Seismic design of RC structures: A critical assessment in the framework of multi‐objective optimization

The assessment of seismic design codes has been the subject of intensive research work in an effort to reveal weak points that originated from the limitations in predicting with acceptable precision the response of the structures under moderate or severe earthquakes. The objective of this work is to evaluate the European seismic design code, i.e. the Eurocode 8 (EC8), when used for the design of 3D reinforced concrete buildings, versus a performance‐based design (PBD) procedure, in the framework of a multi‐objective optimization concept. The initial construction cost and the maximum interstorey drift for the 10/50 hazard level are the two objectives considered for the formulation of the multi‐objective optimization problem. The solution of such optimization problems is represented by the Pareto front curve which is the geometric locus of all Pareto optimum solutions. Limit‐state fragility curves for selected designs, taken from the Pareto front curves of the EC8 and PBD formulations, are developed for assessing the two seismic design procedures. Through this comparison it was found that a linear analysis in conjunction with the behaviour factor q of EC8 cannot capture the nonlinear behaviour of an RC structure. Consequently the corrected EC8 Pareto front curve, using the nonlinear static procedure, differs significantly with regard to the corresponding Pareto front obtained according to EC8. Furthermore, similar designs, with respect to the initial construction cost, obtained through the EC8 and PBD formulations were found to exhibit different maximum interstorey drift and limit‐state fragility curves. Copyright © 2007 John Wiley & Sons, Ltd.     

Seismic performance and new design procedure for chevron‐braced frames

The paper is concerned with the seismic design of steel‐braced frames in which the braces are configured in a chevron pattern. According to EuroCode 8 (EC8), the behaviour factor q, which allows for the trade‐off between the strength and ductility, is set at 2.5 for chevron‐braced frames, while 6.5 is assigned for most ductile steel moment‐resisting frames. Strength deterioration in post‐buckling regime varies with the brace's slenderness, but EC8 adopts a unique q value irrespective of the brace slenderness. The study focuses on reevaluation of the q value adequate for the seismic design of chevron‐braced frames. The present EC8 method for the calculation of brace strength supplies significantly different elastic stiffnesses and actual strengths for different values of brace slenderness. A new method to estimate the strength of a chevron brace pair is proposed, in which the yield strength (for the brace in tension) and the post‐buckling strength (for the brace in compression) are considered. The new method ensures an identical elastic stiffness and a similar strength regardless of the brace slenderness. The advantage of the proposed method over the conventional EC8 method is demonstrated for the capacity of the proposed method to control the maximum inter‐storey drift. The q values adequate for the chevron‐braced frames are examined in reference to the maximum inter‐storey drifts sustained by most ductile moment‐resisting frames. When the proposed method is employed for strength calculation, the q value of 3.5 is found to be reasonable. It is notable that the proposed method does not require larger cross‐sections for the braces compared to the cross‐sections required for the present EC8 method. Copyright © 2005 John Wiley & Sons, Ltd.     

Earthquake‐resistant structural design through energy demand and capacity

An energy‐based earthquake‐resistant structural design method is proposed. The proposed method uses specific input energy spectra, modal or time‐history analyses, and energy distribution among structural members. For a given member strength and stiffness, a relationship between the energy attributable to damage absorbed by a member and its cumulative ductility demand can be determined. Member strength, stiffness and energy capacity are design parameters which are simultaneously used in the design. The method can avoid soft‐storey design. The damage is measured based on a cumulative basis considering earthquake magnitude, frequency, and duration. Tests have been carried out to determine energy absorbing capacities of various structural components. More efforts are needed to make the energy‐based earthquake‐resistant structural design practical, but ssimple formulations for this method are possible. Copyright © 2007 John Wiley & Sons, Ltd.     

Simplified inelastic seismic analysis of base‐isolated structures using the N2 method

In the paper a simplified nonlinear method has been applied to the analysis of base‐isolated structures. In the first part, a three‐linear idealization of the capacity curve is proposed. The initial stiffness is defined based on the first yielding point in the superstructure, whereas the secondary slope depends on the failure mechanism of the superstructure. A consequence is a much more pronounced secondary slope, which does not correspond to the presumptions used in the originally proposed N2 method. A parametric nonlinear dynamic study of single degree of freedom systems with different hardening slopes and damping has been performed for an ensemble of seven EC8 spectrum‐compatible artificial accelerograms. It was concluded that, in the long‐period range, the equal displacement rule could be assumed also for the proposed systems with non‐zero post‐yield stiffness. In the second part, the proposed idealization was used for the analysis of isolated RC frame buildings that were isolated with different (lead) rubber‐bearing isolation systems. The stiffness of the isolators was selected for three different protection levels and for three different ground motion intensities, which have resulted in elastic as well as moderately and fully damaged superstructure performance levels. Three different lateral load distributions were investigated. It was observed that a triangular distribution, with an additional force at the base, works best in the majority of practical cases. It was concluded that the N2 method can, in general, provide a reasonably accurate prediction of the actual top displacement, as well as of the expected damage to the superstructure. Copyright © 2009 John Wiley & Sons, Ltd.     

Probabilistic estimate of seismic response design values of RC frames

Probabilistically controlled design values of the nonlinear seismic response of reinforced concrete frames are obtained using a method previously proposed by the authors. The method allows to calculate conservative design values characterized by a predefined non‐exceedance probability, using a limited number of spectrum‐fitting generated accelerograms. Herein the method is applied to elastic‐strain hardening single degree of freedom systems representative of RC framed structures and is then assessed with reference to four reinforced concrete model frames designed according to EC8. The frames are characterized by different natural periods and aspect ratios. The results, compared with those obtained applying current EC8 recommendations, show the effectiveness of the proposed method. EC8 provides for design values of the seismic response of a structure with a nonlinear behavior computed as the mean value of the responses to seven accelerograms or as the maximum value of the responses to three accelerograms. These two criteria lead to design values characterized by very different and uncontrolled non‐exceedance probability levels, while the proposed method allows the analyst to directly control the non‐exceedance probability level of the calculated design values. Copyright © 2009 John Wiley & Sons, Ltd.     

On the quantification of local deformation demands and adequacy of linear analysis procedures for the seismic assessment of existing steel buildings to EC8-3

The application of performance-based design and assessment procedures requires an accurate estimation of local component deformation demands. In the case of steel moment-resisting frames, these are usually defined in terms of plastic rotations. A rigorous estimation of this response parameter is not straightforward, requiring not only the adoption of complex nonlinear structural models, but also of time-consuming numerical integration calculations. Moreover, the majority of existing codes and guidelines do not provide any guidance in terms of how these response parameters should be estimated. Part 3 of Eurocode 8 (EC8-3) requires the quantification of plastic rotations even when linear methods of analysis are used. Therefore, the aim of the research presented in this paper is to evaluate different methods of quantifying local component demands and also to answer the question of how reliable are the estimates obtained using the EC8-3 linear analysis procedures in comparison to more accurate nonlinear methods of analysis, particularly when the linear analysis applicability criterion proposed by EC8-3 is verified. An alternative methodology to assess the applicability of linear analysis is proposed which overcomes the important limitations identified in the EC8-3 criterion.     

Experimental and analytical investigations of steel panel dampers for seismic applications in steel moment frames

A ductile Vierendeel frame can be constructed by incorporating steel panel dampers (SPDs) into a moment‐resisting frame (MRF). Thus, the stiffness, strength, and ductility of the lateral force–resisting system can be enhanced. The proposed 3‐segment SPD possesses a center inelastic core (IC) and top and bottom elastic joints. This paper discusses the mechanical properties, capacity design method, and buckling‐delaying stiffeners for the SPDs through the use of cyclic loading tests on 2 specimens. Tests confirm that SPDs' cyclic force vs deformation relationships can be accurately predicted using either the Abaqus or PISA3D model analyses. The paper also presents the capacity design method for boundary beams connected to the SPDs of a typical SPD‐MRF. The seismic performance of an example 6‐story SPD‐MRF is evaluated using nonlinear response history analysis procedures and 240 ground accelerations at 3 hazard levels. Results indicate that under 80 maximum considered earthquake ground accelerations, the mean‐plus‐one standard deviation of the shear deformation of the ICs in the SPDs is 0.055 rad, substantially less than the 0.11 rad deformational capacity observed from the SPD specimens. The experimental cumulative plastic deformation of the proposed SPD is 242 times the yield deformation and is capable of sustaining a maximum considered earthquake at least 8 times before failure. This paper introduces the method of using one equivalent beam‐column element for effective modeling of the 3‐segment SPD. The effects of the IC's relative height and stiffness on the overall SPD's elastic and postelastic stiffness, elastic deformation limits, and inelastic deformational demands are discussed.     

Empirical‐based out‐of‐plane URM infill wall model accounting for the interaction with in‐plane demand

The role of masonry infills in the seismic behavior of reinforced concrete buildings has been widely studied in terms of their strength and stiffness contribution in the in‐plane (IP) direction, while fewer studies have been carried out on their response and modeling in the out‐of‐plane (OOP) direction. In this paper, the state of the art in code and literature provisions regarding infills' OOP capacity and seismic demand is presented, together with a review of the experimental tests that have been carried out to investigate infills' OOP behavior and the effects of IP‐OOP interaction. This review aims to collect an experimental database that is used to evaluate the effectiveness of literature and code provisions and to propose a semiempirical approach both for predicting infills' OOP strength, stiffness, and displacement capacity and for modeling the effects of IP displacement demand on OOP behavior and vice versa. Then, the state of the art on modeling of infills' OOP behavior and IP‐OOP interaction is presented together with a new macro model based on the proposed formulations and conceived to represent the IP and OOP behavior by taking into account the mutual interaction effects. Finally, the proposed model is used for an example application on two case‐study buildings, showing the effects of taking into account or neglecting the IP‐OOP interaction phenomena.     

A unified approach for the design of high ductility steel frames with concentric braces in the framework of Eurocode 8

Eurocode 8 (EC8) stipulates design methods for frames with diagonal braces and for chevron braced frames, which differ as regards the numerical model adopted, the value of the behavior factor q and the estimation of the lateral strength provided by braces. Instead, in this paper, the use of the same design method is suggested for both types of concentrically braced frames. The design method is a generalization of the one proposed for chevron braced frames in a previous study. A numerical investigation is conducted to assess the reliability of this design method. A set of concentrically braced frames is designed according to the EC8 and proposed design methods. The seismic response of these frames is determined by nonlinear dynamic analysis. Finally, it is demonstrated that the proposed design method is equivalent to those provided by EC8, because it can ensure the same level of structural safety which would be expected when using EC8. Copyright © 2013 John Wiley & Sons, Ltd.     

Assessment of a capacity spectrum seismic design approach against cyclic and seismic experiments on full‐scale precast RC structures

Within the last decades, simplified methods alternative to dynamic nonlinear analysis have been developed to estimate the seismic performance of structures toward a performance‐oriented design. Considering drift as the main parameter correlated with structural damage, its estimation is of main importance to assess the structural performance. While traditional force‐based design deals with calibrated force reduction factors based on the expected structural ductility, other methods are based on the definition of a viscous damping factor defined as a function of the expected energy dissipated by the structure. An example is the capacity spectrum method. This method can be applied even without any a priori calibration or designer arbitrariness. This allows considering several peculiarities of the seismic behavior of precast structures, which may be influenced by nontraditional hysteresis of connections and members, interaction with the cladding panels, P‐δ effects, etc. The paper aims at verifying the soundness and accuracy of this method through the comparison of its predictions against the results of cyclic and pseudodynamic tests on precast structures, including single‐ and multistory buildings either stiff or flexible, obtained on full‐scale building prototypes tested within the framework of recent research projects (namely, “Precast Structures EC8,” “Safecast,” and “Safecladding”). Two simple methodologies of determination of the equivalent viscous damping from a force‐displacement cycle, based on the dissipated energy in relation to 2 different estimates of the elastic strain energy, are addressed and compared. Comments on the possible use of this procedure for the estimation of the seismic performance of precast structures are provided.     

A rational H∞‐norm–based approach for the optimal design of seismically excited reinforced concrete frames

A rational approach is presented for minimizing the dynamic response of reinforced concrete framed structures forced by a seismic base acceleration. Reference is made to EC8 regulations, but the presented approach may in principle be applied to structures ruled by any regulation code. Governing equations are set in the frequency domain (and not in the periods domain as usual) so as to enable the adoption of sound approaches for analysis and design of dynamic structures that are typical of automatics. Among these, a novel usage of the H_∞‐norm concept is proposed that determines a rational design approach capable to minimize the structural response with reference to any quantity of engineering interest, eg, the overall compliance and the displacement of a specific point or the interstorey drift. A numerical investigation on a 6‐storey 3‐bay frame is performed, and relevant analysis and design results are presented in much detail to validate the theoretical framework.     

Methodology for the development of bridge‐specific fragility curves

A new methodology for the development of bridge‐specific fragility curves is proposed with a view to improving the reliability of loss assessment in road networks and prioritising retrofit of the bridge stock. The key features of the proposed methodology are the explicit definition of critical limit state thresholds for individual bridge components, with consideration of the effect of varying geometry, material properties, reinforcement and loading patterns on the component capacity; the methodology also includes the quantification of uncertainty in capacity, demand and damage state definition. Advanced analysis methods and tools (nonlinear static analysis and incremental dynamic response history analysis) are used for bridge component capacity and demand estimation, while reduced sampling techniques are used for uncertainty treatment. Whereas uncertainty in both capacity and demand is estimated from nonlinear analysis of detailed inelastic models, in practical application to bridge stocks, the demand is estimated through a standard response spectrum analysis of a simplified elastic model of the bridge. The simplified methodology can be efficiently applied to a large number of bridges (with different characteristics) within a road network, by means of an ad hoc developed software involving the use of a generic (elastic) bridge model, which derives bridge‐specific fragility curves. Copyright © 2016 John Wiley & Sons, Ltd.     

Extension of N2 method to plan irregular buildings considering accidental eccentricity

The paper deals with the topic of analyses performed according to modern code provisions, in particular Eurocode 8 (EC8) rules. Non linear static and non linear dynamic analyses of a plan irregular multi-storey r/c frame building designed according to Eurocode 2 (EC2) and EC8 provisions are carried out.The extension of the N2 method to torsionally flexible structures, as applied in previous papers, does not consider the accidental eccentricity, which is prescribed by EC8 also in the case of non linear static analysis. In this paper, three methods combining the accidental eccentricity prescribed by EC8 to the procedure which extends the N2 method to torsionally flexible structures are proposed and discussed. Each of them provides four modal response spectrum analyses (one for each model, corresponding to each position of centre of mass) and eight non linear static analyses (two signs for four models). NLSA(meth. n.2) seems to be the more reliable method of the three proposed, because it better fits absolute displacements obtained by non linear dynamic analysis.In the paper it is also observed that the value of the behaviour factor assigned by EC8 to torsionally flexible systems seems too conservative.     

Seismic collapse risk of precast industrial buildings with strong connections

A systematic seismic risk study has been performed on some typical precast industrial buildings that consists of assemblages of cantilever columns with high shear‐span ratios connected to an essentially rigid roof system with strong pinned connections. These buildings were designed according to the requirements of Eurocode 8. The numerical models and procedures were modified in order to address the particular characteristics of the analyzed system. They were also verified by pseudo‐dynamic and cyclic tests of full‐scale large buildings. The intensity measure (IM)‐based solution strategy described in the PEER methodology was used to estimate the seismic collapse risk in terms of peak ground acceleration capacity and the probability of exceeding the global collapse limit state. The effect of the uncertainty in the model parameters on the dispersion of collapse capacity was investigated in depth. Reasonable seismic safety (as proposed by the Joint Committee on Structural Safety) was demonstrated for all the regular single‐storey precast industrial buildings addressed in this study. However, if the flexural strength required by EC8 was exactly matched, and the additional strength, which results from minimum longitudinal reinforcement, was disregarded as well as large dispersion in records was considered, the seismic risk might in some cases exceed the acceptable limits. Copyright © 2009 John Wiley & Sons, Ltd.     

A statistically based runoff‐yield model coupling infiltration excess and saturation excess mechanisms

A statistically based runoff‐yield model is proposed in this paper. The model considers spatial heterogeneities of rainfall, soil infiltration capacity and soil water storage capacity that are main factors controlling runoff‐yield process. It assumes that the spatial variation of rainfall intensity at each time step can be characterized by a probability density function, which is estimated by matching the hyetograph through goodness‐of‐fit measure, whereas the spatial heterogeneities of soil infiltration capacity and soil water storage capacity are described by parabola‐type functions. Surface runoff is calculated according to infiltration excess mechanism; the statistical distribution of surface runoff rate can be deduced with the joint distribution of rainfall intensity and soil infiltration rate, thus obtaining a quasi‐analytical solution for surface runoff. Based on saturation excess mechanism, the groundwater flow (flows below the ground are collectively referred to as groundwater flow) is calculated by infiltration and the probability distribution of soil water storage capacity. Consequently, the total runoff is composed of infiltration excess and saturation excess runoff components. As an example, this model is applied to flood event simulation in Dongwan catchment, a semi‐humid region and a tributary of Yellow River in China. It indicates that the proposed runoff‐yield model could achieve acceptable accuracy. Copyright © 2011 John Wiley & Sons, Ltd.     

Response simulation and seismic assessment of highway overcrossings

Interaction of bridge structures with the adjacent embankment fills and pile foundations is generally responsible for response modification of the system to strong ground excitations, to a degree that depends on soil compliance, support conditions, and soil mass mobilized in dynamic response. This paper presents a general modeling and assessment procedure specifically targeted for simulation of the dynamic response of short bridges such as highway overcrossings, where the embankment soil–structure interaction is the most prevalent. From previous studies it has been shown that in this type of interaction, seismic displacement demands are magnified in the critical bridge components such as the central piers. This issue is of particular relevance not only in new design but also in the assessment of the existing infrastructure. Among a wide range of issues relevant to soil–structure interaction, typical highway overcrossings that have flexible abutments supported on earth embankments were investigated extensively in the paper. Simulation procedures are proposed for consideration of bridge‐embankment interaction effects in practical analysis of these structures for estimation of their seismic performance. Results are extrapolated after extensive parametric studies and are used to extract ready‐to‐use, general, and parameterized capacity curves for a wide range of possible material properties and geometric characteristics of the bridge‐embankment assembly. Using two instrumented highway overpasses as benchmark examples, the capacity curves estimated using the proposed practical procedures are correlated successfully with the results of explicit incremental dynamic analysis, verifying the applicability of the simple tools developed herein, in seismic assessment of existing short bridges. Copyright © 2009 John Wiley & Sons, Ltd.     

Risk‐based seismic design for collapse safety

Risk‐based seismic design, as introduced in this paper, involves the use of different types of analysis in order to satisfy a risk‐based performance objective with a reasonable utilization rate and sufficient reliability. Differentiation of the reliability of design can be achieved by defining different design algorithms depending on the importance of a structure. In general, the proposed design is iterative, where the adjustment of a structure during iterations is the most challenging task. Rather than using automated design algorithms, an attempt has been made to introduce three simple guidelines for adjusting reinforced concrete frames in order to increase their strength and deformation capacity. It is shown that an engineer can design a reinforced concrete frame in a few iterations, for example, by adjusting the structure on the basis of pushover analysis and checking the final design by means of nonlinear dynamic analysis. A possible variant of the risk‐based design algorithm for the collapse safety of reinforced concrete frame buildings is proposed, and its application is demonstrated by means of an example of an eight‐storey reinforced concrete building. Four iterations were required in order to achieve the risk‐based performance objective with a reasonable utilization rate. Copyright © 2016 John Wiley & Sons, Ltd.     

Strong ground motion record selection for the reliable prediction of the mean seismic collapse capacity of a structure group

How to select a limited number of strong ground motion records (SGMRs) is an important challenge for the seismic collapse capacity assessment of structures. The collapse capacity is considered as the ground motion intensity measure corresponding to the drift‐related dynamic instability in the structural system. The goal of this paper is to select, from a general set of SGMRs, a small number of subsets such that each can be used for the reliable prediction of the mean collapse capacity of a particular group of structures, i.e. of single degree‐of‐freedom systems with a typical behaviour range. In order to achieve this goal, multivariate statistical analysis is first applied, to determine what degree of similarity exists between each selected small subset and the general set of SGMRs. Principal Component analysis is applied to identify the best way to group structures, resulting in a minimum number of SGMRs in a proposed subset. The structures were classified into six groups, and for each group a subset of eight SGMRs has been proposed. The methodology has been validated by analysing a first‐mode‐dominated three‐storey‐reinforced concrete structure by means of the proposed subsets, as well as the general set of SGMRs. The results of this analysis show that the mean seismic collapse capacity can be predicted by the proposed subsets with less dispersion than by the recently developed improved approach, which is based on scaling the response spectra of the records to match the conditional mean spectrum. Copyright © 2010 John Wiley & Sons, Ltd.     

Estimation of the behavior factor of existing RC-MRF buildings

In recent years, several research groups have studied a new generation of analysis methods for seismic response assessment of existing buildings. Nevertheless, many important developments are still needed in order to define more reliable and effective assessment procedures. Moreover, regarding existing buildings, it should be highlighted that due to the low knowledge level, the linear elastic analysis is the only analysis method allowed. The same codes (such as NTC2008, EC8) consider the linear dynamic analysis with behavior factor as the reference method for the evaluation of seismic demand. This type of analysis is based on a linear-elastic structural model subject to a design spectrum, obtained by reducing the elastic spectrum through a behavior factor. The behavior factor (reduction factor or q factor in some codes) is used to reduce the elastic spectrum ordinate or the forces obtained from a linear analysis in order to take into account the non-linear structural capacities. The behavior factors should be defined based on several parameters that influence the seismic nonlinear capacity, such as mechanical materials characteristics, structural system, irregularity and design procedures. In practical applications, there is still an evident lack of detailed rules and accurate behavior factor values adequate for existing buildings. In this work, some investigations of the seismic capacity of the main existing RC-MRF building types have been carried out. In order to make a correct evaluation of the seismic force demand, actual behavior factor values coherent with force based seismic safety assessment procedure have been proposed and compared with the values reported in the Italian seismic code, NTC08.     

Fundamental periods of steel concentrically braced frames designed to Eurocode 8

A two‐phase research program has been undertaken to investigate fundamental natural periods of concentrically braced frames (CBFs) designed according to Eurocode 8 (EC8). In the first phase of the program, over 83,700 buildings were designed, and the accuracy of the lower bound expressions given in well‐known design specifications was evaluated. The results indicated that the lower bound expressions given in EC8 and National Building Code of Canada (NBCC) are acceptable. Although all structures had periods longer than the ones estimated by the EC8 expression, a few structures had shorter periods than the ones estimated by the NBCC expression. In general, the lower bound expressions given in EC8 and NBCC were found to provide over conservative estimates for most cases. In the second phase of the program, a simple hand method was developed to estimate the fundamental natural periods of CBFs designed to EC8. This method requires the use of inelastic top story drift ratio as a parameter to quantify stiffness characteristics. The drift ratios were extracted from the design pool developed as a part of the first phase and represented by simple mathematical relationships. Evaluation of the proposed method indicated that the method is accurate in providing estimates of the fundamental period. To safeguard against providing unconservative estimates, the method was modified to arrive at a new lower bound expression, which significantly improves the estimates compared with the ones provided by the existing expressions. Copyright © 2013 John Wiley & Sons, Ltd.