Axial Force Interaction Research Articles

Flexural behavior of reinforced concrete arch ribs

For many years, arch bridges have been celebrated for their striking appearance and structural effectiveness. However, the response of arch bridges to dynamic loadings, particularly during earthquakes, remains poorly understood, and reliable seismic design guidelines are lacking. Previous research has suggested that reinforced concrete (RC) arch ribs may experience flexural yielding at their springings due to the interaction of axial force and bending moment under earthquake loading. To assess the ductile behavior and ensure the adequate performance of RC arch ribs, a comprehensive investigation combining experimental and analytical approaches was conducted in this study, taking into account the influence of high axial load and the hollow section configuration present in RC arch ribs. The test results revealed that all RC arch ribs exhibited a typical flexural failure mode. As the axial load increased, the lateral load bearing capacity also increased, but the displacement ductility decreased significantly. Comparing different section configurations, the RC arch rib specimen with a double-cell boxed section demonstrated higher lateral load bearing capacity but lower displacement ductility compared to the single-cell boxed section, while the energy dissipation capacity was approximately similar for both section configurations.

Optimization of Reinforcement Ratio in Reinforced Concrete Columns Using Interaction Diagrams

Reinforced concrete columns are structural members used to carry compressive loads. Column planning is important, considering that the column is the main structural element supporting the loads on a building. Column planning is generally used in moment and axial force interaction diagrams for a certain reinforcement ratio. Although there is currently much software available, Interaction diagrams made in this paper can be said to be a simple way of column planning. The method used in this paper is a numerical calculation method with the help of Ms Excel. This paper aims to optimize the planning of reinforced concrete columns using Mn and Pn interaction diagrams. Furthermore, the optimization results of the column planning interaction diagram have been obtained. A reinforcement ratio of 2% is a better result to apply. Keywords: column, interaction diagram, reinforcement ratio.

Prediction of Ultimate Capacity of Concrete Columns Reinforced with FRP Bars.

FRP bars are used in concrete structures as an alternative to steel bars as they have many advantages such as high tensile strength, high strength-to-weight ratio, electromagnetic neutrality, lightweight and no corrosion. There is a perceived lack of standard regulations for the design of concrete columns with FRP reinforcement, e.g., in Eurocode 2. This paper describes a procedure for predicting the bearing capacity of concrete columns with FRP reinforcement based on the interaction of axial force and bending moment, which was developed on the basis of existing design recommendations and standards. It was shown that the bearing capacity of eccentrically loaded RC sections depends on two parameters, which are the mechanical reinforcement ratio ω and the location of the reinforcement in the cross-section expressed by the β factor. The analyses carried out showed the existence of a singularity in the n-m interaction curve indicating the fact that in a certain loaded range, the curve is concave, and more it was shown that the balance failure point for sections with FRP reinforcement takes place for eccentric tension. A simple procedure for calculating the required reinforcement from any FRP bars in concrete columns was also proposed. Nomograms developed from n-m interaction curves provide for the accurate and rational design of FRP reinforcement in columns.

Plastic behavior of metal sandwich beams with foam-filled sinusoidal corrugation

In this paper, the plastic behavior of metal sandwich beams with foam-filled sinusoidal corrugation is studied theoretically and numerically. The yield criterion of foam-filled sinusoidal corrugation sandwich cross-section is established, considering the effects of metal foam strength and sinusoidal corrugation strength. Based on the yield criterion, an analytical model for the plastic behavior of fully clamped foam-filled sinusoidal corrugation sandwich beams under transverse loading is developed, considering the interaction of axial force and bending moment. Finite element calculations are carried out to verify the analytical model. The influences of geometrical and material parameters on the load-carrying capacity and energy absorption of foam-filled sinusoidal corrugation sandwich beams are discussed. The results show that, with the increase of foam strength, face-sheet thickness, sinusoidal corrugation strength, sinusoidal corrugation sheet thickness, sinusoidal amplitude, sinusoidal half wavelength and punch width, the load-carrying capacity and energy absorption of foam-filled sinusoidal corrugation sandwich beams increase. In addition, when the loading position moves from the midspan to the clamped ends, the load and absorbed energy for the same deflection increase obviously.

Behavior of stiffened and multi-cell L-shaped CFST columns under eccentric compression

The mechanical behavior of the traditional special-shaped concrete-filled steel tubular (CFST) columns can be improved by employing longitudinal stiffeners or using multi-cell cross-section. In practical application, the stiffened and multi-cell L-shaped CFSTs are often subjected to bi-directional loading. However, there are only few research studies on their performance as loaded eccentrically with different orientations of the loading and there is no relevant design guideline. This paper reports tests on 16 L-shaped CFST columns (nine stiffened, six multi-cell specimens and one reference specimen) loaded in eccentric compression. The main variables were the angle indicating the orientation of the load action line (0°, 45°, 135°, 180° and 225°), load eccentricity ratio (0, 0.25 and 0.5) and slenderness ratio (31.5 and 41.9). Finite element models for the eccentrically loaded stiffened and multi-cell L-shaped CFST columns were developed. Based on the parametric analysis, practical design methods were proposed for predicting the bearing capacity based on the stability loss and the axial force vs. bending moment interaction diagrams for the members considering the influence of the load orientation at the end face of the column.

Effect of bidirectional excitation on seismic performance of regular RC frame buildings designed for modern codes

The existing practice to estimate seismic performance of a regular building is to carry out nonlinear time history analysis using two-dimensional models subjected to unidirectional excitations, even though the multiple components of ground motion can affect the seismic response, significantly. During seismic shaking, columns are invariably subjected to bending in two orthogonal vertical planes, which leads to a complex interaction of axial force with the biaxial bending moments. This article compares the seismic performance of regular and symmetric RC moment frame buildings for unidirectional and bidirectional ground motions. The buildings are designed and detailed according to the Indian codes, which are at par with the other modern seismic codes. A fiber-hinge model, duly calibrated with the biaxial experimental results, is utilized to simulate the inelastic behavior of columns under bidirectional bending. A comparison of the estimated seismic collapse capacity is presented, illustrating the importance of considering the bidirectional effects. The results from fragility analysis indicate that the failure probabilities of buildings under the bidirectional excitation are significantly higher as compared to those obtained under the unidirectional excitation.

Axial Force and Biaxial Bending Interaction for I-Shaped Cross Section

AbstractThis paper presents new formulae for the determination of the plastic strengths of steel I-sections subjected to uniaxial bending about major or minor axis combined with an axial compressio...

Behaviour of rectangular concrete filled tubular flange girders under combined loading

AbstractSteel‐concrete composite construction can provide an efficient structural solution by utilizing the two component materials to create a single effective composite section. The high tensile strength and ductility of steel combined with the excellent compressive strength and robustness of concrete results in an effective composite cross‐section which can be used in a wide variety of applications. There are a number of different shapes of composite beam, and this paper is focussed on a relatively new structural solution called concrete filled tubular flange girders (CFTFGs). These comprise a steel beam in which the top flange plate is replaced with a concrete‐filled hollow section. The compression flange can be any shape (e.g. circular, rectangular, and pentagonal) and the focus in the current paper is on simply supported girders with a rectangular section for the compression flange (i.e. RCFTFGs). These members have very high lateral torsional buckling resistance compared with conventional steel I‐girders of similar depth, width and steel weight and are therefore capable of carrying very heavy loads over long spans. However, they are complex to analyse and their behaviour is governed by several inter‐related parameters which are investigated and discussed herein. Given the most common applications of these girders, such as in bridges and carparks for example, they are frequently exposed to a simultaneous combination of high axial loads and bending moments. Although current design codes offer rules for the design of composite columns under combined loading, the design of RCFTFGs, which are asymmetric in nature under the combined effects of tension and bending, are not explicitly included. This work aims to investigate the ultimate strength of RCFTFGs with stiffened webs under the combined effects of various levels of axial tension and positive (sagging) bending moment. Nonlinear three‐dimensional finite element analyses using the ABAQUS computer software package have been developed to facilitate the study. The model is validated using available experimental data and then employed to conduct an extensive parametric study. It is shown that the moment capacity of RCFTFGs is reduced in most situations under the presence of an axial tensile force in the steel beam. In addition, the tensile capacity of the RCFTFGs is limited by the axial capacity of the steel beam alone, with little contribution from the concrete infill. Several influential parameters are examined and conclusions are discussed. Based on the finite element analysis, the moment–axial force interaction relationship is presented and discussed.

A crack model for corroded reinforced concrete elements subject to cyclic loading

Corrosion of embedded reinforcement is the main cause of deterioration of existing reinforced concrete infrastructure. Corrosion can significantly affect the seismic response and failure mode of reinforced concrete elements, causing premature concrete crushing, size reduction of reinforcement, degradation of mechanical properties of steel and concrete, and degradation and breaking of stirrups. The latter effects trigger inelastic buckling of the longitudinal reinforcement. In this paper, a non-linear finite-element approach, based on multi-layer shell elements and a crack model, is presented. The fixed crack model was developed at the University of Parma (Italy) and is implemented as a subroutine in standard finite-element software. The model incorporates cyclic constitutive laws for steel able to account for buckling of longitudinal rebars and the effects of corrosion. The effectiveness of the proposed model is validated through comparison with experimental data available in the literature. Finally, the capability of the proposed shell modelling to implicitly consider axial force, shear force and bending moment interaction is discussed and comparisons with analytical model and non-linear finite-element analysis results are provided.

Pushover analysis of R.C. framed structures with infill panels made of masonry having various properties

The seismic performances of R.C. frame structures were determined in terms of inter-storey drifts at two limit states, internal forces and moments (axial forces and bending moments), and the in-plane behaviour of infills. A nonlinear static analysis (pushover) was carried out in order to assess the seismic performance of buildings, to identify the expected plastic mechanisms and to plot the capacity curves. In pushover analysis, the vertical distribution of the monotonically increasing horizontal loads, was performed according to the first mode pattern. The nonlinear behaviour of structural members for pushover analysis was modelled by using the lumped plasticity, from where it derives that the potential plastic hinges were situated at the beams ends (which yield due to the bending moment), at the top and bottom of the columns at any storey (which yield based on the interaction of axial force and bending moment) and in the struts (which yield due to the axial force).

Design and analysis of concrete-filled tubular flange girders under combined loading

This paper is concerned with the behaviour of concrete-filled tubular flange girders (CFTFGs) under the combination of bending and tensile axial force. CFTFG is a relatively new structural solution comprising a steel beam in which the compression flange plate is replaced with a concrete-filled hollow section to create an efficient and effective load-carrying solution. These members have very high torsional stiffness and lateral torsional buckling strength in comparison with conventional steel I-girders of similar depth, width and steel weight and are there-fore capable of carrying very heavy loads over long spans. Current design codes do not explicitly include guidance for the design of these members, which are asymmetric in nature under the combined effects of tension and bending. The current paper presents a numerical study into the behaviour of CFTFGs under the combined effects of positive bending and axial tension. The study includes different loading combinations and the associated failure modes are identified and discussed. To facilitate this study, a finite element (FE) model is developed using the ABAQUS software which is capable of capturing both the geometric and material nonlinearities of the behaviour. Based on the results of finite element analysis, the moment–axial force interaction relationship is presented and a simplified equation is proposed for the design of CFTFGs under combined bending and tensile axial force.

Progressive collapse of reinforced concrete buildings considering flexure-axial-shear interaction in plastic hinges

Progressive collapse assessment of a reinforced concrete (RC) building designed only for gravity loads and lacking a dedicated lateral load resisting system was carried out using the alternate load path (ALP) method and finite element method (FEM) numerical model created in software SAP2000. Plastic hinge capacity of the members was evaluated considering flexure (M), axial force (N) and shear force (V) interaction and a validated procedure was devised to incorporate the plastic hinge capacity based on M-N-V interaction into the results obtained from the FEM model. It was found that consideration of M-N-V interaction resulted in plastic hinge capacities that were lower than the flexure-only capacity of the plastic hinges available in the FEM software which caused the progressive collapse to initiate at a lower load and also resulted in increased collapse area. In the second part of the study, it was demonstrated that the progressive collapse resistance of the building for the interior and the edge column removal scenarios was appreciably improved after ordinary moment frames were cost-effectively designed at selected locations without increasing member cross-sectional dimensions. However, key element design concept approach was needed for improving the progressive collapse performance for the corner column loss scenarios. Relative reduction in the plastic hinge capacity due to M-N-V interaction as compared to flexure-only hinge capacity was found to be lower for the redesigned building due to improved member capacity.

Fire resistance of high-strength steel tubes infilled with ultra-high-strength concrete under compression

Ultra-high strength concrete (UHSC) and high strength steel (HSS) have been found to be attractive alternatives to normal strength materials for high-rise construction. The uses of HSS and UHSC can reduce member sizes and payload acting on foundation, which will free up more usable floor space and require less construction materials and handling works. The combination of them to form concrete-filled steel tubular (CFST) columns is more attractive compared with the columns employing either UHSC or HSS due to enhanced strength and stiffness. To better understand the structural behavior of CFST columns using UHSC and HSS, experimental and analytical studies on their fire resistance are presented in this paper. Fire tests were carried out on square S690 HSS tubes infilled with C170/185 UHSC to form the CFST columns. The fire resistance time under Standard ISO fire was recorded and checked against the conventional simple calculation model of EN1994-1-2 and the newly proposed axial force and moment interaction model. It is revealed that the column buckling curve in EN1993-1-1 can be used for fire-resistant design of CFST columns employing UHSC and HSS when the load level is less than 0.65. The use of UHSC is beneficial to improve the fire resistance of CFST columns but the use of high strength steel is not when compared with their counterparts using normal strength materials.

Dynamic Behavior of Pile-Supported Structures with Batter Piles according to the Ground Slope through Centrifuge Model Tests

Pile-supported structures incorporating batter piles are commonly used, and can be installed both on the horizontal and inclined ground. Recent studies have considered the positive role of batter piles during earthquakes, highlighting their satisfactory contribution to structural seismic performance. However, in these structures, even though the dynamic system responses can vary greatly depending on the ground slope, few previous studies have evaluated the seismic performance of batter piles relative to the ground slope. Therefore, this study evaluates the seismic performance of pile-supported structures with batter piles, relative to the ground slope using dynamic centrifuge model tests. The acceleration, displacement, moment, and axial force of the system were experimentally derived and reviewed, and the pile moment and axial force (M–N) interaction diagrams of the pile cross-sections were analyzed. The installation of the batter piles resulted in a greater reduction in the system response in the inclined-ground model (acceleration: −48%, displacement: −50%, and moment: −84%) compared to that in the horizontal-ground model (acceleration: −27%, displacement: +650%, and moment: −77%). Overall, batter piles showed better seismic performance in the inclined-ground model than in the horizontal-ground model.

Optimal Design of Seismic Resistant RC Columns.

Although the author is well aware that it is nothing special, presented here is the method that he uses to design the columns of a seismic resistant reinforced concrete structure, in hopes that this could be of use to someone. The method, which is directed at satisfying the capacity design requirements without excessively large sections, consists of proportioning the column so that the seismic action effects shall be resisted by the maximum of the bending moment–axial force interaction curve. That design condition is defined by two equations whose solution provides the optimal aspect ratio (or, alternatively, the optimal section side length) and the maximum feasible reinforcement ratio. The method can be used directly to determine the optimal column for given beam spans and vertical loads, or indirectly to determine the optimal beam spans and vertical loads for given cross-sectional dimensions. The paper presents the method, including its proof, and some applications together with the analysis on the optimality of the obtained solutions. The method is intended especially for the practicing structural engineer, though it may also be useful for educators, students, and building officials.

A unified approach to evaluate axial force-moment interaction curves of concrete encased steel composite columns

This paper presents a unified approach to evaluate the axial force and moment interaction strength curve of Concrete Encased Steel (CES) composite columns made of different steel and concrete grades. A database was established by collecting the test results of CES composite columns in the literature covering concrete compressive strength ranging from 20 to 104 MPa and steel yield strength from 280 to 913 MPa. A sensitivity study was then carried out to investigate the effect of different design parameters on the accuracy of the current design method EN 1994-1-1 in predicting the ultimate strength of CES composite columns. These design parameters include characteristic strength of materials, steel contribution ratio, concrete cover thickness ratio, longitudinal reinforcement ratio, and volumetric ratio of transverse reinforcement. Analytical study was performed through a self-compiled computer program which was developed based on materials strain compatibility principle. The comparison between the analytical results and test results confirms the validity of the proposed method to provide reasonable prediction of cross-sectional axial-moment interaction curves for CES columns for a wide range of steel and concrete grades. The existing EC4 method, which is based on plastic design principle, was found to be un-conservative in predicting the cross section resistance of CES composite columns with high strength concrete and high strength steel. Further enhancement was made to the proposed method to include both the strain gradient effect and concrete confinement effect to achieve a better agreement with the test results reported in literature. Finally, a simplified method was proposed to construct the axial-moment interaction curves of CES columns, which can be used as a unified approach to design such columns with normal and high strength steel and concrete materials.

Load capacity of corroded welded hollow spherical joints subjected to bending moment and axial force

Welded hollow spherical joints (WHSJs) have been extensively used in space lattice structures. Corrosion is inevitable in the service life of WHSJs, and it can significantly reduce their load capacity and seriously threaten their structural safety. A series of nonlinear numerical analyses was conducted to investigate the moment and axial force interaction for corroded WHSJs. The moment-rotation surface of corroded WHSJs subjected to axial force was derived. The influence of the location, size, and thickness of corrosion of WHSJs on their compressive capacity were revealed in this study. Two types of corroded shapes were investigated. Results indicate that the geometrical parameters exert a significant influence on the moment and axial force interaction. An analytical equation has been proposed to quantify the influence of axial force on the bending stiffness and moment capacity of corroded WHSJs.

Strain Hardening Analysis for M-P Interaction in Metallic Beam of T-Section

This paper derives kinematic admissible bending moment – axial force (M-P) interaction relations for mild steel by considering strain hardening idealisations. Two models for strain hardening – Linear and parabolic have been considered, the parabolic model being closer to the experiments. The interaction relations can predict strains, which is not possible in a rigid, perfectly plastic idealization. The relations are obtained for all possible cases pertaining to the locations of neutral axis. One commercial rolled steel T-section has been considered for studying the characteristics of interaction curves for different models. On the basis of these interaction curves, most significant cases for the position of neutral axis which are enough for the establishment of interaction relations have been suggested. The influence of strain hardening in the interaction study has been highlighted. The strains and hence the strain rates due to bending and an axial force can be separated only for the linear-elastic case because the principle of superposition is not valid for the nonlinear case. The difference between the interaction curves for linear and parabolic hardening for the particular material is small.

Experimental studies on Belleville springs use in the sliding hinge joint connection

The Sliding hinge joint (SHJ) is a low damage beam-to-column connection developed for and widely used in seismic moment-resisting steel frames (MRSFs). The asymmetric friction connection (AFC) is the SHJ's friction sliding energy dissipating component, which has also been used in other seismic resisting structural systems. In current practice, the AFC bolts are yielded at installation by the method of bolt tightening, and they are subjected to moment, shear, and axial force (MVP) interaction during stable sliding. Hence the AFC bolts tension, and as a result, SHJ elastic strength will be reduced after sliding cycles. A remedy to this post-sliding strength reduction could be installing the AFC bolts in the elastic range in conjunction with using Belleville springs (BeSs) to maintain the clamping force, but at the potential cost of deteriorating the SHJ self-centering capability. This paper describes nine real-scale SHJ's AFC component tests at quasi-static and dynamic rates of displacement controlled loading, with bolts either tightened in the elastic range using no BeSs as well as with four different configurations of BeSs which are deliberately not fully deflected at installation, to avoid the system self-centering capability deterioration and to minimize the additional imposed tension on the AFC bolts during stable sliding. It is concluded that using partially deflected BeSs with sufficient axial deformation to reach the installed bolt tension, with these being installed at both head and nut sides of the AFC bolts, will reduce the post-sliding clamping force loss, improve the self-centering capability, increase the system coefficient of friction, reduce the additional imposed tension on the AFC bolts during stable sliding due to prying actions and/or MVP interactions, and reduce the severity of the sliding surfaces' wearing.

Full-scale testing of stiffened extended shear tab connections under combined axial and shear forces

Owing to the lack of a comprehensive published procedure for the design of stiffened extended shear tabs, practicing engineers usually follow design guides for unstiffened shear tabs. The results of recent laboratory experiments and numerical analyses have demonstrated that improvements to this approach are warranted. Furthermore, design methods for this connection type under combined axial and shear forces are not well established. To address these shortcomings, full-scale laboratory tests were carried out on the double-sided configuration of stiffened extended beam-to-girder shear tab connections with full depth shear plates. These experiments were complemented by a continuum finite element (CFE) study, with which the axial force demands along with other critical parameters that affect the connection behaviour were further examined. The experiments supported by the CFE findings indicated that the primary connection damage states are mainly associated with yielding and fracture of the shear plate due to the interaction of flexural, shear, and axial force. The study demonstrated that the direction and magnitude of the applied axial force significantly affected the shear and axial demands along the centerline of the interior bolt line. The current design practice for the double-sided configuration of the full-depth extended beam-to-girder shear tab was also evaluated; a significant underestimation was observed in the prediction of a connection’s ultimate resistance.