Adapting earthquake actions in Eurocode 8 for performance‐based seismic design

Performance‐based seismic design (PBSD) can be considered as the coupling of expected levels of ground motion with desired levels of structural performance, with the objective of achieving greater control over earthquake‐induced losses. Eurocode 8 (EC8) already envisages two design levels of motion, for no collapse and damage limitation performance targets, anchored to recommended return periods of 475 and 95 years, respectively. For PBSD the earthquake actions need to be presented in ways that are appropriate to the estimation of inelastic displacements, since these provide an effective control on damage at different limit states. The adequacy of current earthquake actions in EC8 are reviewed from this perspective and areas requiring additional development are identified. The implications of these representations of the seismic loads, in terms of mapping and zonation, are discussed. The current practice of defining the loading levels on the basis of the pre‐selected return periods is challenged, and ideas are discussed for calibrating the loading‐performance levels for design on the basis of quantitative earthquake loss estimation. Copyright © 2005 John Wiley & Sons, Ltd.     

Performance‐based design using structural optimization

A new methodology for seismic design is proposed based on structural optimization with performance‐based constraints. Performance‐based criteria are introduced for the seismic design of new buildings. These criteria are derived from the National Guidelines for Seismic Rehabilitation of Buildings (Reference [19], Federal Emergency Management Agency (FEMA), ‘NHERP Guidelines for seismic rehabilitation of buildings’, Report Nos 273 and 274, Washington, DC, 1997) for retrofitting existing structures. The proposed design methodology takes into account the non‐linear behaviour of the structure. The goal is to incorporate in the design the actual performance levels of the structure, i.e. how much reserve capacity the structure has in an earthquake of a given magnitude. The optimal design of the structure minimizes the structural cost subjected to performance constraints on plastic rotations of beams and columns, as well as behavioural constraints for reinforced concrete frames. Uncertainties in the structural period and in the earthquake excitation are taken into account using convex models. The optimization routine incorporates a non‐linear analysis program and the procedure is automated. The proposed methodology leads to a structural design for which the levels of reliability (performance levels) are assumed to be quantifiable. Furthermore, the entire behaviour of the structure well into the non‐linear range is investigated in the design process. Copyright © 2000 John Wiley & Sons, Ltd.     

Performance‐based seismic design via yield frequency spectra‡

Yield frequency spectra (YFS) are introduced to enable the direct design of a structure subject to a set of seismic performance objectives. YFS offer a unique view of the entire solution space for structural performance. This is portrayed in terms of the mean annual frequency (MAF) of exceeding arbitrary ductility (or displacement) thresholds, versus the base shear strength of a structural system having specified yield displacement and capacity curve shape. YFS can be computed nearly instantaneously using publicly available software or closed‐form solutions, for any system whose response can be satisfactorily approximated by an equivalent nonlinear single‐degree‐of‐freedom oscillator. Because the yield displacement typically is a more stable parameter for performance‐based seismic design compared with the period, the YFS format is especially useful for design. Performance objectives stated in terms of the MAF of exceeding specified ductility (or displacement) thresholds are used to determine the lateral strength that governs the design of the structure. Both aleatory and epistemic uncertainties are considered, the latter at user‐selected confidence levels that can inject the desired conservatism in protecting against different failure modes. Near‐optimal values of design parameters can be determined in many cases in a single step. Copyright © 2016 John Wiley & Sons, Ltd.     

Seismic performance and probabilistic collapse resistance assessment of steel moment resisting frames with fluid viscous dampers

This paper evaluates the seismic resistance of steel moment resisting frames (MRFs) with supplemental fluid viscous dampers against collapse. A simplified design procedure is used to design four different steel MRFs with fluid viscous dampers where the strength of the steel MRF and supplemental damping are varied. The combined systems are designed to achieve performance that is similar to or higher than that of conventional steel MRFs designed according to current seismic design codes. Based on the results of nonlinear time history analyses and incremental dynamic analyses, statistics of structural and non‐structural response as well as probabilities of collapse of the steel MRFs with dampers are determined and compared with those of conventional steel MRFs. The analytical frame models used in this study are reliably capable to simulate global frame collapse by considering full geometric nonlinearities as well as the cyclic strength and stiffness deterioration in the plastic hinge regions of structural steel members. The results show that, with the aid of supplemental damping, the performance of a steel MRF with reduced design base shear can be improved and become similar to that of a conventional steel MRF with full design base shear. Incremental dynamic analyses show that supplemental damping reduces the probability of collapse of a steel MRF with a given strength. However, the paper highlights that a design base shear equal to 75% of the minimum design base shear along with supplemental damping to control story drift at 2% (i.e., design drift of a conventional steel MRF) would not guarantee a higher collapse resistance than that of a conventional MRF. At 75% design base shear, a tighter design drift (e.g., 1.5% as shown in this study) is needed to guarantee a higher collapse resistance than that of a conventional MRF. Copyright © 2014 John Wiley & Sons, Ltd.     

Uniform hazard versus uniform risk bases for performance‐based earthquake engineering of light‐frame wood construction

This paper investigates the implications of designing for uniform hazard versus uniform risk for light‐frame wood residential construction subjected to earthquakes in the United States. Using simple structural models of one‐story residences with typical lateral force‐resisting systems (shear walls) found in buildings in western, eastern and central regions of the United States as illustrations, the seismic demands are determined using nonlinear dynamic time‐history analyses, whereas the collapse capacities are determined using incremental dynamic analyses. The probabilities of collapse, conditioned on the occurrence of the maximum considered earthquakes and design earthquakes stipulated in ASCE Standard 7‐05, and the collapse margins of these typical residential structures are compared for typical construction practices in different regions in the United States. The calculated collapse inter‐story drifts are compared with the limits stipulated in FEMA 356/ASCE Standard 41‐06 and observed in the recent experimental testing. The results of this study provide insights into residential building risk assessment and the relation between building seismic performance implied by the current earthquake‐resistant design and construction practices and performance levels in performance‐based engineering of light‐frame wood construction being considered by the SEI/ASCE committee on reliability‐based design of wood structures. Further code developments are necessary to achieve the goal of uniform risk in earthquake‐resistant residential construction. Copyright © 2010 John Wiley & Sons, Ltd.     

Error estimation of closed‐form solution for annual rate of structural collapse

With the increasing emphasis of performance‐based earthquake engineering in the engineering community, several investigations have been presented outlining simplified approaches suitable for performance‐based seismic design (PBSD). Central to most of these PBSD approaches is the use of closed‐form analytical solutions to the probabilistic integral equations representing the rate of exceedance of key performance measures. Situations where such closed‐form solutions are not appropriate primarily relate to the problem of extrapolation outside of the region in which parameters of the closed‐form solution are fit. This study presents a critical review of the closed‐form solution for the annual rate of structural collapse. The closed‐form solution requires the assumptions of lognormality of the collapse fragility and power model form of the ground motion hazard, of which the latter is more significant regarding the error of the closed‐form solution. Via a parametric study, the key variables contributing to the error between the closed‐form solution and solution via numerical integration are illustrated. As these key variables cannot be easily measured, it casts doubt on the use of such closed‐form solutions in future PBSD, especially considering the simple and efficient nature of using direct numerical integration to obtain the solution. Copyright © 2008 John Wiley & Sons, Ltd.     

Improved risk‐targeted performance‐based seismic design of reinforced concrete frame structures

This paper presents a procedure for seismic design of reinforced concrete structures, in which performance objectives are formulated in terms of maximum accepted mean annual frequency (MAF) of exceedance, for multiple limit states. The procedure is explicitly probabilistic and uses Cornell's like closed‐form equations for the MAFs. A gradient‐based constrained optimization technique is used for obtaining values of structural design variables (members' section size and reinforcement) satisfying multiple objectives in terms of risk levels. The method is practically feasible even for real‐sized structures thanks to the adoption of adaptive equivalent linear models where element‐by‐element stiffness reduction is performed (2 linear analyses per intensity level). General geometric and capacity design constraints are duly accounted for. The procedure is applied to a 15‐storey plane frame building, and validation is conducted against results in terms of drift profiles and MAF of exceedance, obtained by multiple‐stripe analysis with records selected to match conditional spectra. Results show that the method is suitable for performance‐based seismic design of RC structures with explicit targets in terms of desired risk levels.     

IM‐based and EDP‐based decision models for the verification of the seismic collapse safety of buildings

Decision models for the verification of seismic collapse safety of buildings are introduced. The derivations are based on the concept of the acceptable (target) annual probability of collapse, whereas the decision making involves comparisons between seismic demand and capacity, which is familiar to engineering practitioners. Seismic demand, which corresponds to the design seismic action associated with a selected return period, can be expressed either in terms of an intensity measure (IM) or an engineering demand parameter (EDP). Seismic capacity, on the other hand, is defined by dividing the near‐collapse limit‐state IM or EDP by an appropriate risk‐targeted safety factor (γ _im or γ _edp ), which is the only safety factor used in the proposed decision model. Consequently, the seismic performance assessment of a building should be based on the best possible estimate. For a case study, it is shown that if the target collapse risk is set to 10^?4 (0.5% over a period of 50 years), and if the seismic demand corresponds to a return period of 475 years (10% over a period of 50 years), then it can be demonstrated that γ _im is approximately equal to 2.5 for very stiff buildings, whereas for buildings with long periods the value of γ _im can increase up to a value of approximately 5. The model using γ _edp is equal to that using γ _im only if it can be assumed that displacements, with consideration of nonlinear behavior, are equal to displacements from linear elastic analysis.     

An efficient method for estimating the collapse risk of structures in seismic regions

Assessing the probability of collapse is a computationally demanding component of performance‐based earthquake engineering. This paper examines various aspects involved in the computation of the mean annual frequency of collapse (λ_c) and proposes an efficient method for estimating the sidesway collapse risk of structures in seismic regions. By deaggregating the mean annual frequency of collapse, it is shown that the mean annual frequency of collapse is typically dominated by earthquake ground motion intensities corresponding to the lower half of the collapse fragility curve. Uncertainty in the collapse fragility curve and mean annual frequency of collapse as a function of the number of ground motions used in calculations is also quantified, and it is shown that using a small number of ground motions can lead to unreliable estimates of a structure's collapse risk. The proposed method is shown to significantly reduce the computational effort and uncertainty in the estimate. Copyright © 2012 John Wiley & Sons, Ltd.     

Alternative non‐linear demand estimation methods for probability‐based seismic assessments

Alternative non‐linear dynamic analysis procedures, using real ground motion records, can be used to make probability‐based seismic assessments. These procedures can be used both to obtain parameter estimates for specific probabilistic assessment criteria such as demand and capacity factored design and also to make direct probabilistic performance assessments using numerical methods. Multiple‐stripe analysis is a non‐linear dynamic analysis method that can be used for performance‐based assessments for a wide range of ground motion intensities and multiple performance objectives from onset of damage through global collapse. Alternatively, the amount of analysis effort needed in the performance assessments can be reduced by performing the structural analyses and estimating the main parameters in the region of ground motion intensity levels of interest. In particular, single‐stripe and double‐stripe analysis can provide local probabilistic demand assessments using minimal number of structural analyses (around 20 to 40). As a case study, the displacement‐based seismic performance of an older reinforced concrete frame structure, which is known to have suffered shear failure in its columns during the 1994 Northridge Earthquake, is evaluated. Copyright © 2008 John Wiley & Sons, Ltd.     

Performance‐based optimum seismic design of reinforced concrete structures

A fully automated design methodology based on nonlinear response history analysis is proposed for the optimum seismic design of reinforced concrete (RC) structures. The conventional trial‐and‐error process is replaced by a structural optimization algorithm that serves as a search engine capable of locating the most efficient design in terms of cost and performance. Two variations of the proposed design methodology are introduced. The first approach treats the optimum design problem in a deterministic manner, while in the second variation the optimum design is sought in the framework of a reliability‐based optimization problem. The reliability‐based approach seems to be a more rational procedure since more meaningful design criteria that correlate better with the performance‐based design concept can be adopted. Thus, the practice of using the mean annual frequency of a limit‐state being exceeded to assess the candidate designs is compared with the use of deterministic criteria. Both formulations take into consideration the structural response for a number of limit‐states, from serviceability to collapse prevention. The proposed design procedure is specifically tailored to the design of RC structures, where a preliminary design step of generating tables of concrete sections is introduced. In order to handle the large size of the tables, the concept of multi‐database cascade optimization is implemented. The final design has to comply with the provisions of European design codes. The proposed methodology allows for a significant reduction of the direct construction cost combined with improved control of the seismic performance under earthquake loading. Copyright © 2008 John Wiley & Sons, Ltd.     

Modified seismic design of concentrically braced frames considering flexural demand on columns

Special concentrically braced frames (SCBFs) are considered as one of the most economical and effective lateral force‐resisting systems in structures located in the regions of high seismicity. Steel braces in a braced frame undergo large axial deformations in tension and compression to dissipate the seismic energy. However, past studies have shown that SCBFs exhibit the soft‐story hinge mechanisms and unpredictable failure patterns under earthquake loading conditions. These inelastic responses along with the use of continuous structural sections as columns over consecutive floors induce flexural demand that is not considered in the current design practice. In this study, the evaluation of seismic performance of nine SCBFs designed as per the current practice has been carried out for three different story heights (i.e., three‐story, six‐story, and nine‐story) and three types of brace configurations (namely, chevron, split X, and single X). Three additional design techniques are also explored based on (i) the inclusion of column moments in the design; (ii) the theory of formation of plastic hinges; and (iii) the design of braces considering the forces computed at their post‐buckled stages. Nonlinear dynamic analyses of these study frames have been evaluated numerically using a computer software Perform‐3D for a suite of 40 ground motions representing the design basis earthquake and maximum considered earthquake hazard levels. Analyses results showed that the SCBFs designed as per the modified procedures achieved the desired performance objectives without the formation of soft‐story mechanism. Copyright © 2017 John Wiley & Sons, Ltd.     

Response prediction,experimental characterization and P‐spectra design of frames with viscoelastic–plastic dampers

Viscoelastic–plastic (VEP) dampers are hybrid passive damping devices that combine the advantages of viscoelastic and hysteretic damping. This paper first formulates a semi‐analytical procedure for predicting the peak response of nonlinear SDOF systems equipped with VEP dampers, which forms the basis for the generation of Performance Spectra that can then be used for direct performance assessment and optimization of VEP damped structures. This procedure is first verified against extensive nonlinear time‐history analyses based on a Kelvin viscoelastic model of the dampers, and then against a more advanced evolutionary model that is calibrated to characterization tests of VEP damper specimens built from commercially available viscoelastic damping devices, and an adjustable friction device. The results show that the proposed procedure is sufficiently accurate for predicting the response of VEP systems without iterative dynamic analysis for preliminary design purposes. A design method based on the Performance Spectra framework is then proposed for systems equipped with passive VEP dampers and is applied to enhance the seismic response of a six‐storey steel moment frame. The numerical simulation results on the damped structure confirm the use of the Performance Spectra as a convenient and accurate platform for the optimization of VEP systems, particularly during the initial design stage. Copyright © 2016 John Wiley & Sons, Ltd.     

A design procedure for tied braced frames

The paper deals with the analysis of the seismic behaviour and design of tied braced frames (TBFs). The behavioural properties of TBFs are described and a comparison drawn with standard eccentrically braced frames. A design procedure is then proposed that aims to achieve optimal collapse seismic behaviour, i.e. a global collapse mechanism characterized by uniform plastic rotations of links. The procedure is based on the displacement‐based approach so as to achieve direct and efficient control of the peak ground acceleration of collapse. Applications are carried out on systems with different numbers of storeys and lengths of links to obtain confirmation of the accuracy of the design hypotheses and methodologies. Copyright © 2007 John Wiley & Sons, Ltd.     

Performance spectra based method for the seismic design of structures equipped with passive supplemental damping systems

A new direct performance‐based design method utilizing design tools called performance‐spectra (P‐Spectra) for low‐rise to medium‐rise frame structures incorporating supplemental damping devices is presented. P‐Spectra are graphic tools that relate the responses of nonlinear SDOF systems with supplemental dampers to various damping parameters and dynamic system properties that structural designers can control. These tools integrate multiple response quantities that are important to the performance of a structure into a single compact graphical format to facilitate direct comparison of different potential solutions that satisfy a set of predetermined performance objectives under various levels of seismic hazard. An SDOF to MDOF transformation procedure that defines the required supplemental damping properties for the MDOF structure to achieve the response defined by the target SDOF system is also presented for hysteretic, linear viscous and viscoelastic damping devices. Using nonlinear time‐history analyses of idealized shear structures, the accuracy of the transformation procedure is verified. A seismic performance upgrade design example is presented to demonstrate the usefulness of the proposed method for achieving design performance goals using supplemental damping devices. Copyright © 2012 John Wiley & Sons, Ltd.     

Need of performance‐based earthquake engineering in Taiwan: a lesson from the Chichi earthquake

The objectives of seismic engineering are to design and build better and more economic earthquake‐resistant structures. Performance, which is measured as the amount of damage of a facility and the impact of damage to the society after an earthquake, is the main concern. Performance‐based earthquake engineering (PBEE) implies design, evaluation, and construction of engineered facilities whose performance under common and extreme earthquake ground motions responds to the diverse needs and objectives of the owners, users and society. Observations on the performance or damage of structures after strong earthquake ground motions have always served as an effective means to evaluate the current seismic regulations and guidelines and make further improvements afterwards. This paper presents some of the typical damage evidence after the Chichi earthquake occurred recently in Taiwan. Important issues in performance‐based earthquake engineering that need to be considered in future seismic regulations of Taiwan are addressed accordingly. Copyright © 2000 John Wiley & Sons, Ltd.     

Effectiveness of simple approaches in mitigating residual deformations in buildings

Developments in performance‐based seismic design and assessment approaches have emphasized the importance of considering residual deformations. Recent investigations have also led to a proposed direct displacement‐based design (DDBD) approach which includes an explicit consideration of the expected residual deformations as an integral part of the design process. Having estimated the expected residual deformations in a structure, engineers are faced with the problem of reducing them to meet the targeted performance levels under pre‐defined seismic hazard levels. Previous studies have identified the post‐yield stiffness as a primary factor influencing the magnitude of residual deformations in single degree of freedom and multiple degree of freedom structures. In this paper, a series of simple approaches to increase the post‐yield stiffness of traditional framed and braced systems for the purpose of reducing residual deformations are investigated. These methods do not utilize recentring post‐tensioned technology. This contribution addresses the feasibility of altering the lateral post‐yield stiffness of structural systems by: (i) using different reinforcement materials with beneficial features in their stress–strain behaviour; (ii) re‐designing the section geometry and properties of primary seismic‐resisting elements; and (iii) introducing a secondary elastic frame to act in parallel with the primary system. The efficiency of each of these techniques is investigated through monotonic and cyclic moment‐curvature and non‐linear time‐history analyses. Of these approaches the design and introduction of an elastic secondary system was found to be most effective and consistent in reducing residual deformations. A simplified design approach for achieving the desired increase of a system's post‐yield stiffness is also presented. Copyright © 2007 John Wiley & Sons, Ltd.     

Seismic response analysis using characteristic ground motion records for risk‐based decision‐making (3R method)

The concept of intensity‐based assessment for risk‐based decision‐making is introduced. It is realized by means of the so‐called 3R method (response analysis, record selection and risk‐based decision‐making), which can be used to check the adequacy of design of a new building or of the strengthening of an existing building by performing conventional pushover analysis and dynamic analysis for only a few ground motions, which are termed characteristic ground motions. Because the objective of the method is not a precise assessment of the seismic risk, a simple decision model for risk acceptability can be introduced. The engineer can decide that the reliability of a no‐collapse requirement is sufficient when collapse is observed in the case of less than half of, for example, seven characteristic ground motions. From the theoretical point of view, it is shown that the accuracy of the method is acceptable if the non‐linear response history analyses are performed at a low percentile of limit‐state intensity, which is also proven by means of several examples of multi‐storey reinforced concrete frame buildings. The 3R method represents a compromise between the exclusive use of either pushover analysis or dynamic analysis and can be easily introduced into building codes provided that its applicability is further investigated (e.g. asymmetric structures and other performance objectives) and that the procedure for the selection of characteristic ground motions is automated and readily available to engineers (www.smartengineering.si).     

Rigid‐plastic seismic design of reinforced concrete structures

In this paper a new seismic design procedure for Reinforced Concrete (R/C) structures is proposed—the Rigid‐Plastic Seismic Design (RPSD) method. This is a design procedure based on Non‐Linear Time‐ History Analysis (NLTHA) for systems expected to perform in the non‐linear range during a lifetime earthquake event. The theoretical background is the Theory of Plasticity (Rigid‐Plastic Structures). Firstly, a collapse mechanism is chosen and the corresponding stress field is made safe outside the regions where plastic behaviour takes place. It is shown that this allows the determination of the required structural strength with respect to a pre‐defined performance parameter using a rigid‐plastic response spectrum, which is characteristic of the ground motion alone. The maximum strength demand at any point is solely dependent on the intensity of the ground motion, which facilitates the task of distributing required strength throughout the structure. Any artificial considerations intended to adjust results according to empirical observations are avoided, which, from a conceptual point of view, is considered to be an advantage over other simplified design procedures for seismic design. The procedure is formulated using a step‐by‐step format followed by a design example of a 4‐storey‐R/C‐plane‐frame. Results are compared with refined NLTHA and found to be extremely encouraging. Copyright © 2006 John Wiley & Sons, Ltd.