Fiber Beam Element Research Articles

Finite element analysis on the seismic behavior of side joint of Prefabricated Cage System in prefabricated concrete frame

The Prefabricated Cage System (PCS) has the advantages of high bearing capacity and good ductility. Meanwhile, it is convenient for factory production and it is beneficial to the cost savings, construction period shortening. Side joint is the weak region of PCS concrete frame and has great influence on seismic behavior of the whole structure. Thus systematically study on the seismic behavior of PCS concrete side joint is necessary. This paper presents a finite element study on behavior of the side joint under seismic loading. In the finite element model, PCS concrete and the reinforced concrete (RC) is modeled by the solid element and fiber-beam element, respectively. The numerical results is compared with the experimental results and it is found that the results of model based on fiber-beam element is in better agreement with the experimental results than solid element model. In addition, the overall seismic behavior of the side joints in PCS concrete is better than that of the RC with the same strength.

Integrating of Nonlinear Shear Models into Fiber Element for Modeling Seismic Behavior of Reinforced Concrete Coupling Beams, Wall Piers, and Overall Coupled Wall Systems

Reinforced concrete (RC) coupled wall systems, compared with RC shear wall without opening, have more complex nonlinear behavior under the extreme earthquake loads due to the existence of coupling beams. The behavior characteristics induced by nonlinear shear deformation such as shear–flexure interaction, pinching effect, strength and stiffness deterioration are clearly observed in numerous cyclic tests of RC coupling beams and shear walls. To develop an analytical model capable of accurately and efficiently assessing the expected seismic performance of RC coupled wall systems, it is critical to define the appropriate key components models (i.e., nonlinear models of RC wall piers/shear walls and coupling beams). Classic fiber beam element based on the theory of Euler–Bernoulli beam is frequently adopted to simulate the nonlinear responses of slender RC wall piers and coupling beams in the literature because it is able to accurately model the response characters from interaction of axial–bending moment at the section level. However, classic fiber beam element cannot capture the nonlinear behaviors of non-slender structures mainly controlled by nonlinear shear deformation. To overcome this shortcoming, a modified force-based fiber element (MFBFE) including shear effect is introduced and used as the analysis element of non-slender RC coupling beams and shear walls. At the section level, a novel shear model for RC coupling beams and an existed shear model for RC shear walls are respectively added to this fiber element to simulate nonlinear responses of these two key components. The analytical model for RC coupled walls hence is formed through integrating the proposed models of these two key components. The validations with different experimental results of cyclic tests including key components and structural system reported in the literature using these proposed models are performed. Good agreements are achieved for all of these proposed models via comparisons between predicted results and experimental data.

Modeling the impact of corrosion on seismic performance of multi-span simply-supported bridges

The corrosion of steel rebar negatively affects the serviceability and capacity of RC bridges and increases their vulnerability in earthquakes. Most of existing numerical models rely on either solid elements with a detailed corrosion damage model, involving impractical computational costs, or fiber beam elements with an incomplete corrosion damage model, requiring careful justification. A time-dependent corrosion damage model based on fiber beam elements was herein proposed as a numerical tool conserving both computational efficiency and appropriate accuracy. The proposed corrosion damage model comprehensively incorporates most of the potential corrosion-induced damage patterns on reinforced concrete, including cross-section loss, ductility degradation and compressional buckling of rebar; deterioration of cover concrete and core concrete; and deteriorated strain penetration effect. This corrosion damage model was implemented in OpenSees via fiber beam elements in which the strain penetration effect was simulated by the Bond_SP01 material with the Zero Length element. The accuracy of corrosion damage model was validated with existing experimental data of cyclic loading tests on corroded RC columns. A multi-span simply supported (MSSS) bridge was selected to showcase how to implement the proposed corrosion damage model in the time-dependent seismic fragility analysis of RC bridges. A sensitivity analysis was conducted to illustrate the roles of different corrosion damage patterns in altering seismic fragility of RC bridges. It revealed that the corrosion-induced deterioration of strain penetration and rebar yield strength significantly increase the seismic fragility of the corroded MSSS bridge.

Displacement and mixed fibre beam elements for modelling of slender reinforced concrete structures under cyclic loads

In this paper, two fibre-based beam elements with enhanced capabilities to consider large displacements and rotations of slender reinforced concrete members are developed. Fibre beam elements were comprehensively used before to model the behaviour of different structural systems with great accuracy. To upsurge the use of the fibre beam elements in modelling complex reinforced concrete (RC) systems such as slender walls and columns, the elements are improved by including the second order effect. Available research from the literature related to large displacements focused mainly on modelling steel and composite members due to the limitations in their material model behaviour. Conversely, the newly developed elements introduced in this paper can precisely model RC members by accounting for their more complex nonlinear material behaviour under reversed cyclic loads. The first element is formulated using a displacement formulation, while the second element is based on a mixed approach that is computationally more complicated but numerically more efficient. Further, the adopted concrete constitutive law accounts for the effect of compression post-peak softening as well as tension stiffening and degradation under cyclic loads. Several correlation studies are presented to highlight the efficiency of the new elements in modelling slender RC structures.

Generalized Finite Element Formulation of Fiber Beam Elements for Distributed Plasticity in Multiple Regions

AbstractA generalized fiber beam element formulation is proposed to accurately capture the formation of multiple plastic regions with a coarse mesh, which usually occurs in the process of structural collapses. The strong gradient of displacement near plastic regions in a fiber beam element can be accurately described using a special plastic enrichment function. The two types of the plastic enrichment functions are suggested for the cases where the plastic region is located fully inside an element and spread over a node, respectively. In this approach, the optimal shape of the plastic enrichment function can be updated by reflecting plastic deformation at the previous loading step. Furthermore, if plastic regions appear in multiple locations in an element, the corresponding plastic enrichment function can be adaptively reconstructed on the basis of plastic region distribution without introducing additional degrees of freedom. The effectiveness of the proposed method is investigated in terms of accuracy and computational cost through several numerical experiments.

Explicit Fiber Beam-Column Elements for Impact Analysis of Structures

The solution of impact problems requires advanced computational techniques to overcome the difficulties associated with large short-duration loads. In this case, the explicit time integration method is typically used, since it provides a stable solution for problems such as the analysis of structures subjected to shock and impact loads. However, most explicit-based finite elements were developed for continuum models such as membrane and solid elements, which renders the problem computationally expensive. On the other hand, the development of fiber-based beam finite elements allows for the simulation of the global structural behavior with very few degrees of freedoms, while accounting for the detailed material nonlinearity along the element length. However, explicit-based fiber beam elements have not been properly formulated, in particular for the case of the emerging force-based beam element. In this paper, two developed fiber plane beam elements that consider an explicit time integration scheme for the solution of the dynamic equation of motion are presented. The first element uses a displacement-based formulation, while the second element uses a force-based formulation. For the latter case, a new algorithm that eliminates the need for iterations at the element level is proposed. The developed elements require the use of a lumped mass matrix and a small time increment to ensure numerical stability. No iterations or convergence checks are required, which renders the problem numerically efficient. The developed explicit fiber beam-column models, particularly the force-based element, represents a simple yet powerful tool for simulating the nonlinear complex effect of impact loads on structures accurately while using very few finite elements. The traditional implicit method of analysis typically fails to provide numerical stable behavior for such short time duration problems. Two correlation studies are presented to highlight the efficiency of the developed elements in modelling impact problems where the strain rate effect is considered in the material models. These examples confirm the accuracy and efficiency of the presented elements.

Progressive Collapse Analysis of Reticulated Shell Structure under Severe Earthquake Loading Considering the Damage Accumulation Effect

A reticulated shell is one of the conventional long span space structures, prone to progressive collapse under a severe earthquake due to its unique single layer feature. This is. However, the collapse mechanism of this type of structure is not well studied. In this paper, a numerical modelling technique using the fiber beam elements is developed. The correspondent material model based on the inclusion of damage accumulation was also developed in order to determine the failure criteria of structural members. An effective way to simulate the buckling behavior of the structural members is also used in the numerical simulation. The relevant numerical method is developed and validated against experimental tests: good agreement is achieved. Based on this numerical method, a parametric study of the reticulated shell under severe earthquake loading is performed and the responses of the structure is investigatedand a three-stages collapse mechanism of this type of structure was observed.

Cascaded multi-dithering technique using PZT modulators for high control bandwidth in coherent laser beam combining

A cascaded multi-dithering (CMD) technique using piezoelectric ceramic transducer (PZT) tubes as phase modulators is proposed as a tool for obtaining high control bandwidth in coherent laser beam combination. To prove its validity, eight coherent fiber beam elements were combined using the CMD technique with PZT tubes. As a result, residual phase error was recorded to be λ/54 at 100 Hz control bandwidth, which is comparable to that of a four laser beam combination in the previous experiment. To our knowledge, this is the first case to date of combining eight laser beam elements using PZT tubes as phase modulators and achieving such good results.

Dynamic analyses of square RC pier column subjected to barge impact using efficient models

Material non-linearity of pier members is an important factor that needs to be considered for dynamic analysis of the bridge pier subjected to barge impact. However, many existing studies pertaining to barge impact on the bridge pier are based on the assumption that the pier is rigid or elastic. High-resolution finite-element simulation serves as the main strategy for dynamic analysis of the bridge pier subjected to barge impact considering material non-linearity of pier members. However, high-resolution finite-element simulations are expensive regarding both calculation time and computing resources, thus efficient models are often required. This paper develops the numerical model of the square RC pier column with fixed base. By coupling the simplified mass-spring model developed by the authors previously with the RC pier column at the impact position using fibre beam elements, the efficient model is developed to predict the impact force time-history and dynamic responses of the RC pier column subjected to barge impact. The studies in this paper show that the prediction quality of the proposed efficient model is adequate for different impact scenarios.

Incremental dynamic analysis of seismic collapse of super‐tall building structures

SummaryIn the present work, the incremental dynamic analysis is performed for the super‐tall building structure of ZhongNan Center, which is more than 700 m high and is currently under construction in Suzhou, China. The Chi‐Chi earthquake record is used as the ground motion input. The peak ground accelerations are scaled to five levels including 0.2 g, 0.4 g, 0.8 g, 1.4 g, and 2.0 g. The plastic damage model is adopted to represent the material failure. The finite element model is developed by using fiber beam elements for beam‐columns and laminated shell elements for shear walls and slabs. Under the attack of strong seismic ground motions, the super tall structure experiences overall collapse, which is well captured by the developed finite element model. More importantly, the collapse patterns of the super tall structure are rather different under the excitations of earthquake records with same wave pattern but different peak accelerations.

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.

全尺寸钢筋混凝土桥墩柱ABAQUS动力分析

本文提出两个纤维梁单元混凝土模型。模型由拉压骨架曲线和加载卸载路径组成，其中，受拉骨架曲线由弹性和线性软化两段组成；受压骨架曲线由线性弹性和随后EN 1992版欧盟混凝土规范建议公式结合KENT-PARK模型组成，其混凝土峰值压应力，对于非约束混凝土采用圆柱体抗压强度，对于约束混凝土采用KENT-PARK模型计算。加载卸载路径分别采用OpenSees的CONCRETE01和CONCRETE02模型路径。依据ABAQUS平台的用户材料接口UMAT，开发了两个适用于纤维梁单元的混凝土模型用户子程序，F1-CON和F2-CON。通过对比全尺寸振动台试验各项结果，本文开发用户子程序与模拟方法的可靠性得到验证，结果表明用户子程序能很好地反映受地震荷载作用的钢筋混凝土柱强度与刚度的退化，模型可以广泛用于精细化模拟钢筋混凝土柱及其它弯曲构件。 Two fiber-beam-element concrete models are presented. The models are comprised of a tension/compression envelope and unload/reload path. The tension envelope contains an elastic range and a linear soft zone. The compression envelope also includes a linear elastic range followed by the formulation of Eurocode No. EN 1992 and KENT-PARK model, whose peak stress is the concrete cylinder compressive strength for the unconfined concrete and is calculated by the KENT-PARK model for the confined concrete. The unload/reload paths of OpenSees CONCRETE01 and CONCRETE02 are used. According to UMAT interface provided by ABAQUS platform, two user subroutines of concrete, F1-CON and F2-CON, are developed for fiber beam element. By means of comparison with the results of a full scale shaking table test, reliabilities of the user subroutines and modeling methods were validated. The results show that the subroutines can well reflect strength and stiffness degradation of reinforced concrete columns produced by earthquake loading. The subroutines are widely applicable to refined simulation of concrete columns or other flexural members widely.

Stiffness degradation-based damage model for RC members and structures using fiber-beam elements

To meet the demand for an accurate and highly efficient damage model with a distinct physical meaning for performance-based earthquake engineering applications, a stiffness degradation-based damage model for reinforced concrete (RC) members and structures was developed using fiber beam-column elements. In this model, damage indices for concrete and steel fibers were defined by the degradation of the initial reloading modulus and the low-cycle fatigue law. Then, section, member, story and structure damage was evaluated by the degradation of the sectional bending stiffness, rod-end bending stiffness, story lateral stiffness and structure lateral stiffness, respectively. The damage model was realized in Matlab by reading in the outputs of OpenSees. The application of the damage model to RC columns and a RC frame indicates that the damage model is capable of accurately predicting the magnitude, position, and evolutionary process of damage, and estimating story damage more precisely than inter-story drift. Additionally, the damage model establishes a close connection between damage indices at various levels without introducing weighting coefficients or force-displacement relationships. The development of the model has perfected the damage assessment function of OpenSees, laying a solid foundation for damage estimation at various levels of a large-scale structure subjected to seismic loading.

Progressive Collapse Analysis of Concrete-filled Steel Tubular Column to Steel Beam Connections Using Multi-scale Model

The multi-scale model which combined the fiber beam element with the fine element was used to investigate the progressive collapse performance of steel beam to concrete-filled steel tubular (CFST) column connections. By using the nonlinear static analysis method and taking into account the influence of the adjacent framework of joints, the resistance of progressive collapse, the failure modes and the stress distribution revealed the resistance mechanism of these joints during the process of progressive collapse. And the vertical displacement time history curves of joints which displayed the progressive collapse resistance demands of these joints were obtained by using the nonlinear dynamic analysis method. The relationship between resistance capacity and resistance demand of these joints were obtained by analyzing the nonlinear static analysis results and the nonlinear dynamic analysis results. These analysis results showed that the frame structure with these joints which enabled to form the resistance mechanism and new alternate path of unbalanced loads can prevent the occurrence of progressive collapse after the failure of column connected to joints. And the adjacent framework can improve the ability of anti-progressive collapse of these joints.

An effective model for analysis of reinforced concrete members and structures under blast loading

The traditional fiber beam model has been widely used in the seismic analysis of reinforced concrete members and structures. However, the inability to capture shear failure restricts its application to blast loadings. In this article, a numerical model that considers both rate-dependent shear behavior and damage effect is proposed based on the traditional fiber beam element. This is achieved using the modified compression-field theory with a concrete damage model and bilinear steel model in the principal directions. Meanwhile, a condensed three-dimensional stress–strain relation from the isotropic hardening plasticity model is implemented to simulate longitudinal reinforcement bars, as large shear strain would be produced under severe blast loads. The proposed model is validated by comparing the numerical and test results. The high-fidelity physics-based finite element model, validated by the same experiment, is also used in the study to prove the efficiency of the proposed model. Case studies of a reinforced concrete beam and a six-story reinforced concrete frame structure subjected to blast loads are then carried out. The results indicate that the proposed model is reliable compared with the high-fidelity physics-based model. In addition to the accuracy, comparisons of the computational time show an excellent performance with respect to the efficiency of the proposed model.

Elastoplastic time history analysis of reinforced engineered cementitious composite or engineered cementitious composite–concrete composite frame under earthquake action

Engineered cementitious composite is a class of high-performance cementitious composites with pseudo-strain hardening behavior and excellent crack control capacity. Substitution of concrete with engineered cementitious composite can greatly reduce the cracking and durability problems associated with low tensile strength and brittleness of concrete and can significantly increase structural seismic resistance. In this article, a pair of beam–column joints with various matrix types has been tested under reversed cyclic loading to study the effect of substitution of concrete with engineered cementitious composite in the joint zone on the seismic behaviors of composite members. After that, a simplified constitutive model of engineered cementitious composite under cyclic loading is proposed, and the structural performance of steel reinforced engineered cementitious composite members is simulated by fiber beam elements. The accuracy of the model is verified with test data. Finally, three frame structures with different matrixes subjected to earthquake actions were numerically modeled to verify the contribution of ductile engineered cementitious composite material to structural seismic resistance. The seismic responses or failure mechanisms, deformation patterns, and energy dissipation capacities for each frame structure are analyzed and compared. The simulation results indicate that the application of engineered cementitious composite can reduce the maximum story drift ratio, and the distributions of the dissipated energy are more uniform along the building height when engineered cementitious composite is strategically used in ground columns and beam–column joints of the frame structure. The seismic performance of the reinforced engineered cementitious composite-concrete composite frame is found to be even better than the frame with all concrete replaced by engineered cementitious composite.

Progressive Collapse Analysis of a Typical Super-Tall Reinforced Concrete Frame-Core Tube Building Exposed to Extreme Fires

A number of disastrous incidents have indicated that extreme fires can act as a trigger event to initiate the progressive collapse of reinforced concrete (RC) structures. Hence, research on progressive collapse risks of RC structures under extreme fires is most important. However, limited studies have been undertaken in the fire-induced progressive collapse of tall and super-tall RC buildings. Hence, a high-performance finite element model was developed for this study to simulate the mechanical behavior of RC members in fire-induced progressive collapse. Fiber beam and multi-layer shell elements were used, in conjunction with appropriate material constitutive laws and elemental failure criteria under high temperature conditions. Extreme fire scenarios were also considered, based on the actual fire-induced progressive collapse events of the WTC towers and the Windsor Tower. The simulation results indicated that a progressive collapse of a super-tall building was triggered by the flexural failure of the peripheral columns, approximately 7 h after being exposed to fire. The bending deformations of the peripheral columns increased significantly, due to the outward thermal expansion of the upper floors and the inward contraction of the lower floors, a result of the fire-induced damage. The results also revealed that, when multiple stories are subjected to fire, the internal forces in the components are redistributed in the horizontal and vertical directions by way of the Vierendeel truss mechanism, leading to a maximum increase (of approximately 100%) of the axial forces in the columns. The present work identified the mechanisms of the fire-induced progressive collapse of a typical RC super-tall building, and provided an effective analysis framework for further research on the fire safety of tall and super-tall RC buildings.

A simplified simulation method for progressive collapse of reinforced concrete slabs

Floor slabs are important components of frame structures which largely affect the structural progressive collapse performance. This paper presents a simplified numerical simulation method for reinforced concrete (RC) slabs. A RC slab is discretized along two directions transferring into a beam network. The meshes at each direction are simulated by fiber beam elements to consider the composite mechanical behavior of steel reinforcement and concrete. In this method, beam-slab joints at the edge area of slabs are simulated by fiber beam elements with T/L sections, by which the effects of slabs on the bending behavior and the damage mode of the beams under small deformation in progressive collapse are considered. On the other hand, fiber beam elements with rectangle sections are used to simulate the interior area of slabs, by which the tensile membrane action of slabs under large deformation can be considered. This method can not only avoid the high stiffness problem when using shell elements, but also greatly improve the efficiency of the calculation of the whole structure. Finally, existing tests on special-shaped columns (T/L cross sections), one-way slabs and two-way slabs are simulated, respectively. The results show that the simplified method can efficiently and accurately simulate the reinforced concrete slabs under large deformation, providing a powerful tool for the simulation of progressive collapse analysis of whole structures.

Simplified nonlinear simulation of shield tunnel lining reinforced by epoxy bonded steel plates

A high-efficiency simplified modeling approach based on fiber-beam elements and discrete elements is proposed for investigating the nonlinear response of shield tunnel reinforced concrete linings. The proposed approach focus on following main features: modeling simplicity and computational efficiency, the considerations of critical material and geometric nonlinearity associated with the entire loading process, including the stage of reinforcing the deformed concrete lining by steel plates. Comparison between the analysis results of the proposed numerical model and the experimental results from the full-scale structural test are presented to validate the developed model. The results show that the proposed model can capture the essential characteristics of the nonlinear load–deformation response of segmental tunnel lining. The modeling approach presents a balance between simplicity and accuracy, and serves as a viable alternative to detailed finite elements analysis.

Investigating the Hysteretic Behavior of Concrete-Filled Steel Tube Arch by Using a Fiber Beam Element

A fiber beam finite element that could account for the nonlinear constitutive relationship between steel and concrete was applied to investigate the hysteretic behavior of concrete filled steel tube (CFT) arch ribs of bridges. At first, the effectiveness of this fiber beam element using for nonlinear analysis was verified by comparing the analytical results with the experimental data, and then this composite element was applied to analyze the hysteretic performance of CFT arch ribs. The following hysteretic behavior of CFT arch ribs of bridges was investigated such as the hysteretic behaviors of moment-curvature of arch ribs in vertical direction of bridge and the hysteretic relationship between load and displacement of arch ribs in longitudinal and transverse direction of bridge. Finally, some parameters affecting the hysteretic behaviors of CFT arch ribs were presented by evaluating the capacity of ductility of CFT arch ribs.