Hybrid simulation testing of a self‐centering rocking steel braced frame system

The self‐centering rocking steel frame is a seismic force resisting system in which a gap is allowed to form between a concentrically braced steel frame and the foundation. Downward vertical force applied to the rocking frame by post‐tensioning acts to close the uplifting gap and thus produces a restoring force. A key feature of the system is replaceable energy‐dissipating devices that act as structural fuses by producing high initial system stiffness and then yielding to dissipate energy from the input loading and protect the remaining portions of the structure from damage. In this research, a series of large‐scale hybrid simulation tests were performed to investigate the seismic performance of the self‐centering rocking steel frame and in particular, the ability of the controlled rocking system to self‐center the entire building. The hybrid simulation experiments were conducted in conjunction with computational modules, one that simulated the destabilizing P‐Δ effect and another module that simulated the hysteretic behavior of the rest of the building including simple composite steel/concrete shear beam‐to‐column connections and partition walls. These tests complement a series of quasi‐static cyclic and dynamic shake table tests that have been conducted on this system in prior work. The hybrid simulation tests validated the expected seismic performance as the system was subjected to ground motions in excess of the maximum considered earthquake, produced virtually no residual drift after every ground motion, did not produce inelasticity in the steel frame or post‐tensioning, and concentrated the inelasticity in fuse elements that were easily replaced. Copyright © 2014 John Wiley & Sons, Ltd.     

Seismic behaviour of multistorey RC wall–frame system versus bare ductile frame system

The wall–frame systems have many known advantages, namely increase of the system's lateral strength and stiffness thereby allowing for a good tangential inter‐storey drift control, and the retention of a satisfactory energy dissipation capacity. However, rocking of the wall could occur as a result of uplifting wall base or concentrated plastic hinge deformations. Problems arising from this phenomenon have significant impact on the system behaviour and hence require extended study. This paper focuses on the wall‐rocking phenomenon due to the concentrated plastic hinge rotation at the wall base. To facilitate a comprehensive evaluation, a six‐storey three‐bay RC wall–frame structure is investigated with comparison to a bare ductile frame by means of earthquake simulation tests. The results revealed that, despite a superior performance over the ductile frame under low to moderate seismic actions, the wall–frame structure deteriorated more rapidly than the bare frame during advanced inelastic response. The increasingly significant rocking of the wall resulted in severe material damage at localized critical regions. Mitigating the wall rocking is seen to be a key to the further improvement of the system performance, and the extent to which this may be achieved by incorporating the three‐dimensional effects is explicitly illustrated by an analytical evaluation. Copyright © 2001 John Wiley & Sons, Ltd.     

Seismic performance of hybrid ductile‐rocking braced frame system

A new hybrid ductile‐rocking seismic‐resistant design is proposed which consists of a code‐designed buckling‐restrained braced frame (BRBF) that yields along its height and also partially rocks on its foundation. The goal of this system is to cost‐effectively improve the performance of BRBFs, by reducing drift concentrations and residual deformations, while taking advantage of their large ductility and their reliable limit on seismic forces and accelerations along a building's height. A lock‐up device ensures that the full code‐compliant lateral strength can be achieved after a limited amount of column uplift, and supplemental energy dissipation elements are used to reduce the rocking response. This paper outlines the mechanics of the system and then presents analyses on rocking frames with both ductile and elastic braces in order to highlight the large higher mode demands on elastic rocking frames. A parametric study using nonlinear time‐history analysis of BRBF structures designed according to the proposed procedure for Los Angeles, California is then presented. This study investigates the system's seismic response and the effect of different energy dissipation element properties and allowable base rotation values before the lock‐up is engaged. Finally, the effect of vertical mass modeling on analysis results was investigated. These studies demonstrated that the hybrid ductile‐rocking system can in fact improve the global peak and residual deformation response as well as reduce brace damage. This enhanced performance could eliminate the need for expensive repairs or demolition that are otherwise to be expected for conventional ductile fixed base buildings that sustain severe damage.     

Rolling and rocking of rigid uplifting structures

Allowing structures to uplift modifies their seismic response; uplifting works as a mechanical fuse and limits the forces transmitted to the superstructure. However, engineers are generally reluctant to construct an unanchored structure because the system could overturn due to lacking redundancy. Using a safety factor for the design of a flat rocking foundation, ie, designing it wider, goes against the main idea of this seismic modification method as the force demand for the structure increases. We propose to extend the flat base of a rocking block with curved extensions to better protect the block from overturning, yet not prevent its uplifting. After investigating the seismic response of such rocking blocks, we extend the study to investigate the seismic response of rolling and rocking frames comprising columns with curved base extensions. The equations of motion are derived, time history analyses are performed, and rocking spectra are constructed. We draw two important conclusions: (a) the response of a class of rocking oscillators with curved base extensions is equivalent to the response of a flat-base rocking oscillators of the same slenderness, yet larger size; (b) the rotation demand on two negative stiffness rocking and rolling oscillators with the same uplifting acceleration and the same size is roughly the same as long as the rocking oscillators are not close to overturning. The above findings can serve as a basis for the rational seismic design of structures supported on rocking columns with curved bases, a system that has been used since the 1960s.     

An evaluation of force-based design vs. direct displacement-based design of jointed precast post-tensioned wall systems

The unique features of jointed post-tensioned wall systems, which include minimum structural damage and re-centering capability when subjected to earthquake lateral loads, are the result of using unbonded post-tensioning to attach the walls to the foundation, along with employing energy dissipating shear connectors between the walls. Using acceptance criteria defined in terms of inter-story drift, residual drift, and floor acceleration, this study presents a multiplelevel performance-based seismic evaluation of two five-story unbonded post-tensioned jointed precast wall systems. The design and analysis of these two wall systems, established as the direct displacement-based and force-based solutions for a prototype building used in the PREcast Seismic Structural Systems （PRESSS） program, were performed at 60% scale so that the analysis model could be validated using the PRESSS test data. Both buildings satisfied the performance criteria at four levels of earthquake motions although the design base shear of the direct displacement-based jointed wall system was 50% of that demanded by the force-based design method. The study also investigated the feasibility of controlling the maximum transient inter-story drift in a jointed wall system by increasing the number of energy dissipating shear connectors between the walls but without significantly affecting its re-centering capability.     

Shake‐table test performance of an inertial force‐limiting floor anchorage system

A new floor connecting system developed for low‐damage seismic‐resistant building structures is described herein. The system, termed Inertial Force‐Limiting Floor Anchorage System (IFAS), is intended to limit the lateral forces in buildings during an earthquake. This objective is accomplished by providing limited‐strength deformable connections between the floor system and the primary elements of the lateral force‐resisting system. The connections transform the seismic demands from inertial forces into relative displacements between the floors and lateral force‐resisting system. This paper presents the IFAS performance in a shake‐table testing program that provides a direct comparison with an equivalent conventional rigidly anchored‐floor structure. The test structure is a half‐scale, 4‐story reinforced concrete flat‐plate shear wall structure. Precast hybrid rocking walls and special precast columns were used for test repeatability in a 22‐input strong ground‐motion sequence. The structure was purposely designed with an eccentric wall layout to examine the performance of the system in coupled translational‐torsional response. The test results indicated a seismic demand reduction in the lateral force‐resisting system of the IFAS structure relative to the conventional structure, including reduced shear wall base rotation, shear wall and column inter‐story drift, and, in some cases, floor accelerations. These results indicate the potential for the IFAS to minimize damage to the primary structural and non‐structural components during earthquakes.     

Seismic evaluation of rocking structures through performance assessment and fragility analysis

Numerical studies have been conducted for low- and medium-rise rocking structures to investigate their efficiency as earthquake-resisting systems in comparison with conventional structures. Several non-linear time-history analyses have been performed to evaluate seismic performance of selected cases at desired ground shaking levels, based on key parameters such as total and flexural story drifts and residual deformations. The Far-field record set is selected as input ground motions and median peak values of key parameters are taken as best estimates of system response. In addition, in order to evaluate the probability of exceeding relevant damage states, analytical fragility curves have been developed based on the results of the incremental dynamic analysis procedure. Small exceedance probabilities and acceptable margins against collapse, together with minor associated damages in main structural members, can be considered as superior seismic performance for medium-rise rocking systems. Low-rise rocking systems could provide significant performance improvement over their conventional counterparts notwithstanding certain weaknesses in their seismic response.     

Seismic retrofit of low‐rise steel buildings in Canada using rocking steel braced frames

This article examines the use of rocking steel braced frames for the retrofit of existing seismically deficient steel building structures. Rocking is also used to achieve superior seismic performance to reduce repair costs and disruption time after earthquakes. The study focuses on low‐rise buildings for which re‐centring is solely provided by gravity loads rather than added post‐tensioning elements. Friction energy dissipative (ED) devices are used to control drifts. The system is applied to 2‐storey and 3‐storey structures located in 2 seismically active regions of Canada. Firm ground and soft soil conditions are considered. The seismic performance of the retrofit scheme is evaluated using nonlinear dynamic analysis and ASCE 41‐13. For all structures, rocking permits to achieve immediate occupancy performance under 2% in 50 years seismic hazard if the braces and their connections at the building's top storeys are strengthened to resist amplified forces due to higher mode response. Base shears are also increased due to higher modes. Impact at column bases upon rocking induces magnified column forces and vertical response in the gravity system. Friction ED is found more effective for drift control than systems with ring springs or bars yielding in tension. Drifts are sufficiently small to achieve position retention performance for most nonstructural components. Horizontal accelerations are generally lower than predicted from ASCE 41 for regular nonrocking structures. Vertical accelerations in the gravity framing directly connected to the rocking frame are however higher than those predicted for ordinary structures. Vertical ground motions have limited effect on frame response.     

Seismic behaviour of steel plate shear wall systems with staggered web configurations

Unstiffened steel plate shear walls (SPSWs) are used as lateral load‐resisting systems in building structures. The energy dissipation mechanism of SPSWs consists of the tension yielding of web plates and the formation of plastic hinges at the ends of horizontal boundary elements. However, vertical boundary elements (VBEs) of high‐rise SPSWs may experience high axial forces under lateral loading. This study explores the effectiveness of staggering of web plates on the reduction of VBE forces and drift response of SPSWs during an earthquake event. An analytical study has been conducted to determine the base shear reduction factor so as to match the overstrength of staggered systems with conventional SPSWs. A design methodology has been proposed for staggered SPSWs. Six‐, 9‐, and 20‐storey staggered and conventional SPSWs with varying aspect ratios are considered in this study to compare their seismic response. These study frames are modelled and analysed in OpenSEES platform. Nonlinear static and dynamic analyses are performed to compare the drift response, hinge mechanisms, and steel tonnage. Staggered SPSWs showed uniform drift distribution and reduction in interstorey drift and axial force demand on the VBEs.     

Centrifuge modeling of rocking‐isolated inelastic RC bridge piers

Experimental proof is provided of an unconventional seismic design concept, which is based on deliberately underdesigning shallow foundations to promote intense rocking oscillations and thereby to dramatically improve the seismic resilience of structures. Termed rocking isolation, this new seismic design philosophy is investigated through a series of dynamic centrifuge experiments on properly scaled models of a modern reinforced concrete (RC) bridge pier. The experimental method reproduces the nonlinear and inelastic response of both the soil‐footing interface and the structure. To this end, a novel scale model RC (1:50 scale) that simulates reasonably well the elastic response and the failure of prototype RC elements is utilized, along with realistic representation of the soil behavior in a geotechnical centrifuge. A variety of seismic ground motions are considered as excitations. They result in consistent demonstrably beneficial performance of the rocking‐isolated pier in comparison with the one designed conventionally. Seismic demand is reduced in terms of both inertial load and deck drift. Furthermore, foundation uplifting has a self‐centering potential, whereas soil yielding is shown to provide a particularly effective energy dissipation mechanism, exhibiting significant resistance to cumulative damage. Thanks to such mechanisms, the rocking pier survived, with no signs of structural distress, a deleterious sequence of seismic motions that caused collapse of the conventionally designed pier. © 2014 The Authors Earthquake Engineering & Structural Dynamics Published by John Wiley & Sons Ltd.     

Seismic performance of a 3D full‐scale high‐ductile steel–concrete composite moment‐resisting frame—Part II: Test results and analytical validation

This paper presents the results of a multi‐level pseudo‐dynamic seismic test program that was performed to assess the performance of a full‐scale three‐bay, two‐storey steel–concrete composite moment‐resisting frame built with partially encased composite columns and partial‐strength beam‐to‐column joints. The system was designed to develop a ductile response in the joint components of beam‐to‐column joints including flexural yielding of beam end plates and shear yielding of the column web panel zone. The ground motion producing the damageability limit state interstorey drift caused minor damage while the ultimate limit state ground motion level entailed column web panel yielding, connection yielding and plastic hinging at the column base connections. The earthquake level chosen to approach the collapse limit state induced more damage and was accompanied by further column web panel yielding, connection yielding and inelastic phenomena at column base connections without local buckling. During the final quasi‐static cyclic test with stepwise increasing displacement–amplitudes up to an interstorey drift angle of 4.6%, the behaviour was ductile although cracking of beam‐to‐end‐plate welds was observed. Correlations with numerical simulations taking into account the inelastic cyclic response of beam‐to‐column and column base joints are also presented in the paper together. Inelastic static pushover and time history analysis procedures are used to estimate the structural behaviour and overstrength factors of the structural system under study. Copyright © 2008 John Wiley & Sons, Ltd.     

Seismic response of precast concrete walls

Large panel precast concrete structures are built in major seismic regions throughout the world. The seismic behaviour of such structures is strongly dependent upon the characteristics of both the horizontal and vertical connections. The limiting behaviour of precast systems, however, is basically dependent upon the horizontal connection. The influence of horizontal connections can be studied in terms of the behaviour of a simple wall—a vertical stack of panels having only horizontal connections. This paper reports on research into the seismic behaviour of simple precast concrete walls. The research was carried out through the development of computer-based modelling techniques capable of including the typical behavioural characteristics associated with horizontal joints. The model assumes that all non-linear, inelastic behaviour is concentrated in the connection regions and that the precast panels remain linear elastic. This assumption allows the precast panels to be modelled as statically condensed ‘super-elements’ and the connection regions as interface elements. The above modelling technique allows for non-linear-inelastic seismic analysis that is capable of handling both rocking type motions throughout the height of the structure and slippage due to shear in the plane of the connection. A series of parametric studies are presented to illustrate the potential influence of rocking and slip on precast walls with both regular reinforcement and post-tensioning. These studies demonstrate the period elongation associated with the nonlinear-elastic rocking phenomenon. Shear slip is found to occur only when friction coefficients are extremely low or when the normal forces across the connections are low. This latter case occurs only in low buildings or in the upper floors of tall buildings. The paper concludes with a brief discussion of the design implications of these results. Particular attention is paid to the problems stemming from the force concentrations associated with rocking and shear slip.     

Mechanisms to limit higher mode effects in a controlled rocking steel frame. 1: Concept,modelling, and low‐amplitude shake table testing

Controlled rocking steel frames have been proposed as an efficient way to avoid the structural damage and residual deformations that are expected in conventional seismic force resisting systems. Although the base rocking response is intended to limit the force demands, higher mode effects can amplify member design forces, reducing the viability of the system. This paper suggests that seismic forces may be limited more effectively by providing multiple force‐limiting mechanisms. Two techniques are proposed: detailing one or more rocking joints above the base rocking joint and providing a self‐centring energy dissipative (SCED) brace at one or more levels. These concepts are applied to the design of an eight‐storey prototype structure and a shake table model at 30% scale. A simple numerical model that was used as a design tool is in good agreement with frequency characterization and low‐amplitude seismic tests of the shake table model, particularly when multiple force‐limiting mechanisms are active. These results suggest that the proposed mechanisms can enable better capacity design by reducing the variability of peak seismic force demands without causing excessive displacements. Similar results are expected for other systems that rely on a single location of concentrated nonlinearity to limit peak seismic loads. Copyright © 2012 John Wiley & Sons, Ltd.     

Ductile steel plate external end diaphragms for steel tub girder straight highway bridges

The end diaphragm of bridges are normally designed to resist lateral seismic forces imposed on the superstructure in earthquake prone regions. Using ductile diaphragms with high deformation capacity could reduce the seismic demands on the substructure and prevent costly damage under strong ground motions. The end diaphragms of steel tub girder bridges with high lateral stiffness and dominant shear behavior have a potential to be used as ductile fuse elements. In this study, a steel plate shear diaphragm(SPSD) is introduced as an external end diaphragm of tub girder steel bridges to reduce the seismic demands imposed on the substructure. Quasi static nonlinear analyses were conducted to evaluate responses of sixteen SPSDs with different boundary conditions, aspect ratios and diaphragm plate thicknesses. Moreover, nonlinear time history analyses were performed using three different ground motions corresponding to DBE and MCE level spectrums. Cyclic and time history analyses proved the proper behavior of SPSD and its efficiency to reduce seismic demands by more than 25%.     

不对称大底板多塔楼隔震结构的地震响应分析

针对不对称大底板多塔楼隔震结构体系,通过建立地震响应的动力分析简化模型,推导出不对称大底板多塔楼隔震结构体系地震作用下的运动方程。对一实际的不对称大底板多塔楼隔震结构进行地震响应仿真分析,探讨塔楼质量偏心率和塔楼质量比对结构周期比、位移比和层剪力比的影响。结果显示,不对称大底板多塔楼隔震结构扭转角主要由隔震层产生;与不隔震结构相比,不对称大底板多塔楼隔震体系的扭转角减小,可取得较好的减震效果;塔楼与底板的位置分布和质量分布会影响体系的扭转效应和减震效果,应尽量使塔楼的质心与底板质心重合,塔楼质量分布均匀,以减小结构的扭转效应,提高减震效果。     

Rocking response of SDOF systems on shallow improved sand: An experimental study

Recent studies have highlighted the potential advantages of allowing inelastic foundation response during strong seismic shaking. Such an alternative seismic design philosophy, in which soil failure is used as a “fuse” for the superstructure has recently been proposed, in the form of “rocking isolation”. Within this context, foundation rocking may be desirable as a means of bounding the inertia forces transmitted onto the superstructure, but incorporates the peril of unacceptable settlements in case of a low static factor of safety FS_v. Hence, to ensure that rocking is materialized through uplifting rather than sinking, an adequately large FS_v is required. Although this is feasible in theory, soil properties are not always well-known in engineering practice. However, since rocking-induced soil yielding is only mobilized within a shallow layer underneath the footing, “shallow soil improvement” is considered as an alternative approach to release the design from the jeopardy of unforeseen inadequate FS_v. For this purpose, this paper studies the rocking response of relatively slender SDOF structures (h/B ratio equals 3 and rocking dominates over sliding), with emphasis on the effectiveness of shallow soil improvement stretching to various depths below the foundation. A series of reduced-scale monotonic and slow-cyclic pushover tests are conducted on SDOF systems lying on a square surface foundation. It is shown that shallow soil improvement may, indeed, be quite effective provided that its depth is equal to the width of the foundation. For lightly-loaded systems, an even shallower soil improvement may also be considered effective, depending on design requirements. The effectiveness of shallow soil improvement is ameliorated with the increase of cyclic rotation amplitude, and with repeating cycles of loading.     

Single precast concrete rocking walls as earthquake force‐resisting elements

Precast concrete walls with unbonded post‐tensioning provide a simple self‐centering system. Yet, its application in seismic regions is not permitted as it is assumed to have no energy dissipation through a hysteretic mechanism. These walls, however, dissipate energy imparted to them because of the wall impacting the foundation during rocking and limited hysteretic action resulting from concrete nonlinearity. The energy dissipated due to rocking was ignored in previous experimental studies because they were conducted primarily using quasi‐static loading. Relying only on limited energy dissipation, a shake table study was conducted on four single rocking walls (SRWs) using multiple‐level earthquake input motions. All walls generally performed satisfactorily up to the design‐level earthquakes when their performance was assessed in terms of the maximum transient drift, maximum absolute acceleration, and residual drift. However, for the maximum considered earthquakes, the walls experienced peak lateral drifts greater than the permissible limits. Combining the experimental results with an analytical investigation, it is shown that SRWs can be designed as earthquake force‐resisting elements to produce satisfactory performance under design‐level and higher‐intensity earthquake motions. Copyright © 2016 John Wiley & Sons, Ltd.     

双防线可恢复性能斜交网格结构耗能机制和抗震性能研究

为提高斜交网格结构的抗震性能,提出一种双防线可恢复性能斜交网格结构。双防线可恢复性能斜交网格结构采用剪切耗能段和特定梁端塑形铰进行集中耗能,使主体结构构件保持弹性。剪切耗能段不承受和传递重力荷载,易在震后修复或更换,使建筑可迅速恢复功能。为实现目标耗能机制,对等效能量塑形设计法进行改进以适用于可恢复性能斜交网格结构,并进行结构设计举例。采用OpenSees软件对所设计结构建立详细的有限元计算模型,进行非线性动力时程分析,以验证双防线耗能机制并评估抗震性能。分析结果表明:（1）小震、中震和大震下的结构顶部位移角分别为0.28%、0.8%和1.7%,与性能设计目标基本相同;（2）中震时剪切耗能段屈服,特定梁端未出现塑性铰;（3）大震时,特定梁端出现塑性铰以增加结构耗能能力,剪切耗能段屈服且处于延性范围内。因此新型可恢复性能斜交网格结构具有有效的双防线耗能机制,在中震后可迅速修复,在大震中可保持延性,实现"中震可修,大震不倒"的性能目标。     

Shake-table testing of a self-centering precast reinforced concrete frame with shear walls

The seismic performance of a self-centering precast reinforced concrete (RC) frame with shear walls was investigated in this paper. The lateral force resistance was provided by self-centering precast RC shear walls (SPCW), which utilize a combination of unbonded prestressed post-tensioned (PT) tendons and mild steel reinforcing bars for flexural resistance across base joints. The structures concentrated deformations at the bottom joints and the unbonded PT tendons provided the self-centering restoring force. A 1/3-scale model of a five-story self-centering RC frame with shear walls was designed and tested on a shake-table under a series of bi-directional earthquake excitations with increasing intensity. The acceleration response, roof displacement, inter-story drifts, residual drifts, shear force ratios, hysteresis curves, and local behaviour of the test specimen were analysed and evaluated. The results demonstrated that seismic performance of the test specimen was satisfactory in the plane of the shear wall; however, the structure sustained inter-story drift levels up to 2.45%. Negligible residual drifts were recorded after all applied earthquake excitations. Based on the shake-table test results, it is feasible to apply and popularize a self-centering precast RC frame with shear walls as a structural system in seismic regions.     

The seismic shear of ductile cantilever wall systems in multistorey structures

The distribution of seismic base shear demand among ductile flexural cantilever walls, comprising the lateral load resisting system of a multistorey building, is studied. It is shown that the base shear force demand depends on the sequence of hinge formation at the wall bases, and this in turn depends on the relative wall lengths. Hence, the routine elastic approach in which the shear forces are allocated per relative flexural rigidity or (when some consideration is given to plastic hinge formation) to moment capacity at the wall base, may appreciably underestimate the shear force demand on the walls, particularly the shorter (usually the more flexible) ones. A simple procedure yielding the results of ‘cyclic’ pushover analysis is proposed to predict the peak seismic wall forces for a given total base shear when plastification is confined to the wall base. The effects of plastic hinges developing at higher floors on (1) shear distribution among the walls and (2) the in‐plane floor forces are also considered. Two numerical examples are presented to demonstrate the main points made. Copyright © 2004 John Wiley & Sons, Ltd.