Target Ductility Research Articles

Influence of the mean period of ground motion on the inelastic dynamic response of single and multi degree of freedom systems

AbstractThis paper focuses on examining the effects of frequency content of the ground motion on the inelastic demands imposed on both single degree of freedom (SDF) and multi degree of freedom (MDF) steel‐framed systems. A detailed literature review is conducted to identify the indicator that best represents the frequency content of ground motion. The mean period (Tm) of ground motion is selected owing to its ability to distinguish between various spectral shapes of ground motion, and its relationship with magnitude, distance and site characteristics. Inelastic displacement demands on SDF systems for target ductility levels are first studied in the light of Tm, using a suite of 128 ground motion records. The study is then extended to MDF systems with the help of incremental dynamic analysis by employing the same ground motion ensemble to assess the influence of Tm on various engineering demand parameters. The results obtained indicate that, for SDF systems, the amplification of displacements occurs when the period ratio between elastic period (Te) and Tm is lower than unity. For MDF systems, the results demonstrate that the influence of higher modes on the base shear and maximum storey drift profile becomes more pronounced, as Tm approaches the higher mode periods of the structure. These observations, for both SDF and MDF systems, tend to be more evident for higher levels of inelasticity. The significance of the results, with particular reference to European seismic design procedures, is highlighted. Copyright © 2010 John Wiley & Sons, Ltd.

교량의 구조특성에 따른 손상확률과 목표연성도 결정

현행의 내진설계의 성능목표는 인명피해를 최소화하기 위한 구조물의 붕괴방지에 있으며 기존구조물의 내진보강도 이를 만족하도록 수행되고 있다. 그러나, 최근의 해외 지진피해사례를 살펴보면 큰 지진에서도 이러한 내진성능목표는 비교적 잘 달성되었지만 엄청난 경제적 손실이 동반되어 새로운 문제점으로 제기되고 있다. 이러한 큰 경제적 손실을 줄이기 위해서는 현행 붕괴방지성능에서 벗어나 구조물의 손상을 제어할 수 있도록 손상확률에 기반하여 내진성능목표를 설정하는 새로운 내진설계개념이 필요하다. 본 연구에서는 다양한 구조적특성을 지닌 교량을 대상으로 하여 비선형지진해석을 수행하여 지진거동특성을 확인하고, 기준손상도에 대한 취약도곡선을 산정하였다. 이로부터 목표손상확률에 따른 교량구조물의 목표연성도의 특성을 분석하였다. The target performance of a current seismic design code is to achieve collapse-prevention in order to minimize casualties. Existing structures are also being retrofitted to meet this target performance. This seismic performance seems to have been achieved in recent great overseas earthquakes, but the accompanying enormous economic loss is pointed out as a new problem. A new seismic design concept over the current target performance is required to reduce economic loss, in which a target performance is determined by the damage probability in order to control the damage levels of structures. In this study, the seismic behavior of bridges having different characteristics was investigated by nonlinear seismic analyses, and fragility curves with respect to a reference damage level were derived. Based on these results, the characteristics of target ductilities satisfying a target damage probability were investigated.

Analytical Models and Guidelines for the Ductility Enhancement of Circular Reinforced Concrete Single-Column Bents Using Fiber-Reinforced Polymers

The target displacement ductility requirements for circular RC single-column bridge bents are considered using a proposed multifailure mode algorithm to determine the required thickness of fiber-reinforced polymer wraps FRPs. The procedure is developed using two in-house computer algorithms, PACCC plastic analysis of circular concrete columns and PACCC-FRP, to generate a moment- curvature analysis using circular segment slices and subsequent failure mode predictions in single-column bents for both FRP-wrapped and unwrapped circular RC sections. The results of the study showed good comparison to published experimental tests at the ultimate force-deflection states of RC sections and against three commercial software test beds. The study uses PACCC-FRP to show that single columns experiencing a brittle failure may be retrofitted with FRP wraps in order to increase the displacement ductility and satisfy target ductility values within the ductility wrap envelope, or wrap-saturation level, as established herein. DOI: 10.1061/ASCEBE.1943-5592.0000136 CE Database subject headings: Brittle failures; Failure modes; Concrete columns; Column beams; Fiber reinforced polymer; Lateral displacement; Ductility. Author keywords: Brittle failure; Failure modes; Concrete columns; Fiber-reinforced polymers; Lateral displacement; Ductility.

New Lateral Force Distribution for Seismic Design of Structures

In the conventional seismic design methods, heightwise distribution of equivalent seismic loads seems to be related implicitly on the elastic vibration modes. Therefore, the employment of such a load pattern does not guarantee the optimum use of materials in the nonlinear range of behavior. Here a method based on the concept of uniform distribution of deformation is implemented in optimization of the dynamic response of structures subjected to seismic excitation. In this approach, the structural properties are modified so that inefficient material is gradually shifted from strong to weak areas of a structure. It is shown that the seismic performance of such a structure is better than those designed conventionally. By conducting this algorithm on shear-building models with various dynamic characteristics, the effects of fundamental period, target ductility demand, number of stories, damping ratio, postyield behavior, and seismic excitations on optimum distribution pattern are investigated. Based on the results, a more adequate load pattern is proposed for seismic design of building structures that is a function of fundamental period of the structure and the target ductility demand.

Seismic vulnerability evaluation of axially loaded steel built-up laced members II: evaluations

The test results described in Part 1 of this paper (Lee and Bruneau, 2008) on twelve steel built-up laced members (BLMs) subjected to quasi-static loading are analyzed to provide better knowledge on their seismic behavior. Strength capacity of the BLM specimens is correlated with the strength predicted by the AISC LRFD Specifications. Assessments of hysteretic properties such as ductility capacity, energy dissipation capacity, and strength degradation after buckling of the specimen are performed. The compressive strength of BLMs is found to be relatively well predicted by the AISC LRFD Specifications. BLMs with smaller kl/r were ductile but failed to reach the target ductility of 3.0 before starting to fracture, while those with larger kl/r could meet the ductility demand in most cases. The normalized energy dissipation ratio, EC/ET and the normalized compressive strength degradation, Cr″/Cr of BLMs typically decrease as normalized displacements δ/δb,exp increase, and the ratios for specimens with larger kl/r dropped more rapidly than for specimens with smaller kl/r; similar trends were observed for the monolithic braces. The BLMs with a smaller slenderness ratio, kl/r, and width-to-thickness ratio, b/t, experienced a larger number of inelastic cycles than those with larger ratios.

Optimum strength distribution for seismic design of tall buildings

AbstractThis paper examines the effects of strength distribution pattern on seismic response of tall buildings. It is shown that in general for an MDOF structure there exists a specific pattern for height‐wise distribution of strength and stiffness that results in a better seismic performance in comparison with all other feasible patterns. This paper presents a new optimization technique for optimum seismic design of structures. In this approach, the structural properties are modified so that inefficient material is gradually shifted from strong to weak areas of a structure. This process is continued until a state of uniform deformation is achieved. It is shown that the seismic performance of such a structure is optimal, and behaves generally better than those designed by conventional methods. The optimization algorithm is then conducted on shear building models with various dynamic characteristics subjected to a group of severe earthquakes. Based on the results, a new load pattern is proposed for seismic design of tall buildings that is a function of fundamental period of the structure and the target ductility demand. The optimization method presented in this paper could be useful in the conceptual design phase and in improving basic understanding of seismic behavior of tall buildings. Copyright © 2007 John Wiley & Sons, Ltd.

エネルギー応答に基づいた地震を受ける鉄筋コンクリート建物におけるダンパーと変形制御機構の設計

In this study, a system combined of viscous damper and displacement controller with hardening type force-displacement relationship is proposed. By applying the proposed system to a multi-story structure, displacement controller device restricts the displacement of the all stories and uniform ductility distribution can be obtained, with no significant change in acceleration and inertia force values. Moreover, an energy-based damper design method, with the assumption of uniform ductility distribution, is proposed to determine the necessary viscous damping coefficient and the adequate gap of displacement controller. The results show that, seismic displacement response of the reinforced concrete multi-story structure is effectively reduced under the target ductility value, with the viscous damping coefficient that is obtained by the proposed method.

Experimental validation of seismic code provisions for RC columns

The aim of the experimental programme was to check the validity of the provisions of Eurocode 8 regarding the confining reinforcement of columns. 37 full-scale specimens were subjected to large cyclic displacements under constant axial load. Single rectangular hoops, even closely spaced, proved to be inadequate, as in most cases the target ductility was not reached. On the contrary, double or triple arrangement of hoops ensured satisfactory behaviour; they ensured acceptable force response degradation (lower than 20%), when the columns were subject to large displacement reversals (compatible with the target ductility).

Simple method to estimate the seismic nonlinear response of nonstructural components in buildings

An approximate method is proposed to estimate the seismic response of nonlinear nonstructural components attached to nonlinear building structures. The method is based on a previously developed procedure for the analysis of linear secondary systems mounted on a linear primary structure, the introduction of simplifying assumptions similar to those made in the derivation of the equivalent lateral force procedure for the seismic analysis of conventional buildings, and the use of strength reduction factors to account for the nonlinear behaviour of nonstructural components and supporting structure. Its application to any given nonstructural component only requires knowing the geometric characteristics, weights, and target ductilities of the nonstructural component and the structure to which it is connected, in addition to the fundamental natural period of the structure and the elastic response spectrum specified for the design of the structure. Presented also are a numerical example that illustrates the application of the method and the results of a comparative numerical study that is carried out to assess the method’s adequacy. Based on its simplicity and rationality and the results from the comparative study, it is concluded that the proposed method represents a simple but effective procedure for the seismic design of nonstructural components in buildings.

Energy-based seismic design of buckling-restrained braced frames using hysteretic energy spectrum

An energy-based seismic design procedure for framed structures with buckling-restrained braces is proposed using hysteretic energy spectra and accumulated ductility spectra. The procedure is based on the premise that the gravity load-resisting elements, such as beams and columns, are designed to remain elastic during earthquake, and all the seismic input energy is dissipated by the buckling-restrained braces. The proposed design procedure requires hysteretic energy spectra and accumulated ductility spectra corresponding to various target ductility ratios. The cross-sectional area of braces required to meet a given target displacement is obtained by equating the hysteretic energy demand to the accumulated plastic energy dissipated by braces. The design procedure was applied to three- and eight-story framed structures with buckling-restrained braces. Twenty earthquake records were utilized to construct the spectra and to verify the validity of the design procedure. According to analysis results, the mean values for the top story displacement correspond well with the given performance target displacements. Also, the inter-story drifts turned out to be relatively uniform over the structure height, which is desirable because uniform inter-story drifts indicate uniform damage distribution.

Toward more rational criteria for determination of design earthquake forces

The preliminary design of most buildings is based on equivalent static forces specified by the governing building code. The height wise distribution of these static forces seems to be based implicitly on the elastic vibration modes. Therefore, the employment of such a load pattern in seismic design of normal structures does not guarantee the optimum use of materials. This paper presents a new method for optimization of dynamic response of structures subjected to seismic excitation. This method is based on the concept of uniform distribution of deformation. In order to obtain the optimum distribution of structural properties, an iterative optimization procedure has been adopted. In this approach, the structural properties are modified so that inefficient material is gradually shifted from strong to weak areas of a structure. This process is continued until a state of uniform deformation is achieved. It is shown that the seismic performance of such a structure is optimal, and behaves generally better than those designed by conventional methods. By conducting this algorithm on shear-building models with various dynamic characteristics subjected to 20 earthquake ground motions, more adequate load patterns are introduced with respect to the period of the structure and the target ductility demand.

A Damage Model for Practical Seismic Design that Accounts for Low Cycle Fatigue

The structural properties of a structure deteriorate when deformations reach the range of inelastic behavior. A possible consequence of deterioration of the hysteretic behavior of a structure is failure of critical elements at deformation levels that are significantly smaller than its ultimate deformation capacity. Seismic design methodologies that account for low cycle fatigue can be formulated using the concept of target ductility. The practical use of one such methodology requires the consideration of simple low cycle fatigue models that consider the severity of repeated loading through a normalized plastic energy parameter. The inconsistencies inherent to the use of such indices can be corrected through simple empirical rules derived from an understanding of the effect of the history of energy dissipation in the assessment of the level of structural damage.

On the non‐iterative procedure of direct displacement‐based seismic design for portal R.C. bridges: Using inelastic design spectrum

In general, iterative procedures are required by the direct displacement‐based seismic design method. This paper presents a non‐iterative displacement‐based method for the design of portal R.C. bridges based on the inelastic design response spectrum. By combining the properties of structural stiffness and yielding, a rational, efficient and accurate method is established, where not only the strength and stiffness of members depend on the pre‐selected target displacement and ductility ratio, but the cross‐sections of those can also directly be determined form the two pre‐chosen values without any iteration. In addition to the examples that are used to illustrate the proposed procedure, the dynamic inelastic time history analysis and the static nonlinear analysis (pushover analysis) are also included to verify this procedure. It is concluded by the study that iterations are not needed in direct displacement‐based design if the force‐deformation relationships of designed structures can be derived.

Ground motion duration effects on nonlinear seismic response

The study presented in this paper addresses the question of which nonlinear demand measures are sensitive to ground motion duration by statistical analyses of several case studies. A number of single degree of freedom (SDOF) structures were selected considering: (1) four oscillation periods; (2) three evolutionary and non-evolutionary hysteretic behaviours; (3) two target ductility levels. Effects of duration are investigated, by nonlinear dynamic analysis, with respect to six different demand indices ranging from displacement ductility ratio to equivalent number of cycles. Input is made of six real accelerogram sets representing three specific duration scenarios (small, moderate and large duration). For all considered demand quantities time-history results are formally compared by statistical hypothesis test to asses the difference, if any, in the demand concerning different scenarios. Incremental dynamic analysis curves are used to evaluate duration effect as function of ground motion intensity (e.g. spectral acceleration corresponding to the SDOF's oscillation period). Duration impact on structural failure probability is evaluated by fragility curves. The results lead to the conclusion that duration content of ground motion is statistically insignificant to displacement ductility and cyclic ductility demand. The conclusions hold regardless of SDOF's period and hysteretic relationship investigated. Copyright © 2005 John Wiley & Sons, Ltd.

Optimum strength distribution for seismic resistant shear buildings

Structures with inappropriate distributions of strength and stiffness have performed poorly in recent earthquakes, and most of the observed collapses have been related to some extent to configuration problems or a wrong conceptual design. Shear building models of multi-story structures are considered in this study and are subjected to a group of severe earthquakes. It is shown that the strength distribution patterns suggested by the seismic codes do not lead to a uniform distribution and minimum amount of ductility, drift, and damage. A new pattern is proposed that is a function of the period of the structure and the target ductility. An iterative approach is also developed to determine the design strength (and stiffness) pattern needed to achieve a prescribed ductility (or drift) distribution according to different dynamic characteristics of the structure and earthquake. Utilizing this approach, a performance-based design methodology is introduced. This approach is shown to be efficient in finding the optimum strength and stiffness distribution patterns and can also be used to determine the optimum stiffness distribution within buildings with hysteretic dampers, and thus can be used to devise efficient retrofitting schemes using hysteretic dampers.

A Non-Iterative Direct Displacement-Based Design Procedure for SDOF Steel Columns: Using Substitute Structure

AbstractTraditionally, the yield displacement of a nonlinear structure was calculated by using the direct displacement-based seismic design method which usually requires a repeatedly iterative procedure no matter whether the substitute structure or inelastic design spectra has been adopted in the procedure. This will sometimes result in inefficiency if too many iterative cycles need to be produced in a design case for convergency. To avoid this disadvantage, this paper presents a non-iterative direct displacement-based design procedure for SDOF steel columns using the substitute structure approach. By combining the yielding property with the stiffness property of the designed steel columns, the procedure can immediately obtain the column's cross-section via the chosen target displacement and ductility ratio.

이력에너지 스펙트럼을 이용한 비좌굴 가새골조의 내진설계

본 연구에서는 단자유도계 시스템에서 작성한 이력에너지 스펙트럼과 누적된 변위 연성비 스펙트럼을 이용하여 비좌굴 가새골조의 내진설계법을 제안하였다. 먼저 목표 연성비에 해당하는 이력에너지 스펙트럼과 누적된 연성비 스펙트럼을 작성하였다. 주어진 목표 변위를 만족하기 위하여 필요한 가새의 단면적은 이력에너지 요구량과 가새에 의하여 소산된 누적 소성에너지를 같다고 하여 산정하였다. 스펙트럼을 작성하고 설계절차의 유효성을 검증하기 위하여 20개의 지진기록을 이용하였다. 제안된 방법에 따라 설계된 3층과 8층 비좌굴 가새골조의 해석결과에 따르면 최상층 변위의 평균값이 성능 목표 변위에 잘 부합됨을 알 수 있다. 또한 층간변위는 구조물 높이에 따라 비교적 일정하였는데 이것은 손상 분포가 일정하기 때문에 바람직하다. 그러므로 제안된 에너지 설계법은 기존 강도설계법의 대안으로 비좌굴 가새골조의 신뢰할만한 설계법이라고 할 수 있다. In this study seismic design procedure for buckling-restrained braced frame systems was proposed using hysteretic energy spectrum and accumulated ductility spectrum constructed from single degree of freedom systems. The hysteretic energy spectra and accumulated ductility spectra corresponding to target ductility ratio were constructed first. The cross-sectional area of braces required to meet a given target displacement was obtained by equating the hysteretic energy demand to the accumulated plastic energy dissipated by braces. Twenty earthquake records were utilized to construct the spectra and to verify the validity of the design procedure. According to analysis results of three- and eight-story buckling-restrained braced frame structures designed using the proposed method, the mean values for the top story displacement correspond well with the given performance target displacements. Also, the inter-story drifts turned out to be relatively uniform over the structure height, which is desirable because uniform inter-story drifts indicate uniform damage distribution. Therefore if was concluded that the proposed energy-based method could be a reliable alternative to conventional strength-based design procedure for structures with buckling-restrained braces.

Carbon-Fiber-Reinforced Polymer Seismic Retrofit of RC Bridge Bent: Design and In Situ Validation

Analysis and design procedures are presented for a carbon-fiber-reinforced polymer (CFRP) composite seismic retrofit of a reinforced concrete (RC) three-column bridge bent. The CFRP jacket was designed using performance-based criteria to provide a target displacement ductility based on seismic retrofit measures for the columns, bent cap, and bent cap-column joints. In situ quasi-static cyclic tests of a bent in the as-built condition and a bent retrofitted with the CFRP jacket were carried out in 1998. The seismic retrofit was successful, and the bridge bent retrofitted with CFRP composites reached a displacement ductility level in excess of the target ductility and double the hysteretic energy dissipation of the as-built bent. A description of the CFRP composite layout and validation of the design assumptions from the experimental results is presented. Recommendations for improvement of the original CFRP composite seismic retrofit design are offered based on the lessons learned from the in situ tests.

Simplified Restrainer Design Procedure for Multiple-Frame Bridges

The collapse of existing bridges due to unseating at supports and intermediate (in-span) hinges with inadequate seat-width can be prevented by the use of restrainers to limit the relative hinge opening. A new simplified procedure for the design of restrainers in bridges accounts for the dynamic characteristics and out-of-phase motion of adjacent frames as well as the inelastic behavior of the bridge. The simplified procedure is developed from an empirical relationship for the restrainer stiffness as a function of the frame stiffnesses, initial hinge displacement, target displacement, and target ductility of the structure. Parameter studies and case studies show that the simplified procedure limits the relative hinge displacement to a designer-specified value.

Near-Fault Ground Motion Effects on Simple Structures

Ground motion records obtained from sites at known locations relative to earthquake faults were used to study near-fault (NF) ground shaking effects on the inelastic response of simple structures. The structures were idealized as single-degree-of-freedom oscillators with periods ranging from 0.05 to 3.0 s, a damping ratio of 2%, and target ductilities of 2, 4, and 6. The severity of inelastic response was described by a relationship between the oscillator period, the target ductility, and the lateral force reduction factor obtained from analysis. It was found that the inelastic demands of medium and longer period oscillators responding to NF strike-normal shaking increased for sites close to the fault as the distance along the fault from the epicenter increased. The inelastic response of short-period oscillators was not affected as much by NF shaking. A methodology for obtaining average and design level demands for structures at specific locations relative to the epicenter and fault is described. A design...