Fiber Beam-column Element Research Articles

Thermomechanical responses of steel frames under aftershock after fires

A novel advanced fiber beam-column element, which incorporates stability functions and the fiber distributed plasticity model to capture geometric and material nonlinearities, respectively, has been successfully developed to predict the nonlinear inelastic thermo-mechanical behaviors of steel frames subjected to aftershock after fires. To address the nonlinear dynamic problems resulting from aftershocks after fires, a sequential nonlinear thermal incremental-iterative solution scheme has been developed, which is based on the Newton-Raphson algorithm and Newmark-β method. In addition, a transcendental probability-based method is employed to express the statistical characteristics of aftershock intensity relative to the mainshock. The proposed method is applied to analyze three framed structures: a steel portal frame, a two-story plane steel frame, and a four-story asymmetric space steel frame. This analysis shows the accuracy, computational performance, and applicability of the proposed method. Remarkably, the results obtained from the code work, using just one or two elements per member, are in close agreement with all the results analyzed by Abaqus. This emphasizes that the proposed method effectively predicts the response of framed structures under aftershock after fires with excellent computational efficiency, significantly surpassing traditional finite element approaches in commercial software like Abaqus. The successful results of the dynamic analysis of the frames under aftershocks following fires underscore the importance of considering aftershocks after a fire incident. It is demonstrated that the occurrence of an aftershock accelerates the failure of the frame compared to the case when the frame is subjected to fire alone. This highlights the critical need to account for aftershocks when assessing the safety and structural integrity of framed structures after a fire event.

Development of a numerical model for RC columns considering seismic dynamic effect and different failure modes

Due to the strain rate sensitivity of concrete and reinforcing steel materials, the mechanical behaviors of RC column members subjected to dynamic loading are significantly different from those measured under static loading, i.e. the dynamic effect. In this paper, a numerical model capable of reflecting the dynamic effect and different failure modes is innovatively developed for RC columns by adding the modified sub-elements to the fiber beam-column element on the OpenSees platform. The methods for considering the dynamic effect on multiple deformation components, including the flexural, shear and bond-slip deformations are put forward. Moreover, the accuracy and effectiveness of the proposed model are verified by comparing the numerical and experimental hysteretic curve and deformation components of RC columns under different failure modes and loading rates. By analyzing the simulated results of hysteretic behavior using the modified and unmodified model, the necessity of dynamic modification to the deformation sub-elements are highlighted. It is revealed that the proposed numerical model can provide reasonable predicted results to the dynamic hysteretic behavior and failure mode of RC column members, and can be further applied to improve the accuracy of seismic performance assessment for RC structures.

Dynamic responses of multi-story structural systems with separated gravity and lateral resisting systems under seismic action considering connection semi-rigidity effects

This paper investigates the dynamic behaviour of an innovative structural system with separated gravity and lateral resisting systems (SGLR system), which is proposed for the prefabricated structures in multi-story buildings by enhancing the standardization of beams, under earthquake excitation. The seismic performance of SGLR system is benchmarked against the conventional rigid frame system (RF system) designed with the same maximum inter-story drift ratios, and the influences of connection semi-rigidity on the dynamic responses of SGLR system are focused on. Numerical models are built using the self-developed fiber beam-column elements for composite frames, beam elements for semi-rigid connections and multi-layer shell elements for shear walls based on a six-story prototype structure. The modal analysis indicates that the natural vibration periods of SGLR system are smaller than those of RF system and the connection semi-rigidity will further significantly decrease the periods for the first three orders. Nonlinear time history analysis is conducted under eight sets of ground motions at two different levels in two horizontal directions. The shear walls in SGLR system bear the majority of seismic action with damage concentrated in the bottom. The connection semi-rigidity will decrease the lateral deformation and increase the involvement of the frame part in the lateral resisting mechanism of SGLR system, which can be more significant when the semi-rigidity is higher. SGLR system exhibits better control of inter-story drift ratios considering connection semi-rigidity in low-rise buildings and higher economic efficiency in mid-rise buildings.

An advanced beam-column element for analysis of frames in fires

A novel advanced fiber beam-column element, which utilizes the stability functions and the fiber distributed plasticity model to capture the geometric and material nonlinearities, is proposed for the first time to predict the nonlinear inelastic thermo-mechanical behaviors of framed structures in fires by using the Fortran programming language. The element stiffness matrix is integrated via the Gauss-Lobatto numerical integration scheme, and geometric nonlinearity is considered by using the stability functions and a geometric matrix for P-δ and P-Δ effects, respectively. A nonlinear thermal incremental-iterative solution scheme based on the Newton-Raphson algorithm is also developed and operated to solve the nonlinear problems due to thermal expansion and material degradation in fires. The proposed element has the novelty of simultaneously taking advantage of the benefits of the stability functions with low computational cost and the capacity of tracing the gradual space spread of plasticity of the fiber model. At the moment it is not possible for the normal beam-column element in commercial software that allows for considering the effects of temperature to provide both low computational cost and accurate representation of the spread of plasticity. To demonstrate the proposed element's capacity in dealing with various scenarios, it will be investigated with both uniform fire, compartment fire, and localized fire with members made of steel and concrete. The accuracy of the proposed element is verified by comparing the obtained results with those from test data and the Abaqus program. Results show that the proposed element can provide exact solutions with excellent computational performance, which is more significantly effective than the traditional finite element in commercial software like Abaqus.

Damage Analysis of Reinforced Concrete Columns Based on Fiber Beam–Column Element

The method of damage analysis of reinforced concrete columns based on the fiber element model is established by combining the uniaxial damage constitutive model of concrete and steel with the fiber beam–column element model. The quasi-static test and the shaking table test of reinforced concrete columns are simulated and analyzed, respectively. The results show that the established fiber element model can predict nonlinear mechanical behavior and the damage distribution of reinforced concrete columns with good accuracy. Furthermore, the model can effectively simulate the evolution process of damage of columns, and describe weak parts of columns, and has high computational efficiency and solution accuracy, thus providing a practical analysis method for the simulation of building structures during earthquake.

Structural performance assessment of RC flexural members through crack-based fibre beam-column model updating

For reinforced concrete (RC) structures in service, original finite element models (FEMs) based on design information usually deviate from actual structures due to structural damage such as cracks, displacement and material degradation. Although conventional FEMs can be updated to give results that match the response data used during the updating process, they can hardly predict the subsequent structural performance. In this study, an innovative fibre beam-column model updating method based on static deflection and crack width is proposed. First, the self-developed fibre beam-column finite element program COMPONA-MARC is modified to efficiently simulate the nonlinear cracking behaviour of RC flexural members. Second, sensitivity studies using the discrete central difference method based on the Lagrange interpolation function are conducted to select updating parameters. Third, with the combination of modified COMPONA-MARC and an automation program written in Python, plenty of sample data are obtained, and artificial neural networks (ANNs) are trained by Bayesian Regularization Backpropagation (BRB). Finally, the updated parameters are acquired by inputting the measured static deflections and crack widths. Typical RC beams and RC slabs from the literature are utilized to validate the proposed methodology and explore potential implementation scenarios. The results show that updated FEMs can satisfactorily predict mechanical behaviour and assess structural performance. The proposed method offers enlightening insights about combining structural health monitoring and inspection (SHMI) results with model updating, which can promote the applications of digital twins in performance assessments of RC structures.

An advanced computational method for nonlinear inelastic thermo-mechanical analysis of spatial steel frames in fires

A novel advanced computational method incorporating the stability functions and the distributed plasticity model into the fiber beam-column element is proposed for the first time to predict the nonlinear inelastic thermo-mechanical behavior of spatial steel frames in fires. The space spread of plasticity is captured by tracing the uniaxial temperature-stress–strain relation of each fiber on sections at integration points. The element stiffness matrix is integrated via the Gauss-Lobatto numerical integration scheme. The nonlinear material behavior is captured by adopting the distributed plasticity model with the force-based interpolation function whereas the geometric nonlinearity of P-δ and P-Δ effects are considered by using the stability functions and a geometric matrix, respectively. The shear deformation and residual stresses which normally exist in steel frames are also considered. For the implementation, a nonlinear thermal incremental-iterative solution scheme based on the Newton-Raphson and Gaussian Elimination algorithm is also developed to address the nonlinear problems due to thermal expansion and material degradation. By taking advantage of the computational benefits of stability functions and the force-based interpolation function, the proposed method offers a novel computational framework for nonlinear structural analysis in a fire with excellent computational efficiency. The reliability and accuracy of the proposed program are verified by comparing the obtained results with results from test data, existing studies, and Abaqus. In addition, the computational performance of the proposed numerical program is about 10 times more effective than the Abaqus commercial software, thus would offer an extremely valuable tool for practical fire resistance designs.

Rapid Seismic Evaluation of Continuous Girder Bridges with Localized Plastic Hinges.

In seismic assessment of continuous girder bridges, plastic hinges form in bridge piers to dissipate seismic energy through nonlinear restoring forces. Considering temporal and spatial variations of ground motions, seismic evaluation of the bridges involves nonlinear stochastic vibration and expensive computation. This paper presents an approach to significantly increase the efficiency of seismic evaluation for continuous girder bridges with plastic hinges. The proposed approach converts nonlinear motion equations into quasi-linear state equations, solves the equations using an explicit time-domain dimension-reduced iterative method, and incorporates a stochastic sampling method to statistically analyze the seismic response of bridges under earthquake excitation. Taking a 3 × 30 m continuous girder bridge as an example, fiber beam-column elements are used to simulate the elastic–plastic components of the continuous girder bridge, and the elastic–plastic time history analysis of the continuous girder bridge under non-uniform seismic excitation is carried out. Results show that the computation time is only 5% of the time of the nonlinear time history approach while retaining the accuracy. This study advances the capability of rapid seismic assessment and design for bridges with localized nonlinear behaviors such as plastic hinges.

Sensitivity-based constitutive parameter identification of nonlinear structures with unknown input earthquake excitation

System identification methods are widely developed in structural health monitoring, in which the force or structural damage is identified from a linearised structure. However, the real-world civil infrastructures are generically nonlinear and subject to extreme loading conditions, such as earthquake. This study proposes a system identification method for material constitutive nonlinear structures subject to earthquake, where sensitivity analysis is developed to accelerate the complicated nonlinear system identification. First, the nonlinear structural model based on the material constitutional law is constructed by fiber beam-column elements. The earthquake input is parameterized by Chebyshev orthogonal polynomials in a recognizable form. Afterwards, the dynamic response sensitivities with respect to the constitutive parameters and the orthogonal factors of earthquake excitation are derived to accelerate the system identification from a complex material constitutive model. Finally, the constitutive parameters and the earthquake input are simultaneously identified by an optimization process. Numerical structures subjected to earthquake excitation are employed to verify the accuracy of the proposed method, by which the influence of parameter's order, input intensity and measurement noise is discussed. The proposed method develops Chebyshev parameterization to recognize the earthquake input and sensitivity analysis to accelerate the optimization, which leads to an accurate nonlinear system identification of civil structures.

Seismic Response Analysis of Isolated and Nonisolated Continuous Girder Bridges under Multidimensional Near-Field Ground Motions

In this study, the responses of isolated bridges and nonisolated bridges are studied under multidimensional seismic motions. First, damage constitutive models of steel bars and concrete materials were combined with the fiber beam-column element model, and the isolated bearing model considering bearing failure was selected. The bridge numerical analysis model was then established. The seismic responses of isolated and nonisolated bridges were analyzed under near-field ground motions (fling-step and forward-directivity ground motions) and far-field ground motions. It was found that the seismic responses of nonisolated bridges, such as deck acceleration, pier displacement, pier damage, and bearing displacement under near-field ground motions, were higher than those under far-field ground motions. Under far-field ground motions, isolation bearings effectively reduced various seismic responses of structures and had isolation effects. Under forward-directivity TCU102 ground motions, the minimum isolation ratios of isolation bearings for peak acceleration of the girder in the Z direction, pier displacement, and pier shear force were −0.14, −2.65, and −0.05, respectively. The low-isolation ratio and significant damage to the isolation bearings indicate that the isolation bearings cannot be directly used under near-field conditions.

Seismic Response and Damage Analysis of an Isolated Bridge Subjected to Near-Fault Ground Motion

In this study, the seismic response and damage behavior of an isolated bridge under near-fault ground motion are studied and compared with the non-isolated bridge. To consider the local damage of the bridge pier and its evolution process, the nonlinear behavior of the bridge pier in the analysis is simulated by the fiber beam-column element model combined with the damage constitutive model of steel and concrete materials. The mechanical behavior of the isolation bearing is simulated by the three-dimensional isolation bearing model that can consider the instability and failure of the bearing. It is found that the isolation bearings do not work, and even amplify the seismic response of the bridge (pier displacement and pier shear) under the near-fault ground motion. This amplification also leads to more severe damage to the piers of the isolated bridge. In the case of the analyzed concrete bridge type and near-fault earthquake data, it can be concluded that the used isolating lead rubber bearings should not be recommended. In general, it can be stated that the selection of the types of bridge bearings in near-fault areas should always be analyzed in detail by designers in order to avoid unintentional amplifying of the bridge’s seismic response.

Numerical Modeling and Shake Table Test for Seismic Response Evaluation of an Auxiliary Building in NPP with Reinforced Concrete Shear Wall

The dynamic responses of three storied auxiliary building of a nuclear power plant (NPP) constructed with a monolithic reinforced concrete shear wall are investigated in this study. The dynamic characterization is weighed through a shake table test and evaluated the efficiency of various structural modeling systems for evaluating seismic responses. The shear wall was subjected to a collaborative research round-robin analysis conducted by the Korea Atomic Energy Research Institute to forecast seismic responses of the auxiliary building in the NPP using a shake table test. The shake table test was performed with five different levels of intensity measures of the base excitation to obtain acceleration responses from different positions of the building in one horizontal direction (front-back). The main motivation of this study is to develop a nonlinear numerical model and examine the efficiency of various modeling approaches for evaluating the performance under seismic loading. Three numerical modeling approaches, i.e., multi-layer shell element modeling (MLSM), fiber beam-column element modeling (FBCM), and beam-truss element modeling (BTM), are generated to simulate the seismic response behaviors of the auxiliary building structure. Modal analysis, floor response spectra, acceleration amplification factor along with height, and story shear force of the building are compared as they are critical responses for evaluating the seismic vulnerability of the structure. The comparison shows that all the nonlinear numerical modeling approaches, i.e., MLSM, FBCM, and BTM, can predict the complex behavior of a shear wall system for low earthquake level, but for high earthquake level, MLSM shows better agreement with the shake table experiment. So, it is recommended to use MLSM modeling for nonlinear analysis with an earthquake intensity measure of 1 g or more.

A novel macroelement for seismic analysis of unreinforced masonry buildings based on MVLEM in OpenSees

Unreinforced masonry (URM) buildings are susceptible to extraordinary actions such as earthquakes compared to steel or reinforced concrete buildings. Various methods have been developed for the computational analysis of URM buildings in the last few decades. The equivalent frame method (EFM) is one of the numerical modeling approaches widely used for the nonlinear analyses of URM buildings. Different macroelements in the context of the EFM have been proposed. However, there is still a need for an efficient modeling approach in the computational effort that can predict the real behavior of URM structural components with sufficient agreement and available in opensource structural analyses software packages. For this purpose, a new macroelement based on the multiple vertical line element method (MVLEM) element has been developed in this study. The MVLEM is available in the OpenSees software platform comprising vertical uniaxial macro-fibers and a shear spring as an efficient macroelement for nonlinear analysis of flexure-dominated reinforced concrete walls. The novel macroelement, double modified MVLEM (DM-MVELM) element has been proposed consisting of two modified MVLEM elements tied with a nonlinear shear spring at the middle with a trilinear backbone behavior. DM-MVLEM can capture the axial-flexural interaction with lower computational effort than finite element models and fiber beam-column elements. The DM-MVLEM has been validated against the test results at the structural components level and a full-scale perforated URM wall. Unified method (UM) and composite spring method (CSM) are two existing EFMs that are presented in this study. A study is performed by comparing the seismic behavior of the perforated URM walls modeled using the UM, CSM, and DM-MVLEM modeling strategies. Results show that the DM-MVLEM can predict the damage patterns, and nonlinear behavior of spandrels can be simulated that was usually modeled with linear behavior in EFMs.

Efficient numerical model for progressive collapse analysis of prestressed concrete frame structures

Prestressed concrete (PC) frames are becoming an attractive solution for building structures due to the lightweight, aesthetics, and high resistance of their structural members. Nonetheless, few experimental and numerical studies have been carried out to investigate the progressive collapse resistance of PC frame structures, which is a key capacity feature to withstand extreme events. In this paper, a numerical model is proposed for progressive collapse analysis of PC beam-column sub-assemblages. The model was developed in OpenSees finite element software, simulating frame members via fiber beam-column elements, prestressing tendons (PTs) through corotational truss elements, the bond-slip behavior at the beam-column joint by zero-length elements, and coupling between the reinforced concrete beam and the PTs through kinematic compatibility conditions. The proposed modeling approach was validated through simulation of seven previously tested sub-assemblages under middle column removal. Numerical results indicate that the model allows a satisfactory simulation of vertical load–displacement pushdown curves, horizontal reaction–displacement curves, as well as local behaviors (e.g., rebar slip and fracture). Furthermore, a parametric study was conducted based on the validated numerical model to analyze the influence of effective prestress, tendon-concrete bond behavior, and tendon profile on the progressive collapse performance of PC sub-assemblages.

Evaluation of seismic torsional response of ductile RC buildings with soft first story

This study investigates the inelastic torsional response of plan asymmetric ductile RC buildings with a soft first story. The buildings of Rectangular, L, T, and U plan shapes are considered for the study. Force-based fiber beam-column elements are modeled for the inelastic response prediction of the buildings. Masonry infill walls are uniformly distributed in the plan and considered for the evaluation of torsional response. The pushover methods, Extended N2 and Extended Capacity Spectrum Method – FEMA 440 are adopted to estimate the inelastic torsional response. Bi-directional nonlinear time history analysis is carried out on the buildings considering near-field and far-field ground motions. Story drift ratio and curvature demand-capacity (D/C) ratio of columns are reported at the stiff, flexible side of buildings. The torsional response of infill wall buildings is compared with that of bare frame buildings. It was observed that the torsionally irregular ductile buildings with soft first story exhibit higher seismic demand on the flexible side corner columns. Infill wall interaction amplifies the torsional response at the bottom story, causing an increase in displacements higher at the flexible side and moderate near the stiff side. This study concludes that the flexible side corner column in plan asymmetric building with a soft first story can be conservatively designed for 1.5 times the design forces obtained from the analysis. This conservative design ensures stable energy dissipation in the corner column under load reversals, without significant strength reduction under higher excitation levels. The designer shall properly distribute lateral load resisting elements in a plan to prevent premature failure of the columns located internally and close to the initial center of rigidity. The designer can avoid the collapse of columns located internally in the buildings with stiff peripheral frames by designing for forces 1.5 times higher than obtained.

Force-based finite element formulation for nonlinear behaviour of reinforced concrete frames

This paper presents a nonlinear force-based finite element formulation which can predict the behaviour of reinforced concrete frames, explicitly satisfying section-level equilibrium. In the existing nonlinear force-based fibre beam–column element formulation, two nested iterative procedures are utilized at the structure and element levels. In the element-level iterative procedure, the strain states of the fibre level are iteratively altered by following the corrective forces suggested by the element level. When this algorithm is implemented with uniaxial material models, the element residual deformations can be minimized effectively by altering the axial strains, which is the only variable at the fibre level, implicitly achieving the section-level equilibrium to a reasonable accuracy. However, when a cracked reinforced concrete constitutive model, which accounts for axial–flexure–shear interaction, is implemented, element-level convergence becomes problematic because element residual deformations have to be minimized by altering all three strain components with additional constraints at the fibre level. To address this issue, this paper proposes a novel force-based finite element formulation by implementing an iterative procedure at the section level in order to minimize section unbalanced forces at section level itself, rather than transferring errors of the section level to element level. The current study focuses to test this algorithm for only axial force–bending moment interaction response. The proposed formulation was experimentally validated and was proved to be stable and accurate to predict the nonlinear responses of RC frames.

Nonlinear inelastic analysis of semi-rigid steel frames with circular concrete-filled steel tubular columns

A reliable and effective method for the nonlinear inelastic analysis of frames using circular concrete-filled steel tubular (CFST) columns is developed in this paper. In the proposed method, the CFST columns and steel beams of the frame are modeled by using a fiber beam-column element that accounts for the nonlinear behaviors of both geometry and materials of the structure. The cross-sections of the elements are discretized into many small fibers and the stiffness matrix of the beam-column element is integrated through the Gauss-Labatto integration. The semi-rigid connections are modeled by using a zero-length element model where the nonlinear relationship of moment and rotation is formulated using a three-parameter power model. The accuracy and efficiency of the proposed method for modeling CFST columns are validated first by comparing the numerical results with multiple experimental results. Two CFST structures including the circular CFST column cantilever and the full-scale portal CFST frame with a variety of beam-to-column connections are then analyzed and verified with finite element models implemented in ABAQUS. The obtained results showed that the proposed method is highly accurate and can be utilized as an extremely useful tool for the nonlinear inelastic analysis of the CFST structures.

Fully nonlinear inelastic analysis of rectangular CFST frames with semi-rigid connections

In this study, an effective numerical method is introduced for nonlinear inelastic analyses of rectangular concrete-filled steel tubular (CFST) frames for the first time. A steel-concrete composite fiber beam-column element model is developed that considers material, and geometric nonlinearities, and residual stresses. This is achieved by using stability functions combined with integration points along the element length to capture the spread of plasticity over the composite cross-section along the element length. Additionally, a multi-spring element with a zero-length is employed to model the nonlinear semi-rigid beam-to-column connections in CFST frame models. To solve the nonlinear equilibrium equations, the generalized displacement control algorithm is adopted. The accuracy of the proposed method is firstly verified by a large number of experiments of CFST members subjected to various loading conditions. Subsequently, the proposed method is applied to investigate the nonlinear inelastic behavior of rectangular CFST frames with fully rigid, semi-rigid, and hinged connections. The accuracy of the predicted results and the efficiency pertaining to the computation time of the proposed method are demonstrated in comparison with the ABAQUS software. The proposed numerical method may be efficiently utilized in practical designs for advanced analysis of the rectangular CFST structures.

Numerical study on the response of composite shear walls with steel sheets under cyclic loading

As an alternative to conventional reinforced concrete walls, composite shear walls have been studied recently due to their great advantages in terms of structural performance under seismic loading. Researchers usually use ready-made profiles for composite shear walls, but in this study L-shaped cold-formed steel sheets were selected for numerical analysis under lateral cyclic forces. A macroscale numerical model was developed using a fiber beam-column element with a shear spring model to reproduce the actual behavior of composite shear walls. In addition, the OpenSees-based model was verified against three experimentally tested composite shear walls and showed robust simulation ability. Moreover, in order to fully explain their effect on the performance of composite shear walls, the properties of L-shaped steel sheets were studied parametrically with the help of the numerical model in terms of thickness and yield strength. It was clear that increases in the sheets’ yield strength and thickness increased the lateral load-displacement capacity of the walls. It was thought that the two factors were connected in terms of their effects, and the L-shaped steel sheet arrangement in the boundary zone had essential participation in the total response of the composite shear wall under the applied loads.

Behavior of eccentrically loaded square spiral-confined high-strength concrete-filled steel tube columns

Concrete-filled steel tube (CFST) columns have been widely used in super tall buildings. Since these columns are subjected to very high axial loads, the use of high-strength concrete (HSC) is preferred in order to reduce their cross-sectional size. For applications in seismic regions, additional confinement to the HSC may be needed to ensure ductility. Among various approaches, spiral confinement is an effective and practical way for square CFST columns. Six spiral-confined concrete-filled steel tube (SCCFST) columns and three CFST columns with the concrete compressive strength of 111 MPa were tested under eccentric axial loading. The behavior of the columns under different levels of eccentricity ratio was investigated, and the use of high-strength spirals to further enhance confinement was also examined. Concrete crushing was found to be the main cause for the loss of the load-carrying capacity. Spiral reinforcement is not effective in increasing the load-carrying capacity; however, it can considerably improve ductility, which is improved with an increase of the yield strength of spiral reinforcement. Based on the test results, an equivalent uniaxial stress–strain model was developed for the HSC in CFST and SCCFST columns. A fiber beam-column element using the proposed stress–strain models was found to provide good predictions of the measured load–displacement responses. Such fiber element can be used for modeling of SCCCFST columns with HSC in nonlinear structural analysis of tall buildings.