Seismic Design Method Research Articles

Performance‐Based Seismic Design With Consideration of Safe Storage From Errors in Reinforced Concrete Member Estimated Yield Deformation

ABSTRACTWhile performing the capacity spectrum method in seismic design, it is essential to select a reasonable objective. In practice, the design objective is typically determined by estimated structural response. However, factors like ground‐motion randomness, the deviation between the structural analysis model and the actual behavior, and other factors would introduce errors in estimation. Therefore, a redundancy design with consideration of safe storage from these errors is necessary. This study focused on errors in the structural analysis model specifically, particularly reinforced concrete members’ estimated yield deformation—an essential parameter in estimating structural response. Initially, the influence on yield deformation of the structure due to each member's estimated yield deformation was clarified theoretically in the capacity spectrum method. To supplement theoretical analysis, a pushover analysis was conducted based on an E‐defense shaking table test specimen. Then, the effect of structural yield deformation on estimated response deformation was deduced according to Japanese seismic design guidelines and was verified based on a single‐degree‐of‐freedom (SDOF) numerical analysis. By integrating these discussions, errors in estimated structural response caused by members’ estimated yield deformation can be evaluated. Consequently, a redundancy factor was proposed to include the safe storage from errors in RC member estimated yield deformation.

Effect of soil profile-related parameters on seismic performance of ductile reinforced concrete building frames in California

Strong ground motions with specific site characteristics can lead to structural damage. Comprehending the effects of site characteristics on the dynamic response of structures is crucial for evaluating seismic performance and thereby implementing design that can mitigate potential damage. This study explores how the site characteristics, including the average shear wave velocity, soil depth to rock, and site period, influence the seismic response of reinforced concrete buildings. Soil column models were created using 319 soil profiles located in California and were employed to perform the nonlinear site response analysis of 80 rock motions to generate surface motions. Subsequently, low-to high-rise reinforced concrete moment-resisting frames with four, eight, twelve, and twenty stories that are representative of California were modeled to conduct nonlinear structural analyses. In this process, the influence of the three site characteristics on the response of the surface motions and structures was investigated. This investigation revealed that structural responses tend to increase when the average shear wave velocity ranges from 180 to 360 m/s or when the depth exceeds 135 m. Additionally, structures with a natural period exceeding 1 s were found to be more vulnerable as the number of stories increased. The outcomes will promote the development of seismic design methods based on different site characteristics.

Performance-based seismic design of low-rise steel moment-resisting frames targeting collapse fragility curve

The aim of this study is to develop a performance-based seismic design method targeting a desirable collapse fragility curve. This direct fragility-based design method is developed and validated for low-rise steel moment-resisting frames. To this end, a relationship is first defined between target fragility curve and design displacement. To this end, 4-story buildings are designed with the design drift ratios of 1.5 % to 4 % and the seismic fragility analysis is performed via the Monte Carlo simulation. The mentioned relationship is derived by plotting the median collapse spectral acceleration versus the design drift ratio. With regard to have this relationship, a modified version of performance-based plastic design method is then proposed. The direct fragility-based design method has been proposed for the low-rise buildings located in Log Angeles. However, its efficiency is also validated for two other regions of Vancouver, Canada and San Francisco, U.S. It can be found from the results that the fragility curve of designed buildings is very close to the target fragility curves. Therefore, the direct fragility-based design method is capable of achieving a target fragility curve and can be considered as an effective design method for low-rise steel moment-resisting frames.

A direct energy-based design method for damping control reinforced concrete structure: methodology and application

Energy-based seismic design, which integrates both the accumulated hysteretic energy and plastic deformation of the structure, provides a more comprehensive evaluation of structural seismic performance compared to other performance-based seismic design methods. In damping control structures, the distribution of hysteretic energy is clearly defined, with the expected positions for energy dissipation and damage concentrated in the dampers. This facilitates the application of an energy-based design method in such structures. This research presented a novel direct energy-based design (DEBD) method for damping control reinforced concrete (RC) structures, following the principle that the energy dissipation capacity of the structural members and dampers exceeds the hysteretic energy dissipation demand. With this principle, an energy-based damage index, which is directly correlated with structural damage state, was introduced. Subsequently, a detailed energy-based design process was provided. To achieve the desired seismic performance, the required energy dissipation capacity of dampers was determined using a pre-select damage index, and thereby, identifying the design parameters of the dampers. Finally, to validate the feasibility of the proposed design method, an 8-story RC frame with friction dampers was chosen as an example. The energy dissipation capacity and damage state of the designed structure were evaluated through nonlinear time-history analyses, and the results demonstrate the successfully achievement of the predefined seismic performance.

Experimental and numerical investigation of failure modes in RC frame structures designed using the equivalent linearization method

The codes of many countries currently employ the column-to-beam flexural strength ratio (CBFSR) based on frequent earthquake internal forces to achieve the expected strong-column-weak-beam (SCWB) ductile failure mode. However, real earthquake damage indicates a general failure to achieve SCWB. The design method based on frequent earthquake internal forces struggles to consider factors such as internal force redistribution and variable axial forces under rare earthquakes. Therefore, developing a seismic design method directly based on rare earthquake internal forces is crucial. The equivalent linearization method is a practical approach for obtaining the internal forces of RC frame structures under strong earthquakes without extensive nonlinear computations. In this paper, nonlinear finite element analyses of RC frame structures with expected SCWB failure modes under various structural parameters were conducted to obtain ductility coefficients under rare earthquakes. Using the equivalent linearization method based on secant stiffness, the equivalent stiffness and damping of beams and columns were calculated. Simplified parameters were determined for engineering applications to facilitate seismic design based on rare earthquake internal forces. Two RC frame structures were designed using both the equivalent linearization method and the CBFSR code method, and then subjected to pseudo-static low-cycle reciprocating loading tests. The study investigated failure modes and hysteretic energy dissipation, as well as overall stiffness and bearing capacity under earthquake conditions. Results showed that the equivalent linearization method can effectively direct RC frame structures to achieve the expected strong earthquake failure mode.The dynamic time history analysis was performed on finite element models of different heights, and the results indicated that the equivalent linearization method significantly reduced plastic hinge occurrences and ductility coefficients of column ends, resulting in improved seismic performance compared to the CBFSR code method.

Collapse-based seismic design method

Continuing the structural analysis until the model reaches its ultimate capacity using an incremental nonlinear time history analysis can incorporate all the behavioral complexities of the structure. This approach ensures that all factors influencing the seismic behavior of structures, which can be simulated in numerical modeling, are fully considered in the analysis. This technique addresses many shortcomings in seismic analysis and structural design, using simple criteria for the accurate design of members. With this perspective, this paper explores the collapse-based seismic design method and provides an approach to determine the ultimate tolerable seismic intensity for a structure, or an appropriate collapse seismic intensity. It also establishes design criteria based on the maximum capacity of structural members under maximum loading and utilizes the endurance time method to perform incremental nonlinear time history analysis quickly and easily. Evaluations show that models designed using this method achieve the desired performance level at different seismic hazard levels, provide sufficient seismic capacity, meet all minimum requirements of the seismic code and standards, and are optimized. Therefore, the procedure presented in this paper is introduced for the analysis, design, evaluation, and retrofitting of structures with simple, accurate, and uniform principles.

Theoretical derivation and seismic design method on self-centering piers with ED members validated using numerical simulations and quasi-static tests

Theoretical derivation and seismic design method on self-centering piers with ED members validated using numerical simulations and quasi-static tests

Performance-Based Design Method of Hinged Wall with Buckling-Restrained Braces at Base Using the Elastic Displacement Spectrum

A performance-based seismic design method using the elastic displacement design spectrum based on equal displacement approximation is proposed for the Hinged Wall with BRBs at Base (HWBB) structural system. HWBB is simplified as an Equivalent Single Degree of Freedom (ESDOF) system. Design flowcharts are given. The proposed design approach aims to limit the lateral displacements to an allowable target displacement. Design examples are presented and target displacements are compared with numerical results. The results indicate that the plastic response of the HWBB structural system is accurately predicted by the elastic displacement spectrum, which verified that the performance-based design method of HWBB is accurate.

A Review of Seismic Optimization Design of Building Structures with Uniform Response

Earthquakes threaten human survival with powerful destructive power, and the performance of buildings in earthquakes is crucial. The seismic design of traditional building structures has the limitations of non-uniform response to displacement and acceleration, which can easily lead to partial damage to the building, unreasonable structure and difficulty in post-earthquake repair, which seriously affects the comfort and safety of the building. It is emphasized that improving the seismic safety of buildings is not only an inevitable requirement to ensure the safety of people's lives, but also to meet people's needs for continuous improvement of building comfort. The review shows that it is of great practical significance to study the seismic optimization design method of building structures with uniform response, which provides an important reference direction for the future design of building structures.

Seismic behavior of CFDST frame with metallic dampers: Damage-controlled design and performance assessment

Current investigations on performance-based seismic design of structures generally employed story drift as performance objectives. However, the story drift could only partially reveal the global damage of a structure and not control the damage of important components. In order to control the damage of various components in a structure, this paper proposed a new damage-controlled seismic design method using the Park & Ang indexes of components. Firstly, the Park & Ang damage index was simplified as an equivalent ductility damage index for various components. The energy balance concept was used to observe the hysteretic energy demand which was subsequently distributed to all stories. Thus, the components of each story could be designed based on their damage indexes under design-based and maximum-considered earthquakes. Four concrete filled double skin tubular (CFDST) moment resisting frames equipped with metallic dampers with various layouts were designed based on the proposed design method. Time history analyses on these four structures were performed after validating the accuracy of nonlinear model by Opensees. Analysis results showed that the components in four structures exhibited expected damage states as illustrated by the design method. It also verified that proposed seismic design method was effective to control the damage of various components, which was beneficial for protecting the important components in a structure by setting low damage indexes for them. The seismic design method and analysis results also provided a reference for the design of moment resisting frame with energy devices.

Analytical calculation method of circular-section rocking steel piers under horizontal cyclic load

The research object of this paper is to investigate the mechanical behavior and develop an analytical model of the prestressed circular-section rocking steel piers with external energy-dissipating devices under the horizontal cyclic load. Based on the method of monolithic beam analogy under monotonic loading, the concept of generalized rotation angle and intercept strain in the pre-decompression state was introduced. The geometrical equations for the pre- and post-decompression stages are deduced. The calculation formulas for internal forces of each component and the analytical calculation method for the entire process of the rocking steel pier under horizontal cyclic loading are established in detail. To reproduce the hysteresis curve of the test, some special test conditions, such as the retraction effect of prestressed tendons and increase of the compressed area due to the vertical plates, were considered in the analytical model. The results show that the analytical method based on generalized rotation angle and intercept strain can ensure an ideal transition of the hysteresis curve of the pier in pre- and post-decompression stages. Except for the pier with particularly severe local buckling and ovalization deformation, the calculated results obtained from the proposed analytical model agrees well with the test results for the rocking steel bridge piers. The effect of prestressed tendons and the P–Δ effect on the lateral load–displacement curve of rocking steel bridge biers was further analyzed through parametric study using the proposed model. The analytical calculation method presented in this paper provides a theoretical tool for seismic design of the rocking steel pier in engineering practice. This paper provides important guidance for the establishment of seismic design method of rocking steel piers.

Energy-based seismic design method for seismically isolated structures with friction pendulum systems

Friction pendulum systems (FPSs) serve as effective isolators that can help ensure adequate seismic performance of structures against significant aftershocks. A commonly used method for FPS design is the equivalent static analysis method outlined in ASCE 7-22. However, this method risks underestimating the seismic performance of FPSs due to its inability to account for energy dissipation from multiple hysteresis loops exceeding two cycles. Moreover, it is not well-suited for designing FPSs with conical friction surfaces, which exhibit nonlinear elastic behavior and hysteresis. A straightforward solution to address these issues is to apply an energy-based seismic design method. In this study, we propose and analytically validate one such method tailored for seismically isolated structures employing FPSs. Our analysis considers FPSs with both spherical (ISF) and conical (ICF) friction surfaces. For ISFs, the design follows the energy-based seismic design method proposed by Akiyama, whereas, for ICFs, it is based on the energy input to the device and its geometric approximation to an ISF. The conclusions of this study are summarized as follows: (1) the proposed energy-based design method effectively predicts the maximum FPS deformation, facilitating a rough estimation of FPS size; (2) because the design assumes symmetrical seismic response of the isolation layer in both the positive and negative directions and the friction surfaces of the ISF and ICF are geometrically similar, in the proposed method, the maximum deformation of an isolation layer with a natural period greater than 2 s depends solely on the friction coefficient, regardless of the friction surface type; (3) to satisfy the relevant conditions, the appropriate FPS design range is determined through nonlinear analysis. The results of this study demonstrate that the proposed energy-based seismic design method provides a reliable and effective means of designing FPSs for enhanced seismic performance.

Code Requirements for the Seismic Design of Irregular Elevation RC Structures

The recent seismic activity highlights the crucial need to enhance seismic design and safety assessment methods, particularly for irregular structures, in both new and existing constructions. The present study focuses on structural irregularities in elevation for buildings, as the design of structural systems involves multiple variables that often result in irregularities in many buildings. This work aims to perform a comparative assessment of the criteria adopted for the evaluation of the structural irregularities in elevation present in European and international seismic codes. This paper is structured as follows: Firtsly, it discusses structural irregularities and more specifically the most common types of structural damage due to seismic events. Then, it shows the documented experiences of structural damages in seismic events associated with structural irregularities in China, Italy, Spain, Nepal and Mexico. Additionaly, it discusses the requirements of the standards on irregularities and their limitation in that matter. At the end of this section, the different approaches of each code in irregularities in elevation are compared. All assessed seismic codes addresses the structural irregularity issue, attributing the desired characteristics of a seismic-resistant structure. However, there are considerable development differences between norms, demonstrated on ambiguity of few codes on criteria of vertical irregularies.

Comparison and study of different seismic calculation methods for underground stations in Shanghai

In terms of seismic design methods for subway stations in the Shanghai area, both national and local standards have presented several pseudo-static methods, including response displacement, response acceleration, equivalent earthquake acceleration, and equivalent inertial force methods. However, certain issues are encountered when these methods are applied to the seismic design of real subway projects. The load input and results obtained from different calculation methods differ from each other. To address such discrepancies and compare the diversity of different methods, this study performs a comparative analysis based on the project case of a ground station in Shanghai. The seismic design is conducted using five different calculation methods. By referring to the results of the dynamic time history analysis, the causes of errors in the calculation results of the displacement and internal force are analyzed. The applicability of the methods is comprehensively explored in terms of a calculation model, determination of the equivalent load, error in the results, and project application. The results show that the response acceleration method exhibits the least error compared to the dynamic time history method. Therefore, the response acceleration method is recommended as the preferred method for the seismic design of underground stations in Shanghai.

Performance-based Seismic Design of reinforced concrete Structure - A Review

In recent times, in multistory buildings, the seismic demands were met using the code-based method of seismic analysis and design of the structure ,although the design of building can be more optimized by a more modern and realistic design approach in the form performance based design .As per the code, the building performance under seismic response are categorized into different levels of performance checks for the actual ground motions or some sets of ground motions ,limiting the global damage and thereby creating a scope for optimization at material level and at cross section level of the reinforced concrete structure .The building can be designed or checked based on this code prescribed performance levels, reducing the potential risk of the future earthquake as well as the damage or the loss caused due the earthquake. This review paper highlights numerous studies done by researchers comparing the responses from the code-based design and performance-based design, paving the way for use of performance-based design in the structure.

Seismic design and performance evaluation of steel braced frames with post-tensioned and disc-spring-based self-centering buckling-restrained braces

In this study, we focus on two types of self-centering buckling-restrained braces (SC-BRBs), which are post-tensioned (PT) SC-BRB and disc-spring-based SC-BRB, and develop a seismic design method for steel braced frames with these braces according to the displacement-based design theory. The whole independent parameters that describe the hysteretic behavior of the SC-BRBs are first determined. Then nonlinear time history analysis (NLTHA) is conducted to explore the effects of these hysteretic parameters on the ductility demands of the nonlinear single-degree-of-freedom (SDOF) system. Based on the analysis results, a ductility demand spectral model is developed, followed by a nonlinear displacement ratio spectral model. Subsequently, the seismic design procedure for SC-BRB frames is proposed based on the two spectral models. Finally, a total of 24 six-story steel frames with the two types of SC-BRBs, two target inter-story drifts, and different parameter combinations are designed at the maximum considered earthquake (MCE) level. The pushover analysis and NLTHA results indicate that a smaller strength ratio β and a larger initial stiffness ratio αs are beneficial for reducing the base shear and obtain an economical design when the designed frames achieve the same target inter-story drift. Considering the initial stiffness of the SC-BRBs is highly sensitive to machining errors, it is recommended that the value of β be taken within 0.25 to reduce the influence of the initial stiffness uncertainty of the braces on seismic design results. Moreover, controlling β within 0.25 also helps to reduce the higher-mode effect and peak floor acceleration responses of the designed structures effectively.

A new performance‐based seismic design method using endurance time analysis for linked column frame system and a comparison of structural systems and seismic analysis methods

SummaryThis paper presents a new performance‐based seismic design method for the design of repairable linked column frame (LCF) and linked column system (LCS). Currently, the biggest problem of these systems is the lack of a simple and practical design method that leads to the design of optimal models with sufficient seismic capacity. The interaction of the primary and secondary systems, changing the lateral load pattern during an earthquake, and the implementation of the target performance objectives have complicated the design of these systems. The evaluations carried out in this research show that the rotation of link beams must be controlled in the design. Therefore, the ultimate plastic rotation of links is determined to be 0.01 rad for the seismic intensity of design base earthquake and 0.015 rad for maximum considered earthquake. The results show that the models designed using the presented method are optimal, have sufficient seismic capacity, and achieve the target performance objectives. In addition, although previous researches have shown that these systems have a suitable seismic behavior, their seismic behavior have not been compared with other structural systems. Comparing can show the behavioral characteristics of a new structural system; hence, the elastic and plastic behavior of the LCF and LCS models have been compared with other common steel structural systems using all analysis methods. Moreover, in the presented method for the design of LCF and LCS systems, nonlinear time history analysis using the endurance time method (ETM) is used, and due to the newness of the endurance time method, its results are compared with the median results of nonlinear time history analysis at different seismic hazard levels and incremental dynamic analysis (IDA), in 45 samples. The results show that the endurance time analysis is a reasonable and efficient method, and in this comparison, the difference between the results of ETM and IDA methods is 6% on average.

Conservativeness Study on the Seismic Analysis Method for Research Reactor Plant Structure Based on TMSR-LF1

The seismic performance analysis of research reactor plants is crucial for ensuring the safety of the entire reactor system. This paper analyzes the plant structure seismic performance of the 2WMt Thorium Molten Salt Reactor-Liquid Fuel 1 (TMSR-LF1) at the Shanghai Institute of Applied Physics, Chinese Academy of Sciences under the action of frequent earthquakes, fortification earthquakes, and rare earthquakes was analyzed by finite element software PKPM based on the seismic design method of civil code +1°. On this basis, a comparison was made between the seismic responses of structural pushover analysis and elastoplastic time history analysis under the action of rare earthquakes, and the conservatism of these two commonly used methods for elastoplastic analysis was systematically analyzed. The results indicate that the TMSR-LF1 plant structure exhibits well bearing and deformation capacity. It meets the seismic design goal of “no damage under small earthquakes,” “no unrepairable damage under medium earthquakes,” and “no collapse under large earthquakes (using static pushover analysis),” and the critical regions are entirely within the elastic range. Furthermore, the analysis reveals that the elastoplastic time history analysis method produced a significantly higher seismic response than the pushover analysis method, which indicates the conservativeness of the time history method. Therefore, it is recommended to use the elastoplastic time history analysis method to evaluate the seismic performance of research reactor plants under rare earthquake actions. The research in this paper provides important references for the seismic performance analysis of other Class II research reactor plants.

Analysis of Bridge Tests on Sandy Overburden Site with Fault Dislocating

Performance-based seismic design methods for bridges are advancing, yet limited research has explored the damage mechanisms of bridges subjected to extreme seismic effects, such as those near or across faults. To investigate the damage mechanisms under bedrock dislocation and bridge rupture resistance, providing essential insights for the standardized design and construction of bridges in close proximity to seismic rupture sites, we developed a large-scale device to model bridges in the immediate vicinity of tilted-slip strong seismic rupture sites. This included a synchronous bedrock dislocation loading system. Four sets of typical sandy soil modeling tests were concurrently conducted. The results indicate: (1) The overall shear deformation zone of the foundation and surface uneven deformation primarily concentrate the overburdened soil body along the fault dip. The damaged area under the low-dip reverse fault is lighter on the surface and inside the soil body compared to the high-dip-positive fault. (2) The presence of bridges reduces the width of the main rupture zone and avoidance distance to some extent. However, this reduction is not as significant as anticipated. The damage to the bridge pile foundation along the fault dislocation tendency notably leads to the bending damage of the bridge deck. (3) Input parameters for fracture-resistant bridge design (surface rupture zone location, extent, maximum deformation, etc.) can be deduced from the free site. Within the rupture zone, a “fuse” design can be implemented using simply supported girders. Additionally, combining the “fuse” design with simple supported girders on both sides and utilizing simple support beams for “fuse” design within the rupture zone, along with structural “disconnection”, allows for reinforcing measures on the bridge structure’s foundation platform and pile in the soil body.

Performance-based seismic design method for disc spring-based self-centering viscous dissipative braced steel frame

Disc spring-based self-centering viscous damper (SCVD) has emerged as a novel technology, offering velocity-dependent energy dissipation and exceptional self-centering capabilities. Integrating this damper in structural bracing systems can effectively enhance passive control over critical structural demands such as peak deformation, residual displacement, and floor acceleration. Nevertheless, a seismic design method specifically tailored for self-centering viscous dissipative braced steel frames (SCVDFs) needs further refinement. This study proposes a performance-based seismic design (PBSD) method for SCVDFs, which is grounded in the performance-based plastic design (PBPD) approach. The proposed procedure primarily considers the effects of two critical hysteresis parameters: the post-activation stiffness ratio and the viscous damping ratio. To verify the effectiveness of the design method, a set of SCVDFs was designed, each utilizing different combinations of design parameters. Nonlinear static and dynamic analyses were performed on these archetypes to evaluate their seismic performance. The evaluation findings demonstrated that the properly designed SCVDFs can achieve the expected design performance and effectively suppress the peak inter-story drift, residual inter-story drift, and peak absolute floor acceleration of the structure, thereby achieving a favorable trade-off in the design outcome and maximizing the advantages of the SCVDF in seismic resilience.