Direct Displacement-based Seismic Design Research Articles

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.

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.

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

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.

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.

Efficient direct displacement-based seismic design approach for structures with viscoelastic dampers

Viscoelastic damper (VED) is one of most effective structural control techniques, because it provides both additional stiffness and damping to the structures. Current seismic standards implement force-based methods for the design of VEDs, which generally require extensive iterative calculations. It also causes inconsistent risk degree and economic efficiency because it is displacements, rather than forces, that are directly related to structural damage. In the past decades, researchers have developed a direct displacement-based design (DDBD) methodology. The DDBD approach begins with selecting a target displacement and estimating of the equivalent damping ratio, and then calculate the seismic demand of the structure using a substitutive equivalent elastic system. However, because of the strong nonlinearity of the VED devices, it is difficult to appropriately proportion the key parameters (i.e., damping, period) of the VED controlled structure system, which makes the DDBD method ineffective. To solve this problem, this paper proposed an efficient DDBD approach that is in accordance with the Chinese seismic design principles. The relationship between the equivalent damping and structure period of the VED-structure system is established, so the proposed approach requires minimum iterative calculations and the efficiency improves significantly. A step-by-step description of the approach is presented, in which the two key VED parameters, namely the strain amplitude and its additional damping ratio contribution to the structure, are determined by the target displacements. The approach is further examined and verified by a 24 story building. Nonlinear history analysis results confirm that, by using the proposed DDBD procedure, the designed target story drift is achieved with no iterative calculations and the structural responses of the VED-structure system satisfy the code requirements.

An improved displacement based seismic design method of prestressed fabricated concrete frame

Due to the randomness of ground motion and the variation of the material itself, it is unreasonable to regard the inter-layer target displacement angle of the structure as a certain amount in the direct displacement-based seismic design. In this paper, an improved displacement seismic design method is proposed, which is characterized by: (1)Considering the reliability when determining the target displacement angle between layers, and combining the probability characteristics of the target displacement angle between layers, the seismic design of the structure has a certain probability meaning.(2)According to the quantitative relationship between damage index and displacement ductility, combining structural damage performance target, the displacement ductility of the structure is determined by the damage index in the displacement-based design method, and the determination of displacement ductility is directly related to the damage performance target. Finally, it is applied to the design of prestressed precast concrete frame structure, then OpenSees modeling is used to verify the improved displacement design method, and at the same time compared with the original design method. The results show that the improved displacement seismic design method proposed in this paper can well control the elastoplastic response of the structure and meet the performance of the structure. The original displacement design method is more conservative than the improved displacement seismic design method.

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.

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.

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.

Performance-Based Seismic Design of Nonstructural Building Elements

ABSTRACT Performance-based earthquake engineering requires the harmonization of performances between structural and nonstructural elements. This paper discusses the performance-based seismic design of nonstructural elements through a direct displacement-based methodology applicable to nonstructural elements attached to a single location in the supporting structure and for which damage is the result of excessive displacements. The fundamentals of direct displacement-based seismic design are presented along with a description of the modifications required for its application to nonstructural elements. As an example, the direct displacement-based seismic design of a suspended piping restraint installation is presented. The design approach is appraised by nonlinear dynamic time-history analyses.

A novel non-iterative direct displacement-based seismic design procedure for self-centering buckling-restrained braced frame structures

Self-centering buckling-restrained braces (SCBRBs) were proposed recently to minimize residual deformation of the braces induced by yielding or buckling. Although earthquake resilience of structures equipped with the SCBRBs can be well achieved using displacement based designs (DBDs), previously proposed DBD procedures generally involve iterations. In this study, a novel direct displacement-based design method with a non-iterative procedure, named R–CR DDBD, is proposed and applied to design of steel braced frame structures with SCBRBs. Unlike previously adopted DBD, the yield displacement does not need to be assumed initially in the proposed procedure. Instead, the yield strength and yield displacement are determined directly by the predetermined objective drift (ratio), using the relation of the strength reduction factor (R) and constant-strength inelastic displacement ratio spectra (CR spectra), i.e. the R–CR relation. Since the derived R–CR relation is independent with the peak ground acceleration of the earthquake records when stiffness and strength degradation are not considered, the proposed procedure can be accurate for any seismic level. The R–CR DDBD is supposed to begin with the knowledge of the seismic excitation level (according to the structure category, site classification and owner’s requirements) and the corresponding target drift; the end of the design is to obtain the cross sections of main frame members and all the bracing parameters. The result of two 7-story buildings designed according to the R–CR DDBD procedure demonstrates that this procedure can be effective and fairly simple for practical seismic design.

Simplified seismic resistant design of base isolated single pylon cable-stayed bridge

The seismic vulnerability of single pylon cable-stayed bridges under strong ground motions in the transverse direction is of great concern to earthquake engineering researchers and bridge engineers. Introduction of base isolation to cable-stayed bridges has been proved very effective in reducing seismic forces in the bridges in previous studies. This paper proposes a direct displacement based seismic design (DDBD) procedure for base isolated cable-stayed bridge under transverse seismic excitation. One of the key aspects of the DDBD is the realization of a uniform transverse target displacement of the deck under seismic excitation, which is achieved by appropriate design of the isolator stiffness at the bottom of the pylon and the ends of the deck. The proposed DDBD procedure is applied in this paper to the seismic design of a single pylon cable-stayed bridge isolated by friction pendulum bearings. The effectiveness and the accuracy of the resulting design are checked by nonlinear time history analyses. The numerical results indicate that the proposed DDBD procedure can predict the deck displacement profile and amplitudes, as well as the base shear within a reasonable degree of accuracy. The case study demonstrates that the proposed DDBD procedure is sufficiently accurate and practical for the seismic design of base isolated single pylon cable-stayed bridges.

Direct displacement-based seismic design of flexible-base structures subjected to pulse-like ground motions

In this paper, a practical displacement-based framework is presented for seismic design of flexible-base structures in near-fault regions. Particular attention is given to pulse-like motions that may cause significant damage to building structures. The proposed design methodology utilises displacement response spectra constructed using a new procedure, which takes into account the effect of pulse period. An equivalent fixed-base single-degree-of-freedom oscillator is adopted to capture the salient features of an actual soil-structure interaction (SSI) system in order to facilitate the design process. Two step-by-step direct-displacement based design (DDBD) procedures based on compatible inelastic spectra and equivalent linearisation are introduced. The effectiveness of the stated design procedures is examined using results of nonlinear response history analysis of two example SSI systems subjected to a set of sixteen spectrum-compatible near-fault pulse-like ground motions. The results of this study suggest that the procedure based on inelastic design spectra, in general, provides a better design solution than using an elastic linearisation method, especially when structures are designed with a higher ductility demand.

Direct displacement-based seismic assessment of concrete frames

Five previously-tested reinforced concrete frames were modelled using a nonlinear finite element analysis procedure to demonstrate the accurate response simulations for seismically-deficient frames through pushover analyses. The load capacities, story drifts, and failure modes were simulated. This procedure accounts for the effects of shear failures and the shearaxial force interaction, and thus is suitable for modeling seismically-deficient frames. It is demonstrated that a comprehensive analysis method with a capability of simulating material constitutive response and significant second-order mechanisms is essential in achieving a satisfactory response simulation. It is further shown that such analysis methods are invaluable in determining the expected seismic response, safety, and failure mode of the frame structures for a performance-based seismic evaluation. In addition, a new computer program was developed to aid researchers and engineers in the direct displacementbased seismic design process by assessing whether a frame structure meets the code-based performance requirements by analyzing the analysis results. As such, the proposed procedure facilitates the performance-based design of new buildings as well as the numerical assessment and retrofit design of existing buildings. A sample frame analysis was presented to demonstrate the application and verification of the approach.