On the design and seismic response of RC frame buildings designed with Eurocode 8

Performance-Based Seismic Design is now widely recognized as the pre-eminent seismic design and assessment methodology for building structures. In recognition of this, seismic codes may require that buildings achieve multiple performance objectives such as withstanding moderate, yet frequently occurring earthquakes with minimal structural and non-structural damage, while withstanding severe, but rare earthquakes without collapse and loss of life. These objectives are presumed to be satisfied by some codes if the force-based design procedures are followed. This paper investigates the efficacy of the Eurocode 8 force-based design provisions with respect to RC frame building design and expected seismic performance. Four, eight, and 16-storey moment frame buildings were designed and analyzed using the code modal response spectrum analysis provisions. Non-linear time-history analyses were subsequently performed to determine the simulated seismic response of the structures and to validate the Eurocode 8 force-based designs. The results indicate the design of flexural members in medium-to-long period structures is not significantly influenced by the choice of effective member stiffness; however, calculated interstorey drift demands are significantly affected. This finding was primarily attributed to the code’s enforcement of a minimum spectral ordinate on the design spectrum. Furthermore, design storey forces and interstorey drift demand estimates (and therefore damage), obtained by application of the code force-based design procedure varied substantially from those found through non-linear time-history analysis. Overall, the results suggest that though the Eurocode 8 may yield life-safe designs, the seismic performance of frame buildings of the same type and ductility class can be highly non-uniform.     

Multiobjective optimization for performance‐based seismic design of steel moment frame structures

The performance‐based seismic design of steel special moment‐resisting frame (SMRF) structures is formulated as a multiobjective optimization problem, in which conflicting design criteria that respectively reflect the present capital investment and the future seismic risk are treated simultaneously as separate objectives other than stringent constraints. Specifically, the initial construction expenses are accounted for by the steel material weight as well as by the number of different standard steel section types, the latter roughly quantifying the degree of design complexity related additional construction cost; the seismic risk is considered in terms of maximum interstory drift demands at two hazard levels with exceedance probabilities being 50% and 2% in 50 years, respectively. The present formulation allows structural engineers to find an optimized design solution by explicitly striving for a desirable compromise between the initial investment and seismic performance. Member sizing for code‐compliant design of a planar five‐story four‐bay SMRF is presented as an application example using the proposed procedure that is automated by a multiobjective genetic algorithm. Copyright © 2004 John Wiley & Sons, Ltd.     

Simplified seismic design approach for steel portal frame piers with hysteretic dampers

A simplified seismic design procedure for steel portal frame piers installed with hysteretic dampers is proposed, which falls into the scope of performance‐based design philosophy. The fundamental goal of this approach is to design a suite of hysteretic damping devices for existing and new bridge piers, which will assure a pre‐defined target performance against future severe earthquakes. The proposed procedure is applicable to multi‐degree‐of‐freedom systems, utilizing an equivalent single‐degree‐of‐freedom methodology with nonlinear response spectra (referred to as strength‐demanded spectra) and a set of formulae of close‐form expressions for the distribution of strength and stiffness produced in the structure by the designed hysteretic damping devices. As an illustrative example, the proposed procedure is applied to a design of a simple steel bridge pier of portal frame type with buckling‐restrained braces (one of several types of hysteretic dampers). For the steel portal frame piers, an attempt is made to utilize not only the displacement‐based index but also the strain‐based index as pre‐determined target performance at the beginning of design. To validate this procedure, dynamic inelastic time‐history analyses are performed using the general‐purpose finite element program ABAQUS. The results confirm that the proposed simplified design procedure attains the expected performance level as specified by both displacement‐based and strain‐based indices with sufficient accuracy. Copyright © 2006 John Wiley & Sons, Ltd.     

Influence of deterioration modelling on the seismic response of steel moment frames designed to Eurocode 8

This paper assesses the influence of cyclic and in‐cycle degradation on seismic drift demands in moment‐resisting steel frames (MRF) designed to Eurocode 8. The structural characteristics, ground motion frequency content, and level of inelasticity are the primary parameters considered. A set of single‐degree‐of‐freedom (SDOF) systems, subjected to varying levels of inelastic demands, is initially investigated followed by an extensive study on multi‐storey frames. The latter comprises a large number of incremental dynamic analyses (IDA) on 12 frames modelled with or without consideration of degradation effects. A suite of 56 far‐field ground motion records, appropriately scaled to simulate 4 levels of inelastic demand, is employed for the IDA. Characteristic results from a detailed parametric investigation show that maximum response in terms of global and inter‐storey drifts is notably affected by degradation phenomena, in addition to the earthquake frequency content and the scaled inelastic demands. Consistently, both SDOF and frame systems with fundamental periods shorter than the mean period of ground motion can experience higher lateral strength demands and seismic drifts than those of non‐degrading counterparts in the same period range. Also, degrading multi‐storey frames can exhibit distinctly different plastic mechanisms with concentration of drifts at lower levels. Importantly, degrading systems might reach a “near‐collapse” limit state at ductility demand levels comparable to or lower than the assumed design behaviour factor, a result with direct consequences on optimised design situations where over‐strength would be minimal. Finally, the implications of the findings with respect to design‐level limit states are discussed.     

Estimation of seismic drift demands for frame structures

A process is outlined and evaluated for the estimation of seismic roof and storey drift demands for frame structures from the spectral displacement demand at the first mode period of the structure. The spectral displacement demand is related to the roof drift demand for the multi‐degree‐of‐freedom (MDOF) structure using three modification factors, accounting for MDOF effects, inelasticity effects, and P‐delta effects. Median values and measures of dispersion for the factors are obtained from elastic and inelastic time history analyses of nine steel moment resisting frame structures subjected to sets of ground motions representative of different hazard levels. The roof drift demand is related to the storey drift demands, with the results being strongly dependent on the number of stories and the ground motion characteristics. The relationships proposed in this paper should prove useful in the conceptual design phase, in estimating deformation demands for performance assessment, and in improving basic understanding of seismic behaviour. Copyright © 2000 John Wiley & Sons, Ltd.     

Yield frequency spectra and seismic design of code‐compatible RC structures: an illustrative example

The seismic design of an eight‐story reinforced concrete space frame building is undertaken using a yield frequency spectra (YFS) performance‐based approach. YFS offer a visual representation of the entire range of a system's performance in terms of the mean annual frequency (MAF) of exceeding arbitrary global ductility or displacement levels versus the base shear strength. As such, the YFS framework can establish the required base shear and corresponding first‐mode period to satisfy arbitrary performance objectives for any structure that may be approximated by a single‐degree‐of‐freedom system with given yield displacement and capacity curve shape. For the eight‐story case study building, deformation checking is the governing limit state. A conventional code‐based design was performed using seismic intensities tied to the desired MAF for safety checking. Then, the YFS‐based approach was employed to redesign the resulting structure working backwards from the desired MAF of response (rather than intensity) to estimate an appropriate value of seismic intensity for use within a typical engineering design process. For this high‐seismicity and high‐importance midrise building, a stiffer system with higher base shear strength was thus derived. Moreover, performance assessment via incremental dynamic analysis showed that while the code‐design did not meet the required performance objective, the YFS‐based redesign needed only pushover analysis results to offer a near‐optimal design outcome. The rapid convergence of the method in a single design/analysis iteration emphasized its efficiency and practicability as a design aid for practical application. Copyright © 2017 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.     

Optimized earthquake response of multi‐storey buildings with seismic isolation at various elevations

The response of multi‐storey structures can be controlled under earthquake actions by installing seismic isolators at various storey levels. By vertically distributing isolation devices at various elevations, the designer is provided with numerous options to appropriately adjust the seismic performance of a building. However, introducing seismic isolators at various storey levels is not a straightforward task, as it may lead to favourable or unfavourable structural behaviour depending on a large number of factors. As a consequence, a rather chaotic decision space of seismic isolation configurations arises, within which a favourable solution needs to be located. The search for favourable isolators' configurations is formulated in this work as a single‐objective optimization task. The aim of the optimization process is to minimize the maximum floor acceleration of the building under consideration, while constraints are specified to control the maximum interstorey drift, the maximum base displacement and the total seismic isolation cost. A genetic algorithm is implemented to perform this optimization task, which selectively introduces seismic isolators at various elevations, in order to identify the optimal configuration for the isolators satisfying the pre‐specified constraints. This way, optimized earthquake response of multi‐storey buildings can be obtained. The effectiveness of the proposed optimization procedure in the design of a seismically isolated structure is demonstrated in a numerical study using time‐history analyses of a typical six‐storey building. Copyright © 2012 John Wiley & Sons, Ltd.     

Comparative response assessment of minimally compliant low‐rise conventional and base‐isolated steel frames

In this study, the multi‐intensity seismic response of code‐designed conventional and base‐isolated steel frame buildings is evaluated using nonlinear response history analysis. The results of hazard and structural response analysis for three‐story braced‐frame buildings are presented in this paper. Three‐dimensional models for both buildings are created and seismic response is assessed for three scenario earthquakes. The response history analysis results indicate that the design objectives are met and the performance of the isolated building is superior to the conventional building in the design event. For the Maximum Considered Earthquake, isolation leads to reductions in story drifts and floor accelerations relative to the conventional building. However, the extremely high displacement demands of the isolation system could not be accommodated under normal circumstances, and creative approaches should be developed to control displacements in the MCE. Copyright © 2010 John Wiley & Sons, Ltd.     

Seismic reliability of steel moment resisting framed buildings retrofitted with buckling restrained braces

The present paper investigates the seismic reliability of the application of buckling restrained braces (BRBs) for seismic retrofitting of steel moment resisting framed buildings through fragility analysis. Samples of regular three‐storey and eight‐storey steel moment resisting frames were designed with lateral stiffness insufficient to comply with the code drift limitations imposed for steel moment resisting frame systems in earthquake‐prone regions. The frames were then retrofitted with concentrically chevron conventional braces and BRBs. To obtain robust estimators of the seismic reliability, a database including a wide range of natural earthquake ground motion records with markedly different characteristics was used in the fragility analysis. Nonlinear time history analyses were utilized to analyze the structures subjected to these earthquake records. The improvement of seismic reliability achieved through the use of conventional braces and BRBs was evaluated by comparing the fragility curves of the three‐storey and eight‐storey model frames before and after retrofits, considering the probabilities of four distinct damage states. Moreover, the feasibility of mitigating the seismic response of moment resisting steel structures by using conventional braces and BRBs was determined through seismic risk analysis. The results obtained indicate that both conventional braces and especially BRBs improve significantly the seismic behavior of the original building by increasing the median values of the structural fragility curves and reducing the probabilities of exceedance of each damage state. Copyright © 2011 John Wiley & Sons, Ltd.     

Interaction between cladding and structural frame observed in a full‐scale steel building test

Interaction between the external wall cladding and the seismic load resisting frame was examined in a full‐scale cyclic loading test of a three‐storey steel building structure. The building specimen had Autoclaved Lightweight Concrete (ALC, also designated as Autoclaved Aerated Concrete) panels installed and anchored to the structural frame as external wall cladding, using a standard Japanese method developed following the 1995 Kobe earthquake. ALC panelling is among the most widely used material for claddings in Japan. In the test, the ALC panel cladding contributed little to the stiffness and strength of the overall structure, even under a very large storey drift of 0.04 rad. No visible damage was noted in the ALC panels other than minor cracks and spalling of the bottom of the panels in the first storey. Consequently, in a Japanese steel building with properly installed ALC panel cladding, the structural frame is likely to be little affected by its cladding, and the ALC panels are capable of accommodating the maximum storey drift generally considered in structural design without sustaining discernible damage. Copyright © 2006 John Wiley & Sons, Ltd.     

钢框架结构的地震损伤研究

基于预定损伤法对钢框架构件主要设计参数进行损伤敏感度分析,研究主要设计参数与钢框架结构梁、柱损伤的关系;揭示钢框架结构梁、柱的损伤及梁、柱线刚度比、结构高宽比、柱轴压比、锈蚀率对楼层损伤的影响规律;获得楼层的损伤与整体结构损伤的关系,最终建立钢框架结构的损伤演化模型。研究成果可为建立地震激励下钢框架结构的损伤模型提供理论基础和数据支持。     

Seismic design methodology for friction damped braced frames

This paper is concerned with the design of steel frames using friction damped slotted bolted connections (SBCs) in the diagonal braces. A dynamic model is developed to describe the behaviour of a single‐degree‐of‐freedom (SDOF) steel frame that uses bilinear hysteretic behaviour for the damper. This model is generalized to MDOF systems. A novel algorithm for displacement reversal in the transition from slip to stick is presented. It uses numerical noise for its success. A design procedure that attains the stiffness of the individual braces and their elongation at the threshold of activation is then applied to a 10‐storey steel frame. This design process is a two‐phase iterative procedure that converges quite fast. Copyright © 2000 John Wiley & Sons, Ltd.     

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.     

多层钢结构基础隔震性能研究

本文用算例按基底剪力法,振型反应谱法和时程分析法分析了多层基础隔震钢结构和多层钢筋混凝土结构及其对应的非隔震结构的地震力和层间剪力。     

Experimental testing and numerical modelling of a heavy timber moment‐resisting frame with ductile steel links

This paper presents the development, experimental testing, and numerical modelling of a new hybrid timber‐steel moment‐resisting connection that is designed to improve the seismic performance of mid‐rise heavy timber moment‐resisting frames (MRF). The connection detail incorporates specially designed replaceable steel links fastened to timber beams and columns using self‐tapping screws. Performance of the connection is verified through experimental testing of four 2/3 scale beam‐column connections. All 4 connection specimens met the acceptance criteria specified in the AISC 341‐10 provisions for steel moment frames and exhibit high strength, ductility, and energy dissipation capacity up to storey drifts exceeding 4%. All of the timber members and self‐tapping screw connections achieved their design objective, remaining entirely elastic throughout all tests and avoiding brittle modes of failure. To assess the global seismic performance of the newly developed connection in a mid‐rise building, a hybrid timber‐steel building using the proposed moment‐resisting connection is designed and modelled in OpenSees. To compare the seismic performance of the hybrid MRF with a conventional steel MRF, a prototype steel‐only building is also designed and modelled in OpenSees. The building models are subject to a suite of ground motions at design basis earthquake and maximum credible earthquake hazard levels using non‐linear time history analysis. Analytical results show that drifts and accelerations of the hybrid building are similar to a conventional steel building while the foundation forces are significantly reduced for the hybrid structure because of its lower seismic weight. The results of the experimental program and numerical analysis demonstrate the seismic performance of the proposed connection and the ability of the hybrid building to achieve comparable seismic performance to a conventional steel MRF.     

Design of friction damped structures using lateral force procedure

A trilinear model is used to simulate the seismic resisting mechanism of a single‐degree‐of‐freedom friction‐damped system to reflect the situation in which both dampers and frame members lose their elastic resistance. The seismic response of the friction‐damped system is normalized with respect to the response of its corresponding linear system by an approach that incorporates a credible equivalent linearization method, a damping reduction rule and the algebraic specification of the design spectrum. The resulting closed‐form solutions obtained for the normalized response are then used to define a force modification factor for friction‐damped systems. This force modification factor, together with the condensation procedure for multi‐degree‐of‐freedom structures, enables the establishment of a quasi‐static design procedure for friction‐damped structures, which is intended for the benefit and use of structural practitioners. A curve‐fitting technique is employed to develop an explicit expression for the force modification factor used with the proposed design procedure; it is shown that this simplification results in satisfactory accuracy. Finally, a design example is given to illustrate the validation of the proposed design procedure. Copyright © 2000 John Wiley & Sons, Ltd.     

An assessment of IS codal provisions for the design of low rise steel moment frames through incremental dynamic analysis

The current Indian Standard (IS) code for seismic design of structures (IS 1893:2002) specifies the use of time history analysis for structures with height greater than 40m. However, for structures less than 40m it recommends the concept of equivalent static analysis. This study attempts to investigate the adequacy of the current design code when it comes to the actual evaluation of structures shorter than 40 m subjected to seismic loading using dynamic analysis as opposed to the code specified static analysis. Incremental dynamic analysis, which subjects a structure to a progressively increasing series of intensity measures, has been adopted here for the purpose. Three 2D moment resisting steel structures under the 1991 Uttarkashi and the 2001 Bhuj earthquakes (both of which predate the current IS1893) have been studied—a single storeyed portal frame, a 2 storey 3 bay frame and a 3 storey 2 bay frame. While it can be argued that two records are never enough for any generalization, and that only a full probabilistic analysis can determine if the limiting collapse prevention probability has been exceeded for these structures, the IS code in both cases does significantly under predict the seismic demands on the structures. At the same time, and perhaps why the codal provisions usually work, the structural capacities are in most cases underestimated as well. These suggest that a thorough study is in order and that there is scope for rationalization in the IS codal provisions.     

DUAL-LEVEL SEISMIC DESIGN: A RELIABILITY-BASED METHODOLOGY

The seismic design provisions of most building codes in the United States specify ground motion parameters for various regions of the country and provide simple formulae to determine a distribution of lateral forces for which the structure should be designed. Although the code provisions are very simple to use, they oversimplify a complex problem and are based on many implicit assumptions which many designers may not appreciate. Furthermore, the reliability of the final design is not easily determined. This paper describes a reliability-based seismic design procedure for building structures. It is a performance-based design procedure which requires the designer to verify that a particular structural design satisfies displacement-based performance criteria. An equivalent system methodology and uniform hazard spectra are used to evaluate structural performance. The performance criteria are expressed in probabilistic terms, and deterministic design-checking equations are derived from these criteria. The design-checking equations incorporate design factors (analogous to load and resistance factors) which account for the uncertainty in the seismic hazard, the uncertainty in predicting site soil effects, and the approximate nature of the simplified models of the structure. The alternative procedure should enable designers to achieve code-specified target performance objectives for moderate and severe levels of earthquake excitation.