Menegotto-Pinto Model Research Articles

A Continuously Derivable Uniaxial Tensile Stress-Strain Model of Cold-Formed Circular Steels

Promoting prefabricated steel structures is considered one of the crucial approaches to meeting the objectives of “carbon peak” and “carbon neutrality” in the construction industry. Due to insufficient practical experience and incomplete fine engineering techniques in civil construction, the sustainable development of prefabricated building systems in China faces many challenges. Taking steel components as an example, the design process of tubular columns does not pay enough attention to the influence of the cold-working effect on material mechanical properties, and the constitutive relationship of cold-formed steels is not clear, which will cause an engineering economic burden and may affect the judgment of catastrophic problems. To serve the refined design and meet the intelligent construction technology using the computer platform, a modified Menegotto-Pinto model using a continuously derivable function is proposed in the paper. The proposed model can successfully describe the complete stress-strain curve of cold-formed circular mild steels as long as the basic mechanical parameters of the parent material are determined. Taking into account the influence of the strength and thickness of the parent steel sheets, as well as the internal bending radius r, on the cold-rolling effect, the model can also flexibly track the elastic-plastic nonlinearity of the cold-formed materials. In addition, the research shows that the cold-rolling effect will weaken with the increase of the yield strength fsy,0 of the parent steels and r/t ratio, and may disappear when fsy,0 reaches 1748 MPa or the r/t ratio is approximately 60, which can be used as economic indicators during the design process.

Optimal Procedure for Determining Constitutive Parameters of Giuffrè–Menegotto–Pinto Model for Steel Based on Experimental Results

Optimal Procedure for Determining Constitutive Parameters of Giuffrè–Menegotto–Pinto Model for Steel Based on Experimental Results

Research on the multi-shear spring model for circular-section steel piers

The main damage caused by earthquakes to single-column circular-section steel piers is the bulged deformation at the bottom, generated by local instability. The refined shell-based finite element (FE) model can accurately simulate the deformational behavior, but it is still cumbersome and time-consuming to apply to the engineering design currently. Further, the existing simplified methods cannot be used in seismic response analyses under horizontal bidirectional earthquakes. Therefore, this paper uses the multi-shear spring (MSS) mechanical model as the basic model and proposes an MSS calculation model for circular-section steel piers. This model is applicable for horizontal bidirectional seismic response analysis and considers the local instability effect of steel plates. In this study, the load–deformation relationship of the modified Menegotto-Pinto model is employed in all directions as the hysteresis curve equation of the springs. The basic parameters of the corresponding models for different structures are determined according to the calculation results of the refined-shell models. In addition, the Ibarra-Krawinkler degradation rule is employed to simulate the degradation process of structural bearing capacity and stiffness, and the degradation parameters are identified. The pseudostatic and seismic time-history response analyses of steel piers with different width-to-thickness ratios verify that the proposed model has reliable calculation accuracy and greatly improved efficiency. The research in this paper provides a practical calculation method for the seismic response analysis of steel bridge piers.

Three-dimensional finite element analyses for cyclic responses of precast segmental bridge piers accounting for bond-slip degradation

Precast segmental piers are attracting the bridge community due to the merits of faster construction speed, smaller site disruption and higher construction quality. Compared to numerous experimental studies, accurate finite element (FE) models to investigate seismic responses of precast piers are rather rare. Among them, an apparent insufficiency is ignorance or inappropriate treatment of bond behavior. To this end, a zero-thickness interface element is adapted between 1 D truss element (rebars) and solid element (concrete). The bond behavior is implemented within the interface element, especially the strength degradation subject to cyclic loading, which renders simulations more realistic. The models further incorporate the softened damage-plasticity model for concrete and Menegotto-Pinto model for rebars. Viscous regularization scheme is adopted to circumvent the convergence difficulty brought out by the strain softening. The 3 D FE models are validated by the experimental works recently performed by authors. All analyses are performed on Abaqus/Standard platform, with the implicit incremental-iterative Newton-Raphson algorithm. The source code (UEL subroutine) is disclosed on github to faciliate relevant researches.

TENSILE BEHAVIOR AND STRENGTH OF STEEL PLATE BONDED WITH UV-CURABLE GLASS FIBER REINFORCED POLYESTER RESIN SHEET ON BOTH SIDES

Steel structures in social infrastructures often undergo corrosion and the thickness of these steel plates decreases. Then, the strength of steel structures decreases according to the residual plate thickness. Applications of a steel plate attaching method and a fiber reinforced polymer/plastic (FRP) bonding method are effective for repair and strengthening for these steel structures. In this study, UV-curable glass fiber reinforced polyester resin (UV-GFRPR) sheet was focused instead of FRPs. The aims of this study are to confirm repair and strengthening effects of the UV-GFRPR sheet bonded on both sides of steel plate. The UVGFRPR sheet consists of a polyester resin and chopped glass fibers and is hardened by radiation of UV source for a certain time. The tensile behavior and strength of steel plate bonded with UV-GFRPR sheets were assessed under axial tensile load. After that, the tensile behavior and strength of specimens were numerically estimated from each stress-strain curve of UV-GFRPR and steel modeled by using Menegotto-Pinto model. Furthermore, nonlinear finite element analysis (FEA) taking into account of the properties of bond layers was carried out to compare the numerical results. From the test results, the yield and ultimate strengths of specimens increased linearly according to the number of laminated layers of UV-GFRPR. Both results of the numerical calculation and the FEA agreed well with the test results. It is concluded that the numerical calculation without the contribution of bond layers can estimate the tensile behavior and strength of steel plate bonded with UVGFRPR on both sides

The role of bond strength in structural behaviors of UHPC-NC composite beams: Experimental investigation and finite element modeling

The booming application of UHPC-NC composite members renders the interfacial behavior a critical role in their macro-scale structural behaviors. Four composite beams were monotonically loaded to failure, with various thickness of the UHPC layer. The occurrence of UHPC-NC interface debonding demonstrated the role of bond strength. To this end, the standard slant shear test was improved and performed to quantify the bond strength in a realistic manner. For the computational aspects, reliable finite element (FE) models are constructed, which adopt the localizing gradient-enhanced model for the bulk region (UHPC and NC), the Menegotto-Pinto model for rebars, and a coupled cohesive-friction model for the interface. The meso-mechanical assumption is employed to smoothly integrate the cohesion with the friction. Viscous regularization is adopted to suppress the instability and the convergence problem. Identification of model parameters is well performed and presented. These FE models are verified with the tested composite beams, which offer a valuable insight to the evolution and distribution of normal and tangential tractions along the UHPC-NC interface. It is demonstrated that all the analyses are realized with the implicit incremental-iterative algorithm.

Seismic damage pattern analysis of high piers of RC bridges based on the fiber model

The practical method of the seismic damage analysis of high piers of RC bridges is established using the uniaxial modified Faria-Oliver damage model for concrete and modified Menegotto-Pinto model for rebars, based on the fiber beam-column element, in the FEA software ABAQUS. Furthermore, the seismic damage analysis of short pier and high piers of different section sizes are conducted, respectively. The results indicate that for the short piers the damage zone is located at the bottom of piers. However, the high piers tend to have multi-location damage zones, and the tendency is more obvious for the high piers with a more slender shape.

A regularized force-based Timoshenko fiber element including flexure-shear interaction for cyclic analysis of RC structures

Reinforced concrete (RC) columns are the most critical structural components in buildings/bridges. For those with small span-to-depth ratios and/or insufficient transverse reinforcing details, it will suffer from shear type or flexure-shear type failure modes, which are challenge to be represented in numerical simulation. For instance, conventional fiber element employs the Euler–Bernoulli beam theory which neglects the shear deformation, thus it will over-estimate the structural responses of flexure-shear and shear-critical columns. This paper presents a new fiber element to include the flexure-shear interaction for cyclic analysis of RC structures. The element adopts a force-based formulation and extends the original fiber element from the Euler-Bernoulli theory basis to the Timoshenko theory basis by introducing shear deformations at the section level. Then the multi-axial softened damage-plasticity model is used for concrete fibers and the uniaxial modified Menegotto–Pinto model is used for reinforcement fibers. The concrete-steel coupling effect that is typical for reinforced concrete subjected to shear, i.e., tension-stiffening and compression softening, are also considered through modifying the material constitutive laws. To overcome the difficulties in force-based element state determination and enhance the computational efficiency, the non-iterative state determination strategy is adopted for the element implementation. Meanwhile, to avoid the localization issue (i.e., integration point-dependency) arising from strain-softening behavior, an interpolatory quadrature is used for the numerical integration of the element. Finally, the element is validated through numerical simulations of a series of column tests under cyclic loadings. The results indicate that the element can retain the performance in modeling flexure-critical columns as conventional Euler–Bernoulli fiber element, while demonstrating significant superiors in modeling flexure-shear and shear-critical columns.

Cyclic behavior modeling of reinforced concrete shear walls based on softened damage-plasticity model

In this paper, a rational analysis procedure is presented to model the typical cyclic behavior of reinforced concrete (RC) shear wall structures. A recently developed multi-dimensional softened damage-plasticity damage model, where the compression-softening effect of reinforced concrete is considered, is adopted to describe the concrete material behaviors. The steel material behaviors follow a modified Menegotto-Pinto model that including strain hardening, Bauschinger effect and tension stiffening. The multi-layer shell element, which is capable of simulating the coupled in-plane/out-of-plane bending as well as in-plane direct shear and the coupled bending-shear behavior of RC shear walls, is used for the finite element modeling of the structures. To overcome the convergence issues in the analysis procedure, the quasi-Newton method is adopted to solve the nonlinear finite equations and the iterative secant stiffness with plasticity offset for cyclic loading is introduced. Finally, several numerical simulations of RC shear walls with different failure modes are given, illustrating that the developed numerical model can accurately predict the cyclic behavior of RC shear wall structures.

Cyclic stress-strain model incorporating buckling effect for steel reinforcing bars embedded in FRP-confined concrete

Buckling of steel reinforcement usually causes a sudden loss of the load-carrying capacity and the ultimate state of conventional reinforced concrete (RC) cylinders. However, reinforcing bars behave differently in fiber-reinforced polymer (FRP)-confined RC cylinders due to the lateral confinement effect of FRP. This paper presents a theoretical study into the buckling behavior of longitudinal steel reinforcing bars embedded in FRP-confined concrete subjected to cyclic axial compression. An empirical monotonic compressive stress-strain model considering the buckling effects proposed previously for laterally supported reinforcing bars is extended to a cyclic model by combining the monotonic envelope and the Menegotto-Pinto model accounting for the cyclic loops. The cyclic stress-strain models for both laterally supported reinforcing bars and FRP-confined plain concrete are then implemented into the OpenSees software platform and validated through comparisons with compressive test results on cyclically loaded FRP-confined plain and RC cylinders. The proposed cyclic stress-strain model for laterally supported reinforcing bars is expected to serve as a fundamental model for predicting the seismic behavior of FRP-strengthened RC cylinders with widely-spaced transverse ties under cyclic axial compression, in which case the local buckling of reinforcing bars usually occurs between two adjacent transverse ties.

EFFECT OF STRAIN-STRESS RELATIONSHIP OF STEEL TUBE ON THE INITIAL STIFFNESS OF SQUARE CFT COLUMNS

The restoring force characteristic of a concrete filled steel tubular (CFT) column is modeled with three straight lines which show the relation of M-R. The initial stiffness is calculated by assuming that the steel and concrete portions are fully effective and materials are elastic. The first break point is the yield bending moment of the CFT column. The yield bending moment is defined by the bending moment when a part of the cross-section yield or the allowable strength for short-term loading obtained by the superposed strength method. It is supposed that the theoretical initial stiffness obtained by assuming that the whole cross section is effective is different from the real one. This study aims to clarify effects of strain-stress relation on the yield strength and allowable strength for short-term loading and the initial stiffness. Three types of stress-strain relations for steel are used, elastic-perfectly plastic model, Menegotto-Pinto's model and Morino's model. According to the analytical results, the difference between allowable strength and yield strength becomes larger as the axial load ratio, indexes Rh and k which are used in Menegotto-Pinto's model and Morino's model increase.

A flexure-shear Timoshenko fiber beam element based on softened damage-plasticity model

In this paper, a displacement-based fiber beam element including flexure-shear interaction is developed. The element is based on the conventional Timoshenko beam theory, and the section behavior is modeled with the well-known fiber section approach, where the section is divided into steel fibers and concrete fibers. The Menegotto-Pinto model is used for steel fibers and a multi-dimensional softened damage-plasticity model, which accounts for the compression-softening effect of reinforced concrete, is adopted for concrete fibers. The axial-flexure-shear interaction can be well reflected in both section level and material level since the normal-shear coupling is reflected naturally in the multi-dimensional material constitutive law. Besides, the concrete material parameters are related to fracture energy to avoid mesh-sensitivity issue of softening problems. The numerical implementation of the proposed element, including the finite element approximation and fiber state determination, is also discussed in detail. The element is validated through the test results for a series of simply supported reinforced concrete beams under monotonic loading and reinforced concrete columns and wall under cyclic loading, and the results indicate that the element is capable to reproduce the shear behaviors of reinforced concrete members under different loading cases.

Seismic Retrofit of a Three-Span RC Bridge with Buckling-Restrained Braces

AbstractThis study evaluated the potential benefits of using buckling-restrained braces (BRBs) to seismically rehabilitate straight bridges. For this purpose, a three-span RC box girder bridge was used as a case study. A three-dimensional model was developed using software to incorporate BRBs between bent columns. The BRB inelastic behavior was represented using the Menegotto–Pinto model to reproduce its isotropic and kinematic strain-hardening properties. Nonlinear time-history analyses were performed to assess the seismic performance of the BRBs and the existing RC bridge. The structure was evaluated under several performance limit states using far-field records, which were scaled to the maximum considered earthquake level at the site using an average interval scaling method. The results show that BRB components improve the seismic performance of bridges under serviceability and ultimate limit states by decreasing drifts in the bents and by reducing the steel and concrete strains of the original RC colu...

A 3D flexure–shear fiber element for modeling the seismic behavior of reinforced concrete columns

In order to model the nonlinear seismic behavior of reinforced concrete (RC) columns under a combined loading of axial force, biaxial bending moment and shear force, a displacement-based 3D flexure–shear fiber element accounting for the effect of shear–bending interaction is developed and presented. The element is based on the Timoshenko beam theory and the section is discretized into two types of fibers: fiber representing the longitudinal reinforcement bar and fiber representing the concrete with smeared stirrups. The constitutive law of the steel material follows the Menegotto–Pinto model, in which strain hardening and Bauschinger effects are considered. The 3D constitutive model for reinforced concrete follows the basic assumptions of the enhanced Modified Compression Field Theory (MCFT), where plastic strains are introduced as offsets to account for cyclic loading. The axial, shear and bending effects are fully coupled at both the section and the element level, since normal–shear interaction has been taken into account in the enhanced MCFT. The developed fiber element is implemented as a user-defined element in a FEA program, and validated with experimental results for columns under in-plane (2D) and bilateral (3D) cyclic loading. It is found that the proposed 3D flexural–shear fiber element is able to capture the complex hysteretic behavior of shear-dominated RC columns under 2D as well as 3D cyclic loading reasonably well.

Modified Microplane Model for Reinforced Concrete under Static and Dynamic Loadings

A smeared dynamic constitutive model is proposed for reinforced concrete based on microplane Model M4, in which the modified Menegotto-Pinto model for steel was adopted and the strain rate effect was taken into account by introducing parallel moving of envelope line. The model was established based on the hypothesis that the strains of concrete and steel bars have parallel coupling. Then the contribution of steel to total stress tensor was derived by projecting the section area of steel bars to three orthogonal directions. This model was calibrated by fitting with the test data, and its validity was verified by simulating a bridge-ship collision application using LS-DYNA embedded with a user-defined material subroutine.

Modeling of the seismic behavior of shear-critical reinforced concrete columns

Inelastic failure of reinforced concrete (RC) structures under seismic loadings can be due either to loss of flexural, shear, or bond capacity. This paper describes the formulation of an inelastic nonlinear beam element with axial, bending, and shear force interaction. The element considers shear deformation and is based on the section discretization into fibers with hysteretic models for the constituent materials. The steel material constitutive law follows the Menegotto–Pinto model. The concrete model is based on a smeared approach of cracked continuous orthotropic concrete with the inclusion of Poisson effect. The concrete model accounts for the biaxial state of stress in the directions of orthotropy in accordance with the Softened Membrane Model, in addition to degradation under reversed cyclic loading. The shear mechanism along the beam is modeled using a Timoshenko beam approach. Transverse strains are internal variables determined by imposing equilibrium between concrete and transverse reinforcements. Element forces are obtained by performing equilibrium based numerical integration on section axial, flexural and shear behaviors along the length of the element. Dynamic behavior was accounted for by adopting the well-known Newmark approach. Rayleigh damping was assumed to simulate the damped behavior under seismic excitations. In order to establish the validity of the proposed model correlation studies were conducted between analytical results and experimental data of RC columns tested under the shake table.

Nonlinear Model-Based System Identification of Lead–Rubber Bearings

A nonlinear model-based system identification method is proposed, formulated, implemented, and applied to a three-span continuous base-isolated bridge. Transverse and rotational rigid-body motions of the bridge superstructure are formulated into two degrees-of-freedom dynamic governing equations. To model hysteretic behavior of lead–rubber bearings, the Menegotto–Pinto model is used. The proposed system identification procedures consist of two phases to address ill-conditioning issues. The uncertainty of parameters is considered, which results in probability distributions instead of single values for identified parameters. The proposed system identification is adopted in the comparison of experimental data sets. Hypothesis testing is used to determine the closeness of identification results. The proposed method is applied to quick-release field experiments on the bridge to investigate aging and temperature dependent effects in lead–rubber bearings.

Standardized mathematical expression for stress-strain relations of structural steel under monotonic and uniaxial tension loading

Tension tests on 36 specimens of steel plates produced in Japan are carried out according to the testing method proposed by RILEM TC 83. The stress-strain curves obtained from the tests are mathematically expressed by determining the material constants included in a modified Menegotto-Pinto model. These results give standardized stress-strain relations with respect to SS41 and SM50A steels generally used in Japan as structural steels for building structures. These kinds of data are expected to be accumulated by many countries and should be then compared internationally to establish a more reasonable stress-strain relationship usable for structural analyses.

高炉厚板鋼板の機械的性質と応力-ひずみ関係の数式表示

Coupon tension tests for steel plates of SS 41 and SM 50 A are carried out in order to obtain the stress-strain diagrams up to the maximum load. The specimens consist of 36 coupons supplied from 6 mill-makers with blast furnaces in Japan. The thickness of the plates are ranging from 6 mm to 50 mm. Testing methods are compared between JIS (Z 2241) and RILEM (TC83-CUS Testing Recommendation), where the strain rate according to the former is higher than the latter, especially in plastic range. The values of the representative points on the stress-strain curves, for exsample, upper yield strength, lower yield strength, strain-hardening point, tensile strength, rupture load, reduction of area, Young's modulus, Poisson's ratio, some points on the strain-hardening region, etc., are measured. The results are discussed by comparing with the difference of testing methods. The values of the mechanical properties from the inspection certificates (socalled Millsheet values) are also ref. erred. Moreover, mathematical expressions for strain-hardening region of the stress-strain diagrams are tried by applying a modified Menegotto-Pinto model which is proposed in RILEM recommendation. The two material constants including in this model are determined for SS 41 and SM 50 A, respectively. Finally, a standard stess-strain diagram expessesed by the model is given and the scatter or deviation is evaluated.