Force-based Beam-column Element Research Articles

Nonlinear Analysis for Investigating Seismic Performance of a Spun Pile-Column of Viaduct Structure

Slab-on-pile SOP viaducts have been constructed on several highways and railways in Indonesia, but there are certain doubts about some practical structural seismic design concepts. Therefore, this study aims to investigate the seismic performance of a single spun pile column for the SOP viaduct using nonlinear analysis. The essential variables used include the effect of top pile reinforced concrete infill treatment, soil-pile structure interaction (SPSI), and different response modification factors (R). Moreover, the single spun pile column was designed as a macro model with a force-based beam-column element having a fiber section in the plastic hinge. The static pushover analysis and quasi-static cyclic were also conducted to determine the displacement limit state and the equal viscous damping, respectively. Furthermore, seven pairs of ground motion excitations were used to investigate seismic performance in line with ASCE 7-10 and ASCE 61-14. The results showed that the implementation of the top-pile reinforced concrete infill treatment slightly reduced seismic response but evoked more severe pile curvature in the embedded zone. In addition, the behavior and seismic performance were slightly better than those without treatment when considering the SPSI. This study recommends the spun pile column for the SOP viaduct with a response modification factor of 1.5 to avoid probable brittle failure occurrence under earthquake load. Doi: 10.28991/CEJ-2023-09-07-02 Full Text: PDF

Effect of material regularization in plastic hinge integration analysis of slender planar RC walls

Recently, mesh-objective (i.e., mesh insensitive) fiber-based numerical models have been developed to simulate RC walls with compression-controlled softening failure modes (i.e., concrete crushing and rebar buckling). These models regularize the post-peak stress-strain behavior of concrete and steel materials based on experimentally-calibrated failure energy equations. While the ultimate displacements of RC walls predicted by these models have been accurate, the local curvature and material strain demands are very sensitive to the selected mesh. Consequently, subsequent normalization of the section curvatures based on an assumed plastic hinge length has been proposed in the literature, resulting in a two-step analysis process. This normalization step uses approximate equations that are dependent on the structural configuration and that can be challenging to implement in cyclic analysis. In accordance with these limitations, this paper studies the effect of material regularization in force-based beam-column elements with a plastic hinge integration method to accurately simulate, in a one-step process, the softening behavior of slender planar RC walls under lateral loading. Numerical results are evaluated using available experimental measurements of eight slender flexural walls with compression-controlled failure modes from the literature. Previous research has shown that one of the biggest limitations of using conventional material models (i.e., without regularization of the stress-strain curves) is that the predicted ultimate displacements are significantly sensitive to the length of the critical integration point over which the nonlinear strains concentrate. This paper demonstrates that this sensitivity of the analysis results can be significantly reduced by using regularized material models and a plastic hinge integration method over a wide range of assumed plastic hinge lengths. The combination of material regularization and plastic hinge integration analysis can also predict the section curvatures and strains of RC walls, with no need for a separate normalization step, though these local responses are more sensitive to the assumed plastic hinge length.

Methodology for Regularization of Force-Based Elements to Model Reinforced Concrete Columns with Short Lap Splices

In reinforced concrete structures built before the 1970s, it was common for columns to be constructed with short lap splices and widely spaced transverse bars at the column base, leading to increased likelihoods of pull-out failures and structural collapse during seismic events. In the modeling and analysis of reinforced concrete columns with short lap splices, several challenges arise, particularly with softening behavior that leads to strain localization and scaling and convergence issues in analyses. This research presents a methodology to regularize force-based beam-column elements with softening lap-splice material response. In the methodology, a constant energy release criterion is imposed with the constant postpeak energy of the lap-splice region determined from relevant experimental data. With the proposed regularization, the numerical model shows objective results that are independent of the length of the element and number of integration points used. Whereas the accuracy in estimating, for example, the displacement at 20% strength drop using existing nonregularized models changes with the number of integration points, the accuracy using the proposed model remains constant across numbers of integration points used with a mean accuracy of 94% compared with experimental tests. Results from static pushover and cyclic analyses show an order of magnitude decrease in standard deviation of the response using the regularized model. Increased accuracy and increased convergence for the method across the number of integration points used is shown in static and dynamic analyses. The proposed regularization approach is able to alleviate strain localization issues and facilitates the scaling of analyses from small-scale to full-scale structures.

3D Fiber-Based Frame Element with Multiaxial Stress Interaction for RC Structures

A three-dimensional fiber-based frame element accounting for multiaxial stress conditions in reinforced concrete structures is presented. The element formulation relies on the classical Timoshenko beam theory combined with sectional fiber discretization and a triaxial constitutive model for reinforced concrete consisting of an orthotropic, smeared crack material model based on the fixed crack assumption. Torsional effects are included through the Saint-Venant theory of torsion, which accounts for out-of-plane displacements perpendicular to the cross section due to warping effects. The formulation was implemented into a force-based beam-column element and verified against monotonic and cyclic tests of reinforced concrete columns in biaxial bending, beams in combined flexure-torsion, and flexure-torsion-shear.

Computational performance of beam-column elements in modelling structural members subjected to localised fire

In the past decades, increasing attention has been directed to understanding the structural response to various scenario fires, which is stimulated by the trend of considering localised burning in large open plan compartments. Beam-column elements as widely used in modelling steel frames have been extended to account for the thermal impact in OpenSees, the development of which is undertaken to formulate the displacement and force-based beam elements. After including the non-uniform thermal expansion along the element length caused by localised heating, the force-based beam-column element has shown greater efficiency compared to the displacement-based element. A detailed discussion regarding the computational performance of both beam-column elements has been presented in this paper, which concludes that force-based beam-column elements can better represent the localised plasticity of fibres caused by non-uniform heating. A generic simply supported steel beam can be modelled even with two force-based elements to reproduce accurate mid-span deflection under localised heating. A steel beam subjected to a localised fire is presented as a case study in this paper, experiencing run-away collapse after 15 min of exposure when the load ratio reaches 50%. Using a 12 element force-based beam-column model and shows equivalent accuracy against 48 element displacement-based beam-column model.

Homogenization of heterogeneous masonry beams

This study presents a two-scale model to describe the out-of-plane masonry response. One-dimensional (1D) structural elements, like masonry columns or strips of long wall characterized by the periodic repetition of bricks and mortar arranged in stack bond, are considered. A damage-friction plasticity law is adopted to model the mortar joint constitutive response, while the bricks are assumed as linear elastic. A 1D beam formulation is introduced at both the structural and micromechanical scale, linking the two levels by means of a kinematic map. This expresses the microscopic beam strains in the masonry unit cell (UC) as function of the macroscopic generalized strains. The kinematic field in the UC is completed by adding an unknown periodic fluctuation term. A nonlinear homogenization procedure is developed, proposing a semi-analytical solution for the micromechanical problem, based on the fiber discretization of the mortar joints. A force-based beam-column finite element procedure is adopted at the structural scale and the solution algorithm for the element state determination is illustrated in details. Some numerical applications, showing the UC constitutive response and the behavior of masonry structural elements, are finally presented.

Numerical Investigation of Variable Length of Seismic Damage Region for Reinforced Concrete Columns

ABSTRACTThe seldom investigation of variable length of damage region prevents the estimation of probabilistic drift limits of reinforced concrete columns at different performance levels for the performance-based seismic design. However, if using the numerical approach to predict the variability of damage region within the framework of force-based beam-column element, the current force-based beam-column element is unable to model the spreading of damage region. Therefore, a new numerical simulation method is proposed to compute the emergence, propagation and termination of damage region of reinforced concrete columns. Then, based on the developed numerical simulation method, the measured response of experimental testing is calibrated. From the calibration, it can be observed that there is a rapid increase on the variable length of damage region with the increasing of lateral displacement and then followed by a stable stage. The propagation of the longitudinal reinforcement yielding and concrete tensile cracking mainly occurs in the ascending branch of the load–displacement response. Then, based on the growth characteristic of the damage region from the numerical simulation, an empirical equation is proposed to describe the variable length of damage region by using the least-square regression analysis to fit the computed responses for its simplicity to use in engineering practices. Finally, the stable length of damage region is reinvestigated by carrying out a parametric study with the developed numerical simulation method, indicating that two critical design parameters, specifically the axial load ratio and the shear span ratio, have considerable influences on this quantity of interest.

Seismic Analysis of Precast Concrete Bridge Columns Connected with Grouted Splice Sleeve Connectors

AbstractReinforcing bar couplers are used in prefabricated bridge elements and bridge systems for accelerated bridge construction. Grouted splice sleeve connectors are used in bridge substructures because of the enhanced construction tolerances they offer. This paper presents a simplified modeling strategy for seismic assessment of precast bridge columns connected to precast footings using grouted splice sleeve connectors. A computational model was developed and validated using three half-scale bridge subassemblies tested to failure. Cyclic quasi-static loading was applied to two precast subassemblies and one cast-in-place specimen. The connectors were located in the footing, for the first precast alternative, and in the column end for the second precast alternative along with debonding of reinforcing bars in the footing. Force-based beam-column elements with fiber sections were used to construct the computational model based on plastic hinge weighted integration; the model included low-cycle fatigue and ...

Optimal Force-Based Beam-Column Element Size for Reinforced-Concrete Piles in Bridges

AbstractThe nonobjective disadvantages of the force-based frame element, such as the nonobjective curvature prediction, have been discussed by many researchers. The trial-and-error method is commonly used to determine element size, but it could cost tremendous computational efforts. This paper proposes and analytically studies the optimal element size for reinforced-concrete piles for bridges when using force-based beam elements. In this study, the relationship between the optimum element size and integration point number is investigated, and the equivalent plastic hinge length is used and correlated to the optimal element size, on the basis of which the moment-curvature and force-displacement responses are objective and the soil effects on the pile response could be simulated sufficiently as required. The results of a case study show that both the local and global responses can be very well predicted, and the nonobjective disadvantage of the force-based element could be eliminated using the proposed opti...

Analysis on Dynamic Response of Reinforced Concrete Frame for Resisting Progressive Collapse

In order to investigate the dynamic response of reinforced concrete spatial frames caused by initial damages, a six-story frame model is analyzed by employing the nonlinear dynamic methodology in accordance with the alternate path method issued by General Services Administration. In this paper, the fiber model and force-based beam-column element are utilized in OpenSees. Four various scenarios are separately analyzed with incremental dynamic analysis. It is shown that the model does not collapse and the internal force redistribution mainly appears in the components adjacent to the failure column. The model has the worst capacity to resist progressive collapse in the inner column demolition scenario. It is observed that the plastic hinges mainly concentrate on the beam ends of the failure bay at the beginning of the demolition of columns. Several plastic hinges emerge at the top-floor beam ends of some other bays in latter period. The number of plastic hinges in columns is much less than that in beams, which corresponds to the design principle ‘strong column and weak beam’.

Stochastic Nonlinear Behavior of Reinforced Concrete Frames. II: Numerical Simulation

AbstractExperimental investigations on the stochastic nonlinear behavior of eight half-scale reinforced concrete (RC) frames with the same conditions in the companion paper indicates that the coupling effect between randomness and nonlinearity of concrete will cause a remarkable fluctuation in structural nonlinear responses. In the current paper, a validation program is presented through numerical simulation. Deterministic nonlinear analysis of test specimens is performed on the basis of a force-based beam–column element model. Probability density evolution method (PDEM) is introduced to analyze the stochastic response analysis of structures. Probability density functions of the stochastic structural responses of the specimens are provided at both the load–displacement level and internal-force level. Comparative studies between numerical and experimental results reveal that the numerical method in conjunction with PDEM can not only qualify the fundamental trend of stochastic nonlinear responses of structu...

A modified stress-strain model accounting for the local buckling of thin-walled stub columns under axial compression

A novel stress–strain model accounting for elastic and inelastic local buckling of thin-walled steel plates was proposed in this paper based on an energy method. The proposed model was then implemented in a fibre force-based beam-column element for the advanced analysis of thin-walled and concrete-filled steel stub columns under axial compression. Both geometric and material nonlinearities are included in the fibre model. The obtained results were compared with independent experimental results and those predicted by ABAQUS using shell and solid elements. As shown in the numerical examples, the proposed stress–strain models can reasonably predict the ultimate strength and local and post-local buckling behaviour of thin-walled and concrete-filled steel stub columns under axial compression.

Calibration and Validation of Analytical Models for Predicting the Seismic and Axial-Load Response of Circular Bridge Columns

AbstractThe objective evaluation of the capacity of a bridge to carry self-weight and traffic loads after an earthquake is essential for a safe and timely reopening of the bridge; this performance goal gains in importance with the recognition of the economic losses caused by the reduced traffic capacity of the transportation systems of a region affected by an earthquake. An analytical model of a bridge column was developed, calibrated, and validated to facilitate the quantitative evaluation of the remaining traffic-load capacity of a typical California highway overpass bridge after an earthquake. The bridge-column model was developed using a fiber cross section, force-based beam-column element with distributed plasticity. The model was calibrated using the data from a series of bidirectional quasi-static tests and validated using the data from hybrid simulations of the bridge earthquake response. It was found that the postpeak degrading slope of the confined-concrete core has a significant influence on th...

Modeling of different bracing configurations in multi-storey concentrically braced frames using a fiber-beam based approach

This study presents a modeling approach for concentrically braced frames to be used in multi-storey buildings. The model for an inelastic beam-column brace consists of two inelastic force-based beam-column elements, each of which having five integration points and a discretized fiber section. The hysteretic response of such elements can be derived by integration of uniaxial stress-strain relations.To capture the effects of gusset end restraint, in addition to the two inelastic beam-column elements, this study uses an additional inelastic force-based beam-column element of length 2t (where t is the thickness of the gusset plate) at each end of the brace. This study presents the correlation of the axial force–axial displacement and the axial force–lateral displacement responses obtained from the brace model with the available experimental results.Based on the comparison of numerical hysteretic responses with the experimental results, it can be concluded that the brace model which includes two additional force-based beam-column elements at the ends of the brace can capture the hysteretic responses of axial force–axial displacement and axial force–lateral displacement more accurately. Finally, this study sets the limits of slenderness and the width-to-thickness ratio in which inelastic beam-column brace model can predict the hysteretic responses of a brace member with adequately accuracy.

고정반복법에 의한 암시적 HHT 시간적분법을 이용한 철근콘크리트 골조구조물의 실시간 하이브리드실험

고정반복법에 의한 암시적 HHT 시간적분법을 이용하여 3층 3경간 철근콘크리트 골조구조물을 수치해석모형과 물리적 분구조모형으로 나누어 실시간 하이브리드실험을 실시하였다. 물리적 부분구조모형으로는 1층 내부 비연성기둥 1개소가 선택되었고, 수치해석모형에 일축 방향의 지진하중을 시편이 심한 손상에 의하여 파괴에 이를 때까지 작용시켰다. 비선형 유한요소해석 프로그램인 Mercury가 실시간 하이브리드실험을 위하여 새로이 개발 및 적용되었다. 실험결과는 물리적 부분구조모형의 상부 수평방향 층간변위비를 OpenSees에 의한 수치해석시뮬레이션과 진동대실험의 그것과 비교하였다. 본 실험은 가장 복잡한 실시간 하이브리드실험 중의 하나이고, 하드웨어, 알고리즘 그리고 모형에 대한 기술적인 내용을 본 논문에 자세히 설명하였다. 수치해석모형의 개선, 물리적 부분구조 모형 접선강성행렬의 유한요소해석 프로그램에서의 평가 그리고 하중기반 보-요소의 요소상태결정의 연산시간을 줄이기 위한 소프트웨어의 개선이 이루어진다면 실시간 하이브리드실험과 진동대실험결과의 비교는 권장할 만하다. 그리고 "지진과 같은 동적하중하의 복잡한 구조물의 수치해석시뮬레이션"이라는 목적을 위하여 실시간 하이브리드실험은 동적하중에 대한 실험적 검증을 점진적으로 수치해석모형으로 대체하기 위한 저비용-고효율 실험법으로서의 가치를 충분히 가지고 있다고 할 수 있다. A real-time hybrid test of a 3 story-3 bay reinforced concrete frame which is divided into numerical and physical substructure models under uniaxial earthquake excitation was run using a fixed iteration implicit HHT time integration method. The first story inner non-ductile column was selected as the physical substructure model, and uniaxial earthquake excitation was applied to the numerical model until the specimen failed due to severe damage. A finite-element analysis program, Mercury, was newly developed and optimized for a real-time hybrid test. The drift ratio based on the top horizontal displacement of the physical substructure model was compared with the result of a numerical simulation by OpenSees and the result of a shaking table test. The experiment in this paper is one of the most complex real-time hybrid tests, and the description of the hardware, algorithm and models is presented in detail. If there is an improvement in the numerical model, the evaluation of the tangent stiffness matrix of the physical substructure model in the finite element analysis program and better software to reduce the computational time of the element state determination for the force-based beam-column element, then the comparison with the results of the real-time hybrid test and the shaking table test deserves to make a recommendation. In addition, for the goal of a "Numerical simulation of the complex structures under dynamic loading", the real time hybrid test has enough merit as an alternative to dynamic experiments of large and complex structures.

An Improved Three-Strut Model for Masonry Infills in RC Frame Structures

In Wenchuan Earthquake, masonry-infilled frames have the quite critical failures. In this paper, the reason of the failure phenomenon is analyzed and the influence of the infilled wall to performance of the frame is highlighted. An improved three-strut model for masonry-infilled frame structures is presented. Then, two RC frame specimens, which are modeled by the presented three-strut model and force-based beam-column element combined with fiber section considering compression-bending coupling in Opensees, are analyzed. The analytical results agree well with the experimental results. It is shown that the presented three-strut model is sufficient to simulate the performance of the infilled wall.

Plastic Hinge Integration Methods for Force-Based Beam–Column Elements

A new plastic hinge integration method overcomes the problems with nonobjective response caused by strain-softening behavior in force-based beam-column finite elements. The integration method uses the common concept of a plastic hinge length in a numerically consistent manner. The method, derived from the Gauss-Radau quadrature rule, integrates deformations over specified plastic hinge lengths at the ends of the beam-column element, and it has the desirable property that it reduces to the exact solution for linear problems. Numerical examples show the effect of plastic hinge integration on the response of force-based beam-column elements for both strain-hardening and strain-softening section behavior in the plastic hinge regions. The incorporation of a plastic hinge length in the element integration method ensures objective element and section response, which is important for strain-softening behavior in reinforced concrete structures. Plastic rotations are defined in a consistent manner and clearly related to deformations in the plastic hinges.

A force-based model for composite steel–concrete beams with partial interaction

This paper presents a new force-based beam–column element for the nonlinear analysis of composite steel–concrete beams with partial interaction. The element is made up of three components: (a) a fiber beam–column element that models the behavior of the steel girder, (b) a fiber beam–column element that models the behavior of the concrete deck, and (c) a bond element that models the transfer of forces between the steel and concrete elements through shear connectors. The model neglects uplift and frictional effects. The fiber beam–columns are force-based elements that depend on force interpolation functions. A linear bending moment and a constant axial force serve as the interpolation functions. An important factor that favors the use of force-based elements in modeling composite structures is their ability to treat any type of distributed element loads. Distributed element loads are applied internally in a continuous manner by force superposition at the control sections. The state determination of these elements is based on an iterative solution that determines the element resisting forces and stiffness matrix. The bond element is a spring-type element that assumes a linear bond stress variation along the length. The nonlinear behavior of the composite element derives entirely from the constitutive laws of the steel, the concrete and the shear connectors. The paper concludes with a correlation study to investigate the validity of the model. Good agreement between analysis and experimental results was observed.

Response Sensitivity for Nonlinear Beam–Column Elements

Response sensitivity is needed for simulation applications such as optimization, reliability, and system identification. The exact response sensitivity of material nonlinear beam-column elements is derived for the displacement- and force-based formulations. For displacement-based beam.column elements the response sensitivity is straightforward to compute because the displacement field is specified along the element. A new approach is presented for computing the response sensitivity of force-based beam-column elements, in which the displacement field is not specified. In this approach, the response sensitivity depends on the derivative of unbalanced section forces because the element displacement field changes with the element state. Example nonlinear static analyses of steel and reinforced concrete structural systems verify the exact response sensitivity for force-based elements using the new approach.