Seismic design procedure and seismic response of post‐tensioned self‐centering steel frames

Post‐tensioned (PT) self‐centering moment‐resisting frames (MRFs) have recently been developed as an alternative to welded moment frames. The first generation of these systems incorporated yielding energy dissipation mechanisms, whereas more recently, PT self‐centering friction damped (SCFR) moment‐resistant connections have been proposed and experimentally validated. Although all of these systems exhibited good stiffness, strength and ductility properties and stable dissipation of energy under cyclic loading, questions concerning their ultimate response still remained and a complete design methodology to allow engineers to conceive structures using these systems was also needed. In this paper, the mechanics of SCFR frames are first described and a comprehensive design procedure that accounts for the frame behavior and the nonlinear dynamics of self‐centering frames is then elaborated. A strategy for the response of these systems at ultimate deformation stages is then proposed and detailing requirements on the beams in order to achieve this response are outlined. The proposed procedure aims to achieve designs where the interstory drifts for SCFR frames are similar to those of special steel welded moment‐resisting frames (WMRFs). Furthermore, this procedure is adapted from current seismic design practices and can be extended to any other PT self‐centering steel frame system. A six‐story building incorporating WMRFs was designed and a similar building incorporating SCFR frames were re‐designed by the proposed seismic design procedure. Time‐history analyses showed that the maximum interstory drifts and maximum floor accelerations of the SCFR frame were similar to those of the WMRF but that almost zero residual drifts were observed for the SCFR frame. The results obtained from the analyses confirmed the validity of the proposed seismic design procedure, since the peak drift values were similar to those prescribed by the seismic design codes and the SCFR frames achieved the intended performance level under both design and maximum considerable levels of seismic loading. Copyright © 2008 John Wiley & Sons, Ltd.     

Merging energy‐based design criteria and reliability‐based methods: exploring a new concept

This paper examines the potential development of a probabilistic design methodology, considering hysteretic energy demand, within the framework of performance‐based seismic design of buildings. This article does not propose specific energy‐based criteria for design guidelines, but explores how such criteria can be treated from a probabilistic design perspective. Uniform hazard spectra for normalized hysteretic energy are constructed to characterize seismic demand at a specific site. These spectra, in combination with an equivalent systems methodology, are used to estimate hysteretic energy demand on real building structures. A design checking equation for a (hypothetical) probabilistic energy‐based performance criterion is developed by accounting for the randomness of the earthquake phenomenon, the uncertainties associated with the equivalent system analysis technique, and with the site soil factor. The developed design checking equation itself is deterministic, and requires no probabilistic analysis for use. The application of the proposed equation is demonstrated by applying it to a trial design of a three‐storey steel moment frame. The design checking equation represents a first step toward the development of a performance‐based seismic design procedure based on energy criterion, and additional works needed to fully implement this are discussed in brief at the end of the paper. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

Rocking damage‐free steel column base with friction devices: design procedure and numerical evaluation

Earthquake‐resilient steel frames, such as self‐centering frames or frames with passive energy dissipation devices, have been extensively studied during the past decade, but little attention has been paid to their column bases. The paper presents a rocking damage‐free steel column base, which uses post‐tensioned high‐strength steel bars to control rocking behavior and friction devices to dissipate seismic energy. Contrary to conventional steel column bases, the rocking column base exhibits monotonic and cyclic moment–rotation behaviors that are easily described using simple analytical equations. Analytical equations are provided for different cases including structural limit states that involve yielding or loss of post‐tensioning in the post‐tensioned bars. A step‐by‐step design procedure is presented, which ensures damage‐free behavior, self‐centering capability, and adequate energy dissipation capacity for a predefined target rotation. A 3D nonlinear finite element (FE) model of the column base is developed in abaqus . The results of the FE simulations validate the accuracy of the moment–rotation analytical equations and demonstrate the efficiency of the design procedure. Moreover, a simplified model for the column base is developed in OpenSees . Comparisons among the OpenSees and abaqus models demonstrate the efficiency of the former and its adequacy to be used in nonlinear dynamic analysis. A prototype steel building is designed as a self‐centering moment‐resisting frame with conventional or rocking column bases. Nonlinear dynamic analyses show that the rocking column base fully protects the first story columns from yielding and eliminates the first story residual drift without any detrimental effect on peak interstory drifts. The study focuses on the 2D rocking motion and, thus, ignores 3D rocking effects such as biaxial bending deformations in the friction devices. The FE models, the analytical equations, and the design procedure will be updated and validated to cover 3D rocking motion effects after forthcoming experimental tests on the column base. Copyright © 2017 John Wiley & Sons, Ltd.     

Steel frames with bracing mechanism and hysteretic dampers

A new earthquake resistant structural system for multi‐storey frame structures, based on a dual function of its bracing components, is developed. This consists of a hysteretic damper device and a cross‐bracing mechanism with a kinetic closed circuit, working only in tension, so that cable members can be used for this purpose. Solutions are presented regarding the connections' design of three types of structural frame system, that are concerned throughout the study: braced moment free frame, braced moment resisting frame with moment free supports, and with moment resisting supports. The dynamic behaviour of the system is investigated on the basis of an SDOF model, and based on the response spectra method an approximate design approach of the controlled structures is shown. From the time history analysis of the structural systems for the El Centro earthquake the areas of appropriate stiffness relations of the frames to the hysteretic dampers and the cable braces are deduced, so that the energy dissipation of the system may be controlled by the damper‐cable bracing mechanism. Based on the results of these studies, a predesign approach is developed for the implementation of the control system in frame structures. Copyright © 2003 John Wiley & Sons, Ltd.     

Estimation of hysteretic energy demand using concepts of modal pushover analysis

Hysteretic energy dissipation in a structure during an earthquake is the key factor, besides maximum displacement, related to the amount of damage in it. This energy demand can be accurately computed only through a nonlinear time‐history analysis of the structure subjected to a specific earthquake ground acceleration. However, for multi‐story structures, which are usually modeled as multi‐degree of freedom (MDOF) systems, this analysis becomes computation intensive and time consuming and is not suitable for adopting in seismic design guidelines. An alternative method of estimating hysteretic energy demand on MDOF systems is presented here. The proposed method uses multiple ‘generalized’ or ‘equivalent’ single degree of freedom (ESDOF) systems to estimate hysteretic energy demand on an MDOF system within the context of a ‘modal pushover analysis’. This is a modified version of a previous procedure using a single ESDOF system. Efficiency of the proposed procedure is tested by comparing energy demands based on this method with results from nonlinear dynamic analyses of MDOF systems, as well as estimates based on the previous method, for several ground motion scenarios. Three steel moment frame structures, of 3‐, 9‐, and 20‐story configurations, are selected for this comparison. Bias statistics that show the effectiveness of the proposed method are presented. In addition to being less demanding on the computation time and complexity, the proposed method is also suitable for adopting in design guidelines, as it can use response spectra for hysteretic energy demand estimation. Copyright © 2008 John Wiley & Sons, Ltd.     

Displacement-based seismic design of hysteretic damped braces for retrofitting in-plan irregular r.c. framed structures

A displacement-based design procedure is proposed for proportioning hysteretic damped braces in order to attain, for the in-plan least seismic capacity direction and a specific level of seismic intensity, a designated performance level of a reinforced concrete (r.c.) irregular framed building to be retrofitted. To this end, a computer code for the nonlinear static analysis of spatial frames is developed to obtain the pushover curve for an assigned in-plan direction of the seismic loads. The town hall of Spilinga (Italy), a two-storey r.c. framed structure with an L-shaped plan built at the beginning of the 1960s, has been considered as case study. Four alternative structural solutions are examined, derived from the first one by the insertion of hysteretic damped braces, considering: the extended N2 and the extended pushover methods combined with a proportional and an inversely proportional in-plan stiffness distributions of hysteretic damped braces. To check the effectiveness and reliability of the design procedure, the nonlinear static response of the unbraced and damped braced frames is compared for different in-plan directions of the seismic loads. Frame members are simulated with a lumped plasticity model, including a flat surface modeling of the axial load-biaxial bending moment elastic domain, while the behavior of a hysteretic damped brace is idealized through the use of a bilinear law. Vulnerability index domains are adopted to estimate the directions of least seismic capacity at the ultimate (i.e. life-safety and collapse prevention) limit states prescribed by Italian and European seismic codes.     

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.     

新型低损伤自复位混凝土框架节点试验及性能优化研究

提出一种带可更换软钢阻尼器的低损伤自复预制混凝土(LDSCPC)框架节点,并针对该节点在地震作用下的抗震性能、更换阻尼器后的性能恢复等开展足尺试件的拟静力试验。在节点试验基础上,基于ABAQUS精细化有限元模型进行该节点关于螺栓预紧力、水平和竖向耗能条尺寸的参数化分析及优化设计。研究表明,软钢阻尼器LT12的滞回特性和承载能力是最优异的,而LT14是耗能最好的;增加阻尼器耗能条的尺寸和厚度能分别提高LDSCPC框架节点在加载早期和变形较大时的耗能性能。较大的螺栓预紧力能明显提升LDSCPC框架节点的耗能能力,当预紧力为155 kN时,软钢阻尼器几乎达到理想的耗能性能。     

Experimental–numerical investigation on the seismic behaviour of moment‐resisting timber frames with densified veneer wood‐reinforced timber joints and expanded tube fasteners

This paper investigates the seismic behaviour of moment‐resisting timber frames with beam‐column joints fastened with expanded tubes and reinforced with densified veneer wood. Laboratory experiments are carried out on single joints to investigate the cyclic behaviour and, more specifically, the impairment of strength, the ductility ratio and the equivalent viscous damping ratio. A phenomenological numerical model is proposed, where the beams and columns are schematized using linear‐elastic beam elements, and the joints with non‐linear hysteretic spring calibrated on the results of the experimental tests. The model is used to analyse some representative moment‐transmitting structures characterised by different number of bays and storeys. After an estimation of the lateral load‐carrying capacity using a pushover analysis, the numerical model is used to estimate the behaviour factor. An incremental dynamic analysis is performed using a set of accelerograms spectrum consistent with a chosen design spectrum. The analyses lead to an estimation of the behaviour factor of 3 and 6 for a portal frame and a five‐storey, three‐bay frame, respectively, which confirms the highly dissipative behaviour of this kind of moment connection. Copyright © 2017 John Wiley & Sons, Ltd.     

低周反复荷载下两跨两层轻钢框架抗震性能试验研究

本文通过两跨两层轻钢框架试件的低周反复加载试验,研究了轻钢框架结构在地震作用下的滞回性能、耗能机制、耗能能力、刚度退化和破坏形态,结果显示轻钢框架具有很好的抗震性能,节点域耗能能力强。论文结论可为多层轻钢框架的抗震设计提供依据。     

Inclusion of P–Δ effect in displacement‐based seismic design of steel moment resisting frames

A procedure for treating the P– Δ effect in the direct displacement‐based seismic design of regular steel moment resisting frames with ideal elastoplastic material behaviour is proposed. A simple formula for the yield displacement amplification factor as a function of ductility and the stability coefficient is derived on the basis of the seismic response of an inelastic single degree‐of‐freedom system taking into account the P– Δ effect. Extensive parametric seismic inelastic analyses of plane moment resisting steel frames result in a simple formula for the dynamic stability coefficient as a function of the number of stories of a frame and the column to beam stiffness ratio. Thus, the P– Δ effect can be easily taken into account in a direct displacement‐based seismic design through the stability coefficient and the yield displacement amplification factor. A simple design example serves to illustrate the application of the proposed method and demonstrate its merits. Copyright © 2007 John Wiley & Sons, Ltd.     

基于OpenSees的防屈曲支撑加固钢筋混凝土框架数值模拟

提出了一种既有钢筋混凝土框架结构的抗震加固方法,该法采用防屈曲支撑提高框架结构体系的水平承载力和耗能能力,利用外包钢进一步提高柱子的抗弯和抗剪承载力。采用开源有限元程序OpenSees,分别建立空钢筋混凝土框架和防屈曲支撑加固钢筋混凝土框架的分析模型,对2榀钢筋混凝土框架的抗震性能进行模拟。防屈曲支撑采用了弹塑性桁架单元模型,加固框架柱混凝土考虑了外包钢的约束作用。将分析结果与拟静力试验结果进行比较,以检验分析模型的准确性,以及研究防屈曲支撑和外包钢对混凝土框架抗震性能的影响。分析结果表明,数值模拟与试验结果吻合较好,验证了基于OpenSees建立的数值模型的准确性;外包钢有效改善了框架柱的抗弯承载力和变形能力;防屈曲支撑显著提高了加固框架体系的水平刚度、水平承载力和耗能能力。     

Optimal seismic design of moment‐resisting steel frames with hysteretic passive devices

The effectiveness of hysteretic passive devices to protect and mitigate the response of a structure under seismic loading is well established by both analytical and experimental research. Nevertheless, a systematic and well‐established methodology for the topological distribution and size of these devices in order to achieve a desired structural response performance does not exist. In this paper, a computational framework is proposed for the optimal distribution and design of yielding metallic buckling restrained braces (BRB) and/or friction dampers within steel moment‐resisting frames (MRF) for a given seismic environment. A Genetic Algorithm (GA) is used to solve the resulting discrete optimization problem. Specific examples involving two three‐story, four‐bay steel MRFs and a six‐story, three‐bay steel MRF retrofitted with yielding and/or friction braces are considered. The seismic environment consists of four synthetic ground motions representative of the west coast of the United States with 5% probability of exceedance in 50 years. Non‐linear time‐history analyses are employed to evaluate the potential designs. As a result of the evolutionary process, the optimal placement, strength and size of the dampers are obtained throughout the height of the steel MRF. Furthermore, the developed computational approach for seismic design based upon GAs provides an attractive procedure for design of MRFs with hysteretic passive dampers. Copyright © 2009 John Wiley & Sons, Ltd.     

半刚性连接钢框架抗震性能的模型试验研究

通过两榀1／2比例的一跨两层半刚性连接钢框架模型的低周反复荷载试验,研究了框架模型的破坏机制、、出饺顺序、滞回特性、耗能能力等抗震性能。从而得出结论：具有腹板双角钢的顶底角钢连接的钢框架由于节点连接刚度较小,因此框架在侧向力作用下变形较大,但同时此连接也改善了梁柱的内力分布,提高了框架的耗能能力,增加了结构抗震性能。     

Probabilistic seismic performance evaluation of SMA-braced steel frames considering SMA brace failure

This study explores seismic performance of steel frame buildings with SMA-based self-centering bracing systems using a probabilistic approach. The self-centering bracing system described in this study relies on superelastic response of large-diameter cables. The bracing systems is designed such that the SMA cables are always stressed in tension. A four-story steel frame building characterized until collapse in previous research is selected as a case-study building. The selected steel frame building is designed with SMA bracing systems considering various design parameters for SMA braces. Numerical models of these buildings are developed by taking into account the ultimate state of structural components and SMA braces as well as the effect of gravity frames on lateral load resistance. Nonlinear static analyses are conducted to assess the seismic characteristics of each frame and to examine the effect of SMA brace failure on the seismic load carrying capacity of SMA-braced frames. Incremental dynamic analyses (IDA) are performed to compute seismic response of the designed frames at various seismic intensity levels. The results of IDA are used to develop probabilistic seismic demand models for peak inter-story and residual inter-story drifts. Seismic demand hazard curves of peak and residual inter-story drifts are generated by convolving the ground motion hazard with the probabilistic seismic demand models. Results show that steel frames designed with SMA bracing systems provide considerably lower probability of reaching at a damage state level associated with residual drifts compared to a similarly designed steel moment resisting frame, especially for seismic events with high return periods. This indicates reduced risks for the demolition and collapse due to excessive residual drifts for SMA braced steel frames.     

基于OpenSees的RCS组合框架结构抗震性能模拟分析

选取已有钢筋混凝土柱—钢梁组合结构（RCS）框架的低周期反复试验数据,采用地震工程开源模拟软件OpenSees对其进行有限元模拟,对比骨架曲线与滞回曲线,试验结果与有限元结果吻合较好。随后考察弯矩放大系数（Mc/Mb=0.86、1.48、2.04）、柱轴压比（n=0.06、0.2、0.3、0.6、0.8）对抗震性能的影响,得到了各参数下框架的滞回曲线、骨架曲线和各特征阶段的荷载与位移值。分析了框架的破化过程、延性与强度退化。结果表明：RCS组合框架滞回曲线饱满,具有良好的变形及耗能能力;随着弯矩放大系数的减小、柱轴压比的增大,框架的水平极限承载力降低、屈服状态提前、位移延性降低。分析结果可供有关研究或工程应用参考。     

Seismic performance and damage evaluation of a reinforced concrete frame with hysteretic dampers through shake‐table tests

Passive energy dissipation devices are increasingly implemented in frame structures to improve their performance under seismic loading. Most guidelines for designing this type of system retain the requirements applicable to frames without dampers, and this hinders taking full advantage of the benefits of implementing dampers. Further, assessing the extent of damage suffered by the frame and by the dampers for different levels of seismic hazard is of paramount importance in the framework of performance‐based design. This paper presents an experimental investigation whose objectives are to provide empirical data on the response of reinforced concrete (RC) frames equipped with hysteretic dampers (dynamic response and damage) and to evaluate the need for the frame to form a strong column‐weak beam mechanism and dissipate large amounts of plastic strain energy. To this end, shake‐table tests were conducted on a 2/5‐scale RC frame with hysteretic dampers. The frame was designed only for gravitational loads. The dampers provided lateral strength and stiffness, respectively, three and 12 times greater than those of the frame. The test structure was subjected to a sequence of seismic simulations that represented different levels of seismic hazard. The RC frame showed a performance level of ‘immediate occupancy’, with maximum rotation demands below 20% of the ultimate capacity. The dampers dissipated most of the energy input by the earthquake. It is shown that combining hysteretic dampers with flexible reinforced concrete frames leads to structures with improved seismic performance and that requirements of conventional RC frames (without dampers) can be relieved. Copyright © 2014 John Wiley & Sons, Ltd.     

Research on the seismic retrofitting performance of RC frames using SC-PBSPC BRBF substructures

A new type of external substructure to upgrade existing reinforced concrete frames (RCFs) is presented in this paper, namely, a self-centering precast bolt-connected steel-plate reinforced concrete buckling-restrained brace frame (SC-PBSPC BRBF). The upgrade mechanism and three-dimensional simulation model were analyzed based on relevant experiment validations. A quasistatic analysis and parameter study was conducted using 21 scenarios to compare the upgrading effects of the outside substructure. Afterwards, a stiffness-based design procedure was developed and modified for this external substructure, including macro-demand analysis, partial component design, and overall structural evaluations. Dynamic analyses were also performed on a frame building for five cases, before and after strengthening. The proposed numerical model reflected the precast characteristics and displayed the ideal fitting accuracy. The external assembled brace provided sufficient initial stiffness and energy dissipation capacity, while the external prestressed tendon decreased residual displacements and facilitated self-centering of the whole structure. The analyses illustrated that the damage to the existing RCF was transferred and seismic demands were significantly reduced within limitations, accompanied with greater capacity reliability. This research provides a reference for the practical applications of the external upgrading substructures in earthquake-prone areas.     

Seismic behaviour of self‐centring braced frame buildings with reusable hysteretic damping brace

This paper presents the seismic behaviour of a concentrically braced frame system with self‐centring capability, in which a special type of bracing element termed reusable hysteretic damping brace (RHDB) is used. The RHDB is a passive energy dissipation device with its core energy‐dissipating component made of superelastic Nitinol wires. Compared with conventional bracing in steel structures, RHDB has a few prominent performance characteristics: damage free under frequent and design basis earthquakes in earthquake prone areas; minimal residual drifts due to the self‐centring capability of RHDB frame; and ability to survive several strong earthquakes without the need for repair or replacement. This paper also includes a brief discussion of the RHDB's mechanical configuration and analytical model for RHDB. The seismic performance study of RHDB frame was carried out through a non‐linear time history analysis of 3‐storey and 6‐storey RHDB frame buildings subjected to two suites of 20 earthquake ground motions. The analysis results were compared with buckling‐restrained brace (BRB) frames. This study shows that RHDB frame has a potential to outperform BRB frames by eliminating the residual drift problem. Copyright © 2007 John Wiley & Sons, Ltd.