Displacement Of Superstructure Research Articles

Probabilistic ductile deformation limit state prediction of monolithic exterior shear keys based on quantile regression machine learning techniques

Shear strength and ductile deformation capacity of monolithic exterior shear keys play important roles on the seismic behavior of highway bridges. Improving the ductility of the shear key through reasonable design could effectively restrict superstructure displacement and minimize damage to pier columns. However, most existing studies primarily focus on evaluating the shear strength and damage mechanisms of shear keys, with limited attention given to analytical models for assessing ductile deformation capacity. To this end, this study proposes a method that combines quantile regression and machine learning techniques to predict the ductile deformation limit states of shear keys. The proposed numerical modeling method for shear keys is validated using the experimental data on lateral load-displacement curves. On this basis, Latin hypercubic sampling and joint simulation are utilized to establish the ductile deformation limit state database. The ductile deformation limit states of shear keys are characterized by their lateral displacements in three distinct damage states. The main influencing factors of each limit states are investigated by correlation analysis. Three quantile regression machine learning models are trained and constructed to conduct point and interval prediction for the ductile deformation limit states. All three models, particularly the Gaussian process quantile regression model, are proven to demonstrate exceptional prediction accuracy and uncertainty quantification. Experimental data validation confirms that these models outperform the prediction accuracy of existing simplified models.

Live load and long-term response of steel bridges with high skew

High skew in bridges alters live load distribution and creates performance issues such as deck cracking, superstructure in-plane (horizontal) displacements and bearing distress. In-plane superstructure displacements, also called racking, are particularly important as they cause misalignments of superstructure and approach slabs, stress bearings and expansion joints. This study had two objectives: to evaluate live load distribution in skewed bridges and to understand how skew influences in-plane superstructure displacements. The effect of bridge design details on live load distribution and in-plane superstructure displacements was assessed through parametric studies on highly skewed bridges.A three-span, steel girder-concrete deck bridge with a 47-degree skew was load tested. Load test results were employed to validate finite element analyses that were used to understand the impact of varying skew angle, bridge features and bearing fixity on live load distribution and in-plane superstructure displacements. The ability of the American Association of Highway and Transportation Officials Load and Resistance Factor Design Bridge Design Specifications (AASHTO LRFD BDS) to accurately capture live load distribution for steel girder bridges was evaluated.Field test results, consisting of girder bending and vertical shear strains measured through strain gages strategically located on one of the exterior spans, and parametric studies showed that AASHTO LRFD BDS predicted shear and moment distribution very conservatively and closely, respectively. Seasonal temperature changes were sufficient to create in-plane (horizontal) superstructure displacements. These displacements caused the superstructure to rotate towards obtuse and acute corners for negative and positive temperature changes, respectively. Larger skew angles led to greater transverse (i.e., perpendicular to bridge longitudinal axis) displacements at girder bearings. Longitudinal (i.e., parallel to bridge longitudinal axis) displacements were consistently smaller than transverse displacements and were not affected by skew. Mixed bearing fixity arrangements, with both fixed and expansion bearings over the same pier, limited superstructure transverse in-plane displacements.

Effect of Shear Keys on the Quasi-Isolated Behavior of Small-to-Medium-Span Girder Bridges

Small-to-medium-span girder bridges equipped with shear keys play a significant role in the Chinese highway bridge system. However, shear key failure was observed during the 2008 Wenchuan earthquake, which resulted in excessive superstructure displacements and even catastrophic span collapse. For this, six refined bridges were investigated for the quasi-isolated behaviors under different shear key strengths by using the Pushover and IDA methods. Results indicate that the bridges exhibit two distinct damage states upon the shear key strengths. The shear key failure and bearing sliding create a natural quasi-isolated mechanism, with the following damage sequence: shear key failure → bearing sliding → pier undamaged or slight damage. Quasi-isolated behavior leads to higher displacement demands for beams, especially when the peak ground acceleration (PGA) exceeds 0.45 g. By selecting suitable shear key strength, below 9% for 20 m piers and 30% for 10 m piers, quasi-isolated damage is expected to occur in bridges. The study offers a fresh perspective on the concept of seismic design for highway girder bridges in China.

Wind-Induced Impact Behavior of Base-Isolated High-Rise Buildings with Adjacent Structures

The base-isolation technology has been increasingly applied in high-rise buildings in recent years. Previous studies have shown that the unfavorable wind-induced response can be effectively reduced by a certain degree of hysteretic energy dissipation after the yielding of the isolation system under strong wind load. However, a large relative inelastic displacement at the isolation level will occur under this condition, which is likely to exceed the width of seismic gap, and cause a structural impact with the adjacent structures (i.e. retaining wall or other barriers). Such wind-induced impacts may have detrimental consequences on the structural performance and have not been investigated much before. This study prospectively investigated the wind-induced impact behavior of base-isolated high-rise buildings with adjacent structures. The multi-story superstructure is modeled as a linear elastic shear building, while the isolation system is represented by bilinear hysteresis restoring force model. An impact element combined with linear spring and damper is used. The story wind load is determined by its cross power spectral density (PSD). Responses for two kinds of typical impact including crosswind and along-wind impact are examined by time history analysis. The results demonstrate that the impact will increase the fluctuation components of superstructure displacement, shear force and bending moment to some extent compared with that of the base-isolated building without impact. The floor accelerations, especially floors close to the base, are significantly increased during impact. The impact has no effect on the mean component of each response. At last, a parametric analysis is carried out to explore the influences of various impact parameters on the inelastic impact response. The results of this study can help to better understand the impact behavior of base-isolated high-rise buildings under strong wind excitation and be useful for performance-based wind resistance design.

Seismic performance of a continuous bridge with winding rope device activated by a fluid viscous damper

The seismic requirements of piers with fixed bearings (the fixed pier) for continuous girder bridges are relatively high, while the potential seismic capabilities of piers with sliding bearings (the sliding piers) are not fully utilized. To solve this contradiction, a new type of winding rope shock absorption device activated by a fluid viscous damper (WRD-D) was proposed. The WRD-D was installed on the top of the sliding piers, and the both ends of a fluid viscous damper were connected to the superstructure by winding ropes. During an earthquake, the damping force rises with the increase of relative speed between the sliding piers and the superstructure, activating the WRD-D and producing large frictional resistance, subsequently causing the sliding piers and the fixed pier to bear the seismic load cooperatively. In this study, the working mechanism of the WRD-D was researched. The shaking table test of a scaled continuous girder bridge model employing the WRD-D was conducted. The test results reveal that the WRD-D can effectively reduce the seismic requirements of the fixed pier and the superstructure displacements.

Seismic performance of composite rubber bearings for highway bridges: Bearing test and numerical parametric study

For unbonded laminated natural rubber bearings (ULNBs) which are popular in highway bridges with medium-to-small spans especially in China, the linear and single deformation pattern consisting only of rubber shearing leads to a lack of displacement capacity and a great tendency to slide, resulting in severe damages in recent earthquakes. The excessive displacement of superstructures due to bearing sliding can be lowered and controlled by the introduction of external devices or the improvement on bearings themselves, but with disadvantages. Therefore, the objective of this study is to propose a new bearing, the composite rubber bearing (CRB), to enhance the displacement capacity before the total bearing sliding by combining the sections of the LNBs and the sliding rubber bearings (SRBs). Bearing tests including vertical compression tests, quasi-static tests with variable and constant amplitudes have been conducted on 7 full-scale specimens to investigate the mechanical properties of CRBs and the corresponding influencing factors. Then, the restoring force model has been derived based on the design concept. The influences of internal sliding areas and the PGAs on seismic responses of bridge structures have been studied through a numerical parametric study. Compared with LNBs, the test results show a larger vertical stiffness and energy dissipation capacity and a smaller equivalent horizontal stiffness of CRBs, which are related to the pressure, the position as well as the stiffness ratio of the sliding area. The numerical results illustrate an improved seismic performance by increasing internal sliding area to considerably delay the critical point of the bearing sliding.

A high performance hybrid passive base‐isolated system

This paper proposes a novel high performance hybrid passive base-isolated system integrating the base-isolated system (BIS) with the tuned tandem mass damper inerters (TTMDI), referred to as the BIS+TTMDI. To reveal the interaction between two components and their integrated control performance, the proposed configuration is modeled by a simplified four degree-of-freedom model together taking the dynamic characteristics of the isolation system, TTMDI, and superstructure into inclusion. Employing the optimization criterion defined as minimization of the dimensionless variance of superstructure displacement relative to the ground and by resorting to the particle swarm optimization, the system parameters of TTMDI are tuned to get their best integrated control performance. Evaluations are in turn unfolded on the performance taking into diverse TTMDI inertial properties and different isolation layer characteristics account and robustness, to fully explore the effectiveness of reducing both the displacement and acceleration for the isolation layer and superstructure, the TTMDI's energy dissipation mechanism and capacity, evolution of stiffness and damping, stroke, and structural frequency response. Subsequently, the findings of the BIS+TTMDI in the frequency domain is further tested via the time history analyses using the real records including both near-field with pulse and far-field earthquakes. In two analysis domains, the integrated performance of the proposed BIS+TTMDI is compared not only to the BIS but also to the BIS+TMDI, as well as to the BIS+TTMD and BIS+TMD. Results confirm that the BIS+TTMDI is a high performance system, namely, with high control effectiveness, high robustness, highly smaller stroke, and drastically reduced damping demand.

Experimental Study on Seismic Instability of Pile-Supported Structure Considering Different Ground Conditions

The stability of pile-supported structures under earthquake loads involves complex dynamic soil–structure interaction (SSI). A series of large-scale shaking table experiments was performed to investigate the seismic performance and SSI of pile-supported structures considering different ground conditions. Lateral soil resistance and dynamic displacements of superstructures located in nonliquefiable and liquefiable sites as well as a rigid foundation were measured during shaking tests. The measured responses were analyzed to investigate the P-Δ effect on structural stability. It was observed that the soil lateral resistance to the pile cap at the nonliquefiable site was large and represented the main component of the lateral bearing capacity resisting structure overturning. On the other hand, the lateral resistance of liquefied soil on piles was insignificant and the lateral bearing capacity was derived primarily from soil resistance to pile cap. The analysis of the measured dynamic displacements demonstrated that the seismic instability of the structure was mainly due to the P-Δ effect caused by the rotation of the foundation, especially in liquefied sites. In addition, comparison with the results of base shears and bending moments with the rigid base assumption allows for an in-depth discussion of the effect of SSI on structural seismic design.

Application of Viscous Damper and Laminated Rubber Bearing Pads for Bridges in Seismic Regions

Normally, Laminated Rubber Bearing Pads (LRBPs) are directly placed between girders and piers and their role is to provide the bridge span with horizontal movement, and to transmit the gravity loads from the deck to the piers. Although not designed for seismic loads, they can act as a fuse, partially isolating the substructure from the superstructure and keeping the piers intact during earthquakes. However, recent investigations show that large relative displacement of superstructure against substructure caused by sliding at bearing (sliding between girders and LRBPs) can cause expansion joint failure or even bridge span collapse. Accordingly, proper restrainers should be selected to prevent large displacement. Among all types of restrainers, viscous dampers as passive energy dissipation devices have shown a great capacity in damping earthquake energy. This study investigates the effectiveness of a VD-LRBP system, a viscous damper in conjunction with LRBPs, in dissipating energy and reducing the displacement of the superstructure with reference to the substructure caused by sliding at bearing during a seismic event. A Finite Element (FE) model was first developed and validated using available experimental and numerical results. With the validated model, a 3D Nonlinear Time History Analysis (NTHA) was conducted on a reinforced concrete bridge model under various records of earthquakes using OpenSees, an open-source finite element software. The relative displacement histories were recorded for the bridge in two cases: 1- with only LRBPs and 2- with viscous dampers and LRBPs (VD-LRBP system). The results of this study show that applying viscous dampers can reduce the relative displacement of the superstructure with reference to the substructure for up to 60 percent. As importantly, it can also reduce the residual displacement after the earthquake to near zero.

A three-dimensional investigation on performance of batter pile groups in laterally spreading ground

The performance of batter pile groups in laterally spreading ground has rarely been investigated. The present study evaluates the performance of 2 × 1 batter pile groups with four different configurations subjected to lateral spreading displacement through three-dimensional, fully coupled numerical investigations. Pressure dependent multi-yield model for the soil medium complemented with variation in permeability of liquefiable soil for excess pore pressure generation is considered. The nonlinear behaviour of the reinforced concrete pile is also incorporated. The behaviour of batter pile groups is evaluated for various earthquake time histories. The study indicates that the bending moment developed in the pile sections of both upstream and downstream sides of the ground displacement is observed to reduce under combined (kinematic + inertial) loading conditions for batter pile group configurations considered. However, shear and axial forces show increasing trends for batter pile groups, especially with higher batter angles for both kinematic and combined loading conditions. It is also observed that the presence of batter piles reduces both pile cap and superstructure displacements. However, significant pile cap rotations are recorded for pile groups with higher batter angles. The performances of the pile groups are confirmed for earthquake motions with a wide range of peak ground accelerations.

Performance assessment of a concrete railway bridge by diagnostic load testing

AbstractDiagnostic load testing can be a suitable method for condition assessment of existing bridges. This paper presents the evaluation of a concrete railway bridge built in the 1940s based on diagnostic load testing. The test was the outcome of a visual inspection and preliminary theoretical analysis that found the bridge to be in unsatisfactory condition. Unlike the other possibilities that infrastructure management bodies have in such situations, for example, structure replacement, traffic reorganization, closure of the bridge, etc., diagnostic load testing is a low cost and quick method that indicates the bridge response to real traffic load. The paper describes the test plan and implementation covering the static and dynamic load tests. The experimental methods comprise superstructure displacements measurement, strain measurement on concrete and reinforcement and determination of bridge dynamic parameters. The obtained test results analysis enabled more accurate diagnosis of the actual bridge condition. The bridge demonstrated satisfactory load bearing capacity and response to real service load in terms of registered levels of displacement and strain and proper dynamic performance.

Displacement mitigation–oriented design and mechanism for inerter-based isolation system

The inerter-based isolation system, which comprises an inerter, a dashpot, and a spring, has been shown to be effective for improving the dynamic performance of isolated structures. However, the underlying theoretical basis of its vibration control mechanism has not been studied for superstructures with inerter-based isolation system; in particular, the functionality of the inerter has not been explicitly demonstrated. In this study, the displacement mitigation mechanism is established by deriving a fundamental equation, designated as the displacement demand equation. The mechanism is explained by clarifying the functionality of the inerter-based isolation system to determine the theoretical relationship between the displacements of the superstructure and isolation layer. A nominal displacement demand ratio is defined to evaluate the overall displacement demand of the structure–inerter-based isolation system, by considering the contribution of the inerter-based isolation system. Following the displacement mitigation mechanism, design strategies are developed for inerter-based isolation system, where the isolation frequency ratio can be directly determined once the target displacement performance of the entire structure–inerter-based isolation system is prespecified. In addition, the inertance-mass ratio and damping ratio of the inerter-based isolation system can be obtained according to the target demand of the superstructure displacement. Finally, a series of examples are used to verify the derived displacement demand equation and proposed design strategy. In this study, the displacement mitigation mechanism yields an effective design method that is suitable for the inerter-based isolation system and has a clear physical basis. Through the proposed displacement mitigation–oriented optimal strategy, a target displacement demand for a structure can be satisfied directly, which also provides an optimized displacement performance for the isolation layer. The displacement mitigation mechanism and equation are practical for the simplification of the design procedure and help to reveal the advantageous features of the inerter-based isolation system.

Large shaking table tests of pile-supported structures in different ground conditions

This study investigates the dynamic response of structures and the effect of soil-structure interaction for flexible structures supported by pile foundations located in non-liquefiable and liquefiable sites as well as a rigid foundation. A series of large-scale shaking table experiments were performed, and accelerations and dynamic displacements of model superstructures were recorded during the shaking events. It was observed that the structure in non-liquefiable soil deposits had the highest accelerations due to the amplification of ground motion within the soil. On the other hand, the accelerations of the structure in liquefied site was small due to the increased dissipation of seismic energy. The structures founded on soil experienced residual (permanent) lateral displacements, with the permanent lateral displacement and tilting of the structure in the liquefied site being much larger. The structure on rigid foundation (i.e. foundation on rock or fixed base) experienced high accelerations and oscillatory displacement as the seismic energy could not be dissipated. Therefore, structures in liquefiable soil are prone to overturning damage due to failure of their foundations. Furthermore, the base shear force of the structure in the non-liquefied site was significantly larger than that in the liquefied site and fixed-base, indicating it would be more susceptible to shear failure. On the other hand, the fixed-base structure experienced relatively large acceleration and dynamic displacement responses, which indicates increased seismic demands on its structural members.

Shape memory alloy (SMA)-cable-controlled sliding bearings: development, testing, and system behavior

This paper presents an innovative type of friction sliding bearing system incorporating shape memory alloy (SMA) cables. The study commences with cyclic tests on individual SMA cables to understand their fundamental mechanical properties. The working principle of the proposed SMA-cable-controlled friction sliding bearing (SMA-sliding bearing) is subsequently described, followed by physical tests on two SMA-sliding bearing specimens. The bearing specimens show rectangular hysteresis loops induced by Coulomb friction before the SMA cables are stretched, and afterward the load resistance and energy dissipation capacity of the bearings are increased accompanied by certain self-centering capability due to the engagement of the SMA cables. Such action is expected to effectively restrict excessive displacements of the bearings and to help reduce the residual displacement. Following the experimental study, a theoretical model of the new bearing is developed and numerical simulation is carried out. The theoretical and numerical results agree very well with the experimental results. A case study focusing on a three-span continuous bridge subjected to pulse-like near-fault (NF) ground motions is subsequently conducted, where three types of bearing system, namely, conventional sliding bearing system, SMA-sliding bearing system, and steel-cable-controlled (steel-sliding) bearing system are compared. The system-level analysis results show that the proposed SMA-sliding bearing has its superiority in superstructure displacement control, with a limited increase in the curvature ductility of the pier.

Seismic control of a single-tower extradosed railway bridge using the E-Shaped steel damping bearing

An extradosed bridge is a hybrid structure that combines the main elements of the classic cable-stayed bridge and continuous girder bridge. Almost all extradosed bridges have the main girder transversely restrained at the pier locations, which may cause extremely large transverse shear force and bending moment on bridge substructures during strong earthquakes. This study thoroughly investigates the efficacy of using the E-shaped steel damping bearing (ESSDB) for lateral seismic control of a prototype extradosed railway bridge. Firstly, high-fidelity finite element models are developed for nonlinear time history analyses for both the ESSDB isolated bridge and two conventional non-isolated configurations (i.e., rigid frame system and continuous system). Parametric sensitivity study is then carried out, which indicates a tendency of decreasing transverse deck displacements and increasing pier base transverse forces with the increase of the ESSDB yield force. The optimal ESSDB yield force is thus selected mainly based on a tradeoff between maximizing the structural force reduction and limiting the deformation demand of the ESSDB. Finally, through detailed comparisons of bridge seismic responses with the two non-isolated cases, it shows that the ESSDB can significantly reduce the transverse seismic force demands in bridge substructures, at a cost of a moderate increase in superstructure displacements and formation of permanent inelastic deformation in the ESSDB. It is concluded that the ESSDB can provide a simple and efficient solution to the transverse seismic control of the extradosed railway bridge.

Risk analysis of seismic bridge damage: case study after Lombok and Palu earthquake

Indonesia is known as an earthquake-prone region, lies in the ring of fire zone. This potential hazard can impact several infrastructures, including bridges. Seismic bridge damages could possibly disrupt traffic flow furthermore cut off the regional connectivity. In this study, risk analysis is carried out on several bridges after Lombok and Palu earthquake. Visual inspection has been undertaken on 38 bridges on-site, and several damages identification are reported. Risk analysis was then carried out according to the severity of element damages and the frequency of occurrence. From the analysis, it is concluded that embankment settlement in the approach road is found to be the most potential element with the highest risk of damage due to earthquakes. Besides, the superstructure displacement and crack in the wing wall are at moderate risk. This finding makes the substructure become the most vulnerable element which needs more attention. Therefore, it is recommended to specify a higher design specification for substructure to mitigate seismic bridge damages, especially for bridges located in the high seismic zone area.

Substructure Responses of a Concrete Bridge with Different Deck-to-Pier Connections

This paper tried to analyze the effects of deck-to-pier connections on pier design forces of a number of typical bridges. To this end, the behavior of pier connection of several 3D concrete bridge models was studied under service loads. A parametric study is conducted to investigate the different bearing types and pier height effects. The responses of models, such as superstructure displacements, forces, and displacements of deck-to-pier connections, and column forces are presented. The analysis results revealed that an increase in pier height leads to a considerable rise in the pier displacements and a decrease in transferring forces in all types of connections, and the greatest increase was found in the single elastomeric-bearing line. Therefore, rigid connections have better performance compared to other cases in high piers. Moreover, evaluating the effect of deck-to-pier connection on the pier force distribution indicated that the double elastomeric-bearing line connection increases the rigidity and transferred moment in comparison to the single line to the pier. Thus, its restraint lies between rigid and single bearing line conditions, and it should be considered in column design and can be more effective in moderate pier height. It was also revealed that the bearing location has a significant effect on the connection stiffness and transferred forces to the pier and influences its behavior and design.

Experimental Studies on Seismic Response of Skew Bridges with Seat-Type Abutments. I: Shake Table Experiments

Girder unseating in skewed bridges with seat-type abutments has been frequently observed in past earthquakes. This has been attributed to excessive in-plane rotation of the superstructure, and a handful of numerical studies have been conducted to investigate the cause of this rotation. The most common explanation has been pounding between the superstructure and abutment back wall, but this phenomenon has not been verified by experimental testing. Accordingly, this paper describes an experimental investigation into the behavior of skewed bridges, with special attention being given to the interaction between the superstructure and abutment. Shake table experiments are described on a family of four single-span simply supported bridge models with skew angles of 0°, 30°, 45°, and 60° and five different expansion gaps. These models were subjected to a suite of ground motions that varied by type (near field and far field), intensity, and input direction. In total, 876 experiments were conducted. Data collected included superstructure displacements and accelerations, and impact forces at the abutments. The results confirm that a skew bridge experiences large in-plane rotation when the obtuse corner of the span impacts the adjacent back wall with or without slippage along the face of the wall. As a consequence, these bridges can experience large in-plane displacements normal to the back wall at their acute corners, and larger support lengths are required to prevent unseating than for straight bridges. The comprehensive data set obtained in these experiments may be used in future studies to validate numerical models for skew bridges and improve the empirically based minimum support length requirements that are specified for skew bridges in many bridge design codes.

Numerical study on the stochastic response of a long-span sea-crossing bridge subjected to extreme nonlinear wave loads

In current practice, linear wave load theory is widely employed in the wave force evaluation of sea-crossing bridges. However, the observation of nonlinear wave loads in shallow waters suggests that second-order wave loads might be essential to the dynamic behavior of marine structures. In this paper, a framework to investigate the stochastic response of a long-span sea-crossing bridge under extreme nonlinear wave loads was proposed based on the combined use of the spectral wave model MIKE21 SW, the 3D diffraction theory hydrodynamic solver AQWA and the structural analysis tool ANSYS. An extreme wave condition of a 300-year return period at the exact bridge site is estimated from offshore statistical wave data by utilizing the state-of-the-art spectral wave model MIKE21 SW by considering of the complex nearshore wave transformation. Linear as well as nonlinear stochastic wave loads are modeled in AQWA and subsequently fed into the finite-element model to assess the responses. The results indicate that the nonlinear wave loads could remarkably increase the dynamic responses of the internal base forces of bridge foundations as well as displacements of superstructures. The sum-frequency second-order components in nonlinear loads, though not large in magnitude, might overlap with the first few eigenfrequencies of the bridge and thus excite these modes and increase the responses.

Comparative Seismic Fragility Assessment of an Existing Isolated Continuous Bridge Retrofitted with Different Energy Dissipation Devices

Seismic isolation is a commonly adopted approach for designing bridges against earthquakes. However, the period elongation in an isolated bridge will generally lead to a large superstructure displacement, which may result in pounding, bearing unseating, or even span collapse. This study focuses on the implementation of energy dissipation devices for retrofitting an existing bridge isolated by lead rubber bearings (LRBs). Four different retrofit measures, namely yielding steel cables (YSCs), viscous dampers (VDs), friction dampers (FDs), and superelastic shape memory alloy cables (SMAs) were considered in this study. Fragility analyses were performed to evaluate the relative effectiveness of these devices in minimizing the seismic vulnerability of the bridge. The results indicate that all the devices show comparable performance in reducing the probability of damage of the isolation bearings without imposing much additional vulnerability on the bridge piers. The SMAs are the most effective in mitigating the seismic vulnerability of the bridge system at all the damage states, followed by FDs, VDs, and YSCs. Due to the superior self-centering capacity, the SMAs retrofitted bridge exhibits better recentering performance with a reduced residual displacement of superstructure compared with the bridges with other retrofit measures.