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1.
The seismic response of non‐ductile reinforced concrete (RC) buildings can be affected by the behaviour of beam‐column joints involved in the failure mechanism, especially in typical existing buildings. Conventional modelling approaches consider only beam and column flexibility, although joints can provide a significant contribution also to the overall frame deformability. In this study, the attention is focused on exterior joints without transverse reinforcement, and a possible approach to their modelling in nonlinear seismic analysis of RC frames is proposed. First, experimental tests performed by the authors are briefly presented, and their results are discussed. Second, these tests, together with other tests with similar features from literature, are employed to calibrate the joint panel deformability contribution in order to reproduce numerically the experimental joint shear stress–strain behaviour under cyclic loading. After a validation phase of this proposal, a numerical investigation of the influence of joints on the seismic behaviour of a case study RC frame – designed for gravity loads only – is performed. The preliminary failure mode classification of the joints within the analysed frame is carried out. Structural models that (i) explicitly include nonlinear behaviour of beam‐column joints exhibiting shear or anchorage failure or (ii) model joints as elements with infinite strength and stiffness are built and their seismic performance are assessed and compared. A probabilistic assessment based on nonlinear dynamic simulations is performed by means of a scaling approach to evaluate the seismic response at different damage states accounting for uncertainties in ground‐motion records. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

2.
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.  相似文献   

3.
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.  相似文献   

4.
Given their excellent self‐centering and energy‐dissipating capabilities, superelastic shape memory alloys (SMAs) become an emerging structural material in the field of earthquake engineering. This paper presents experimental and numerical studies on a scaled self‐centering steel frame with novel SMA braces (SMAB), which utilize superelastic Ni–Ti wires. The braces were fabricated and cyclically characterized before their installation in a two‐story one‐bay steel frame. The equivalent viscous damping ratio and ‘post‐yield’ stiffness ratio of the tested braces are around 5% and 0.15, respectively. In particular, the frame was seismically designed with nearly all pin connections, including the pinned column bases. To assess the seismic performance of the SMA braced frame (SMABF), a series of shake table tests were conducted, in which the SMABF was subjected to ground motions with incremental seismic intensity levels. No repair or replacement of structural members was performed during the entire series of tests. Experimental results showed that the SMAB could withstand several strong earthquakes with very limited capacity degradation. Thanks to the self‐centering capacity and pin‐connection design, the steel frame was subjected to limited damage and zero residual deformation even if the peak interstory drift ratio exceeded 2%. Good agreement was found between the experimental results and numerical simulations. The current study validates the prospect of using SMAB as a standalone seismic‐resisting component in critical building structures when high seismic performance or earthquake resilience is desirable under moderate and strong earthquakes. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

5.
A refined component model is proposed to predict the inelastic monotonic response of exterior and interior beam‐to‐column joints for partial‐strength composite steel–concrete moment‐resisting frames. The joint typology is designed to exhibit ductile seismic response through plastic deformation developing simultaneously in the column web panel in shear, the bolted end‐plate connection, the column flanges in bending and the steel reinforcing bars in tension. The model can handle the large inelastic deformations consistent with high ductility moment‐resisting frames. Slip response between the concrete slab and the beams was taken into account. A fibre representation was adopted for the concrete slab to accurately capture the non‐uniform stress distribution and progressive crushing of the concrete at the interface between the concrete slab and the column flange. The model is validated against results from full‐scale subassemblages monotonic physical tests performed at the University of Pisa, Italy. A parametric study is presented to illustrate the capabilities of the model and the behaviour of the joints examined. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

6.
Performance‐based engineering (PBE) methodologies allow for the design of more reliable earthquake‐resistant structures. Nonetheless, to implement PBE techniques, accurate finite element models of critical components are needed. With these objectives in mind, initially, we describe an experimental study on the seismic behaviour of both beam‐to‐column (BTC) and column‐base (CB) joints made of high‐strength steel S590 circular columns filled with concrete. These joints belonged to moment‐resisting frames (MRFs) that constituted the lateral‐force‐resisting system of an office building. BTC joints were conceived as rigid and of partial strength, whereas CB joints were designed as rigid and of full strength. Tests on a BTC joint composed of an S275 steel composite beam and high‐strength steel concrete‐filled tubes were carried out. Moreover, two seismic CB joints were tested with stiffeners welded to the base plate and anchor bolts embedded in the concrete foundation as well as where part of a column was embedded in the foundation with no stiffeners. A test programme was carried out with the aim of characterising these joints under monotonic, cyclic and random loads. Experimental results are presented by means of both force–interstory drift ratio and moment–rotation relationships. The outcomes demonstrated the adequacy of these joints to be used for MRFs of medium ductility class located in zones of moderate seismic hazard. Then, a numerical calibration of the whole joint subassemblies was successfully accomplished. Finally, non‐linear time‐history analyses performed on 2D MRFs provided useful information on the seismic behaviour of relevant MRFs. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

7.
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.  相似文献   

8.
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.  相似文献   

9.
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.  相似文献   

10.
The feasibility and efficiency of a seismic retrofit solution for existing reinforced concrete frame systems, designed before the introduction of modern seismic‐oriented design codes in the mid 1970s, is conceptually presented and experimentally investigated. A diagonal metallic haunch system is introduced at the beam–column connections to protect the joint panel zone from extensive damage and brittle shear mechanisms, while inverting the hierarchy of strength within the beam–column subassemblies and forming a plastic hinge in the beam. A complete step‐by‐step design procedure is suggested for the proposed retrofit strategy to achieve the desired reversal of strength hierarchy. Analytical formulations of the internal force flow at the beam–column‐joint level are derived for the retrofitted joints. The study is particularly focused on exterior beam–column joints, since it is recognized that they are the most vulnerable, due to their lack of a reliable joint shear transfer mechanism. Results from an experimental program carried out to validate the concept and the design procedure are also presented. The program consisted of quasi‐static cyclic tests on four exterior, ? scaled, beam–column joint subassemblies, typical of pre‐1970 construction practice using plain round bars with end‐hooks, with limited joint transverse reinforcement and detailed without capacity design considerations. The first (control specimen) emulated the as‐built connection while the three others incorporated the proposed retrofitted configurations. The experimental results demonstrated the effectiveness of the proposed solution for upgrading non‐seismically designed RC frames and also confirmed the applicability of the proposed design procedure and of the analytical derivations. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

11.
Recent research developed and experimentally validated a self‐centering buckling‐restrained brace (SC‐BRB) that employs a restoring mechanism created using concentric tubes held flush with pretensioned shape memory alloy rods, in conjunction with a buckling‐restrained brace (BRB) that dissipates seismic energy. The present computational study investigated how the SC‐BRB can be implemented in real buildings to improve seismic performance. First, a computational brace model was developed and calibrated against experimental data, including the definition of a new cyclic material model for superelastic NiTi shape memory alloy. A parametric study were then conducted to explore the design space for SC‐BRBs. Finally, a set of prototype buildings was designed and computationally subjected to a suite of ground motions. The effect of the lateral resistance of gravity framing on self‐centering was also examined. From the component study, the SC‐BRB was found to dissipate sufficient energy even with large self‐centering ratios (as large as 4) based on criteria found in the literature for limiting peak drifts. From the prototype building study, a SC‐BRB self‐centering ratio of 0.5 was capable of reliably limiting residual drifts to negligible values, which is consistent with a dynamic form of self‐centering discussed in the literature. Because large self‐centering ratios can create significant overstrength, the most efficient SC‐BRB frame designs had a self‐centering ratio in the range of 0.5–1.5. Ambient building resistance (e.g., gravity framing) was found to reduce peak drifts, but had a negligible effect on residual drifts. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

12.
In low‐rise steel‐concrete composite structures, moment‐resisting frames can be designed to develop a ductile response in beam‐to‐column joints and column bases by activating flexural yielding of beams and end plates, shear yielding of column web panel zones and yielding of anchors. To evaluate the performance of these components under differing earthquake intensities, a series of pseudodynamic, quasistatic cyclic and vibration tests were carried out on a two‐storey two‐bay moment resisting structure. The performance‐based seismic design and control of these structures requires that stiffness degradation, strength deterioration and slip are properly modelled. In this context, compact hysteretic models can play a key role and must therefore be striven for. Nonetheless, relevant techniques, like nonlinear system identification, are far from representing standard and reliable tools for the dynamic characterization of full‐scale structural systems. With this objective in mind, we present a restoring force surface‐based technique applied to pseudodynamic test data, in view of the nonlinear identification of multistorey frames. The technique is developed by means of a parametric approach, where a time‐variant stiffness operator is coupled to a modified Bouc–Wen model that allows both for slip and for degradation in stiffness. Strength deterioration is indirectly taken into account too. We also show how model‐based parameters can be correlated to the damage process progressively observed both in the structure and in its components. Finally, the predictive capabilities of the identified model are highlighted. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

13.
This paper reports a study for the seismic performance of one large‐scaled (1/15) model of 30‐story steel‐reinforced concrete frame‐concrete core wall mixed structure. The study was implemented by both shaking table tests, in which the similarity ratio for lateral and gravitational accelerations was kept to 1:1, and numerical nonlinear dynamic analysis. The test observations presented herein include story displacement, interstory drift, natural vibration periods, and final failure mode. The numerical analysis was performed to simulate the shaking table test procedure, and the numerically obtained responses were verified by the test results. On the basis of the numerical results, the progressions of structural stiffness, base shear, and overturning moment were investigated, and the distributions of base shear and overturning moment between frame and core wall were also discussed. The test demonstrates the seismic performance of the steel‐reinforced concrete frame‐core wall mixed structure and reveals the potential overturning failure mode for high rise structures. The nonlinear analysis results indicate that the peripheral frames could take more shear forces after core wall damaged under severe earthquakes. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

14.
The response of low‐ductility reinforced concrete (RC) frames, designed typically for a non‐seismic region, subjected to two frequencies of base excitations is studied. Five half‐scaled, two‐bay, two‐storey, RC frames, each approximately 5 m wide by 3.3 m high, were subjected to both horizontal and/or vertical base excitations with a frequency of 40 Hz as well as a lower frequency of about 4 Hz (close to the fundamental frequency) using a shake table. The imposed acceleration amplitude ranged from 0.2 to 1.2g. The test results showed that the response characteristics of the structures differed under high‐ and low‐frequency excitations. The frames were able to sustain high‐frequency excitations without damage but were inadequate for low‐frequency excitations, even though the frames exhibited some ductility. Linear‐elastic time‐history analysis can predict reasonably well the structural response under high‐frequency excitations. As the frames were not designed for seismic loads, the reinforcement detailing may not have been adequate, based on the crack pattern observed. The effect of vertical excitation can cause significant additional forces in the columns and moment reversals in the beams. The ‘strong‐column, weak‐beam’ approach for lateral load RC frame design is supported by experimental observations. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

15.
Recent earthquakes have confirmed the role played by infills in the seismic response of reinforced concrete buildings. The control and limitation of damage to such nonstructural elements is a key issue in performance‐based earthquake engineering. The present work is focused on modeling and analysis of damage to infill panels, and, in particular, it is aimed towards linear analysis procedures for assessing the damage limitation limit state of infilled reinforced concrete frames. First, code provisions on infill modeling and acceptance criteria at the damage limitation limit state are reviewed. Literature contributions on damage to unreinforced masonry infill panels and corresponding displacement capacity are reported and discussed. Two procedures are then proposed aiming at a twofold goal: (i) the determination of ‘equivalent’ interstory drift ratio limits for a bare frame model and (ii) the estimation of the stiffness of equivalent struts representing infill walls in a linear model. These two quantities are determined such that a linear model ensures a reliable estimation of seismic capacity at the damage limitation limit state, providing the same intensity level as that obtained from nonlinear analyses carried out on structural models with infills. Finally, the proposed procedures are applied to four‐story and eight‐story case study‐infilled frames, designed for seismic loads according to current technical codes. The results of these application examples are presented and discussed. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

16.
The self‐centering prestressed concrete (SCPC) moment resisting frame (MRF) with web friction devices (WFDs) is a new type of structure that integrates advantages of post‐tensioned precast concrete MRFs and self‐centering steel MRFs. In this paper, the configuration of the connection and design guidelines are presented. To further reduce damage to the connection under cyclic loading and facilitate implementation in practice, several significant improvements are proposed and experimentally validated in this study, including the following: (i) the welded connection is replaced by the bolted connection; (ii) aluminum plates are used for friction instead of brass plates to reduce the material costs without decreasing the energy dissipation capacity; and (iii) post‐tensioned tendons at the corners of the beam are replaced by a bundle of tendons at the beam centroid in order to facilitate the field assembly. The resulting improvements of seismic performances are experimentally demonstrated by 10 cyclic tests of two full‐scale SCPC beam–column connections. Numerical simulation of the proposed connection is conducted using the Open System for Earthquake Engineering Simulation (OpenSees) to replicate the experimental results. Seismic behaviors are taken into account, such as the gap opening/closing at the beam–column interface, the self‐centering capacity, and the friction energy dissipation. Good agreement is observed between the numerical simulation and the test results. The proposed SCPC connection with bolted WFDs is demonstrated to have good performance when subjected to cyclic loading. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

17.
The seismic damages commonly observed on beam–column joints of old reinforced concrete structures, built with plain bars and without proper detailing, justifies the need to further study the behaviour of this type of structures. The response of these structures when loaded cyclically, as occurs during the earthquakes, is partially controlled by the bond properties between the reinforcing bars and the surrounding concrete. This paper presents the results of an experimental campaign of unidirectional cyclic tests carried out on six full‐scale beam–column joints built with plain bars. These joint specimens are representative of existing reinforced concrete structures, that is, built without adequate reinforcement detailing for seismic demands. For comparison, an additional specimen is built with deformed bars and tested. The seven specimens are designed and detailed to allow the investigation of the influence of bond properties, lapping of the longitudinal bars in columns and beams, bent‐up bars in the beams, slab contribution and concrete strength. The lateral force–drift relationships, global dissipated energy evolution, contribution of the joint, beams and columns to the global dissipated energy, ductility, equivalent damping, final damage observed, homogenized reinforced concrete damage index, displacement components, curvature evolutions and Eurocode requirements are presented and discussed. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

18.
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.  相似文献   

19.
为了对混凝土框架结构的地震破坏机制和抗震性能进行控制,在框架柱中配置高强钢筋,并将纤维增强混凝土(FRC)用于框架结构的预期损伤部位。结构柱中的高强钢筋用来减小结构的残余变形,FRC材料用来增加结构的耗能能力和损伤容限。设计了三个框架,采用动力弹塑性时程分析方法进行分析。研究结果表明,采用高强钢筋提高了结构的整体承载能力,在层间侧移角达到3%之前避免了柱铰的出现(包括底层柱底),并且减小了结构的残余变形;预期损伤部位采用FRC材料能够提高结构的塑性耗能。  相似文献   

20.
The reinforced concrete frame‐core tube structure is a common form of high‐rise building; however, certain vertical components of these structures are prone to be damaged by earthquakes, debris flow, or other accidents, leaving no time for repair or retrofit. This study is motivated by a practical problem—that is, the seismic vulnerability and collapse resistant capability under future earthquakes when a vertical member has failed. A reduced scale model (1:15 scale) of a typical reinforced concrete frame‐core tube with a corner column removed from the first floor is designed, fabricated, and tested. The corner column is replaced by a jack, and the failure behavior is simulated by manually unloading the jack. The model is then excited by a variety of seismic ground motions on the shaking table. Experimental results concerning the seismic responses and actual process of collapse are presented herein. Finally, the earthquake‐induced collapse process is simulated numerically using the software program ANSYS/LS‐DYNA. Validation and calibration of the model are carried out by comparison with the experimental results. Furthermore, based on both experimental investigations and numerical simulations, the collapse mechanism is discussed, and some suggestions on collapse design are put forward. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

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