Force-displacement Hysteresis Research Articles

Seismic performance of self-centering steel column base with buckling-restrained bars

Self-centering structures, emerging as a vital innovation in earthquake-resilient design, offer notable advantages in structural integrity, rapid functional recovery post-earthquake, and economic efficiency over the building's life cycle. This paper introduces a self-centering steel column base, employing buckling-restrained bars for energy dissipation. Through an analysis of its force mechanism, it conducts low-cycle reciprocating load test on four set of specimens with varying buckling-restrained bars and axial compression ratios. The results demonstrate the column base's superior seismic performance, characterized by its ability to rapidly restore seismic functionality after unloading and replacing the buckling-restrained bars. The force-displacement hysteresis curves exhibit a distinctive double-flag shape, with a minimal residual story drift of 0.001 rad, underscoring the structure's exceptional self-centering capability. The displacement ductility coefficients and equivalent viscous damping coefficients confirm the column base's excellent deformation and energy dissipation capabilities. Furthermore, a refined ABAQUS finite element model is developed and validated against the load test results, further analyzing the seismic performance relative to key structural parameters.

Asymmetric deterioration of reinforced concrete marine piles subjected to nonuniformly localized corrosion: Experimental study

Reinforced concrete (RC) marine piles usually suffer from local stiffness deterioration caused by chloride attack in splash and tidal zones. Moreover, pre-existing concrete cracks and defects at the steel–concrete interface usually lead to nonuniformly localized corrosion, which has seldomly been discussed. In this study, the effects of nonuniformly localized corrosion on the lateral behaviours of piles were experimentally studied. The localized electrochemical chloride erosion (LECE) technique was employed, and the corrosion level was represented by the number of corroded steel bars and the length of the corroded sections. Results show that the nonuniform localized corrosion caused asymmetric force–displacement hysteresis curves and changed the failure mode of pile structure under cyclic loading. The highly contrast mechanical responses suggest the importance of the loading directions in assessing the mechanical behaviours of corroded piles. Skeleton curves, stiffness degradation and energy dissipation capacity were further analysed to investigate the bearing capacity of corroded piles. These findings can benefit the comprehensive understandings and assessment of the asymmetric stiffness deterioration of corroded marine RC piles.

Cyclic loading changes the taproot's tensile properties and reinforces the soil via the shrub's taproot in semi-arid areas, China

This study aimed to reveal the soil reinforcement by shrub root systems after repeated stress from external forces, such as high winds and runoff, for extended periods in the wind-hydraulic compound erosion zone. Using the widely distributed Shandong mine area soil and water-conserving plant species, Caragana microphylla, Hippophae rhamnoides, and Artemisia ordosica, cyclic loading tests were conducted on taproots of the three plant species (1–5 mm diameter) via a TY8000 servo-type machine to investigate the taproots’ tensile properties response to repeated loading–unloading using simulated high wind pulling and runoff scouring. Our study revealed that the tensile force was positively correlated with the root diameter but the tensile strength was negatively correlated under monotonic and cyclic loading of the three plants’ taproots. However, after cyclic loading, the three plant species' taproots significantly enhanced the tensile force and strength more than monotonic loading (P < 0.05). The taproot force–displacement hysteresis curves of the three plant species revealed obvious cyclic characteristics. Structural equation modeling analysis revealed that root diameter and damage method directly affected the taproots' survival rate, reflecting their sustainable soil reinforcement capacity. The damage method significantly influenced the soil reinforcement more than the root diameter. Our findings reveal that the plant species' taproots can adapt more to the external environment and enhance their resistance to erosion after natural low perimeter erosion damage, effectively inducing soil reinforcement. Particularly, the taproots of Caragana microphylla have superior soil-fixing ability and can be used for ecological restoration.

Energy dissipation evaluation of butterfly-shaped steel plate shear keys under different loading protocols

This paper proposes a novel energy dissipation shear key (ED shear key) for small-to-medium-span highway bridges using butterfly-shaped steel plates for enhanced energy dissipation capacity. Reversed cyclic loading tests were conducted on two series of specimens which had different designs of structural dimensions. Four distinctive loading protocols were adopted to allow an in-depth examination of the seismic hysteretic behavior and energy dissipation capacity of the ED shear keys. The test results reveal that the ED shear keys exhibited distinctive characteristics before and after buckling of steel plates. The recorded force-displacement curves of the ED shear keys were plump before buckling and typically became pinched after buckling. The loading protocol had a significant effect on the energy dissipation of the ED shear key specimens, with an over 90% increase in energy dissipation observed under the constant-amplitude loading protocol compared to the incremental-amplitude ones. It was found from the test results that the profile of the force-displacement skeleton curves was hardly affected by the loading protocols, as a result a trilinear skeleton model is developed to characterize the force-displacement relationship of the ED shear keys. Furthermore, by decomposing the force-displacement hysteresis curve into a skeleton part and a Bauschinger part, an evaluation model is established for predicting the energy dissipation capacity of the ED shear keys. Validation against the test results indicates that the evaluation model can provide a satisfactory accuracy for predicting the energy dissipation of the ED shear keys subjected to various loading protocols.

Blast wave attenuation of nonlinear meta-isolation system: Theoretical analysis and experimental validation

In the field of protective engineering, wire rope isolators are usually applied in the isolation floor to mitigate the impact and vibration induced by explosive blast. In this paper, two kinds of meta-isolation systems were proposed and designed based on the local resonance, and investigated by means of theoretical analysis, numerical calculation and experimental research. First, the force-displacement hysteresis loops of the selected wire rope isolators are obtained by the cyclic loading tests, and identified by a mathematical model to make preparations for numerical calculation. Then, in order to discuss the influence of mass ratio, stiffness ratio and damping ratio on the shock isolation, the two-degree-of-freedom (TDOF) linear and nonlinear models are studied based on the mode superposition method and fourth-order Rugga-Kutta method respectively. Finally, the blast-induced ground shock experiments were conducted to evaluate the isolation efficiencies of conventional isolation systems and meta-isolation systems. The experiment results reveal that the isolation efficiency of meta-isolation system can increase by 10% points vertically and 16% points horizontally compared to conventional systems, which indicates that the meta-isolation system has great potential to be adopted in the engineering structures and provides a new idea and reference for protective engineering.

Cyclic test evaluation of double skin composite hybrid coupled wall with frictional steel truss coupling beams

The seismic performance of double skin composite shear walls (DSCSWs) has significant superior to conventional reinforce concrete (RC) shear walls. Previous studies have neglected the changes of axial compressive forces and bending moments actting on the top of wall piers. In addition, behaviors hybrid coupled wall (HCW) under real boundary condition have not been fully investigated. Thus, in this study, a novel quasi-static test which incorporates the boundary conditions of substructures in a prototype building was preformed. And a cyclic test was carried out on a 2/3-scaled double skin composite (DSC) HCW with frictional steel truss coupling beams (FSTCBs) using the proposed method. The seismic behavior of specimen under reversed lateral cyclic loads was investigated. The failure modes of the wall piers mainly included local buckling of the steel faceplate, fracture of the side plate, and concrete crushing at the corners of walls. The force-displacement hysteresis curve of FSTCBs was obtainable from the attached instruments as the force transmission path of the steel truss could be clearly observed. DSCSW pier deformation was evaluated based on the deformative relationship between the wall pier and FSTCB. The FSTCB primarily dissipated 80% of the total energy input prior to damage occurring in the DSCSW. Strain distribution curves along the DSCSW showed that the pre-peak-resistance plane section assumption was still valid.

Performance of special RC shear walls under lateral cyclic and axial loads

Reinforced concrete (RC) shear walls are common structural elements, although their cyclic behavior under different combinations of axial and lateral loading requires further study. The boundaries of flexural-dominated walls experience the greatest stress and strain; thus, rebar layouts are vital in this area and have significant effects on the cyclic behavior of a wall. In the current study, three full-scale walls were designed and constructed using the ACI318-19 special structural wall criteria with boundary elements placed at each end of the wall. Cyclic testing was performed on RC shear walls for different lateral and axial load combinations. These large-scale tests showed how axial loads affect the seismic performance of special RC shear walls. The seismic parameters of the force–displacement hysteresis curves, concrete strain, rebar strain, dissipated energy and stiffness are presented and discussed. The experimental findings demonstrate the effect of axial loading on the wall deformation capacity, strength capacity and mode of failure. Experimental backbone curves for numerical models of walls as recommended by ASCE41-17 revealed that the ASCE model overestimates the effective stiffness of walls with axial loads of less than 10% fcAg, A four-line model is proposed to estimate the force–deformation relationship. It is demonstrated that the effective stiffness coefficient should be a function of the axial load ratio.

Nonlinear analysis of vibration attenuation of ring-spring-resonator based meta-isolation system

Ring-spring-resonator (RSR) based nonlinear meta-isolation system (RSR-M) was proposed and its vibration attenuation characteristic was investigated experimentally and theoretically. The force–displacement hysteresis loops of the selected wire rope isolators (WRIs) exhibit softening under compression and hardening under extension, and are identified by a modified mathematical model combined with the normalized Bouc-Wen model. Frequency response curves of conventional isolation system and RSR-M−2 were calculated based on the single-degree-of-freedom (SDOF) and two-degree-of-freedom (TDOF) models, along with the fourth-order Runge-Kutta method. Shaking table experiments were carried out to evaluate the nonlinear dynamic response and vibration attenuation property of the RSR-M, which proves to be in good agreement with the numerical results of acceptable validity. Dynamic hysteresis loops and phase portraits were plotted to study the dynamic responses and stability of the RSR-M. The experimental results show that, no matter vertical or horizontal direction, the RSR-M possesses better vibration attenuation performance compared to conventional isolation system. In general, the meta-isolation vibration system provides a new reference and idea for the practice designing of the isolation system in some sense.

A novel energetic approach for predicting fatigue crack growth in pseudoelastic NiTi alloys

A novel strain energy-based method for analyzing fatigue crack growth (FCG) in pseudoelastic Nickel-Titanium (NiTi) -based shape memory alloys (SMAs) is proposed. It uses the dissipated energy to predict the FCG. This parameter can be computed either by volume integration of near-crack-tip strain energy or by the force–displacement hysteresis measured at the loading pins of the sample. Eccentrically-loaded single Edge Crack tension samples (ESE(T)) were used for FCG tests. High resolution Digital Image Correlation (DIC) was used to capture near-crack-tip displacement and strain fields. DIC data were also used to estimate the effective stress intensity range by regressing the William’s expansion series. Furthermore, a constitutive model for SMAs was used for FE simulations of ESE(T) samples, and the evolution of the dissipated energy during FCG tests was computed. Experimental FCG rate, plotted against the cyclic dissipated energy, are well fitted by a power law equation (R2 = 0.99). This result would open new perspectives to develop predictive models for FCG in SMAs considering intricate thermomechanical coupling mechanisms and material non-linearities.

Analytical and differential reformulations of the Vaiana–Rosati model for complex rate-independent mechanical hysteresis phenomena

A recent analytical model of hysteresis, developed by the authors to simulate a great variety of complex uniaxial rate-independent mechanical hysteresis phenomena, is reformulated in a twofold manner. First, it is proposed an analytical reformulation that, compared to the current version of the model, does not require the evaluation of any internal variable. Second, the closed form expressions provided by the analytical reformulation are expressed in rate form to foster its use especially in the field of nonlinear dynamics. To verify their accuracy, both formulations are first employed to reproduce four different complex hysteresis phenomena and the related results are compared in terms of generalized force–displacement hysteresis loops, tangent stiffness functions, and work-displacement relations. Subsequently, nonlinear time history analyses are carried out on four single degree of freedom mechanical systems for three different types of external generalized forces. To this end, two solution strategies are adopted. The former combines the model analytical reformulation with an explicit structure-dependent time integration method used to directly integrate the second-order ordinary differential equation of motion. The latter employs the model differential reformulation in conjunction with the Runge–Kutta method implemented to solve the equivalent system of three first-order ordinary differential equations. The comparison of the numerical results obtained by the two solution procedures shows an excellent agreement.

Force-Displacement Hysteresis Model of Exterior PCRB Joints under Low Cyclic Loading.

The seismic behaviors of exterior polyvinyl chloride-carbon-fiber-reinforced polymer (PVC-CFRP) confined concrete (PCCC) column-ring-beam joints (hereafter referred to as exterior PCRB joints) under low cyclic loading were investigated. A total of 11 specimens were tested to analyze the effects of the structural parameters (i.e., the reinforcement ratio of the ring beam, the CFRP-strip spacing, the ring-beam width, the reinforcement ratio of the frame beam, and the axial compression ratio) on the failure modes and hysteretic behavior. Three different failure modes, including the failure of the frame beam, the failure of the junction between the frame beam and the ring beam, and the shear failure of the ring-beam joint, were observed. The experimental results showed that the pinching effects of the hysteresis curves decreased and that the slope of the descending stage of the skeleton curves gradually decreased with the enhancement of the reinforcement ratio of the ring beam, axial compression ratio, and ring-beam width. The effects of the CFRP-strip spacing and the reinforcement ratio of the frame beam on the hysteresis loops and skeleton curves were marginal, while the reinforcement ratio of the frame beam exerted significant effects on the failure modes. Therefore, a model for predicting the skeleton curves of exterior PCRB joints and hysteresis rules was proposed, based on the softening constitutive relation of the concrete and a regression analysis of the test data. Ultimately, a load-displacement hysteresis model of the exterior PCRB joints was established and validated by the test data, with good agreement.

Experimental Investigation on Seismic Performance of Non-Uniformly Corroded RC Moment-Resisting Frames

To investigate the effect of non-uniform corrosion on the seismic performance of reinforced concrete (RC) frame structures, seven RC frame specimens, including one uncorroded and six corroded frames, were tested under quasi-static loading. The damage modes, force-displacement hysteresis curves and skeleton curves, stiffness degradation, ductility and the energy dissipation capacity of specimens were studied. The influences of the corrosion degree, non-uniform corrosion characteristic value, and axial compression ratio on the seismic performance of the specimens were analyzed. The test results show that non-uniform corrosion of longitudinal bars has a significant effect on the development of seismic damage in RC frames. In comparison with non-corroded RC frames, the loading carrying capacity of corroded frames with non-uniform corrosion characteristics values of 0.18, 0.59, and 0.72 decreased by 8.5%, 14.8%, and 22.3%, the displacement ductility ratios decreased by 6.7%, 8.7%, and 10.0%, and the total cumulative energy dissipation at ultimate displacement values decreased by 24%, 41%, and 54%. For corroded frames with low axial compressive ratios, the loading carrying capacity and energy dissipation capacity rose with the increase in the axial compression ratio.

Cyclic Nanoindentation for Local High Cycle Fatigue Investigations: A Methodological Approach Accounting for Thermal Drift

Cyclic nanoindentation allows characterizing the influence of single phases and their interactions on fatigue mechanisms. Herein, a method for high cycle fatigue testing by nanoindentation is presented. By combining high‐ and low‐frequency indentation modes, high cycle numbers are achieved while obtaining sufficient data points to reconstruct force–displacement hysteresis loops. A challenge is the stochastic course of thermal drift which is addressed by measuring drift rate in regular low‐force holding segments. Drift rates are used to correct the displacement values, yielding reproducible cyclic deformation data as it is shown for two very different materials, a ductile metal and a brittle ceramic.

Performance of RC beam-column joints with hybrid GFRP-steel reinforcement under cyclic and axial loads

Structural reinforced concrete (RC) elements incorporating glass fiber-reinforced polymer (GFRP) bars have been claimed to exhibit notable deformability under seismic loading. In this research, an attempt has been made to evaluate the influence of replacing steel bars with GFRP bars on the behaviour of RC beam-column joints. To this end, five ½ scale joints were fabricated and examined under cyclic and axial loading. The joints were the same in terms of specimens’ geometry, material properties and test setup while they differed in the number of beams’ steel bars replaced with GFRP bars. Otherwise noted, GFRP-to-steel bars ratio was changed by 0 (reference specimen), 25%, 50%, 75% and 100%. The crack propagation and force–displacement hysteresis curves are presented as the main test outputs. Moreover, seismic parameters namely displacement ductility, absorbed energy, stiffness and equivalent damping ratio are compared and discussed. Overall, the results demonstrated that incorporating GFRP bars by the ratio of less than 50% could enhance cyclic response of joints in terms of ductility, absorbed energy and equivalent damping ratio.

Analysis of Energy Dissipation on the Sealing Surface of Premium Connection Based on a Microslip Shear Layer Model

In high production gas wells, premium connections are subject to alternating loads and vibration excitation due to the change of fluid pressure exerted on the tubing string. The energy dissipation on the sealing surface of premium connections affects the sealing performance of premium connections. The present study proposes a new energy dissipation analysis method for the sealing performance of premium connections using a microslip shear layer mode, a novel technique to overcome and improve the limitations of existing analysis method of premium connections. In this paper, based on a microslip shear layer model, a vibration equilibrium equation of premium connection was established with the constraints of the taper of the sealing surface, the thread, and the torque shoulder. Then, the control equilibrium equations of the stick and microslip were derived, and the critical microslip tangential force and force–displacement hysteresis curves under different interface parameters were obtained by solving the equilibrium equations. The influence of different interface parameters on the energy dissipation of premium connection was discussed by using a standardized regression coefficient method. It was found that the friction coefficient influenced both the minimum and maximum microslip tangential forces, while the shear layer stiffness influenced only the minimum microslip tangential force. The greater the stiffness of the shear layer, the smaller the minimum microslip tangential force and the relative displacement of the contact surface, which made it easier to generate energy dissipation. The influence of the friction coefficient on energy dissipation was much greater than the stiffness of the shear layer. There was positive correlation between the friction coefficient and energy dissipation. While, there was a negative correlation between the stiffness of shear layer and energy dissipation. The results can provide a theoretical guide for micro sealing failure mechanism of premium connections under dynamic loads and expand the analysis method of metal seals.

Nonlinear damping effects in vertically vibrating systems with violently sloshing liquid

Damping induced by vertically sloshing liquids at large amplitudes is of interest in the understanding of the dynamic response of aircraft wings containing fuel. This work presents the experimental investigation of sloshing-induced damping in two small rectangular tanks (L=100mm, h=37.5mm and 50mm) under vertical excitation at various frequencies (3.3 to 10.3Hz) and amplitudes (up to 1.57 tank heights). The focus is placed on large amplitudes that lead to violent vertical interactions between the liquid and the tank and the nonlinear damping effects they cause. The sloshing-induced dissipative energy in dimensional form shows a deviation from linearity with increasing amplitude of excitation, which is attributed to force–displacement hysteresis sub-cycle formations. When increasing the frequency of excitation, it is shown that the damping increases initially, and then remains constant. These findings are confirmed by a kinematics-based ballistic–harmonic model. Optical flow and a new technique based on pixel intensity standard deviation are employed in correlation with an analysis of the hysteresis cycles in order to offer insight into the sloshing force variation within one liquid cycle of oscillation.

Numerical and experimental study of mechanical behaviors of the steel-confined rubber bearing

The conventional laminated rubber bearing is primarily for the horizontal seismic input. To achieve three-dimensional seismic isolation, the horizontal laminated steel plates in rubber bearings are replaced by externally confined steel plates, which is the steel-confined rubber bearing (SCRB). The external steel cover effectively increases the stability of the rubber bearing, while acting as a U-shaped steel cover and improving the energy dissipation capacity of the isolator. The mechanical properties of the SCRBs were investigated based on finite element analysis and experiments. The test and numerical results show that the SCRB has a low horizontal and vertical stiffness, while the external steel cover provides additional damping for the rubber isolator. The modified Bouc-Wen model was introduced to simulate the horizontal and vertical force–displacement hysteresis relationship of the SCRB. Based on FE model simulations, the effects of area coverage, quantity and length of steel cover on vertical stiffness, horizontal stiffness and equivalent damping ratio of the SCRB were analyzed in detail. A design procedure of the SCRB based on the stiffness is proposed. Finally, the effectiveness of the SCRB on reducing horizontal and vertical seismic responses is validated using a single-degree-of-freedom system.

Effect of Volume Fraction on Shear Mode Properties of Fe-Co and Fe-Ni Filled Magneto-Rheological Elastomers.

In this research, the synergistic behavior of magnetorheological elastomers containing nickel and cobalt along with iron particles as magnetically polarizable fillers is examined experimentally under dynamic shear loading. Two different types of magnetorheological elastomer were fabricated having equal proportions of iron and nickel in one kind, and iron and cobalt in the other. The concentrations of magnetic particles in each type are varied from 10% to 40% and investigated for several frequencies, displacement amplitude, and magnetic field values. A test assembly with moveable permanent magnets was used to vary magnetic field density. Force displacement hysteresis loops were studied for dynamic response of magnetorheological elastomers (MREs). It was observed that MREs showed a linear behavior at low strains while nonlinearity increased with increasing strain. The percentage filler content and frequency increased the MRE stiffness whereas it decreased with displacement amplitude. The computed maximum magnetorheological (MR) effect was 55.56 percent. While MRE with iron and cobalt gave the highest effective stiffness, MRE with iron and nickel gave the highest MR effect.

Classification and unified phenomenological modeling of complex uniaxial rate-independent hysteretic responses

The number and nature of hysteretic responses typically exhibited by mechanical systems and materials are so huge that their modeling and identification are usually carried out on an ad-hoc basis. Thus, with the aim of proposing a unified approach to the modeling of rate-independent hysteretic behavior, we first perform a detailed classification of complex generalized force–displacement hysteresis loops, ranging from the asymmetric, pinched, S-shaped, flag-shaped ones to those obtained by their arbitrary combination, since they typically span the vast majority of loops obtained experimentally. Subsequently, we formulate a novel rate-independent hysteretic model, having an exponential nature, that offers a series of advantages over other hysteretic models available in the literature. Indeed, it adopts closed form expressions for evaluating the output variable, with important benefits in terms of computational efficiency and implementation ease, and it allows for an uncoupled modeling of the generic loading and unloading phases by means of two different sets of eight parameters. In addition, it requires the use of a simple identification procedure thanks to the clear theoretical and/or experimental interpretation of the adopted parameters. The accuracy of the proposed model is experimentally and numerically validated and its computational efficiency is demonstrated. In particular, the experimental validation is carried out by reproducing four different types of complex experimental hysteresis loops retrieved from the literature, whereas the numerical validation is performed by running some nonlinear time history analyses on a single degree of freedom mechanical system and comparing the results with those obtained by using a modified version of the celebrated Graesser–Cozzarelli model.

Cyclic Testing on Seismic Behavior of Segmental Assembled CFST Bridge Pier with External Replaceable Energy Dissipator

In 2009–2022, to meet the requirement of resilient bridge pier structure (e.g., earthquake resistance, energy dissipation, isolation, resilience) for rapid repair after earthquakes and to improve the suitability of precast segmental bridge piers in medium- and high-intensity areas, a segmental assembled CFST bridge pier with external replaceable energy dissipator was proposed. Based on ABAQUS finite element analysis software, the finite element model of the CFST pier is established to analyze the force of the external replaceable energy dissipator, and the feasibility of the external energy dissipator is verified. Thereafter, two groups of segmentally assembled CFST pier model structures were tested for seismic behavior under reciprocating loading. Non-linear mechanical behaviors, such as restoring force-displacement hysteresis, loss of prestressing, and opening of the indirect joint of a segmented precast assembled pier, are analyzed. The results show that compared with a CFST pier with an energy dissipator, the lateral bearing capacity of the CFST pier with an external energy dissipator is increased by 32.8%, the energy dissipation capacity is also significantly improved, the opening size of joints between segments is reduced, and the overall damage of the CFST pier is concentrated on the energy dissipator, which is convenient for rapid disassembly and replacement. At the same time, the seismic performance of the CFST pier after replacing the energy dissipator is analyzed. The results show that the replacement of the external energy dissipator will not affect the seismic performance of a segmental assembled pier.