Plastic Hinge Model Research Articles

Pushover Analysis of Precast Segmental UHPFRC Bridge Columns with Unbonded Posttensioned Tendons

Cyclic loading tests were carried out to research seismic behavior of precast segmental ultrahigh-performance fiber-reinforced concrete (UHPFRC) bridge column with unbonded posttensioned (PT) tendons. Energy dissipation (ED) bars embeded in ultrahigh-performance concrete (UHPC) grout maintained continuous across segment joints and unbonded at the bottom joint. The equivalent method was proposed for ED bars with unbonded length and unbonded PT tendons to obtain the equivalent fiber section conforming to the flat section assumption. A method based on the equivalent plastic hinge model was given to conduct pushover analysis for precast segmental UHPFRC bridge columns. Test results showed that all the specimens exhibited no less than 8% drift capacities, which were remarked with the first fracture of ED bars. Compared with test data, the proposed model was validated to have good accuracy to provide lateral skeleton curve.

Gravity Load Collapse Behavior of Nonengineered Reinforced Concrete Columns

This paper aims at investigating gravity load collapse behavior of extremely poor quality reinforced concrete columns under cyclic loading. Such columns were usually constructed by local people and may not be designed to meet any of the standards. It was found that their concrete strength may be as low as 5 MPa and the amount of longitudinal reinforcement may be lower than 1%. This type of column is deliberately defined as “nonengineered reinforced concrete column,” or NRCC. During earthquake, the gravity load collapse of the NRCC columns caused a large number of death tolls around the world. In this study, four columns as representative of existing NRCC were tested under cyclic loading. The compressive strength of concrete in order of 5 MPa was used to be representative of columns with poor quality concrete. Two axial load levels of 6 and 18 tons were used to study the influence of axial load level on maximum drift at gravity load collapse. To investigate the effect of bar types on drift capacity, 9 mm round bars were used in two specimens and 12 mm deformed bars were used for the rest of the specimens. The maximum drift before gravity load collapse was very dependent on the axial load level. The maximum drift of the specimens subjected to high axial load (18 tons) was extremely low at approximately 1.75% drifts. The use of deformed bars (associated with larger amount of longitudinal reinforcement) caused the damage to severely dissipate all over the height of the columns. Such damage caused columns to collapse at a lower drift compared to those using round bars. Finally, the plastic hinge model was used to predict the maximum drift of the low strength columns. It was found that the model overly underestimates the drift at gravity load collapse.

Implementation and Calibration of Finite-Length Plastic Hinge Elements for Use in Seismic Structural Collapse Analysis

Finite-length plastic hinge (FLPH) models have shown advantages over the concentrated plasticity hinge (CPH) models. However, empirical phenomenological relationships, such as Modified Ibarra–Medina–Krawinkler (ModIMK) deterioration model, were mainly calibrated for use in CPH models. ModIMK relationships are versatile and have been applied to steel, reinforced concrete, and timber structures. Herein, a calibration procedure of FLPH models and a unified algorithm for use of ModIMK relationships in CPH and FLPH models are presented. Results from included examples validate the proposed algorithms, which were implemented in OpenSees. Additionally, results highlight that FPLH models avoid errors and convergence pitfalls of CPH models.

Internally nested self-locked tube system for energy absorption

For energy-absorbing systems constructed by round tubes, boundary constraints and/or inter-tube fasteners are required to prevent splashing of tubes from lateral loadings, which results in extra labor and time costs. To overcome this shortcoming, the self-locked system comprised of dumbbell-shaped tubes was recently proposed, which can prevent the lateral splashing of tubes under impact loadings without any constraints. To improve the energy-absorbing capacity of the self-locked system, the internally nested self-locked system is proposed, of which the basic unit is a dumbbell-shaped tube nested by round tubes inside. The proposed nested self-locked system not only inherits the self-locking effect of dumbbell-shaped tubes, but also significantly improves the energy absorption properties. In order to estimate the energy absorption of the proposed tube, a plastic hinge model is developed based on the analysis of the four-phase deformation process of the tube. Besides, experimental study and FEM simulations are also carried out, and the results agree well with the theoretical prediction. Furthermore, the geometric parameters of inserted round tubes and the stacking arrangement of the proposed nested self-locked systems are investigated, and suggestions on designing an internally nested self-locked energy-absorbing system are provided for practical applications.

Influencia del tipo de rótula plástica en el análisis no lineal de estructuras de hormigón armado

An adequate modelling of the plastic hinges generated during the pushover analysis is crucial in order to obtain accurate results. Thus, empirical expressions must be used appropriately in order to model the generalised force-deformation relationship of plastic hinges. The main aim of this article is to study the influence of different plastic hinge models on the non-linear structural behaviour of reinforced concrete structures. To that end, several non-linear analyses have been performed using the following plastic hinge models: the model included in the code FEMA-356 and two additional models developed by some researchers by using empirical expressions calibrated with different experimental data. The results obtained show that plastic hinges modelled with empirical expressions can be used to more precisely model the behaviour of structural elements in ordinary buildings located in seismic areas, and to compare with the results offered by the models included in seismic building design codes.

Plastic deformation behavior in SEB specimens with various crack length to width ratios

The authors have already proposed a new crack tip opening displacement (CTOD) calculation formula based on the plastic hinge model considering the unique crack tip blunting behavior due to strain hardening of the material. This formula is limited to the standard length-to-width ratio (a0/W) range of between 0.45 and 0.55. However, CTOD calculations are necessary for various other a0/W conditions when the critical CTOD for a specific microstructure must be evaluated in a welded joint. ISO15653, which prescribes CTOD test methods for welds, covers a wide range of a0/W between 0.10 and 0.7 by applying a J-integral based CTOD derived from ASTM E1290 for a0/W from 0.10 to 0.45 and a plastic hinge based CTOD for a0/W from 0.45 to 0.70. This procedure leads to a discontinuity in the evaluated CTOD at a0/W=0.45. This problem results from the fact that the J-integral based CTOD is inconsistent with the conventional plastic hinge based CTOD, especially in low yield-to-tensile ratio materials. Thus, a single CTOD calculation method for the wide range of a0/W is required for rational evaluation. In this study, the plastic deformation behavior of SEB specimens was analytically examined in the a0/W range from 0.05 to 0.70, and the capacity of the plastic hinge based CTOD was discussed with the aim of establishing a unified CTOD calculation formula for SEB specimens with the wide range of a0/W.

Applicability of new CTOD calculation formula to various a0/W conditions and B × B configuration

In the previous report, the authors proposed a new CTOD calculation formula which shows good correspondence with actual CTOD in large thickness materials by introduction of a correction parameter for varied blunting shapes at the crack tip by a strain hardening exponent. However, this formula is limited to the standard range of the crack depth to width ratio, a0/W from 0.45 to 0.55, and hence did not satisfy strong demand for evaluation of a wider a0/W range. Actually, ISO15653 can cover a wider a0/W range from 0.01 to 0.70 in order to respond to this demand, considering the description in the Annex, which specifies a J-integral based CTOD calculation formula. In the context of this situation, the authors’ recent report revealed that the plastic hinge model can be applied to a0/W conditions other than the range from 0.45 to 0.55 based on detailed observation of plastic deformation for wider a0/W conditions. Coordination of the rotational center is steady regardless of the load level and strain hardening exponent. In this study, first, based on a B×2B configuration, expansion of the applicable a0/W range for the proposed CTOD calculation formula is investigated with some modification of the proposed formula. Second, application to the B×B type specimen is investigated. Finally, validation of the FEM analysis for B×B type specimens by the silicone rubber replica method is presented.

Modeling considerations in seismic assessment of RC bridges using state-of-practice structural analysis software tools

The increasing awareness of the general society toward the seismic safety of structures has led to more restrictive performance requirements hence, many times, to the need of using new and more accurate methods of analysis of structures. Among these, nonlinear static procedures are becoming, evermore, the preferred choice of the majority of design codes, as an alternative to complete nonlinear time-history analysis for seismic design and assessment of structures. The many available software tools should therefore be evaluated and well understood, in order to be easily and soundly employed by the practitioners. The study presented herein intends to contribute to this need by providing further insight with respect to the use of commonly employed structural analysis software tools in nonlinear analysis of bridge structures. A comparison between different nonlinear modeling assumptions is presented, together with the comparison with real experimental results. Furthermore, alternative adaptive pushover procedures are proposed and applied to a case study bridge, based on a generic plastic hinge model. The adopted structural analysis program proved to be accurate, yielding reliable estimates, both in terms of local plastic hinge behavior and global structural behavior.

Employing a fiber-based finite-length plastic hinge model for representing the cyclic and seismic behaviour of hollow steel columns

Numerical simulations are prevalently used to evaluate the seismic behaviour of structures. The accuracy of the simulation results depends directly on the accuracy of the modelling techniques employed to simulate the behaviour of individual structural members. An empirical modelling technique is employed in this paper to simulate the behaviour of column members under cyclic and seismic loading. Despite the common modelling techniques, this technique is capable of simulating two important aspects of the cyclic and seismic behaviour of columns simultaneously. The proposed fiber-based modelling technique captures explicitly the interaction between the bending moment and the axial force in columns, and the cyclic deterioration of the hysteretic behaviour of these members is implicitly taken into account. The fiber-based model is calibrated based on the cyclic behaviour of square hollow steel sections. The behaviour of several column archetypes is investigated under a dual cyclic loading protocol to develop a benchmark database before the calibration procedure. The dual loading protocol used in this study consists of both axial and lateral loading cycles with varying amplitudes. After the calibration procedure, a regression analysis is conducted to derive an equation for predicting a varying calibrated modelling parameter. Finally, several nonlinear time-history analyses are conducted on a 6-story steel special moment frame in order to investigate how the results of numerical simulations can be affected by employing the intended modelling technique for columns instead of other common modelling techniques.

Theoretical analysis on the collapse of dumbbell-shaped tubes

Thin-walled round tube systems are widely used in impact protection. However, in these systems, additional installation time and cost is required to constrain the tubes and prevent their splashing under impact loadings. To address this problem, a self-locked system comprised of thin-walled dumbbell-shaped tubes was recently proposed, which can prevent lateral splash from impact loadings without the presence of any constraints on the boundary or between the tubes. This paper provides a theoretical analysis on the deformation and collapse of dumbbell-shaped tubes under quasi-static lateral loads. A plastic hinge model is developed to estimate the force-displacement relationship, deformation efficiency and specific energy absorption of the dumbbell-shaped tube, and besides, an elastic solution is derived to describe the mechanical response of the dumbbell-shaped tube at small deformation. The theoretical models are validated by both finite element method (FEM) simulation and experiments. Based on the theoretical analysis, the effects of the geometry of the dumbbell-shaped tube on energy absorption are studied, and the optimal geometry design of the tube is discussed. The relation between each geometry parameter and energy absorption properties is summarized in a table, which provides important reference for designing dumbbell-shaped tubes in practical applications.

Evaluation of rotational deformation in compact specimens for CTOD fracture toughness testing

In Crack Tip Opening Displacement (CTOD) fracture toughness tests, the plastic hinge model is used for calculating the plastic component of CTOD, but the accuracy of the plastic hinge model has been a matter of controversy. In this study, 3-D elastic-plastic finite element analysis was conducted by using a stepped notch 1T compact specimen model, in which the ratio of crack length to specimen was set at 0.5. Two steel models, the low yield to tensile ratio, Y/T, of 0.6 and the high Y/T of 0.9, were employed for the analysis. The plastic rotational center was determined by using distributions of the plastic strain increment and the total strain increment in the crack opening direction along the ligament on the mid-thickness plane. The effect of Y/T on the plastic rotational factor was quite small in the C(T) specimen model, and the average of their plastic rotational factors was 0.52 in both Y/T steel models. This plastic rotational factor is consistent with conventional ones, and is reasonably used for CTOD calculation.

Seismic behavior of special truss moment frame with double hollow structural sections as chord members

Research work carried out on steel special truss moment frames (STMFs) with double-angle sections as chord members during the 1990s led to the formulation of design code provisions. Further research results using double-channel specimens resulted in a modified equation for the expected vertical shear strength of the central special segments, Vne, and has been incorporated into the current AISC Seismic Provisions for Structural Steel Buildings. Double hollow structural sections (double-HSS) have the advantages of minimizing lateral torsional buckling and maximizing compactness in the flanges as compared to single HSS with the same flexural capacity. In this research, double-HSS members were proposed for the chord and web members of STMFs instead of double-angle, double-channel, or single-HSS. Double-HSS can effectively delay flange local buckling and enhance rotational ductility due to reduced width-to-thickness ratio (b/t) without increasing the wall thickness of the members. A full-scale STMF subassemblage with double-HSS as truss members was tested under large displacement reversals to simulate a severe earthquake ground motion. Testing results indicate that using double-HSS truss members is a viable alternative for STMFs in high seismic regions. Plastic hinge models are also suggested for computer analysis and design of non-yielding members outside of the special segments.

Characterisation of Fracture and HAC Resistance of an Individual Microstructural Constituent with Micro-Cantilever Testing

This paper focuses on the application of miniaturized fracture tests to evaluate the fracture and hydrogen assisted cracking (HAC) resistance of a selected microstructural constituent (acicular ferrite, AF) which only occurs in microscopic material volumes. Site-specific Focused Ion Beam (FIB) micro-machining was used to fabricate sharply notched micro-cantilevers into a region fully constituting of AF. The micro-cantilevers were subsequently tested under uncharged and hydrogen charged conditions with a nanoindenter. The load displacement curves were recorded and analysed with a simplified plastic hinge model for the uncharged specimen, as AF demonstrated an essentially ductile behaviour. The simplified model assisted with FE simulations provided values of the critical plastic crack tip opening displacement (CTOD). A value of the conditional fracture toughness was thereby determined as 12.1 MPa m1/2. With LEFM, a threshold stress intensity factor, Kth, to initiate hydrogen crack propagation in AF was found to range between 1.56 MPa m1/2 and 4.36 MPa m1/2. All these values were significantly below the corresponding values reported for various ferrous alloys in standard macro-tests. This finding indicates that the fracture and HAC resistance at the micro-scale could be very different than at the macro-scale as not all fracture toughening mechanisms may be activated at this scale level.

Incremental-iterative model for time-variant analysis of SFRC subjected to flexural fatigue

Fatigue behaviour of plain (PC) and steel fibre reinforced concrete (SFRC) is of growing interest in concrete engineering since structural reliability often depends on the concrete’s damage state. The current paper deals with its investigation. Starting from a new and universal SN-approach for PC and SFRC based on stress- and material-dependent ductility and a cycle-dependent strain evolution under centric pulsating loads an isotropic and time-dependent material damage parameter is derived. In the framework of the elasto-plastic damage theory, wherein PC and SFRC are idealized homogeneously on macroscopic level, this damage parameter in conjunction with the established envelope concept enables to compute time-dependent stiffness and strength degradations as well as increasing plastic strains. Additionally, an assessment of the total number of cycles to failure of specimens subjected to multi-staged cyclic loading is permitted by a specific damage accumulation procedure. Decisive parameters like fibre type, length, orientation, dosages and bond on the axial static and cyclic material response are covered. To compute numbers of cycles to failure, deflections and stress redistributions of members exposed to flexural fatigue, the findings are integrated into a plastic hinge model. This accounts for localization of damage after cracking in a discontinuity region typical for both, PC and SFRC. Cycle- and crack-width-dependent deflections are obtained for valid states of equilibriums between external loads and internal stress resultants. To assess macroscopic cracking a strain criterion serves. In the numerical simulation, time-increments are performed according to Lemaitre’s jump-in-cycles procedure. For verification test results from literature are recalculated. Theoretical and experimental data are in good accordance on average proving a comparable fatigue behaviour of PC and SFRC in principle. However, fibre’s impact on fatigue life and deformation capacities of concrete is ambivalent, depending on specific material and load characteristics.

Influence of adjusted models of plastic hinges in nonlinear behaviour of reinforced concrete buildings

Among the procedures available for the seismic analysis of structures, pushover analysis is one of the most frequently used methods by structural engineers. An adequate modelling of the plastic hinges generated during the pushover analysis is crucial in order to obtain accurate results. Thus, the yielding and ultimate states of the cross-section must be defined in order to model the generalised force-deformation relation of plastic hinges. For this purpose, the use of empirical expressions that obtain the aforementioned states from the cross-section properties can prove beneficial.The main objective of this work is to study the influence of different plastic hinge models on the structural nonlinear behaviour of reinforced concrete structures. To that end, several nonlinear analyses have been performed with the software SAP2000®, considering the following plastic hinge models: (i) the model of FEMA-356 included in SAP2000®, and (ii) two additional models developed by some researchers by using empirical expressions calibrated with different experimental data. Simplified structures of two buildings have been used as examples.The results obtained show that plastic hinges modelled with empirical expressions can be used by structural engineers to more precisely model the behaviour of structural elements in ordinary reinforced concrete buildings located in seismic areas, and to compare with the results offered by the models included in seismic building design codes.

Behavior of Q690 high-strength steel columns: Part 2: Parametric study and design recommendations

Prediction of the column strength, associated with buckling and material yielding, is vital in a successful design. In this paper, a completely numerical analysis technique is employed for simulating the compressive behavior of Q690 high-strength steel columns with box- and H-sections, and its accuracy is verified by the experimental results as presented in the part 1 of the companion papers. To this, the curved Pointwise-Equilibrating-Polynomial (PEP) is introduced for representing the column deformations with an explicit simulation on the member initial imperfection. Further, the refined plastic hinge model combined with the use of sectional yield surfaces is employed to reflect inelastic yielding at the critical location. A cross-sectional analysis approach allowing for residual stresses modeling is also incorporated into the numerical method. Sequentially, a parametric study is conducted extensively for the Q690 high-strength steel welded columns. At last, the buckling curves from Chinese (GB 50017-2003), European (Eurocode 3), and American (ANSI/AISC 360-10) codes are examined, and some recommendations for design of Q690 high-strength steel columns are presented.

Displacement and curvature estimation for the design of reinforced concrete slender walls

SUMMARY Previous earthquakes, such as the 2010 Maule earthquake in Chile, have demonstrated the need to establish suitable predictors of compressive or tensile strains in concrete or steel in reinforced concrete shear walls, which can provide limit states or confinement requirements. Slender walls are commonly controlled by flexural deformations that can be divided into elastic and inelastic components. This study provides calibrated expressions for the elastic and inelastic components of flexural deformations using a fiber model for slender walls. These expressions are obtained for rectangular and T-shaped walls. The elastic component is dependent on the axial load and the boundary steel reinforcement ratio. The impact of wall coupling is investigated, which requires a correction for the elastic component. The investigation of the inelastic component is based on a plastic hinge model, in which the length of the plastic hinge is a function of the lateral inelastic drift of the wall among other parameters. The traditional linear inelastic curvature distribution over the wall height is also modified for cases with steel reinforcement with a long yield plateau or low strain hardening, which results in a larger curvature at the wall base. The distribution is validated with experimental data from the literature. Copyright © 2016 John Wiley & Sons, Ltd.

Software for biaxial cyclic analysis of reinforced concrete columns

Realistic assessment of the performance of reinforced concrete structural members like columns is needed for designing new structures or maintenance of the existing structural members. This assessment requires analytical capability of employing proper material models and cyclic rules and considering various load and displacement patterns. A computer application was developed to analyze the non-linear, cyclic flexural performance of reinforced concrete structural members under various types of loading paths including non-sequential variations in axial load and bi-axial cyclic load or displacement. Different monotonic material models as well as hysteresis rules, were implemented in a fiber-based moment-curvature and in turn force-deflection analysis, using proper assumptions on curvature distribution along the member, as in plastic-hinge models. Performance of the program was verified against analytical results by others, and accuracy of the analytical process and the implemented models were evaluated in comparison to the experimental results. The computer application can be used to predict the response of a member with an arbitrary cross section and various type of lateral and longitudinal reinforcement under different combinations of loading patterns in axial and bi-axial directions. On the other hand, the application can be used to examine analytical models and methods using proper experimental data.

System reliability evaluation of steel frames with semi-rigid connections

This paper presents an accurate and efficient numerical procedure for evaluating the system reliability of steel frames with semi-rigid connections. The ultimate strength and behaviour of the frame were predicted using a refined plastic hinge model due to its computational efficiency, whilst the nonlinear behaviour of semi-rigid connections was captured using a three-parameter power model. The statistical properties for the three parameter power model were obtained based on available experimental results. The sensitivity of reliability to the model error was also studied. Monte Carlo simulation was used to estimate the probability of failure and the reliability index of a system. Two example frames subjected to combined gravity and wind loads were examined and their system reliability indices for both strength and serviceability limit states were evaluated based on the randomness in loadings, material and geometric properties and semi-rigid connections. The results indicate that the frame reliability is strongly affected by semi-rigid connections.

Geometric and material property dependencies of the plastic rotation factor in the drop-weight-tear test

We carry out significance testing on experimental and computational data sets to determine which material and geometric parameters affect the plastic rotation factor (which is used to estimate the crack-tip-opening angle based on the plastic hinge model) for pipeline steels. It is shown, using the Xue-Wierzbicki damage mechanics model and a statistical analysis, that the rotation factor mainly depends on the Charpy V-notch energy, and empirical fits for the rotation factor are proposed.