Equivalent Plastic Hinge Length Research Articles

Seismic performance and calculation method for plastic hinge length of RC pier reinforced with UHPC

Piers are highly vulnerable load-bearing components, and their seismic performance determines the integral seismic resistance of bridges to a certain degree. They play crucial roles in evacuation during earthquakes and post-earthquake rescue. The manner in which piers meet the seismic performance requirements after reinforcement has become a popular research topic. In this study, ultra-high-performance concrete (UHPC) and HTRB600E high-tensile reinforcements were used to expand the cross section of a cast-in-place square pier with severe bending damage. The earthquake-resistant behaviour indicators of the pier were compared and analysed by conducting pseudo-static tests on a reinforced concrete pier before and after reinforcement. These indicators included the hysteretic curve, skeleton curve, energy dissipation curve, rigidity degradation, residual displacement, and pier body curvature. Based on the results of the seismic reinforcement quasi-static tests, a finite element model (FEM) of the bridge pier was constructed using the ABAQUS software, and the accuracy of the FEM was averaged. The impact of the reinforcement layer height, thickness, longitudinal strength and axial compression ratio on the equivalent plastic-hinge length of the reinforced pier was analysed, and the formula for the equivalent plastic-hinge length of the reinforced pier was obtained based on multiple linear regression fitting. The analysis results demonstrated that the broadened section method, utilising UHPC and high-tensile reinforcement, significantly enhanced the flexural capacity, energy dissipation, and first rigidity of the bridge pier. The earthquake-resistant behaviour of pier was effectively restored and improved, and the seismic reinforcement effect was significant. The equivalent plastic hinge length of the pier after reinforcement is proportional to the height of the reinforcement layer, the thickness of the reinforcement layer, the strength of the longitudinal reinforcement, and inversely proportional to the axial compression ratio.

Base joint hysteresis model for reinforced concrete assembly columns with post-pouring area

In response to the problem of uncontrollable grouting quality of traditional grouting sleeves in the connection between prefabricated components, a column base joint with post pouring area connected by grouting sleeves (PCGS) is proposed. Both the sleeve and post pouring area could cause differences in hysteresis characteristics between prefabricated and cast-in-place components. In order to investigate the hysteresis model of PCGS column base joint, the cyclic load tests and finite element parametric analysis of PCGS column base joint were conducted. The theoretical calculation method for load and displacement of PCGS column base joint at yield, peak, and ultimate characteristic points was established based on equivalent rectangular stress and plastic hinge length in joint area. The average ratios of theoretical calculations to test results for load and displacement at the above three characteristic points are 0.997, 0.983, and 0.983, and 1.020, 1.041, and 0.970, respectively, indicating that the theoretical calculation method can accurately predict the strength and deformation of PCGS column base joint. The dimensionless skeleton curve model with double broken lines in the elastic and strengthening stages, and exponential function in descending stage has been established based on the test and simulated results. The degradation behavior of unloading stiffness and bearing capacity was quantitatively described using the regression fitting method, and the hysteresis rule was defined. The established hysteresis model can effectively reflect the strength and stiffness degradation under cyclic loading, which can provide guidance for the elastic-plastic seismic response analysis of PCGS column base joint.

Numerical investigation on plastic hinge behavior of hybrid steel-FRP reinforced concrete columns

This paper presents a numerical study on the plastic hinge behavior and rotation capacity of concrete columns reinforced with a combination of steel bars and fiber-reinforced polymer (FRP) bars. A meso-scale numerical model, which considers the internal heterogeneity of concrete and bond behavior between concrete and longitudinal reinforcements, was developed and validated. The failure modes, lateral load-displacement responses, and the physical plastic hinge lengths of hybrid steel-FRP reinforced concrete (SFRC) columns were investigated and compared with those of conventional steel-reinforced concrete columns. The results indicated that the steel yielding zone and curvature localization zone of SFRC columns with FRP longitudinal bars were enlarged, due to the relatively low modulus of FRP bars. After that, a parametric analysis was performed to study the plastic hinge length of SFRC columns with respect to the nominal area ratio of FRP longitudinal bars, shear span-to-depth ratio, axial load ratio, and longitudinal reinforcement ratio. A new empirical model was proposed to predict the equivalent plastic hinge length, which was subsequently integrated into an analytical method for predicting the ultimate rotation. The comparison of predictions with simulation and test results demonstrated the accuracy of both the proposed empirical model and analytical method.

Experimental and numerical study on flexural performance of ultra-high performance concrete frame beams reinforced with steel-FRP composite bars

This paper presents the bending tests of four ultra-high performance concrete (UHPC) frame beams and one normal strength concrete (NSC) frame beam, all reinforced with steel-FRP composite bars (SFCBs). A comprehensive analysis was carried out, encompassing evaluation of the failure mode, crack propagation, bearing capacity, deformation, strain response, and plastic rotational capacity of the frame beams. Investigating the effects of concrete type, reinforcement type, and beam-end reinforcement ratio on the flexural performance of the frame beams was a key aspect of this study. A three-dimensional finite element (FE) model of the frame beam was established and rigorously verified. The developed model enabled a detailed parametric analysis involving the steel ratio, the yield strength of the inner core steel bar, the elastic modulus of the FRP, and the ultimate tensile strength of the SFCB. The results indicated a consistent failure mode of all frame beams: crushing of concrete at the beam-end, initiating a sequence of plastic hinge occurrence starting at the beam-end and then progressing to mid-span. The substitution of normal strength concrete with UHPC significantly enhanced various aspects of the frame beams, including the flexural capacity, deformation, ductility, ultimate energy dissipation, and plastic rotational capacity, while inhibiting the generation and expansion of cracks. Notably, the plastic rotation angle of SFCB-UHPC frame beams was 4.9 times greater than those of steel-UHPC frame beams, emphasizing the effectiveness of SFCB in enhancing the beam-end plastic rotational capacity. A decrease in the beam-end reinforcement ratio significantly reduced the flexural capacity, ultimate energy dissipation, and beam-end plastic rotational capacity, while improving ductility. Additionally, the study established a formula for calculating the equivalent plastic hinge length, utilizing the relative compressive zone height and effective section height of the beam-end controlling section as variables, which demonstrated good alignment between predicted and experimental results.

Failure mechanism and plastic hinge of RC joints under impact load acting on column ends

Impact loads often act on columns end during accidents such as vehicle impacts and terrorist attacks. The resulting deformations lead to a redistribution of internal forces in the member as well as a reduction in the load carrying capacity. The integrity of the core area of the joint is threatened, which could trigger a progressive collapse. This study numerically investigated the damage and deformation of reinforced concrete (RC) beam-column joints when they are impacted on the column end. The resistance mechanism of joints and the influence of impact location as well as impact velocity was explored. Besides, the deformation capacity of RC beam-column joints under impact loading was quantified using equivalent plastic hinges. It was found that the damage and plastic deformation is concentrated at the impacted column end. The horizontal reaction force at the beam end provides resistance and plays the role as a bearing. The column bottom reaction force is in the same direction as the impact force. However, it is much smaller than the beam end reaction force. The resistance mechanisms within the joints can be categorized into strut-and-tie near the loading point and arches in the mid-span of the beam and column. The core area rotates and has a significant lateral displacement towards the impact location, whether it is loaded at the beam end or the column end. As the impact location moves away from the core aera, the impacted column end exhibit more bending failure. With increasing impact velocity, the impact force, reaction force and total energy absorption of the joint increase. The deformation increases, with more damage occurring in the core area and spreading to the beam. In addition, the plastic curvature was used to describe the actual plastic deformation of the joints, whose maximum occurring at the interface where the impacted column end meets the core area. A formula for the equivalent plastic hinge length of RC joints was proposed, taking into account the effects of impact location and impact velocity.

Experimental study on GFRP-steel double-skin rubber concrete composite piers under mixed loading

To address the issues related to the insufficient compressive and shear strength of rubberized concrete and to enhance the deformation capacity and longevity of composite piers, a novel approach involving the confinement of rubberized concrete with glass fiber-reinforced polymer (GFRP) tube and steel tube has been proposed. This method aims to create a GFRP-steel double-skin rubberized concrete composite pier. Pseudo-dynamic and quasi-static tests were conducted on the composite pier to assess its seismic response and residual seismic performance. The study investigated the failure mode, hysteretic characteristics, ductility, energy dissipation, stiffness, and self-centering capability of composite piers. Additionally, a correction coefficient for the equivalent plastic hinge length was proposed. The results indicate that the specimen maintains its elastic state when subjected to frequent seismic events. However, when subjected to infrequent seismic events, the glass fiber layer may fracture, leading to the development of white stripes, while the steel tube experiences yielding, transitioning into a plastic state. The shock absorption and toughness of rubberized concrete were effectively utilized when subjected to horizontal low cyclic loading, thereby mitigating the appearance of more pronounced damage in seismic-damaged specimens. The hysteretic curve was complete, demonstrating a significant energy dissipation capacity. This confirmation indicates that the composite pier can be a viable solution for sea-crossing bridges and complex environments.

Pushover Analyses of Slender Cantilever Bridge Piers with Strength and Ductility Degradation

Reinforced concrete bridge piers are often subject to spatially non-uniform deterioration which typically produces strength and ductility degradation. When piers are subject to deterioration, the sectional response is no longer uniform and the determination of the pushover curves from sectional response is no longer immediate. This paper proposes a simplified procedure to accomplish this task for RC bridge cantilever piers. The method is simplified only with respect to geometric nonlinearities and yields an accurate estimate of the ultimate displacement, free of numerical issues typical of fiber-based finite elements. The procedure is based on an iterative approach to enforce the element equilibrium under P-Delta effects induced by vertical loads and can consider arbitrary deterioration patterns through the specification of different moment-curvature response along the elevation. After validating the approach with experimental results, a parametric analysis of the influence of sectional strength and ductility degradation is carried out for the case study of a rectangular hollow RC pier. Results show that significant variations of the pier equivalent plastic hinge length can be expected because of the occurrence of deterioration in the lower part of the pier. Moreover, paper provides quantitative measure of the extent of the strength and ductility degradation.

Equivalent plastic hinge length of sleeve connected precast bridge piers

The paper proposes a method to calculate the deformation capacity of sleeve connected precast piers by assuming different curvature distributions for three types of damage forms. It also presents a calculation method for the displacement capacity of the top of precast piers. The study analyzes test data from 46 sleeve-connected precast piers to determine the classification of the three damage forms and the impact of design parameters on the plastic hinge length. Additionally, an equivalent plastic hinge model for precast piers with sleeve connections is established, considering bending, shear, longitudinal bar slip, and sleeve length. The F-Δ curve is determined through the utilization of the suggested equivalent plastic hinge model and the cast-in-place (CIP) based equivalent plastic hinge model, and the test results of three precast piers are compared. The results show that the precast pier with sleeve connection can experience three distinct types of damage: the pier bottom damage, the double plastic hinge zone damage and the sleeve top damage. According to the theory of correlation degree, the damage form of precast piers is more significantly affected by the axial compression ratio, while its impact on the equivalent plastic hinge length is relatively smaller. As the axial compression ratio increases, the influence of sleeve length on the equivalent plastic hinge length also increases. The proposed four parameter calibration equation for the equivalent plastic hinge length in this study has highly correlated properties. This equation demonstrates improved accuracy in simulating the F-Δ curve for the three distinct damage forms when compared to the CIP model, and the calculated value is well fitted with the experimental value.

Plastic hinge and damage mechanism of RC assembly column base joint with post pouring area

Column base joint with post pouring area connected by grouted sleeves (PPCGS), which can solve the problems of poor controllability of grouting quality in the engineering application of traditional sleeves, is proposed in this paper. Based on the horizontal low-cycle reversed loading test results of six full-scale column base joints under axial pressure, the mechanics characteristic of plastic hinge, the length of equivalent plastic hinge, and the displacement ductility are mainly explored. The research results showed that the plastic hinge was formed above the sleeves in all precast column base joints, and the post pouring area of PPCGS column base joints can provide higher compressive strength, so it could protect the longitudinal rebar under the sleeve from premature buckling deformation, made the plastic hinge fully develop at the top of the sleeves. The ratio of the equivalent plastic hinge length to the section size of PPCGS column base joints decreases as the section size of column and the strength of the post pouring material increase. The average error between the calculated results and the test results of the displacement ductility coefficient of PPCGS column base joints is -3.93%, and the displacement ductility coefficient showed an increasing trend with the increase of the section size and the strength of post pouring material. In addition, a finite element analysis method for the PPCGS column base joint was verified through experimental results, and the influence law of post pouring height and tenon section size on the damage of column base joint was obtained through parametric analysis.

Experimental investigation on plastic hinge length of RC round-ended hollow columns with a variable section

In the ductile design, it is an essential task to accurately estimate the equivalent plastic hinge length of a reinforced concrete (RC) column. The plastic behavior of a RC hollow column is influenced significantly by tension shift and bond-slip according to the test results, which hasn’t yet received adequate attention in the existing models of equivalent plastic hinge in the literatures. Few publications and even no explicit provision in the current codes provide the method to compute the plastic hinge of hollow RC columns, especially those with a variable section. To bridge this knowledge gap, in this study, based on the equivalent principle of plastic displacement, an innovative formula of equivalent plastic hinge length is derived for the hollow columns, which considers both the effects of plastic tension shift and bond-slip based upon the authors’ previous research on solid columns. The quasi-static tests on two rectangular and two round-ended hollow columns were conducted to calibrate the undetermined parameters of the proposed formula. The accuracy and applicability of the proposed formula were then investigated based on the available test results of 30 rectangular and 3 round-ended hollow columns in literature. The results show that different slip behavior leads to distinct plastic deformation between these two types of hollow columns. Compared to the rectangular columns with a uniform section, the plastic hinge length of round-ended columns is longer due to the presence of the bottom solid segment, chamfer, and variable section. For both types of hollow columns, the equivalent plastic hinge region increases with the specimen length, section height, and strain penetration. The comparison suggests that the proposed formula is more appropriate to calculate the plastic hinge length of hollow columns with a uniform or variable section than the existing models.

Study on the equivalent plastic hinge length of superimposed RC shear walls with embedded bracings

The equivalent plastic hinge length of RC shear wall is often regarded as an important index to be studied in the framework of performance-based seismic design, for which a series of evaluation formulae have been widely proposed. However, existing equivalent plastic hinge length calculation formulae are proposed for cast-in-place RC shear walls, while that for superimposed RC shear walls with embedded bracings (SRCXSWs) still needs to be further studied. With an attempt to achieve this goal, a series of research including finite element analysis and theoretical derivation are conducted in this research. Based on the analysis of crack development and failure modes for SRCXSW, the relationship between the ultimate deformation and the equivalent plastic hinge length is established through the theoretical derivation, then 51 finite element models with 10 parameters are analyzed by OpenSEES to summarize the influence modes of different parameters on the equivalent plastic hinge length. Finally, the equivalent plastic hinge length calculation formulae for SRCXSWs are proposed and verified by the numerical and experimental results. The research results illustrate that there exists a function relation between the ultimate deformation and the equivalent plastic hinge length, and decreasing the ratio of deformation caused by shear effect to top deformation or increasing the compressive strain properties of concrete by parameter assignment will be more conducive to the formation and development of the plastic hinge zone of SRCXSWs. The existing formulae cannot effectively estimate the equivalent plastic hinge length of SRCXSWs, while the proposed formulae are suitable for predicting the equivalent plastic hinge length of SRCXSWs.

Deformation ability of precast concrete columns reinforced with steel-FRP composite bars (SFCBs) based on the DIC method

A steel-fiber reinforced polymer (FRP) composite bar (SFCB) is a novel reinforcement composed of an inner steel bar and outer continuous FRP. Moreover, SFCBs have excellent corrosion resistance and stable positive post-yield stiffness and can be used to control structural damage. However, the relatively small fracture strain of the outer FRP may limit the deformation ability of the concrete members reinforced with SFCBs. Bundled reinforcement can weaken the interfacial adhesion to improve the structural deformation capacity and reduce the connections of the reinforced precast structures to enhance the construction efficiency and quality. In this paper, a quasistatic test of six concrete columns was conducted, and the deformation of the column foot was observed by the digital image correlation (DIC) method to investigate the effects of the reinforcement type (steel bar and SFCB), the number of bars in each bundle (1, 2, and 3), and the construction method (cast-in-place, general precast, and precast with full-length grouting) on the deformation capacity. The crack spacing of the precast concrete column reinforced with single-bar SFCBs increased by approximately 10% compared to the precast reinforced concrete (RC) column, and the crack spacing decreased with an increasing number of bars within each bundle. The proportion of the lateral displacement caused by rigid body rotation due to strain penetration of the longitudinal reinforcement at the precast column foot in total lateral drift was approximately 35%; the smaller growth rate of residual rotation in concrete columns reinforced with SFCBs produced a superior post-disaster resetting ability. The curvature distribution range of columns reinforced with SFCBs was wider and more uniform than that of RC columns. Overall, the utilization of SFCBs as longitudinal reinforcement improved the equivalent plastic hinge length by approximately 120% compared with RC columns, thus greatly reducing the curvature requirement of the column bottom. Moreover, the bundled reinforcement reduced the growth rate of plasticity. The precast specimen with full-length grouting altered the failure mode and achieved a considerable deformation capacity with the longest equivalent plastic hinge length of approximately 435 mm, which is 2.77 times that of the conventional RC column.

The quasi-static test of hollow prefabricated circular pier with high-strength reinforcement and calculation method for plastic hinge length

A high-strength hollow prefabricated circular pier with HTRB600E high-strength reinforcement was proposed to realise lightweight prefabricated piers and optimise their seismic performance. Its seismic performance was investigated by comparing and analysing the seismic performance indices of four different types of piers under low-cyclic reciprocating load. The finite element model (FEM) was used to analyse the influences of the grouted sleeve length, axial compression ratio, and longitudinal reinforcement strength on the equivalent plastic hinge length of the proposed pier. The equation for calculating the equivalent plastic hinge length under different working conditions was based on multiple linear regression. The results showed that different parameters had different degrees of influence on the plastic hinge length of the proposed pier, with the axial compression ratio having the strongest influence.

From experimental strain and crack distributions to plastic hinge lengths of RC walls with SMA rebars

Modern-designed reinforced concrete walls can typically achieve the primary performance level of collapse prevention in a moderate-to-large earthquake event. However, the substantial amount of damage sustained by the wall can result in large residual displacements of a building, often requiring costly repairs or even demolition. Localised replacement of reinforcing steel for a pseudoelastic material, such as shape memory alloys, has been offered as a potential solution for reducing residual displacements of reinforced concrete walls. This paper examines two basic assumptions that can be employed for the simulation of reinforced concrete walls with shape memory alloy rebars using distributed and lumped plasticity line models, namely: plane-sections-remain-plane and plastic hinge length. To this purpose, the authors analyse the strain and crack distributions using the experimental data from a recent experimental campaign. Digital image correlation techniques were used to capture the displacement field of the surface of the walls. Experimental findings are presented, including crack distributions and salient crack widths, longitudinal strain profiles along the wall length and height, and curvature profiles. They are used to discuss the validity of the plane-section hypothesis and equivalent plastic hinge length expressions. A conventional wall reinforced with steel rebars is used for comparison purposes. The experimental results presented in this paper are useful for the ongoing international investigations on concrete structures detailed with shape memory alloys.

Design guideline for extended pile shaft incorporating nonlinear pile-soil interaction

Equivalent fixed-based cantilever approach is commonly used for seismic performance-based design of pile foundations supporting marine and bridge structures. In this method, prior knowledge of parameters such as equivalent length of fixity, depth-to-plastic hinge and equivalent plastic-hinge length is essential for reliable assessment of ductility capacity. Available recommendations for these parameters have resulted in contradicting conclusions due to numerical simplifications and/or experimental limitations. In this study, basic concepts of strain wedge model are employed to provide guidelines for the estimation of the key parameters by incorporating nonlinear behavior of the soil-pile system. A set of dimensionless design charts is produced based on an analytical approach covering a range of practical values of soil and pile properties. Finally, the performance of the proposed analytical model in assessing the local curvature ductility of a bridge system induced by an imposed displacement ductility factor is demonstrated through two examples.

Rapid determination method of the seismic failure modes of coastal bridge columns in the whole life cycle

Due to the different corrosive conditions in the atmospheric zone, splash and tidal zone, and submerged zone, coastal bridge columns in marine environment always suffer from non-uniform corrosion along the height. As a result, an important phenomenon of plastic hinge transfer can occur, which has a significant effect on the seismic performance of the coastal structures. However, this problem has seldom been studied. The plastic hinge transfer phenomenon has been observed in previous cyclic loading and shaking table tests of the authors [1,2]. In this study, a further study focusing on the changing time of different failure modes and the plastic hinge length is conducted. First, the possible failure modes resulted from the non-uniform corrosion are discussed, in terms of the distribution of plasticity at the ultimate state. Then, a finite element modeling method of the bridge columns with different service time is developed. Equations that can predict the failure mode are proposed based on multi-parameter regression analysis. Finally, a flowchart describing the rapid determination method of the time-dependent failure mode and the way to obtain the equivalent plastic hinge length is proposed. The results indicate that the prediction method is with high accuracy and efficiency, which is helpful for the seismic performance design and evaluation of the coastal bridges during the entire service life.

Damage localization length in RC frame components: Mechanical analysis and experimental observations

Estimating the extent of reinforced concrete (RC) frame components that may be damaged after an earthquake and the corresponding connection with the physical mechanisms that lead to damage accumulation is of the upmost importance when deciding retrofitting solutions, evaluating the potential repair cost or when selecting a nonlinear modelling technique to be used in seismic demand quantifications. However, relevant criteria to quantify this length (the damage localization length, LD) are still not well defined, leading to the usual adoption of the equivalent plastic hinge length as a reference value for it. To provide further insights on this issue, a mechanical interpretation of the different mechanisms contributing to the damage localization at LD is provided. These mechanisms are formulated in terms of the size-dependent behaviour of the constitutive materials at their ultimate state, namely the strength and stiffness deterioration of the concrete and reinforcing steel compressive and tensile responses. Furthermore, a database including multiple experimental records of the length where substantial damage was observed in RC frame components is compiled from the technical literature. The experimental data is used to assess the adequacy of each of the referred mechanisms to model the observed damage patterns. Recommendations are then made on the most adequate way to quantify LD depending on the characteristics of different RC frame components.

Cyclic loading tests of semi-precast circular steel tubular columns incorporating precast segments containing demolished concrete lumps

This paper is concerned with the cyclic response of circular steel tubular column incorporating precast segments (PSs), a structural component proposed to facilitate the use of demolished concrete lumps (DCLs). Such a semi-precast column has been demonstrated to be easy-to-assemble, and sustain static axial load well; yet its seismic behavior is still a big concern, particularly when the precast construction technique is involved. An experimental program was therefore conducted to see how those columns would fare under simulated seismic action. Sixteen model columns were fabricated and tested cyclically, considering the following variables: compressive strength of post-pouring concrete (PPC), axial load ratio, lateral loading direction, cross-sectional size of PS, and vertical location of spacing between adjacent PSs within potential plastic hinge zones. Experimental outcomes indicated that the proposed columns showed comparable cyclic responses to their cast-in-situ counterparts; generally, integrity between PSs and their outer shell (i.e. PPC) was retained, leading to an overall monolithic flexural-dominated behavior. The effects of the PPC’s strength and the axial load ratio on the columns’ cyclic performances were significant, whilst the other variables appeared to be less influential, thereby allowing a high construction tolerance. A simplified model is suggested to determine the equivalent plastic hinge length of the columns. Moreover, ultimate strength prediction using current standards, as well as fiber-beam based numerical modeling, are made to evaluate their predictive capability for the current case. Overall, this study helps establish initial confidence in applying the semi-precast columns in seismic areas.

Effects of Soil Type on Single Pile-Soil Gap and Force Acting on Pile Body under Low Cyclic Loading

OpenSees software was be used in this paper as an analysis platform to establish a single pile-soil nonlinear numerical model. The nonlinear mechanical properties of pile nonlinearity and pile-soil gap were being mainly considered in the model. The accuracy of the numerical model was verified by combining the full-scale quasi-static test results of a single pile, which from the literature results, showed that the established numerical analysis model could accurately simulate experimental hysteresis curves of the single pile and the sliding behaviour of the pile-soil interface, and verified the reliability of the model. Further comparison analysis for acting under different soils such as soft clay, medium clay and stiff clay. It was found that under the horizontal low-cycle loading, when the soil around the pile was changed from stiff clay to soft clay, the degree of separation of piles and soils, and the length of the free section increased. For the soft clay, the length of the free section was the longest, which reached 21.3% of the length of the pile. There were significant differences in the distribution of bending moment, shearing force and displacement for piles in three soils. The maximum bending moment, maximum shearing force values of the pile body in the stiff clay were the largest, and the position was closest to the surface and the lateral displacement and equivalent plastic hinge length were the smallest.

Numerical Investigation on Plastic Hinge Length of Ultra-high Performance Concrete Column under Cyclic Load

ABSTRACT The unique features of ultra-high performance concrete (UHPC) in terms of damage tolerance, energy absorption, and deformability make this material suitable for applications in piers or columns of structures. However, few studies were available in literature regarding seismic test under cyclic load to investigate the plastic hinges of UHPC columns. As the cost of testing is relatively high, this study focuses on determining the plastic hinge lengths of UHPC columns under cyclic load based on numerical analysis. Analysis is conducted using finite element method (FEM) with the software OpenSees, and calibrated by test results. Parametric study is performed to investigate the effect of horizontal loading angle, axial force ratio, reinforcement diameter, yield strength of reinforcement, and length of the column on the plastic hinge length. The applicability of the empirical models of reinforced concrete (RC) columns for UHPC columns is discussed, and a multivariate regression expression for the equivalent plastic hinge length of a UHPC column is proposed. The results indicate that the length of the plastic zone decreases with the increase in axial load ratio, and monotonously increases with the increase in the length of the column. The trend of initial increase followed by a decrease in the length of plastic zone is observed with the increase in horizontal loading angle, reinforcement diameter, and yield strength of reinforcement. The empirical models are found to underestimate the plastic deformation of UHPC columns. The proposed expression for equivalent plastic hinge length has a reasonable agreement with FEM results.