Displacement-based Design Method Research Articles

Explainable AI model for predicting equivalent viscous damping in dual frame–wall resilient system

A prominent challenge in applying the direct displacement-based design (DDBD) method to the proposed dual frame–wall lateral force-resisting system lies in determining the equivalent viscous damping ratio (EVDR). However, the strong nonlinearity and complexity behind the equivalent procedure lead to limited choice, mostly trial and error based on experience, to explain and predict the EVDR in the context of traditional research. This study employs the XGBoost method to unravel intricate relationships of EVDR using over 5 million data points from nonlinear time-history (NLTH) analyses, encompassing various parameters including the fundamental period, ductility, subsystem stiffness ratios, post-yielding stiffness ratios of the subsystems and ground motion types. SHapley Additive exPlanations (SHAP) values consistently identify critical features relevant to the equivalent procedure. Comprehensive feature ablation tests further illuminate the robustness and susceptibility of each model. Additionally, the incorporation of Local Interpretable Model-agnostic Explanations (LIME) for local interpretability provides insights into the intricate decision-making mechanisms inherent in each model’s predictions. Both the predicting results from machine learning (ML) and traditional method are also compared. Findings highlight the relative importance of features for EVDR and present a refined prediction model. It underscores the pivotal role of model interpretability in reinforcing confidence in complex models and advocates for leveraging ML techniques to enhance the effectiveness and efficiency of the DDBD method in structural design.

Strength reduction factor for inelastic-displacement estimation and design of self-centering viscous-hysteretic systems

This study focuses on developing strength reduction factor Rμ spectrum, a maximum inelastic displacement (MID) estimation method and a displacement-based design method for single-degree-of-freedom (SDOF) bilinear structures with self-centering viscous-hysteretic devices (SC-VHDs). The effects of design parameters on Rμ spectrum are statistically investigated under near-fault pulse-like ground motions (NFPG) and far-field ground motions (FFG), and its prediction formula is fitted according to the statistical data. Following proposed Rμ spectrum, a MID estimation method and a performance-based design method are proposed, respectively. Next, three SC-VHD frames are designed step-by-step to verify the proposed design method, and then their MIDs are calculated step-by-step to validate the MID estimation method. Finally, a risk assessment is conducted on a SC-VHD frame and a conventional frame to compare their collapse performance and the performance exceeding 0.2% residual drift in the probability framework. The results indicate that Rμ spectrum is primarily affected by the ductility ratio, period and viscous damping ratio, while the parameters of ring springs have little effect on it. Rμ spectrum under the NFPE is significantly lower than that under the FFE except for periods from 0.2 s to 0.6 s. The Rμ spectrum formula and the MID estimation method both have errors that are typically less than 10%. The designed SC-VHD frame can achieve the target performance, and its probability of collapse and exceeding 0.2% residual drift in a period of 50-year is significantly smaller than that of the conventional frame.

Substructure-based design method for vertically irregular steel buckling-restrained braced frame structures

Buckling-restrained braces (BRBs) can mitigate the uneven inter-story drifts of vertically irregular steel frame structures during earthquakes, preventing unfavorable seismic forces and failure patterns. However, the structural lateral displacement profile of vertically irregular steel buckling-restrained braced frame structures (VSBFSs) can hardly be predicted; hence, parameter tuning and iterative designing are commonly required in conventional direct displacement-based design (DDBD) methods, which strongly rely on the experience of designers and consumes a considerable amount of time. This study proposes a substructure-based design (SBD) method developed explicitly for VSBFSs. In this method, the substructures of every story of a VSBFS are separated from the entire structure and individually analyzed in the subsequent procedures. The boundary conditions of the substructures are initially simplified as hinges, and an explicit equation of BRB stiffness and inter-story drift for the substructures is established. An iterative calculation procedure is consequently applied to correct the equation by considering the influence of the constraints of adjacent stories. In this manner, the inter-story drifts of all the stories of the entire structure uniformly converge to the predetermined targets, in which the demand of BRBs for each story is also determined. Compared with conventional DDBD methods, the proposed method does not assume the structural lateral displacement profile and is not based on experience, yielding relatively economical and safe design outcomes in a timely manner. The proposed SBD method was first validated by comparing it with existing elastic and elastoplastic design methods through a 15-story VSBFS example. Then, the applicability of the SBD method was further explored through four 6-story VSBFSs with different plan layout reductions and two VSBFSs with heights of 20 stories and 30 stories. Finally, the SBD method was applied to redesign the BRBs of a vertically irregular thermal power plant model (an example of a VSBFS) in a shaking table test.

Seismic performance assessment of post-tensioned CLT shear wall buildings with buckling-restrained axial fuses

Post-tensioned cross-laminated timber (PT-CLT) walls have been demonstrated to be a low-damage seismic force-resisting system (SFRS) due to their self-centering capability. However, there is still a need to examine the seismic performance of such SFRS in high-seismic risk zones. This study evaluates the seismic performance of 6-, 9-, and 12-storey PT-CLT shear wall buildings in Vancouver, Canada, equipped with buckling-restrained axial fuses. The prototype buildings were designed using the displacement-based design method, and the assessment considered the most recent seismic hazard model provided in the 2020 National Building Code of Canada. To conduct nonlinear response history analysis (NLRHA) and incremental dynamic analysis (IDA), numerical models were developed in OpenSeesPy and calibrated based on component- and system-level experimental tests. The NLRHA and IDA results demonstrate that all the studied buildings have adequate collapse margin ratios, with less than a 10% chance of collapsing at the maximum considered earthquakes.

Displacement-based seismic design of SMA cable-restrained sliding lead rubber bearing for isolated continuous girder bridges

The sliding of isolation bearings in a bridge structure can reduce bridge pier damage, but bearing sliding under the strong earthquake may cause excessive displacement of the girders or even falling girders. This study proposes an innovative shape memory alloy (SMA) cable-restrained sliding lead rubber bearing (SMA-SLRB), which can maximise the sliding advantages of the bearing whilst combining the displacement-limiting capacity and self-centering capacity of the SMA cable. The working mechanism of the SMA-SLRB is firstly revealed, and the mechanical model of the SMA-SLRB is verified by tests. Then, the multilevel fortification performance target of isolated continuous girder bridges with SMA-SLRB is proposed. A displacement-based seismic design (DBSD) method for the SMA-SLRB isolated continuous girder bridge is established. Next, with the single pier model of a five-span isolated continuous girder bridge taken as an example, the displacement-based design is implemented, and the seismic performance of the bridge is evaluated. Finally, the seismic responses of bridges with SMA-SLRB and SLRB under extremely rare earthquakes are compared. Results show that the energy dissipation capacity and stiffness of SMA-SLRB are improved to varying degrees compared with SLRB. The bridge basically achieves the design target displacement and meets the requirements of multilevel fortification performance, which confirms the effectiveness of the DBSD method. Under extremely rare earthquakes, the SMA-SLRB can effectively reduce the maximum displacement and residual displacement of the girder compared with the SLRB.

Nonlinear analysis model and seismic resilience assessment of LEM-filled CFS residence

Lightweight EPS materials (LEM)-filled cold-formed steel (CFS) shear wall structure is a new type of green, low-carbon and prefabricated rural residence, which has drawn in expanding consideration due to the promotion of the rural revitalization strategy. However, most of the existing research on this type of residence has focused on its behaviours of components, with little attention was paid to its overall response to resist earthquake disasters. During the past two decades, significant advancements have been made in effectively mitigating building collapses and reducing casualties resulting from earthquakes. Thus, the concept of seismic resilience is proposed, and the seismic performance requirements of structural design have been elevated from “safety” to “resilience”. To analyze the seismic resilience of LEM-filled CFS residence, this paper proposed a strut and tie- equivalent spring model to establish the simplified analysis model of a single composite wall, and the precision of the model was confirmed by test results, in which the nonlinear characteristic and the supporting effect of fillers was considered. Subsequently, three LEM-filled CFS residences are designed using the direct displacement-based design method. Then the three-D models are established for nonlinear analysis, and the inter-drift ratio (IDR) and residual inter-drift ratio (RIDR) are adopted to estimate the seismic response of the three archetypes. The seismic resilience of the three archetypes are assessed based on FEMA P58. This paper would provide a guidance for the nonlinear analysis and seismic resilience assessment of this type of residences, and promote the application and popularization of this kind of residence.

Seismic performance of self-centering braced rocking frame with novel self-centering friction dampers characterized by low-secondary stiffness

Research has demonstrated that self-centering energy dissipation dampers (SCEDs) are effective devices for reducing the residual deformation of structures after a strong earthquake. However, the equivalent damping ratio of SCEDs is relatively lower than that of conventional dampers such as viscous dampers, BRBs, or friction dampers. According to displacement spectrums, the lower damping ratio could result in a lower natural period and higher equivalent stiffness of structures for a given displacement target, and thus the structures could attract more earthquake action to the structures. To alleviate the problem, a novel self-centering damper composed of elastic post-buckling plates and adjustable friction devices (PBSCFD) was proposed and used as the self-centering braces for a self-centering braced rocking frame (SBRF) structure for example. First, the theoretical force-displacement relationship of the PBSCFD was derived based on its configuration and work principle, and then a scaled PBSCFD was manufactured and tested to investigate its mechanical properties and verify the theoretical constitutive model. Subsequently, the SBRF structure with PBSCFDs was designed by the direct displacement-based seismic design method (DDBD), and its seismic performance was examined by elastic–plastic time-history analysis. Finally, the effects of the secondary stiffness ratio of the self-centering braces on seismic mitigation of the SBRF structure were investigated. The results show that PBSCFDs is characterized by classic self-centering behavior with low secondary stiffness, which can be designed to obtain significant control effects on the base/interstorey shear and interstorey drift ratio of the SBRF structure under rare and extremely rare earthquake compared to the conventional SCEDs with significant secondary stiffness.

Hybrid self-centering dual rocking core system for seismic resilience by controlling both structural and nonstructural damage

This study proposes a novel hybrid self-centering dual rocking core (HSDRC) system with structural and nonstructural damage control functions for the building structure’s seismic resilience. The rigid rocking cores (RCs), viscous dampers (VDs), and shear friction spring dampers (SFDs) are introduced in HSDRC systems. The rocking cores with pinned bases are adopted for promoting uniform inter-story drifts over the building height. The SFDs are introduced to dissipate hysteretic energy and bring self-centering capacity by eliminating residual deformation. The VD’s velocity-proportional damping can help HSDRC systems control the nonstructural damage and building content’s damage sensitive to absolute floor accelerations. The expected behavior of HSDRC systems is first described. A direct displacement-based design (DDBD) method is following proposed to achieve the desired nonlinear behavior of HSDRC. Following the developed DDBD procedure, six HSDRC systems are designed. For highlighting the advantages of HSDRC systems compared to the existing self-centering energy-absorbing rocking core (SEDRC) system, two SEDRC systems are also designed. Nonlinear dynamics were included for investigating the performance of the designed systems subjected to seismic events. The numerical results demonstrate that the designed HSDRC systems show the expected nonlinear behavior and achieve the design target, confirming the developed DDBD method’s effectiveness. Compared to SEDRC systems, the newly proposed HSDRC systems show smaller absolute floor acceleration responses while obtaining the comparative capacity in controlling both peak and residual inters-tory drifts, indicating the proposed HSDRC systems can be a promising seismic resilient structural system for both structural and nonstructural damage control.

Probabilistic residual displacement-based design for enhancing seismic resilience of BRBFs using self-centering braces

Buckling-restrained braces (BRBs) can effectively control the structural maximum displacements. However, their full hysteresis tends to cause significant residual drifts after strong earthquakes, resulting in massive economic loss. To improve the resilience of the buckling-restrained braced frames (BRBFs) by reducing the residual drifts, self-centering braces (SCBs) are introduced to BRBFs based on the probabilistic residual displacement-based design (PRDBD) method in this study. Parametric analyses are first carried out on single-degree-of-freedom (SDOF) systems to represent the retrofitted BRBFs subjected to near-fault pulse-like earthquakes, wherein the isotropic strain hardening of BRBs is considered. The probabilistic prediction models for maximum and residual displacement are subsequently developed by employing an artificial neural network (ANN) machine learning algorithm. Subsequently, the PRDBD method is proposed. A benchmark BRBF is retrofitted by SCBs to demonstrate the PRDBD’s effectiveness. System-level nonlinear time-history analyses (THAs) are performed to study the dynamic performance of the enhanced BRBFs. It can be observed from the analysis results that the proposed PRDBD is efficient in controlling residual displacements of the enhanced BRBFs within the prescribed guarantee rate. Moreover, the analysis results confirm that the retrofitted BRBF with partial self-centering behavior can achieve remarkable post-earthquake repairability, as evidenced by residual inter-story drifts below 0.5% with 99% probability subjected to the maximum considered earthquakes.

Design and numerical analysis of Cross-Laminated bamboo (CLB) buildings with different rocking wall configurations

Engineering bamboo attracts increasing attention due to its renewable, low-carbon properties as well as the high strength-to-weight ratio. This paper proposed a displacement-based design (DBD) method for cross-laminated bamboo (CLB) rocking wall buildings based on experimental tests. The DBD was to control the story drift limitation considering the collapse prevention (CP) hazards level. The DBD accounted for the detailed design of prestressed tendons (PT) and conventional friction dampers (CFD). Segmented and monolithic rocking wall configurations were designed based on DBD and applied in the building. The simplified numerical models (SNM) for those two rocking walls were established in ABAQUS using cartesian connectors. Then two three-story CLB building models, i.e., X-LamBR1 with segmented rocking wall and X-LamBR2 with monolithic rocking wall were developed. Modal analysis and time history analysis were conducted with these two models. Smaller inter-story displacement, acceleration, and shear force were observed in X-LamBR2. Simulation results indicated that building with a monolithic rocking wall configuration performed better under earthquake excitation.

SEISMIC VULNERABILITY ASSESSMENT OF BASE-ISOLATED RC FRAME BUILDING USING DDBD METHOD

The direct displacement-based design (DDBD) method is widely used worldwide because it allows structures to be designed based on their expected performance criteria. The DDBD approach is utilized so that base-isolated building structures can meet the seismic performance parameters established by the displacement threshold. In the present study, an 8-story, 10-story and 12-storey base-isolated RC frame building is designed using the latest Indian seismic standards, with lead rubber bearing (LRB) as the base-isolation system. Force-based and DDBD methodology is implemented and compared for the selected base-isolated RC frame buildings. The nonlinear time-history analysis is conducted to evaluate the nonlinear lateral response of the RC frame buildings. The results indicated that the traditional force-based method shows almost 12% less top-storey displacement than the DDBD approach. The DDBD approach provides enhanced reliability, simplicity, and convenience in seismic design for base-isolated building frames with LRBs, making the observations more dependable and easier to employ.

Hybrid force-displacement-based design methods for self-centering wall structures

Self-centering wall structures (SCWs) are well-developed resilient structures and are being gradually implemented in practical engineering. The direct displacement-based design (DDBD) method is commonly adopted for the seismic design of SCWs due to its predictable displacement pattern. Due to the complexity of DDBD, practical engineers still commonly use the present force-based design (FBD) methods. However, the existing FBD method is inapplicable when the deformation of SCWs is large. To make the design procedure more acceptable to engineers and promote SCWs in real practice, three design methods were proposed: a force-based design method by empirical formula, a force-based method by iteration, and a hybrid force-displacement-based design method (HBD). The applicability of FBD by existing empirical formulas of structural periods in several codes for SCWs was discussed. In FBD by iteration, the initial prestress is iterated to determine secant stiffness and the structural period so that SCWs can be designed following its constitutive relationships. HBD is carried out by comparing the resistance of the structure under the target displacement with the earthquake demand according to the deformation mode of the SCWs. Compared with the existing DDBD methods, the proposed design methods can simplify the design process in engineering applications while keeping the design outcomes consistent with DDBD and proved to be reasonable with nonlinear time history analysis. In addition, the FBD method by empirical formula and the HBD method can be implemented in the four-level seismic fortifications currently proposed in China. The proposed methods solve the issues of the existing FBD and could be a reference for engineers to design SCWs in engineering practice.

Development and investigation of a self-centering cable brace with variable slip stiffness for braced frame structure

Extremely rarely occurring earthquake (EROE) level is currently not often considered in most national codes or standards, and the earthquake damage has shown that its consequences are serious. To control the seismic responses of the structures under the EROE level, a novel self-centering cable brace with variable slip stiffness (VSS-SCB) is proposed as the lateral force resisting component of braced frame structure. Firstly, the theoretical analysis of the damper in the VSS-SCB was carried out, it is found that the slope angle, friction coefficient, and compressive stiffness of the disc springs are the main parameters affecting the mechanical behavior of the damper. The combination of strong and weak stacks of disc springs can effectively provide a self-centering damper with adaptive stiffness. Then, pseudo-static tests were carried out on the design specimens of the damper. The test results show that the hysteretic curve of the self-centering cable brace with constant slip stiffness (CSS-SCB) presents a classical flag type, and the residual deformation can be ignored. When the disc spring stacks with different stiffness are combined in series, there are significant strengthened points for the loading and unloading stiffness of the brace. Finally, the displacement-based design method was applied to the design of the braced frame structures with the VSS-SCBs. The dynamic analysis shows that the braced frame structure with the CSS-SCBs has larger displacement response than that with the buckling-restrained braces (BRBs), and the hysteretic curves of the CSS-SCB and VSS-SCB show good self-centering capability. When the deformation of the CSS-SCB and VSS-SCB exceeds the strengthened point, the large strengthened stiffness of VSS-SCB can control the seismic response of the braced frame structure. The seismic fragility curves of the braced frame structures with the BRBs and with the VSS-SCBs are comparable, and are significantly smaller than that with the CSS-SCBs. However, since the BRB is prone to significant residual deformation, the braced frame structure with the VSS-SCBs has more advantages in improving the seismic resilience of the structure.

Effects of beam-column connection rigidities and soil-structure interaction on seismic performance of steel frames

Structures can be exposed to non-linear deformations under earthquake effects. However, linear methods are mostly preferred for designs because of their simplicity and facility. The inelastic behavior of the structure is approximately taken into account by using some coefficients. However, it is possible to make more realistic and economical designs by using methods that consider the inelastic behavior of the structure. In this context, the displacement-based design method is becoming increasingly popular. This study evaluates the seismic performance of steel frames resting on elastic foundations with different beam-column joint stiffnesses using the static pushover analysis method. Static pushover curves, plastic deformations, performance points, and base shear forces were compared. The results show that the base condition greatly affects the seismic performance of the building.

A novel self-centering friction damper with elastic post-buckling plates to retrofit bridge bents

The self-centering energy dissipation dampers (SCEDs) have been demonstrated in mitigating the residual deformation of structures under strong ground motions. However, existing researches show that the damping force demand of SCEDs is higher than conventional dampers such as viscous dampers, BRBs or friction dampers for same design displacement of self-centering retrofitted structures, which could lead to higher base shear and acceleration responses of structures. In order to alleviate the problem, a novel self-centering damper composed of elastic post-buckling plates and adjustable friction devices (PBSCFD) was proposed. Compared with conventional SCEDs, the proposed PBSCFD has low secondary stiffness and adjustable energy dissipation capacity, which is beneficial to control the additional internal force of members adjacent to the damper in self-centering retrofitted structures. Based on the configuration and working principle of the PBSCFD, the theoretical force-displacement relationship of the damper was derived. Subsequently, a scaled PBSCFD was manufactured and tested under quasi-static loading to investigate its mechanical properties and to verify the theoretical constitutive model. In order to demonstrate the seismic performance of PBSCFDs, the double-column bridge bent retrofitted with PBSCFDs was designed by direct displacement-based seismic design method (DDBD), and its seismic performance was examined by elastic-plastic time-history analysis. Finally, effects of secondary stiffness ratio of self-centering dampers on seismic mitigation of self-centering retrofitted bridge bent were investigated. The results show that PBSCFDs have certain advantages in controlling the base shear and acceleration of the retrofitted bridge bent compared to conventional SCEDs with significant secondary stiffness.

Direct displacement-based design of steel-timber hybrid structure with separated gravity and lateral resisting systems

Steel-timber hybrid structure can bring the benefits of timber and steel together in a more effective way. In this paper, a steel-timber hybrid structure with separated gravity and lateral resisting systems (ST-SGLRS) was proposed, and an iterative direct displacement-based design method was developed for this type of structure. Design examples revealed that the direct displacement-based design method with appropriate iterative steps is feasible for the design of steel-timber hybrid structures with separated gravity and lateral resisting systems. Furthermore, four steel-timber hybrid structures were designed based on the proposed design method, including 6-story, 9-story, 12-story structures with deformable steel-timber connections and a 9-story structure with rigid steel-timber connections, and corresponding OpenSees structural models were generated. Static and dynamic analyses were performed on the models to calibrate the structural performance. Comparing with the analytical result, it is found that the post-yield stiffness of the structure with deformable steel-timber connections decreased less than the structure with rigid steel-timber connections. As the earthquake intensity increased, the inter-story drift of the structure with rigid steel-timber connections increased rapidly. Besides, the residual inter-story drift of the structure with rigid steel-timber connections was generally larger than that of the structure with deformable steel-timber connections, indicating that the deformable connections contribute to the structure's ability to recover after a large earthquake. Finally, the seismic performance of the calibrated structures considering far-field and near-field earthquakes and impulse effect was evaluated via the probabilistic seismic demand analysis method. It is found that the maximum inter-story drift and the residual inter-story drift exceedance probabilities of the structures under near-field pulse-like earthquakes were larger than those under near-field no-pulse and far-field earthquakes. The research outcome aims to provide a fundamental basis for the design and engineering application of steel-timber hybrid structures with separated gravity and lateral resisting systems.

Self-centering beam-column joints with variable stiffness for steel moment resisting frame

Different from the self-centering joint with constant post-yield stiffness (CS joint), self-centering joint with various post-yield stiffness (VS joint) is proposed to control the seismic responses and improve the seismic resilience of frame structures under the extremely rarely occurring earthquake (EROE) level. The angle steel connectors and disc springs are adopted to provide the energy dissipation and self-centering capacities of the VS joint, respectively. First, theoretical study and pseudo-static tests are conducted, the results show that the VS joint has two stages of stiffness after the joint gap opens; the joint can deform and dissipate energy during the first stage with ordinary post-yield stiffness when the rotation angle of the joint is small; with the increase of the joint rotation angle, the weak stack of disc springs is flattened, causing the joint to enter the second stage with strengthened post-yield stiffness. It is found that the smaller the deformation capacity of the preloaded weak stack, the smaller the begin rotation angle of the second stage; the larger the stiffness of the strong stack, the larger the strengthened post-yield stiffness. Then, the updated displacement-based design method suitable for the frame structure with the VS joints (VSF structure) is also proposed. The non-linear dynamic time analysis results show that the plastic damage of the general moment resisting frame structure (GF structure) is severe and exceeds the extent of repairability under the EROE level; both the frame structure with the CS joints (CSF structure) and VSF structure have similar structural responses under the frequently occurring earthquake (FOE), the moderately occurring earthquake (MOE) and the rarely occurring earthquake (ROE) levels, and both can avoid plastic damage and have good self-centering capability even under the EROE level; due to the strengthened post-yield stiffness of the VS joints, the displacement responses of the VSF structure under the EROE level can be effectively controlled, while this is difficult for the CSF structure, whose responses exceed the performance target.

Seismic retrofit of torsionally coupled RC soft-storey building using short yielding core BRBs

This study presents seismic retrofitting of medium-rise torsionally coupled Reinforced-Concrete (RC) non-ductile building with soft ground storey. An irregular RC building with T-shaped plan is considered for the present study. In this sample building the presence of plan irregularity results in the torsional coupling of lateral modes. The location of staircase in the sample building significantly enhances the plan irregularity. Therefore, the contribution of stiffness of the staircase slabs is considered in the overall stiffness of the numerical model. Buckling Restrained Braces (BRBs) with short yielding cores are adopted to improve the seismic performance of the sample building. Short yielding core BRBs are installed in the ground storey to control the seismic lateral response induced by the soft-storey and torsional coupling of lateral modes. Displacement-based design method is adopted for the design of short yielding core BRBs to enhance the stiffness and energy dissipation of the structure so that it can endure the considered earthquake without exceeding the target drift level. Nonlinear dynamic analysis of the sample building is carried out before and after retrofit under bidirectional horizontal ground excitations applied simultaneously. The seismic performance is assessed in terms of maximum inter-storey drift, torsional response, plastic hinge distribution, residual displacement. Maximum axial force distribution of BRBs, maximum ductility and cumulative ductility demand of BRBs are discussed for a critical ground motion record. Analysis of the results reveals that the installation of BRBs decouples the torsionally coupled lateral modes of the sample building; and decreases inter-storey drift, torsional response and residual displacement in the soft ground storey. Thus, the retrofit design considered in this study, enhances the overall structural performance of the sample building reducing the lateral response due to the combined effect of the soft-storey and torsional coupling of lateral modes.

Seismic design and shaking table test of continuous girder bridges with winding rope fluid viscous dampers

In order to decrease the seismic response of continuous girder bridges, a winding rope fluid viscous damper (WRFVD) was proposed, which is installed on sliding piers, and connected to the deck by winding ropes. In this paper, the mechanical properties of WRFVD were derived and verified by the dynamic performance test. The direct displacement-based seismic design (DDBD) method of WRFVD was developed. Then, a scaled three-span continuous girder bridge was designed for the shaking table test to investigate the seismic performance of WRFVD and validate the seismic design method. The test results showed that WRFVD can effectively reduce the internal force of the fixed pier and the deck displacement. Additionally, the corresponding numerical simulations were carried out to compare with the test results, which are in good agreement with experimental data with acceptable difference. Then a series of nonlinear time history analyses based on the test model was conducted to evaluate the effectiveness of the DDBD method of WRFVD. The test and numerical results reveal that the DDBD method of WRFVD can effectively calculate the seismic response of continuous girder bridges with WRFVD.

Lateral displacement mode of column-supported modular steel structures with semi-rigid connections

The lateral displacement of a column-supported modular steel structure with semi-rigid connections (CSMSS-SRC) owing to lateral loading was investigated to determine the corresponding lateral displacement mode and establish a foundation for a direct displacement-based seismic design method. Theoretical equations for the lateral displacement caused by the bending deformation of beams and columns, axial deformation of columns, and shear deformation of the vertical inter-module connections were theoretically derived using slope–deflection equations, unit-load method, and shear deformation definition, respectively. Two simplified single frame finite element models were then established to verify the theoretical equations and study the effects of the rotational and horizontal shear stiffnesses of the vertical inter-module connections on the lateral displacement of the CSMSS-SRC. The results showed that the proposed lateral displacement equations are highly accurate. Furthermore, although the rotational stiffness of the vertical inter-module connection did not exert an appreciable effect on the lateral displacement of the CSMSS-SRC, its horizontal shear stiffness did. These results are expected to provide a reference for the engineering design of CSMSS-SRC.