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.     

Determination of the seismic performance factors for post‐tensioned rocking timber wall systems

Post‐tensioned technologies for concrete seismic resistant buildings were first developed in the 1990s during the PREcast Seismic Structural Systems program. Among different solutions, the hybrid system proved to be the most resilient solution providing a combination of re‐centering and energy dissipative contributions respectively by using post‐tensioned tendons and mild steel reinforcement. The system, while providing significant strength and energy dissipation, reduces structural element damage and limits post‐earthquake residual displacements. More recently, the technology was extended to laminated veneer lumber (LVL) structural members, and extensive experimental and numerical work was carried out and allowed the development of reliable analytical and numerical models as well as design guidelines. On the basis of the experimental and numerical outcomes, this paper presents the evaluation of the seismic performance factors for post‐tensioned rocking LVL walls using the FEMA P‐695 procedure. Several archetype buildings were designed considering different parameters such as the building and story height, the type of seismic resistant system, the magnitude of gravity loads and the seismic design category. Lumped plasticity models were developed for each index archetype to simulate the behavioral aspects and collapse mechanisms. Non‐linear quasi‐static analyses were carried out to evaluate the system over‐strength factor; moreover, non‐linear time history analyses were performed using the incremental dynamic analysis concept to assess the collapse of each building. From the results of quasi‐static and dynamic analyses the response modification factor, R, system over‐strength factor, Ω₀, and deflection amplification factor, C_d, values of, respectively, 7, 3.5 and 7.5 are recommended. Copyright © 2016 John Wiley & Sons, Ltd.     

Seismic design and shake table tests of a steel post‐tensioned self‐centering moment frame with a slab accommodating frame expansion

Post‐tensioned (PT) self‐centering moment frames were developed as an alternative to welded moment‐resisting frames (MRFs). Lateral deformation of a PT frame opens gaps between beams and columns. The use of a composite slab in welded MRFs limits the opening of gaps at the beam‐to‐column interfaces but cannot be adopted in PT self‐centering frames. In this study, a sliding slab is used to minimize restraints to the expansion of the PT frame. A composite slab is rigidly connected to the beams in a single bay of the PT frame. A sliding device is installed between the floor beams and the beams in other bays, wherever the slab is allowed to slide. Many shaking table tests were conducted on a reduced‐scale, two‐by‐two bay one‐story specimen, which comprised one PT frame and two gravitational frames (GFs). The PT frame and GFs were self‐centering throughout the tests, responding in phase with only minor differences in peak drifts that were caused by the expansion of the PT frame. When the specimen was excited by the 1999 Chi‐Chi earthquake with a peak ground acceleration of 1.87g, the maximum interstory drift was 7.2% and the maximum lateral force was 270 kN, equal to 2.2 times the yield force of the specimen. Buckling of the beam bottom flange was observed near the column face, and the initial post‐tensioning force in the columns and beams decreased by 50 and 22%, respectively. However, the specimen remained self‐centering and its residual drift was 0.01%. Copyright © 2011 John Wiley & Sons, Ltd.     

Performance‐based earthquake engineering assessment of a self‐centering,post‐tensioned concrete bridge system

Highway bridges in highly seismic regions can sustain considerable residual displacements in their columns following large earthquakes. These residual displacements are an important measure of post‐earthquake functionality, and often determine whether or not a bridge remains usable following an earthquake. In this study, a self‐centering system is considered that makes use of unbonded, post‐tensioned steel tendons to provide a restoring force to bridge columns to mitigate the problem of residual displacements. To evaluate the proposed system, a code‐conforming, case‐study bridge structure is analyzed both with conventional reinforced concrete columns and with self‐centering, post‐tensioned columns using a formalized performance‐based earthquake engineering (PBEE) framework. The PBEE analysis allows for a quantitative comparison of the relative performance of the two systems in terms of engineering parameters such as peak drift ratio as well as more readily understood metrics such as expected repair costs and downtime. The self‐centering column system is found to undergo similar peak displacements to the conventional system, but sustains lower residual displacements under large earthquakes, resulting in similar expected repair costs but significantly lower expected downtimes. Copyright © 2010 John Wiley & Sons, Ltd.     

Seismic demand sensitivity of reinforced concrete shear‐wall building using FOSM method

The uncertainty in the seismic demand of a structure (referred to as the engineering demand parameter, EDP) needs to be properly characterized in performance‐based earthquake engineering. Uncertainties in the ground motion and in structural properties are responsible for EDP uncertainty. In this study, sensitivity of EDPs to major uncertain variables is investigated using the first‐order second‐moment method for a case study building. This method is shown to be simple and efficient for estimating the sensitivity of seismic demand. The EDP uncertainty induced by each uncertain variable is used to determine which variables are most significant. Results show that the uncertainties in ground motion are more significant for global EDPs, namely peak roof acceleration and displacement, and maximum inter‐storey drift ratio, than those in structural properties. Uncertainty in the intensity measure (IM) of ground motion is the dominant variable for uncertainties in local EDPs such as the curvature demand at critical cross‐sections. Conditional sensitivity of global and local EDPs given IM is also estimated. It is observed that the combined effect of uncertainties in structural properties is more significant than uncertainty in ground motion profile at lower IM levels, while the opposite is true at higher IM levels. Copyright © 2005 John Wiley & Sons, Ltd.     

Evaluating performance of post‐tensioned steel connections with strands and reduced flange plates

The seismic performance of post‐tensioned steel connections for moment‐resisting frames was examined experimentally and analytically. Cyclic tests were conducted on three full‐scale subassemblies, which had two steel beams post‐tensioned to a concrete‐filled tube (CFT) column with high‐strength strands to provide recentring response. Reduced flange plates (RFPs) welded to the column and bolted to the beam flange were used to increase the dissipation of energy. Test results indicated that (1) the proposed buckling‐restrained RFP could dissipate energy in axial tension and compression, (2) the subassemblies could reach an interstorey drift of 4% without strength degradation, and (3) buckling of the beam occurred towards an interstorey drift of 5%, causing a loss of the strand force, the recentring response, and the moment capacity. A general‐purpose non‐linear finite element analysis program (ABAQUS) was used to perform a correlation study. The behaviour of the steel beam under both post‐tensioning and flexural loadings was compared to the test results and predictions. Copyright © 2006 John Wiley & Sons, Ltd.     

Hysteretic model development and seismic response of unbonded post‐tensioned precast CFT segmental bridge columns

The study investigated the cyclic behavior of unbonded, post‐tensioned, precast concrete‐filled tube segmental bridge columns by loading each specimen twice. Moreover, a stiffness‐degrading flag‐shaped (SDFS) hysteretic model was developed based on self‐centering and stiffness‐degrading behaviors. The proposed model overcomes the deficiency of cyclic behavior prediction using a FS model, which self‐centers with fixed elastic and inelastic stiffnesses. Experimental and analytical results showed that (1) deformation capabilities of the column under the first and second cyclic tests were similar; however, energy dissipation capacities significantly differed from each other, and (2) the SDFS model predicted the cyclic response of the column better than the FS model. Inelastic time‐history analyses were performed to demonstrate the dynamic response variability of a single‐degree‐of‐freedom (SDOF) system using both models. A parametric study, performed on SDOF systems subjected to eight historical earthquakes, showed that increased displacement ductility demand was significant for structures with a low period and low‐to‐medium yield strength ratio and reduced displacement ductility demand in these systems was effectively attained by increasing energy dissipation capacity. Copyright © 2008 John Wiley & Sons, Ltd.     

Biaxial testing of unbonded post‐tensioned rocking bridge piers with external replacable dissipaters

The biaxial response of two bridge piers is experimentally investigated. A post‐tensioned precast bridge pier with external replaceable mild‐steel dissipaters is tested under biaxial loading. The performance of the post‐tensioned bridge pier is compared with a conventionally reinforced monolithic bridge pier. The experimental biaxial response is then compared with previous uniaxial experimental testing of identical bridge piers to understand the influence of biaxial loading, specifically concerning post‐tensioned rocking sections. A 3‐dimensional moment–curvature and moment–rotation analysis program is created to generate the monotonic section response of a conventional and post‐tensioned bridge pier. After comparing the accuracy of the section analysis program to the experimental testing of the monolithic pier, the program is validated against the experimental testing of the post‐tensioned bridge pier. This section analysis program is then used in the calibration of a macro‐model to capture the entire cyclic response of the post‐tensioned bridge pier. The macro‐model adopts multiple linear‐elastic compression‐only springs at the rocking interface, combined with non‐linear inelastic springs for each of the mild‐steel dissipaters and returns encouraging results at both local and global levels. The paper concludes with a number of biaxial moment‐interaction design charts for monolithic and post‐tensioned bridge piers as a function of mechanical and geometric section properties. The design charts define the biaxial yield surface at nominal yield and at the design section capacity defined by one of three material limit states. Copyright © 2011 John Wiley & Sons, Ltd.     

Near‐collapse response of existing RC building under severe pulse‐type ground motion using hybrid simulation

Column shear‐axial failure is a complex response, which lends itself to physical experimentation. Reinforced concrete structures built prior to the mid‐1970s are particularly susceptible to such failure. Shear‐axial column failure has been examined and studied at the element level, but current rehabilitation practice equates such a column failure with structural collapse, neglecting the collapse resistance of the full structural system following column failure. This system‐level response can prevent a column failure from leading to progressive collapse of the entire structure. In this study, a hybrid simulation was conducted on a representative pre‐1970s reinforced concrete frame structure under severe seismic ground motion, in which three full‐scale reinforced concrete columns were tested at the University of Illinois at Urbana Champaign. The analytical portion of the model was represented in the computer program OpenSees. Failure occurred in multiple physical specimens as a result of the ground motion, and the hybrid nature of the test allowed for observation of the system‐level response of the tested columns and the remaining structural system. The behavior of the system accounting for multiple column shear‐axial failure is discussed and characterized. Copyright © 2016 John Wiley & Sons, Ltd.     

Three‐dimensional beam–truss model for reinforced concrete walls and slabs – part 2: modeling approach and validation for slabs and coupled walls

A three‐dimensional beam–truss model (BTM) for reinforced concrete (RC) walls that explicitly models flexure–shear interaction and accurately captures diagonal shear failures was presented in the first part of this two‐paper series. This paper extends the BTM to simulate RC slabs and coupled RC walls through slabs and beams. The inclination angle of the diagonal elements for coupled RC walls is determined, accounting for the geometry of the walls and the level of coupling. Two case studies validate the model: (1) a two‐bay slab–column specimen experimentally tested using cyclic static loading and (2) a five‐story coupled T‐wall–beam–slab specimen subjected to biaxial shake table excitation. The numerically computed lateral force–lateral displacement and strain contours are compared with the experimentally measured response and observed damage. The five‐story specimen is characterized by diagonal shear failure at the bottom story of the walls, which is captured by the BTM. The BTM of the five‐story specimen is used to study the effects of coupling on shear demand for lightly reinforced RC coupled walls. The effect of mesh refinement and bar fracture of non‐ductile transverse reinforcement is studied. Copyright © 2016 John Wiley & Sons, Ltd.     

Quasi‐static and pseudo‐dynamic testing of unbonded post‐tensioned rocking bridge piers with external replaceable dissipaters

It has been well documented that following a major earthquake a substantial percentage of economic loss results from downtime of essential lifelines in and out of major urban centres. This has thus led to an improvement of both performance‐based seismic design philosophies and to the development of cost‐effective seismic structural systems capable of guaranteeing a high level of protection, low structural damage and reduced downtime after a design‐level seismic event. An example of such technology is the development of unbonded post‐tensioned techniques in combination with rocking–dissipating connections. In this contribution, further advances in the development of high‐performance seismic‐resistant bridge piers are achieved through the experimental validation of unbonded post‐tensioned bridge piers with external, fully replaceable, mild steel hysteretic dissipaters. The experimental response of three 1 : 3 scale unbonded, post‐tensioned cantilever bridge piers, subjected to quasi‐static and pseudo‐dynamic loading protocols, are presented and compared with an equivalently reinforced monolithic benchmark. Minimal physical damage is observed for the post‐tensioned systems, which exhibit very stable energy dissipation and re‐centring properties. Furthermore, the external dissipaters can be easily replaced if severely damaged under a major (higher than expected) earthquake event. Thus, negligible residual deformations, limited repair costs and downtime can be achieved for critical lifeline components. Satisfactory analytical–experimental comparisons are also presented as a further confirmation of the reliability of the design procedure and of the modelling techniques. Copyright © 2008 John Wiley & Sons, Ltd.     

Seismic performance assessment of a hybrid coupled wall system with replaceable steel coupling beams versus traditional RC coupling beams

This study assesses the seismic performance of a hybrid coupled wall (HCW) system with replaceable steel coupling beams (RSCBs) at four intensities of ground motion shaking. The performance of the HCW system is benchmarked against the traditional reinforced concrete coupled wall (RCW). Nonlinear numerical models are developed in OpenSees for a representative wall elevation in a prototype 11‐story building designed per modern Chinese codes. Performance is assessed via nonlinear dynamic analysis. The results indicate that both systems can adequately meet code defined objectives in terms of global and component behavior. Behavior of the two systems is consistent under service level earthquakes, whereas under more extreme events, the HCW system illustrates enhanced performance over the RCW system resulting in peak interstory drifts up to 31% lower in the HCW than the RCW. Larger drifts in the RCW are because of reduced coupling action induced by stiffness degradation of RC coupling beams, whereas the stable hysteretic responses and overstrength of RSCBs benefit post‐yield behavior of the HCW. Under extreme events, the maximum beam rotations of the RSCBs are up to 42% smaller than those of the RC coupling beams. Moderate to severe damage is expected in the RC coupling beams, whereas the RSCBs sustain damage to the slab above the beam and possible web buckling of shear links. The assessment illustrates the benefits of the HCW with RSCBs over the RCW system, because of easy replacement of the shear links as opposed to costly and time‐consuming repairs of RC coupling beams. Copyright © 2016 John Wiley & Sons, Ltd.     

Dual‐plastic hinge design concept for reducing higher‐mode effects on high‐rise cantilever wall buildings

This paper explores the notion of detailing reinforced concrete structural walls to develop base and mid‐height plastic hinges to better control the seismic response of tall cantilever wall buildings to strong shaking. This concept, termed here dual‐plastic hinge (DPH) concept, is used to reduce the effects of higher modes of response in high‐rise buildings. Higher modes can significantly increase the flexural demands in tall cantilever wall buildings. Lumped‐mass Euler–Bernoulli cantilevers are used to model the case‐study buildings examined in this paper. Buildings with 10, 20 and 40 stories are designed according to three different approaches: ACI‐318, Eurocode 8 and the proposed DPH concept. The buildings are designed and subjected to three‐specific historical strong near‐fault ground motions. The investigation clearly shows the dual‐hinge design concept is effective at reducing the effects of the second mode of response. An advantage of the concept is that, when combined with capacity design, it can result in relaxation of special reinforcing detailing in large portions of the walls. Copyright © 2009 John Wiley & Sons, Ltd.     

SRC-RC竖向混合结构过渡层抗震设计方法探讨

首先介绍了SRC-RC竖向混合结构的受力特点和性能优势;并针对我国和日本的相关规程及工程应用实践,结合日本阪神地震中SRC-RC竖向混合结构的主要震害特点,指出国内外SRC-RC竖向混合结构过渡层抗震设计方法所存在的主要问题及不足。在综合分析阪神地震后日本关于SRC-RC竖向混合结构过渡层抗震设计方法的最新研究进展的基础上,提出了SRC-RC竖向混合结构过渡层抗震设计的设计思路和方法,可为SRC-RC竖向混合结构过渡层抗震设计提供参考。     

Seismic response of structures with coupled vertical stiffness–strength irregularities

Several seismic design codes around the world restrict the use of theit Equivalent Lateral Force analysis method to structures satisfying structural regularity limits. These regularity limits are based on engineering judgement and lack quantitative justification. One common irregularity is that of a change in vertical stiffness over the building height. This stiffness irregularity is almost always associated with a change in vertical strength over the building height. For this reason, the effect of various realistic combinations of stiffness–strength irregularity in shear‐type buildings is evaluated to quantify regularity limits. Structures analysed had 3, 5, 9 and 15 storeys, and the floor mass at all the levels were kept the same. Both regular and irregular structures were designed in accordance with the Equivalent Lateral Force procedure to produce the same engineering demand parameter. Structural ductility factors of 1, 2, 3, 4 and 6, and target (design) interstorey drift ratios ranging between 0.5 and 3%, were used in this study. The irregular structures were created by modifying specific storey lateral stiffnesses from that of the regular structure. Strengths at these storeys were also modified to ensure realistic relationships between stiffness and strength. The modified structures were then redesigned until the target interstorey drift ratio was achieved at the critical storey. Inelastic dynamic time‐history analysis was conducted to compare the maximum interstorey drift ratio demands of the regular and irregular structures. Simple equations were developed to estimate possible variations in demand due to vertical stiffness–strength irregularity applied at critical locations in structures. Copyright © 2011 John Wiley & Sons, Ltd.     

Three‐dimensional beam‐truss model for reinforced concrete walls and slabs – part 1: modeling approach,validation, and parametric study for individual reinforced concrete walls

A three‐dimensional beam‐truss model for reinforced concrete (RC) walls developed by the first two authors in a previous study is modified to better represent the flexure–shear interaction and more accurately capture diagonal shear failures under static cyclic or dynamic loading. The modifications pertain to the element formulations and the determination of the inclination angle of the diagonal elements. The modified beam‐truss model is validated using the experimental test data of eight RC walls subjected to static cyclic loading, including two non‐planar RC walls under multiaxial cyclic loading. Five of the walls considered experienced diagonal shear failure after reaching their flexural strength, while the other three walls had a flexure‐dominated response. The numerically computed lateral force–lateral displacement and strain contours are compared with the experimentally recorded response and damage patterns for the walls. The effects of different model parameters on the computed results are examined by means of parametric analyses. Extension of the model to simulate RC slabs and coupled RC walls is presented in a companion paper. Copyright © 2016 John Wiley & Sons, Ltd.     

Numerical models and ductile ultimate deformation response of post‐tensioned self‐centering moment connections

New steel moment‐resisting connections that incorporate post‐tensioning elements to provide a self‐centering capacity and devices to dissipate seismic input energy have recently been proposed and experimentally validated. Experimental studies have confirmed that these connections are capable of undergoing large lateral deformations with negligible residual drifts. To facilitate their implementation, accurate modeling of the behavior of systems incorporating post‐tensioned connections must be readily available to designers and researchers. A number of simplified models have been suggested in the literature by researchers trying to capture experimental results at the beam–column connections and thereby to predict the global response of structures incorporating such connections. To provide a clear set of guidelines for the modeling of post‐tensioned steel frames, for practicing engineers as well as researchers, in this paper three types of numerical models of increasing complexity are presented: (i) a sectional analysis procedure, (ii) a lumped plasticity spring frame leveled approach and (iii) a non‐linear solid finite element analysis to predict the response at ultimate deformation levels. The analytical results obtained from the numerical models predict well the structural behavior of these connections when compared with available experimental data. Even at the ultimate deformation level, analytical results are in good agreement with test results. Furthermore, detailing requirements are proposed to assure that flexural hinges form in the beams in order to improve the cyclic response of steel self‐centering connections when drifts exceeding the design drifts are imposed to the system. Experimental and analytical studies demonstrate that steel post‐tensioned self‐centering connections incorporating the proposed detailing in the beams develop an increased deformation capacity and thereby exhibit a ductile response while avoiding a sudden loss of their strength and stiffness. Copyright © 2008 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.     

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.     

Methodology for preliminary seismic design of extended pile‐shafts for bridge structures

Seismic design of extended pile‐shafts requires a careful consideration of the influence of the surrounding soil on the overall response of the soil–pile system. In this paper, a procedure that incorporates soil properties into the process is developed for preliminary seismic design of extended pile‐shafts. The method follows the well‐accepted approach of using a force reduction factor to determine the lateral strength of the structure. The procedure involves an iterative process to arrive at the required amount of longitudinal reinforcement. Other outcomes of the procedure include the appropriate lateral stiffness and strength, as well as an estimation of the local curvature demand and ultimate drift ratio that can be used to ensure a satisfactory lateral response. The design procedure is capable of providing reliable results for a practical range of structural and soil properties. The versatility of the procedure is illustrated using two numerical examples of extended pile‐shafts constructed in different soil sites. Copyright © 2006 John Wiley & Sons, Ltd.