Steel Piers Research Articles

Life-cycle seismic performance of bridges with thin-walled steel piers under bi-directional excitations

In corrosive environments, steel bridges demonstrate time-dependent seismic performance and varied directional responses to bi-directional excitation at different life-cycle stages. However, current seismic assessment methods for bridges have not adequately addressed the time-dependent effects of bi-directional excitation directionality on seismic responses throughout their entire life cycle. Thus, this study aims to investigate the time-varying directional effects of bi-directional seismic excitations on steel bridges with multiple parameters and to propose a method for predicting the range of critical incident angles while considering the aging effects of bridges. Initially, time-dependent functions that characterize steel corrosion are integrated into multiscale finite element models of the steel bridges to simulate corrosion progression across their life-cycle stages. Subsequently, a quantitative analysis of the bi-directional seismic response of steel bridges is conducted throughout their life cycle, accounting for the directionality of seismic excitation. Finally, a method and process for predicting the range of time-varying bi-directional critical incident angles with 95 % probability are derived by fitting the statistical probability distribution boundary values of the critical incident angle deviation index. The study's findings indicate that the aging effects of steel bridges amplify the displacement response under bi-directional seismic excitation, with the maximum displacement response difference exceeds 40 %. The service time may increase the sensitivity of steel bridges to changes in incident angles, potentially amplifying the displacement response by a factor of 1.69. The study's findings highlight the importance of considering aging effects and bi-directional excitation directionality in bridge seismic assessments.

Simplified Calculation Method for the Critical Load Bearing of Market-based Profile Emergency Steel Pier

A novel emergency steel pier, assembled from market-available profiles, has been developed to address the challenges associated with the "regular stockpiling and rapid emergency deployment" of bridge pier repair equipment. These challenges often involve significant labor and financial costs for manufacturing and maintenance. The buckling modes of the columns and pier-girder connections were considered. Using energy methods and plate-shell theory, an analytical formula for the critical load-bearing capacity of the steel pier under emergency conditions was derived. Numerical simulations were conducted for comparison and validation, resulting in an optimized and simplified method for calculating the critical load capacity, which is suitable for engineering applications.The study shows that the critical load-bearing capacity of the emergency steel pier exhibits distinct patterns under the influence of column buckling modes and pier-girder connection methods. In cases where the column is fixed at one end and hinged at the other, or fixed at both ends, the critical load for axisymmetric buckling is affected by factors such as elastic modulus, Poisson’s ratio, height, radius, wall thickness, and the number of buckling waves. When considering non-axisymmetric buckling, the number of circumferential buckling waves becomes an additional factor. A simplified method for calculating the critical load-bearing capacity was developed. The simplified formula depends only on a correction factor, modified buckling stress, the number of columns, and cross-sectional area. This makes it highly practical for emergency engineering applications.

Rapid design method for composite emergency steel piers with thin-walled steel tube framework and discussion on "temporary-permanent" transition

To address the conflict between the reserve of repair materials for existing bridge piers and the demands for emergency repairs, as well as the challenge of converting temporary emergency structures into permanent ones without significant disassembly, a novel composite emergency steel pier has been developed. This pier utilizes commonly available thin-walled steel tube sections as the framework, I-beams as the connecting elements, and incorporates a "temporary-permanent" transition function. Taking the emergency steel pier for medium-height bridge piers in high-speed rail systems as an example, this study introduces three evaluation metrics—security coefficient (n), stability coefficient k), and variation coefficient (V)—analyzing the factors influencing the design and application thresholds of the emergency steel piers from perspectives of strength, stability, and load distribution uniformity. Based on this, a rapid design method for composite emergency steel piers with thin-walled steel tube frameworks that does not require numerical simulation has been developed and experimentally validated. Research findings indicate that when used for the emergency repair of medium-height or lower bridge piers in high-speed railways, the column line stiffness of the thin-walled steel tube framework composite emergency steel piers should range between 0.34 × 10 exp7 kN/mm to 4.15 × 10 exp7 kN/mm. The transverse and longitudinal spacing of the columns should be 1 m to 3 m and 1.5 m to 3 m respectively. The line stiffness of the plinth beams I and II should be greater than 0.69 kN/mm and 1.01 kN/mm respectively. Within these parameter ranges, the emergency steel pier will not experience strength failure or instability, and the load distribution among the columns remains uniformly favorable. In applications to other scenarios, the rapid generation of composite emergency steel piers with thin-walled steel tube frameworks can be achieved by following three steps: parameter selection and structural configuration determination, calculation of the pier-beam linear stiffness ratio, and criterion-based result verification. The rapid design and implementation of composite emergency steel piers help alleviate the contradiction between material stockpiling and repair demands. Furthermore, the pre-designed "temporary-permanent" transition functionality facilitates integrated operations for emergency repairs and permanent restorations.

Multi-spring model for tubular rocking steel bridge piers subjected to earthquake loading

Recent decades have seen increased interest in using the controlled rocking concept in seismic resisting systems. Unlike conventional systems, where lateral deformation of a member is achieved through the formation of plastic hinges in critical regions, in the rocking systems this is achieved through a gap opening mechanism. Due to gravity load and/or post-tensioning forces, the rocking systems exhibit a self-centering behavior. Conducting a continuum finite element analysis to investigate the seismic response of such a system is quite expensive in terms of computational resources. On the other hand, a simplified macro model using two springs to simulate the gap opening/closing mechanism cannot accurately predict the dynamic response of the system. This study utilizes a multiple-spring model to simulate the nonlinear seismic response of circular tubular steel piers. An efficient optimization procedure based on a genetic algorithm is developed to calibrate the parameters of the springs. The results of continuum finite element analyses are compared with those obtained from the multi-spring model to verify the accuracy of the model. The proposed method is shown to be advantageous for accurately simulating the seismic response of a bridge model subjected to multi-directional ground motions, particularly the hysteretic force-displacement relationship, and dynamic response time history.

Analytical calculation method of circular-section rocking steel piers under horizontal cyclic load

The research object of this paper is to investigate the mechanical behavior and develop an analytical model of the prestressed circular-section rocking steel piers with external energy-dissipating devices under the horizontal cyclic load. Based on the method of monolithic beam analogy under monotonic loading, the concept of generalized rotation angle and intercept strain in the pre-decompression state was introduced. The geometrical equations for the pre- and post-decompression stages are deduced. The calculation formulas for internal forces of each component and the analytical calculation method for the entire process of the rocking steel pier under horizontal cyclic loading are established in detail. To reproduce the hysteresis curve of the test, some special test conditions, such as the retraction effect of prestressed tendons and increase of the compressed area due to the vertical plates, were considered in the analytical model. The results show that the analytical method based on generalized rotation angle and intercept strain can ensure an ideal transition of the hysteresis curve of the pier in pre- and post-decompression stages. Except for the pier with particularly severe local buckling and ovalization deformation, the calculated results obtained from the proposed analytical model agrees well with the test results for the rocking steel bridge piers. The effect of prestressed tendons and the P–Δ effect on the lateral load–displacement curve of rocking steel bridge biers was further analyzed through parametric study using the proposed model. The analytical calculation method presented in this paper provides a theoretical tool for seismic design of the rocking steel pier in engineering practice. This paper provides important guidance for the establishment of seismic design method of rocking steel piers.

Feasibility of using superelastic shape memory alloy in plastic hinge regions of steel bridge columns for seismic applications

AbstractThis paper contributes to the further development of seismic resilient infrastructure by introducing a novel prototype bridge which integrates tubular steel piers with superelastic shape memory alloy (SMA). The proposed bridge pier is composed of a circular steel tube which is bonded to a superelastic SMA tube in regions of high stress. The pier is distinguished by its ability to minimize residual drifts following inelastic deformations induced by cyclic loading. Three‐dimensional continuum finite element (FE) models are utilized to examine its lateral behavior. Experimental data is used to demonstrate the effectiveness of the continuum FE procedure in replicating the cyclic response and capturing both global and localized behaviors. A novel composite material model is proposed to represent the degradation of strength and accumulation of irreversible strains in the cyclic response of superelastic SMAs. An iterative procedure for the calibration of this material is presented. Investigations, employing the calibrated FE procedure, focus on the quasi‐static cyclic response of steel piers with superelastic SMA in the plastic hinge zone, aiming to identify the optimal length of the SMA tube for achieving a self‐centering response with reduced residual deformation. The study is then further expanded to examine the seismic response of a bridge structure incorporating such piers. Development of the FE model for the prototype bridge includes the modelling of the piers using continuum elements, while the superstructure, bearing units, abutment walls, and backfill material are modelled using discrete elements. Nonlinear time history analyses are undertaken to investigate the effects of column wall thickness and materials used in the plastic hinge zones of the piers. Dynamic FE study results indicate that bridges employing such piers are capable of returning to their original position, provided the SMA tube is of adequate length.

Ultra-low cycle fatigue evaluation method for unstiffened steel piers using fiber model

The safety of steel bridge piers is threatened by ultra-low cycle fatigue (ULCF) damage, which dominates the failure mode in those with relatively compact section under strong seismic action. Existing methods for calculating such ULCF damage face the dilemma between accuracy and efficiency. To this end, this paper proposes a simplified evaluation method based on fiber model to expediently evaluate the ULCF damage of unstiffened steel piers, evenly with sound precision. Specifically, the average stress triaxiality is assumed as 0.63 for steel piers, and it is validated by cyclic loading experiments with the modified Coffin-Masson formula and solid element sub-model. The disparity between local plastic strain range in fiber and solid models is compensated by introducing a magnified coefficient. The analyzed results indicate the slenderness ratio, axial compressive ratio, especially the flange thickness and the width-to-thickness ratio, strongly influence the strain concentration effect occurring in the pier bottom. In addition, the proposed close equation for the magnified coefficient fits well with the discrete calculated points. The 3.05% mean absolute error is realized on the predicting half cycles when applying this method in random cyclic loading. Its favorable applicability in practical engineering is also verified with considering different ground motion types.

Performance and damage states assessment of thin-walled steel bridge piers with end-corrosion under earthquake loading

End-corrosion is typical damage to steel bridge piers, which will reduce the seismic performance. Unlike overall uniform corrosion, end-corrosion results in more complex stresses on bridge piers, however, there are few related studies. This study aims to analyze the mechanical performance of corroded bridge piers and to establish a method for evaluating the seismic damage status of steel piers considering circumferential uniform end-corrosion. Firstly, the effect of corrosion parameters on key performance points of bridge piers is quantitatively analyzed using the validated finite element model. The calculation method of critical displacement value corresponding to different damage states of the end-corroded bridge pier is proposed. A high-precision fiber beam element analysis model is developed to simultaneously consider the effects of end-corrosion and shear stiffness variation. The results show that the degradation degree of yield displacement of the end-corroded bridge pier is relatively small. In contrast, the ultimate displacement, capacity point displacement and bearing capacity are significantly affected by corrosion parameters, and the degradation degree after corrosion can reach more than 30%. The pier damage ratio formula proposed in this study can accurately describe the degradation of the ultimate value, and the calculation error is almost controlled within 15%. The multi-node variable section (MNVS) fiber beam model proposed in this study has higher analysis accuracy, which can be improved by more than 16% compared with the traditional fiber beam model. In addition, the accuracy of the MNVS model in the dynamic analysis is verified by inputting the seismic records under three site conditions. Finally, considering the characteristics of end-corrosion, an evaluation method and procedure for seismic damage status of the steel pier with end-corrosion is established.

Use of load‐bearing AAC panels in transportable, prefabricated, pre‐finished, modular housing

AbstractThis article will outline a method of building residential homes as Prefabricated, Prefinished Volumetric Construction (PPVC), using AAC panels. These transportable structures are created from solid AAC modules and designed for Residential Homes and Low‐Rise multi‐residential developments. In this transportable system, thick AAC panels are used as the principal construction material and load‐bearing structural element. The AAC modules are factory assembled and fitted out as completed room pods. They are transported to the site where they are lifted directly from the delivery truck and positioned into their final location on steel piers. Engineered AAC floor and ceiling cassettes connect the modular pods together to form a spacious and modern solid AAC home.

System fragility evaluation of a curved highway bridge structure considering multi-direction seismic excitations

This paper presents the impact of varying the input seismic excitation directions on the system fragility of a geometrically complex highway bridge structure. The traditional approach of fragility derivation in the principal loading directions (longitudinal and transverse) results in an under/overestimation of the system fragility. To reduce such errors, the contribution of all major vulnerable components to the system fragility in the critical loading direction must be considered. For this purpose, a series of nonlinear time-history analyses were conducted for a testbed configured geometrically curved highway bridge structure in Japan. Shear strain, ductility, and distortion strain were considered as engineering demand parameters for bearings, concrete pier, and steel piers, respectively. The demand dependency among the components was considered using the correlation coefficient matrix for fragility estimation. Subsequently, fragility functions with respect to the input loading directions were generated for the bridge components and system to quantify their sensitivity to seismic input excitation directions. The results show that the component fragility is significantly influenced by the input excitation direction. A relative comparison of the system fragility for different loading directions indicated that a 150° loading direction yielded a higher fragility demand. The findings suggest that the critical fragility assessment should not always be decided only along the principal loading directions.

Vibration Analysis of Low Height-to-Span Ratio Pedestrian Bridge under Human-Induced Excitation

Driven by the aesthetic pursuit of the urban landscape, pedestrian bridges become longer, lighter, and slender, which may be susceptible to unacceptable vibrations induced by human activities. This paper presented on-site vibration tests of a pedestrian bridge with a very low height-to-span ratio (1/60). The vibration characteristics and dynamic responses were analyzed using environmental, heel-drop, and walking tests. Then, a verified finite model was established to investigate the effect of the height-to-span ratio and the concrete filling ranges of tree-like steel piers on the vibration characteristics and acceleration responses of this kind of pedestrian bridges. Moreover, the relationship between different peak accelerations under heel-drop and walking at various frequencies by the same person was detailed and studied experimentally and by computer simulation, after which the ratios of the peak acceleration during walking and the one under heel-drop were recommended. Finally, a method that demonstrates the feasibility of predicting the peak acceleration of pedestrian bridges of a small height-to-span ratio across a range of walking frequencies was proposed based on a simplified heel-drop load model developed according to 60 time-history records.

3D response simulation of a bridge with a posttensioned base rocking steel pier under sequential loading of traffic loads, braking force, and earthquake excitations

AbstractThis paper presents finite element (FE) investigations of the seismic response of a bridge incorporating a base rocking steel pier. The pier consists of a circular steel tube, circular end plates, posttensioned (PT) tendon(s), and supplemental energy dissipation devices, and is configured to rock at its interface with the foundation. The main characteristic of such a pier is its ability to ensure small residual drifts after undergoing inelastic deformations during cyclic loading. The system has a tendency to close the gap due to the presence of superstructure dead load (DL) and tendon posttensioning force. Using experimental data, the calibration of the FE procedure is done at the material, component, and global system levels. The FE model of a prototype bridge is developed with the rocking pier modelled by continuum elements while superstructure, bearing units, abutment walls and backfill material modelled by discrete elements. The analysis procedure includes the application of one or two earthquake excitations, traffic loads, and braking force. The varied parameters are the diameter‐to‐thickness ratio of the column, presence of a PT tendon, addition of supplemental energy dissipaters (EDs), base plate dimensions, height of ED chairs, and ED strength. The results of dynamic FE studies demonstrate that a bridge utilizing such a pier has the potential to undergo consecutive earthquakes without sustaining significant damage and return to its original position without requiring abutment component stiffness and strength.

Novel fiber-based seismic response modelling and design method of partially CFST bridge piers considering local buckling effect

Considering the prohibitive computation time and convergence problems of shell-solid models in seismic analysis of partially concrete-filled steel tubular (CFST) bridge piers, a simple fiber-based nonlinear modelling method is proposed and calibrated in this study intended for large-scale seismic analyses. The local buckling effect of the outer steel tube is considered in the proposed method. By comparing the results of the numerical modelling with those from the experiments, the proposed fiber models are demonstrated to capture the hysteretic behavior of CFST piers with a comparable effectiveness but an enhanced efficiency and analysis time and effort over the shell-solid models. Based on the proposed fiber models, extensive cyclic pushover and time-history analyses are conducted to investigate the effect of critical design parameters on seismic performance of partially CFST piers. The analysis results indicate that the parameters of steel tube and infilled concrete should be properly designed in a combined way to mitigate the local buckling of the steel tube and thus improve the overall seismic performance of partially CFST piers. A novel design method using layered concrete filling is proposed for partially CFST piers, which can achieve an improved structural seismic performance. Furthermore, this method is validated to be especially efficient for seismic retrofit of existing hollow steel piers, which can significantly enhance the pier deformation capacity without imposing much extra force demands on pier foundations.

Seismic safety evaluation method based on fiber-element strain for square-section steel piers

Inconsistency and incompatibility exist between the seismic capacity values obtained from shell-element models and the seismic demand results obtained from beam-based models in engineering. In this paper, the improved fiber model which can consider local instability of steel plates is used uniformly to conduct seismic capacity and seismic demand analyses under bidirectional earthquake actions. First, the restoring-force interaction curves of square-section steel piers are obtained under horizontal unidirectional and oblique loading; however, the evaluation method based on the restoring-force interaction curves may produce incorrect evaluation results according to the elastoplastic stability theory. Therefore, a new seismic safety evaluation method, based on the fiber-element strain within the effective damaged length (Led), is further proposed through the quasistatic analysis under the square spiral loading path. Dynamic seismic response analysis is conducted to verify the effectiveness of the proposed strain-based evaluation method. The results show that the ultimate state according to the compressive strain limit obtained via the square spiral loading is consistent with that based on the elastoplastic stability theory under bidirectional earthquake actions. The proposed method can not only coordinate the demand and capacity results, but also avoid misjudgment cases and facilitate engineering application.

Seismic Behavior of Box Steel Bridge Pier with Built-In Energy Dissipation Steel Plates

Based on the design concept of earthquake-resilient structure, a new-type of box-shaped steel piers with embedded energy-dissipating steel plates was proposed. Quasi-static tests of 6 box-shaped steel pier specimens under variable axial pressure and cyclic horizontal loading were carried out. By analyzing the failure mode, load-displacement hysteretic curve, skeleton curve, displacement ductility coefficient, stiffness degradation characteristics, strength degradation coefficient, and cumulative hysteretic energy, the effects of setting energy-dissipating steel plate, axial compression ratio, and thickness of energy dissipation steel plates on the seismic performance of new-type steel piers were discussed. Finite element models of steel bridge piers were established and compared with the test results. The analysis results using FEM agree well with the test results. Results show that the setting of energy-dissipating steel plates can effectively improve the ductility, deformation capacity, and energy-dissipating capacity of box-shaped steel piers, and effectively delay buckling deformation and cracking of wall plates. The steel plate near the bolt hole of the wall plate at the root of the new-type of box-shaped steel piers is easy to crack due to stress concentration, resulting in a rapid reduction of the maximum bearing capacity of the specimens. With the increase of axial compression ratio, the bearing capacity, energy-dissipating capacity, and earthquake-resilient capacity of the specimens increase. The smaller the thickness of the replaceable energy-dissipating steel plates, the smaller the bearing capacity and faster the stiffness degradation of the specimens become, while the ductility and energy-dissipating capacity of the specimens are improved. The axial compression ratio and the thickness of the energy-dissipating steel plate have relatively little effect on the strength degradation of the specimens. In order to facilitate the popularization and application of the new-type steel piers, formulas were also established to calculate the bearing capacity and displacement ductility factor of the new-type of box-shaped steel piers.

Finite-Element Simulation of the Lateral Response of Posttensioned Base Rocking Steel Bridge Piers

This paper presents the results of a finite-element (FE) study on posttensioned (PT) rocking steel bridge piers, each composed of a circular tubular column, welded end plates, PT strands, and axially yielding steel energy dissipators (EDs), and corresponding chairs. The pier is configured so that it rocks at its base. Previously conducted experiments on five scaled rocking steel columns are summarized. Three-dimensional (3D) continuum FE models of the tested specimens are generated with the objective of verifying the capability of the modeling approach in the simulation of the local and global responses. Strain-controlled cyclic coupon tests were performed to quantify the kinematic and isotropic hardening material parameters. A simplified method is proposed to model the cyclic loss of prestressing because of wedge seating in a typical industry monostrand anchorage system. The FE procedure is then calibrated against the experimental data at the material, component, and global pier levels. A parametric study is conducted to examine the effects of key factors such as material model, P-Delta, base plate dimensions, column diameter-to-thickness and initial axial force ratios, ED chairs, and ED location on the lateral cyclic response. It is demonstrated that, for a given target drift, local buckling and the resulting residual lateral deformations of a rocking steel pier are a function of the diameter-to-thickness and initial axial force ratios of the column and the ED chairs. By the proper selection of these variables, a stable and robust self-centering response can be obtained with minimal damage to the bridge pier.

Ultra-low cycle fatigue fracture initiation life evaluation of thick-walled steel bridge piers with microscopic damage index under bidirectional cyclic loading

Strong earthquakes can cause ultra-low cycle fatigue (ULCF) fracture in steel bridge piers. This paper examined the fracture behavior of two thick-walled square section steel bridge piers subjecting to horizontal bidirectional cyclic loading. In addition, a microscope damage index for evaluating ULCF fracture initiation life of steel bridge piers was proposed. The findings show that ductile cracking firstly appeared at the junction between the stiffened base plate and bottom weld at the corner position of steel bridge piers under bidirectional cyclic loading, and that initial crack growth did not reduce the strength capacity. The strength capacity of steel piers began to rapidly decline as cracks propagated into the base metal. The proposed microscope damage index for ULCF fracture initiation life evaluation of steel bridge piers performs well when compared to experimental and evaluation results.

Fiber Model Considering the Local Instability Effect and Its Application to the Seismic Analysis of Eccentrically Compressed Steel Piers

To propose a seismic response calculation model for eccentrically compressed steel piers that can consider the local instability effect and horizontal bidirectional earthquake actions, in-plane and out-of-plane pseudo-static numerical simulation and bidirectional seismic response analysis are performed to study the applicability of the improved fiber model. The comparison results with the refined hybrid-element model show that the improved fiber model can accurately simulate the hysteretic performance of eccentrically compressed steel piers in the in-plane or out-of-plane directions and can be used to calculate the structural seismic requirements under the bidirectional action of rarely met earthquakes.

Research on the multi-shear spring model for circular-section steel piers

The main damage caused by earthquakes to single-column circular-section steel piers is the bulged deformation at the bottom, generated by local instability. The refined shell-based finite element (FE) model can accurately simulate the deformational behavior, but it is still cumbersome and time-consuming to apply to the engineering design currently. Further, the existing simplified methods cannot be used in seismic response analyses under horizontal bidirectional earthquakes. Therefore, this paper uses the multi-shear spring (MSS) mechanical model as the basic model and proposes an MSS calculation model for circular-section steel piers. This model is applicable for horizontal bidirectional seismic response analysis and considers the local instability effect of steel plates. In this study, the load–deformation relationship of the modified Menegotto-Pinto model is employed in all directions as the hysteresis curve equation of the springs. The basic parameters of the corresponding models for different structures are determined according to the calculation results of the refined-shell models. In addition, the Ibarra-Krawinkler degradation rule is employed to simulate the degradation process of structural bearing capacity and stiffness, and the degradation parameters are identified. The pseudostatic and seismic time-history response analyses of steel piers with different width-to-thickness ratios verify that the proposed model has reliable calculation accuracy and greatly improved efficiency. The research in this paper provides a practical calculation method for the seismic response analysis of steel bridge piers.

Detecting Epileptic Seizures Based on Parameter Estimation of a Neural Mass Model

This paper presents two adaptive Kalman filters (KFs) for nonlinear model updating where, in addition to nonlinear model parameters, the covariance matrix of measurement noise is estimated recursively in a near online manner. Two adaptive KF approaches are formulated based on the forgetting factor and the moving window covariance-matching techniques using residuals. Although the proposed adaptive methods are integrated with the unscented KF (UKF) for nonlinear model updating in this paper, they can be alternatively combined with other types of nonlinear KFs such as the extended KF (EKF) or the ensemble KF (EnKF). The performance of the proposed methods is investigated through two numerical applications and compared to that of a non-adaptive UKF and an existing dual adaptive filter. The first application considers a nonlinear steel pier where nonlinear material properties are selected as updating parameters. Significant improvements in parameter estimation results are observed when using adaptive filters compared to the non-adaptive approach. Furthermore, the covariance matrix of simulated measurement noise is estimated from the adaptive approaches with acceptable accuracy. Effects of different types of modeling errors are studied in the second numerical application of a nonlinear 3-story 3-bay steel frame structure. Similarly, more accurate and robust parameter estimations and response predictions are obtained from the adaptive approaches compared to the non-adaptive approach. The results verify the effectiveness and robustness of the proposed adaptive filters. The forgetting factor and moving window methods are shown to have a simpler tuning process compared to the dual adaptive method while providing similar performance.