Five bridge models were used in the analysis to compare the seismic response in both the longitudinal and transverse directions taking into account the number of spans and height irregularity in the bridge models. Numerical analysis showed very obvious results that the base shear calculated by both approaches of the DBD method is found to be smaller than the FBD method indicating that an economic member section be attained for meeting the same design objective. More specifically, the ADBD approach provides the design professionals a more conservative design approach in compared with the DDBD approach keeping an economic design approach comparing with the FBD method.

Deformation-dependent peak floor acceleration for the performance-based design of nonstructural elements attached to R/C structures

This study introduces a simple and efficient method to determine the peak floor acceleration (PFA) at different performance levels for three types of plane reinforced concrete (RC) structures: moment-resisting frames (MRFs), infilled–moment-resisting frames (I-MRFs), and wall-frame dual systems (WFDSs). By associating the structural maximum PFA response with the deformation response, the acceleration-sensitive nonstructural components, and the building contents, can be designed to adhere to the performance-based seismic design of the supporting structure. Thus, the proposed method can accompany displacement-based seismic design methods to design acceleration-sensitive nonstructural elements to comply with the deformation target of the supporting structure. The PFA response shape is represented by line segments defined by key points corresponding to certain floor levels. These key points are defined by explicit empirical expressions developed herein. The maximum PFA response is correlated with the maximum interstory drift ratio (IDR) and other vital characteristics of the supporting structure such as the fundamental period. The proposed expressions are established based on extensive nonlinear dynamic analyses of 19 MRFs, 19 WFDSs, and 19 I-MRFs under 100 far-fault ground motions scaled to capture different deformation targets. Realistic examples demonstrate the efficiency of the proposed method to assess the PFA response at a given IDR, making the method suitable in the framework of performance-based design.

A Nonlinear Static Procedure for the Seismic Design of Symmetrical Irregular Bridges

Displacement-based seismic design methods support the performance-based seismic design philosophy known to be the most advanced seismic design theory. This paper explores one common type of irregular-continuous bridges and studies the prediction of their elastoplastic displacement demand, based on a new nonlinear static procedure. This benefits to achieve the operation of displacement-based seismic design. Three irregular-continuous bridges are analyzed to advance the equivalent SDOF system, build the capacity spectrum and the inelastic spectrum, and generate the new nonlinear static analysis. The proposed approach is used to simplify the prediction of elastoplastic displacement demand and is validated by parametric analysis. The new nonlinear static procedure is also used to achieve the displacement-based seismic design procedure. It is tested by an example to obtain results which show that after several combinations of the capacity spectrum (obtained by a pushover analysis) and the inelastic demand spectrum, the simplified displacement-based seismic design of the common irregular-continuous bridges can be achieved. By this design, the seismic damage on structures is effectively controlled.

A direct displacement-based seismic design method using a MDOF equivalent system: application to R/C framed structures

An improved version of the direct displacement-based design (DDBD) method for the seismic design of plane moment resisting frames in the framework of performance-based design approach is presented. The method employs a multi-degree-of-freedom equivalent system instead of the single-degree-of-freedom equivalent system used by the conventional DDBD method. Thus, the proposed method can take more rationally and with higher accuracy into account the higher mode and P-Δ effects than the conventional one. This is accomplished with the aid of the concept of deformation dependent equivalent modal damping ratios previously developed by the present authors for other purposes and the concept of the design modal displacements developed herein. These design modal displacements are determined on the basis of target inter-storey drift ratios for every performance level and the first few modes significantly contributing to the structural response. Thus, one can determine from the displacement spectrum with high amounts of viscous damping the required modal periods for known values of the design modal displacements. From those modal periods, the corresponding required modal stiffness and hence the modal base shear forces can be obtained. The final required design base shear can be obtained by a combination rule, like the SRSS rule. Numerical examples involving the seismic design of two moment resisting reinforced concrete plane frames are presented in detail for illustrating the proposed approach and demonstrating its merits over the conventional DDBD method and the force-based design method of Eurocode 8.

PERFORMANCE BASED SEISMIC DESIGN OF STRUCTURES – A REVIEW.

This paper presents an overview of the current state of knowledge with regard to literature on Performance based seismic design method. Performance-based earthquake engineering (PBEE) comprises the design, evaluation, and construction of structures performing during design earthquakes and extreme earthquakes to the desires / needs of owners, user, society and environment. The general promise of performance based design is to produce engineered structures with predictable performance during future earthquakes. Presented in this paper is an updated literature review of the Performance -based Seismic design (PBSD) method. Performance based Seismic design is an elastic design methodology done on the probable performance of the building under different ground motions. The derivatives of the PBSD method, known as the Performance ¬based Plastic design (PBPD) and Displacement-based seismic design (DBSD) method that has been widely recognized as an ideal method for use in the future practice of seismic design has also been reviewed.

Rapid assessment of peak storey drift demands on reinforced concrete frame buildings

The peak storey drift demands that an earthquake imposes on a building can be assessed through a detailed engineering seismic assessment or recorded if a building is instrumented. However, for the rapid seismic assessment of a large number of buildings, it is desirable to have a simplified means of estimating storey drift demands. Consequently, this paper proposes a simplified means of quickly estimating storey drift demands on reinforced concrete (RC) frame buildings. Expressions for peak storey drift demand as a function of ground motion intensity are developed by utilising concepts and simplifications available from displacement-based seismic design and assessment methods. The performance of the approach is gauged by comparing predicted storey drift demands with those obtained from rigorous non-linear time-history analyses for a number of case study buildings. The promising results suggest that the approach proposed will be useful for rapidly assessing the likelihood of damage to a range of drift-sensitive elements in modern RC frame buildings.

Seismic Yield Displacement Profile in Steel Eccentrically Braced Frames

Displacement-based methods are recognized as appropriate approaches to reach the goals of performance-based seismic design method. In the direct displacement-based seismic design method, the seismic yield displacement is applied as one of the important design parameters. In this paper, a new relation is suggested to determine the lateral displacement pattern at first yielding of eccentrically braced frame systems subjected to earthquake ground motions. This relation considers the influence of various structural features of frames. It is developed from the results of several nonlinear dynamic analyses containing 30 eccentrically braced frames under 15 far-field and near-field earthquake ground motions. Then, the results of these analyses are processed by nonlinear regression analysis in order to establish the most effective parameters on the yield displacement pattern of the frames. As a result, a comparison between the suggested yield displacement pattern and nonlinear dynamic analyses showed the efficiency and advantages of the suggested approach.

Incorporation of Torsional & Higher-Mode Responses in Displacement-Based Seismic Design of Asymmetric RC Frame Buildings

Direct displacement-based design (DDBD) is currently a widely used displacement-based seismic design method. DDBD accounts for the torsional response of reinforced concrete (RC) frame buildings by using semi-empirical equations formulated for wall-type buildings. Higher-mode responses are incorporated by using equations obtained from only a few parametric studies of regular planar frames. In this paper, there is an attempt to eliminate torsional responses by proportioning frames’ secant stiffnesses so that the centers of rigidity and supported mass (the mass on and above each story) coincide. Once the torsional rotations are significantly reduced and only translational motions are achieved, higher-mode responses are included using a technique developed by the authors in their recent paper. The efficiency of the proposed design procedure in fulfilling the intended performance objective is checked by two plan-asymmetric 20-story RC frame building cases. Case-I has the same-plan configuration while Case-II has a different-plan configuration along the height. Both cases have different bay widths in orthogonal directions. Verification of the case studies by nonlinear time history analysis (NTHA) has shown that the proposed method results in designs that satisfy the performance objective with reasonable accuracy without redesigning members. It is believed that a step forward is undertaken toward rendering design verification by NTHA less necessary, thereby saving computational resources and effort.

Simplified force-based seismic design procedure for linked column frame system

Dual structural systems with structural fuse such as linked column frame system (LCF) have two main performances, including the resistance to lateral seismic loads and the proper function of structural fuse to control deformation of the other members to remain in elastic phase. The achievement of these two functions is necessary for appropriate seismic design of these systems. Undoubtedly, despite the practical complexity, displacement-based seismic design methods are generally the best method for this purpose. In contrast, conventional force-based methods are relatively simple, but it cannot easily guarantee the desired performance. In this paper, a simplified force-based seismic design method is presented for linked column frame system based on parametric studies on different structures, which are designed with displacement-based method. In addition to simplicity, the proposed method has an appropriate accuracy in terms of achieving the performance objectives. For the parametric study, 18 prototype structures with various relative lateral stiffness of moment frame and linked column system are designed with the displacement-based method. Based on the results of the structures designed with desirable performance, the criteria are proposed for the force-based design method. Based on evaluating results, the structures designed by the proposed simplified force-based method properly reached the performance objectives.

Seismic performance of irregular RC frames designed according to the DDBD approach

The Direct Displacement-Based seismic Design (DDBD) method has been a major development in the context of Performance-Based seismic Design of reinforced concrete (RC) frames. The method has been positively received from the engineering community, while, at the same time, significant improvements have been proposed. Even though its field of application is constantly widening, no specific rules are generally provided for specific cases, such as RC frames with setback irregularity, under the claim that, in this case, no modifications in the basic approach are needed. The validity of this assumption is examined by assessing the DDBD provisions through design of such irregular RC structures and assessment of their seismic performance under non-linear static and dynamic analyses. Local ductility associated with global behavior is examined and incompatibilities in demands with the global design displacement are identified, where they occur. Guidelines are provided to ensure that rational performance results are obtained, when the DDBD method is applied.

Displacement-based Mode Pushover Analysis of Self-anchored Cable-stayed Suspension Bridge

As being a typical multi-freedom degree system structure, self-anchored cablestayed suspension bridge is significantly affected by higher modes in the earthquake response. Traditional force-based pushover analysis of reverse triangle or uniform distribution patterns will lead* to a certain error for the results of pushover analysis of self-anchored cable-stayed suspension bridge. An improved method of displacement-based mode pushover analysis is presented in this paper by combining the two stage horizontal displacement pattern with mode pushover. This improved method can take the contributions of higher modes into account. And the applicability of the method can be verified commendably by the selected examples. Traditional force-based pushover analysis considers the seismic load is equivalent to lateral load. And it judges whether the deformation ability of the structure and component can meet the need of design and use function by analysing nonlinear response of structures under the monotonic increasing horizontal lateral load applied to the structure with a certain distribution mode. The selection of the lateral load distribution mode can directly affect the analysis results of the pushover method on the seismic performance of whole structure in traditional force-based pushover analysis. Moreover, the problem of stiffness degradation after failure is not taken into account in this traditional wide application method. Seismic hazard, experiment and theoretical analysis indicate structural collapse is mainly due to the lack of deformation capacity and energy dissipation capacity during severer earthquake. In this case, the deformation capacity and the displacement response of structure will have an certain impact on the damage degree of structural members. Therefore, it is more reasonable to use displacement control on structural seismic response during severer earthquake[4]. Compared with the traditional force-based design, the displacement of structure can reflect the nonlinear reactive state more during severer earthquake, it also can control the behavior of structure better in earthquake. Consequently, the displacement-based seismic design method has been greatly developed[5-10]. There are three commonly used displacement-based seismic design method: ductility factor design, capacity spectrum and direct displacement-based design method. The basic thought of displacement-based mode pushover analysis is as follows: first, put monotonic increasing lateral displacement to bear on structure directly according to a certain horizontal displacement distribution mode, second, the final failure pattern of structure is obtained by pushover the structure to the target displacement, after that, whether the deformation ability of structure and component can meet the need of design and use function can be analyzed.