Axial Load Moment Research Articles

Derivation of Key Characteristics of Columns in Frames with Sway

The paper paper examines columns of elastic frames that are able to displace laterally under axial load. Columns on the same level (story) of such frames may contribute to lateral support (stability) or require lateral support (supported columns). In the former case, maximum moments will occur at column ends, but may occur between column ends in the latter case. The column response, including the formation of moments and shears, is often complicated, often calling for approximate analysis methods and information that presently may not be readily available. Main attention of the paper is paid to providing results that will be helpful in providing, in a rather simple manner, improved understanding of column mechanics, and that may be helpful also as a supplement to full second-order analyses. Towards this goal, the major objective of the paper is threefold: (i) to identify characteristic points, or behavioral“landmarks” in the axial load-moment solution space, through the study of rotationally restrained elastic columns and two-column panels with sidesway; (ii) to derive simple, novel, closed-form expressions for these, thereby providing a tool simplifying the establishment of the variation of end and maximum moments versus axial load; (iii) to identify to what extent isolated (single) column analyses may adequately represent horizontally interacting columns, and potential unwinding, in frames.

Inelastic analysis of octagonal concrete‐filled steel tubular short columns under eccentric loading

AbstractOctagonal concrete‐filled steel tubular (OCFST) columns combine the benefits of circular and square concrete‐filled steel tubular (CFST) columns so that they not only possess higher strength and ductility but also provide the ease of connection to composite beams. However, research studies have been very limited on the performance analysis of OCFST short beam‐columns subjected to eccentric loading. In this study, a fiber‐based numerical model is developed for the performance simulation of high‐strength OCFST short beam‐columns under eccentric loading. The simulation model takes into account material nonlinearities and concrete confinement induced by the octagonal steel tube. Computational methods are given that predict the axial load–moment interaction curves and moment–curvature responses of OCFST beam‐columns. The developed fiber model is verified against available test data with good accuracy. The influences of important parameters on the responses of high‐strength OCFST short beam‐columns are studied by means of utilizing the computational model. It is found that the behavior of OCFST beam‐columns is significantly influenced by the diameter‐to‐thickness ratio of the cross‐section, concrete strength, steel yield stress, and axial load ratio. Interaction equations are proposed for expressing the axial load–moment strength envelopes of the cross‐sections of OCFST beam‐columns and validated against numerical results.

Axial-flexural behaviours of concrete-filled square GFRP tubular columns under low temperatures

This study reported experimental investigations on the axial-flexural behaviours of concrete-filled square glass fiber-reinforced polymer (GFRP) tubular (CFSFT) columns at low temperatures. Twenty CFSFT columns under eccentric loads and two-point loading were conducted to evaluate the influences of low temperatures (T = 20 and −60 °C) and eccentricity ratios (e/r = 0.00, 0.25, 0.50, and 0.75). Failure modes, load–displacement behaviours, and load–strain behaviours at low temperatures have been reported. Test results indicated the load-vertical displacement curves of CFSFT columns under eccentric loads exhibited three different stages, i.e., linear, transition, and strain hardening or softening stage. Meanwhile, the bilinear load–deflection curves were observed for CFSFT columns under four-point bending. Based on these test results, the experimental axial load-moment (NT-MT) curves of CFSFT columns were obtained. These curves indicated that decreasing the temperature from 20 to −60 °C observably increased both the ultimate axial load (NuT) and ultimate bending moment (MuT) of CFSFT columns. However, the increment of both ultimate axial load and ultimate bending moment gradually decreased with the increasing eccentricity ratios.

Serviceability analysis of piled foundations supporting tall structures

Pile foundations supporting tall structures, such as wind turbines, chimneys, silos, elevated water tanks or bridge piers, are subjected during their life span to remarkably eccentric loads. These may lead to significant rotations which, however, cannot exceed the limiting values corresponding to the safe operation of the structure. A physically motivated mathematical framework aimed at the prediction of the serviceability performance of such kind of structures is herein presented and discussed. Piles are idealized as uniaxial nonlinear elements characterized by two yielding loads, one in compression and one in uplift, while pile-to-pile interaction effects are modeled by means of superposition, through an approximate solution. The axial load–moment capacity of the pile group is preliminary determined from a recent closed form, exact solution based on upper and lower bound theorems, allowing the analysis to be performed under load control. The model is capable of accounting for the dependence of the moment–rotation response from the dead load of the structure and the ‘coupling effect’ between generalized loads and displacements. The prediction performance of the proposed calculation method is validated against both numerical and experimental benchmarks. Finally, a parametric study allowed to assess the importance of pile-to-pile interaction on the foundation response under eccentric loads.

Obtaining interaction diagram of concrete section exposed to fire by mathematical optimization

This paper proposes a novel method for obtaining the axial load–moment (P–M) interaction diagrams of reinforced concrete sections exposed to fire. The problem of obtaining the strength of a reinforced concrete section subjected to an eccentric load was converted into determining an optimum solution of a constrained nonlinear optimization problem. The proposed method does not limit the strains of both concrete and reinforcing bars. A sequential quadratic programming algorithm was used to solve the constrained nonlinear optimization. Discontinuity in the arctangent function was avoided by rotating the atan2 function. A bending moment offset from the tilted axis was introduced to solve the asymmetric section and uneven heating condition. The results of the examples confirm that the proposed method can produce the entire P–M interaction surface of an arbitrarily shaped reinforced composite section exposed to fire. The proposed method is much faster and more versatile than the incremental-iterative procedure. The proposed method can calculate equally spaced points on the Mx–My interaction curve which the incremental-iterative procedure cannot obtain. The proposed method can be applied to any combination of cross-sectional shape, material, and temperature history.

Axial load–moment interaction diagram of full-scale circular LWSCC columns reinforced with BFRP and GFRP bars and spirals: Experimental and theoretical investigations

No research has yet been reported on the behavior of lightweight-aggregate self-consolidating concrete (LWSCC) columns reinforced with fiber-reinforced polymer (FRP) bars. LWSCC can be of great interest for reducing dead loads, section dimensions, and project costs, especially for precast elements. This paper presents, for the first time, the test results of a study conducted on 12 circular LWSCC columns reinforced with two types of FRP bars: basalt FRP (BFRP) and glass FRP (GFRP). In addition, columns with steel reinforcement were introduced into the test matrix as references. A mix design for the LWSCC with an equilibrium density of 1,807 kg/m3 and compressive strength of 52 MPa was developed and used to cast the columns. The columns were tested under concentric and eccentric loading. The test variables were the eccentricity-to-diameter ratio, and the type of reinforcement (steel versus GFRP and BFRP). The study was conducted to investigate whether the type of concrete and reinforcement affect the column performance and to develop the experimental load–moment interaction diagram. The load–strain behavior for the concrete, bars, and spirals; the load-deformation curves (axial and lateral); and the experimental P–M interaction diagrams are presented. An analytical study was conducted to predict the axial–flexural capacity. The effect of concrete density was considered in the analysis based on parameters in the codes for conventional and modified rectangular stress blocks. The test results indicate that the LWSCC columns with BFRP and GFRP reinforcement had behavior and strength comparable to their steel-reinforced counterparts when tested under different levels of eccentricity. The analytical results show that the column capacity was sensitive to variations in the rectangular stress-block parameters. Lastly, this study demonstrated the effectiveness of integrating GFRP and BFRP reinforcement into lightweight-aggregate concrete would play a role in producing lighter and more durable concrete members for precast applications.

Seismic behaviour of RC jacketed columns under different axial loads

This study examines the flexural performance of reinforced concrete (RC) columns strengthened through a seismic jacket technique developed using a prefabricated steel bar unit that forms peripheral closed hoops and supplementary V ties, satisfying the design requirements of the ACI 318-14 seismic provisions. Three RC jacketed columns were prepared with a parameter of axial load levels and tested under a constant concentric axial load and cyclic lateral loads. Analytical approaches were also applied to examine the axial load–moment interaction of the RC jacketed columns when considering the confinement effect provided by the jacket section and to investigate the applicability of the previous performance-based design models proposed for virgin seismic columns. The test results show that the developed jacket technique possesses a good potential in enhancing the flexural stiffness, strength and ductility of deficient columns, even under a high axial load. Reinforced concrete jacketed columns possess a higher ductility than that estimated using the ductility parameter model, regardless of the axial load level. Thus, the jacket section including the seismic details of a transverse reinforcement can be conservatively designed, based on the axial load–moment interaction and ductility parameter model for the moment and ductility enhancements required by deficient columns.

Behavior of slender UHPC columns under eccentric loading

The behavior of slender ultra-high performance concrete (UHPC) columns under eccentric loading was investigated in this study. Eight slender UHPC columns were tested, with the major experimental variables being the amounts of confinement steel and steel fibers. The behavior of the columns was evaluated using various performance measures, including the failure pattern, load–deflection relationship, ductility, steel reinforcement strain, and axial load–moment interaction diagram. Results showed that the inclusion of steel fibers with a volume fraction of 0.75% or more effectively restrained spalling and crushing of the slender UHPC columns. In particular, the inclusion of a 1.5% volume fraction of steel fibers was able to compensate a 70% reduction in the confinement steel while still promoting the ductility of the slender columns under eccentric loading. Furthermore, analytical studies were conducted to estimate the crushing strain of the UHPC material in the outermost fiber of the column section under a combined flexural and axial action. The applicability of an analytical procedure and the current design codes for evaluating the total moment demand of the slender UHPC columns under the influence of the P-Delta effect were also evaluated.

Capacity of exposed column base connections subjected to uniaxial and biaxial bending moments

ABSTRACT Current guidelines do not address the design of column base connections under combined biaxial bending moment and axial load. An analytical study is conducted to develop a biaxial moment-axial load interaction curve for design of exposed, unstiffened column base plates. First, a 3D finite element analysis model is developed for these connections. The response of the model is validated through a series of existing experimental data. Next, the model is used to investigate the response of a few connections subjected to various biaxial moments and axial loads. Based on simulation results, a simple and reasonably accurate interaction equation is proposed. Since the uniaxial capacities of the connection are involved in the interaction curve, an analytical method for predicting the uniaxial capacities, is also presented. This analytical method, which is based on formation of plastic mechanisms, is able to predict the strength of flexible base plates with high accuracy. The behavior of exposed base plates with I-shaped columns under minor-axis moments is also studied. Findings of this study assists practitioners with a reliable and convenient column base connection design.

Axial Load–Moment Interaction Diagram of Circular Concrete Columns Reinforced with CFRP Bars and Spirals: Experimental and Theoretical Investigations

AbstractNorth America’s current design codes and guidelines allow the use of fiber–reinforced polymer (FRP) bars as the primary reinforcement in concrete structures and provide design recommendations for using these bars. Because of a lack of experimental data, however, FRP bars have not been recommended for resisting compression stresses as longitudinal reinforcement in columns or compression reinforcement in flexural elements. This paper presents test results of an experimental program to investigate the structural performance of 10 full-scale circular concrete columns reinforced with carbon fiber–reinforced polymer (CFRP) bars and spirals subjected to combined axial compression loads and bending moments. The test variables include different eccentricity-to-diameter ratios and two types of reinforcement (CFRP and steel). The test results show that the CFRP- and steel-reinforced concrete columns behaved similarly up to their peak loads. The failure of the test specimens under different levels of eccentri...

하이브리드 해상풍력발전 지지구조물의 콘크리트 베이스-슬리브 연결부에 대한 실험 연구

In this paper, concrete base to sleeve connections of hybrid substructures for offshore wind turbines were suggested and investigated experimentally. Punching shear strength tests with well-instrumented three connections under different reinforcement ratios and loading conditions were conducted to investigate the punching shear strength and the behavior of the concrete base to a sleeve connection. The test results showed that the punching strength and stiffness of the connections are affected mainly by the reinforcement ratios. The loading conditions with an axial load and proportional moment cannot affect the stiffness but affect the strength of the connections because of the axial load-moment interaction. The punching shear failure and critical section of the each test specimen are also discussed.

The lateral load-deformation response of RC walls with a consideration of the height–length ratio

Reinforced concrete (RC) walls play an important role in resisting earthquakes, so understanding the lateral load-deformation response of an RC wall subjected to an axial load, shear, and moment is essential to nonlinear structural analysis. In this study, the moment-bending deformation response of an RC wall under an axial load and moment is obtained from moment–curvature analysis using the wall’s proper plastic hinge length. Furthermore, modified compression-field theory, adjusted according to the height–length ratio of the wall, is used to calculate the shear–shear deformation response of the wall under an axial load and shear. By integrating the moment-bending deformation and the shear–shear deformation responses, the lateral load-deformation response of the RC wall under axial load–moment–shear interaction can be reasonably determined. To confirm the reliability of the proposed method, experimental results for 67 RC walls are compared with analysis results from the proposed method. The statistical results show that the proposed method accurately predicts the lateral ultimate load but somewhat underestimates the lateral ultimate deformation. Finally, this paper gives an example using an equivalent column to simulate an RC wall using SAP2000 pushover analysis.

Analysis of rectangular hybrid steel-GFRP reinforced concrete beam columns

In this study, nominal moment-axial load interaction diagrams, moment-curvature relationships, and ductility of rectangular hybrid beam-column concrete sections are analyzed using the modified Hognestad concrete model. The hybrid columns are primarily reinforced with steel bars with additional Glass Fiber Reinforced Polymer (GFRP) control bars. Parameters investigated include amount, pattern, location, and material properties of concrete, steel, and GFRP. The study was implemented using a user defined comprehensive <TEX>$MATLAB^{(R)}$</TEX> simulation model to find an efficient hybrid section design maximizing strength and ductility. Generating lower bond stresses than steel bars at the concrete interface, auxiliary GFRP bars minimize damage in the concrete core of beam-column sections. Their usage prevents excessive yielding of the core longitudinal bars during frequent moderate cyclic deformations, which leads to significant damage in the foundations of bridges or beam-column spliced sections where repair is difficult and expensive. Analytical results from this study shows that hybrid steel-GFRP composite concrete sections where GFRP is used as auxiliary bars show adequate ductility with a significant increase in strength. Results also compare different design parameters reaching a number of design recommendations for the proposed hybrid section.

New theoretical model for SSTT-confined HSC columns

The concrete-confining method using low-cost steel straps, also known as the steel-strapping tensioning technique (SSTT), has proven to be effective in increasing the load-carrying capacity and ductility of high-strength concrete (HSC). However, the technique is restricted to short columns subjected to concentric loads as most of the studies on the SSTT have focused on concentrically loaded short HSC specimens. The performance of the SSTT in confining eccentrically loaded slender HSC columns is not fully understood due to a scarcity of experimental and theoretical data. Against this background, a theoretical model for analysing slender SSTT-confined cylindrical HSC columns is developed based on a numerical integration method. A previously proposed stress–strain empirical model is employed to develop the theoretical model. The model is used to generate the load–deflection curves and axial load–moment interaction diagrams of SSTT-confined HSC columns. Based on comparisons with existing experimental results, the proposed theoretical model accurately captured the behaviour of SSTT-confined HSC columns. It is also concluded that the previously proposed stress–strain empirical model is reasonably accurate for SSTT-confined HSC columns of both circular and rectangular cross-section.

Analysis of steel-GFRP reinforced concrete circular columns

This paper presents results from an analytical investigation of the behavior of steel reinforced concrete circular column sections with additional Glass Fiber Reinforced Polymers (GFRP) bars. The primary application of this composite section is to relocate the plastic hinge region from the column-footing joint where repair is difficult and expensive. Mainly, the study focuses on the development of the full nominal moment-axial load (M-P) interaction diagrams for hybrid concrete sections, reinforced with steel bars as primary reinforcement, and GFRP as auxiliary control bars. A large parametric study of circular steel reinforced concrete members were undertaken using a purpose-built MATLAB© code. The parameters considered were amount, location, dimensions and mechanical properties of steel, GFRP and concrete. The results indicate that the plastic hinge was indeed shifted to a less critical and congested region, thus facilitating cost-effective repair. Moreover, the reinforced concrete steel -GFRP section exhibited high strength and good ductility.

Rigid Spread Footings Resting on Soil Subjected to Axial Load and Biaxial Bending. I: Simplified Analytical Method

AbstractA simplified analytical method that determines the axial load and biaxial moment capacities of a rigid spread footing of regular or arbitrary shape resting on soil is presented. Three different types of pressure distribution at the soil-footing interface are considered: uniform, linear, and parabolic. The proposed algorithm can be used to determine (1) the maximum soil-bearing stress under rigid spread footings subjected to vertical load and biaxial bending moments; (2) the vulnerability of exceeding the maximum soil-bearing stress by comparing the biaxial moment-axial load interaction diagrams of the footing with those of the attached wall or column; and (3) the development of nomograms for the analysis and design of spread rigid footings of different shapes. Three comprehensive examples are included that show the first two applications. The third application is shown in a companion paper that deals with development of design aids for the analysis and design of rectangular and trapezoidal spread ...

Rigid Spread Footings Resting on Soil Subjected to Axial Load and Biaxial Bending. II: Design Aids

AbstractDesign aids (nomograms) for rectangular and symmetrical trapezoidal rigid spread footings are developed using a method previously developed by the writers in a companion paper. The nomograms can be used by designers to directly determine their maximum axial load and biaxial moment capacities without exceeding the bearing capacity of the supporting soil. Three different types of pressure distribution at the soil-footing interface are considered: uniform, linear, and parabolic. The results obtained can then be compared with the biaxial moment-axial load interaction diagrams of the attached concrete walls or columns. This allows the structural designer to determine the vulnerability and likelihood of exceeding the bearing capacity of the supporting soil. Four examples are presented that show the effectiveness and simplicity of the proposed nomograms in the analysis of isolated rectangular and trapezoidal rigid spread footings resting on soil.

High strength thin-walled rectangular concrete-filled steel tubular slender beam-columns, Part I: Modeling

High strength thin-walled rectangular concrete-filled steel tubular (CFST) slender beam-columns under eccentric loading may undergo local and overall buckling. The modeling of the interaction between local and overall buckling is highly complicated. There is relatively little numerical study on the interaction buckling of high strength thin-walled rectangular CFST slender beam-columns. This paper presents a new numerical model for simulating the nonlinear inelastic behavior of uniaxially loaded high strength thin-walled rectangular CFST slender beam-columns with local buckling effects. The cross-section strengths of CFST beam-columns are modeled using the fiber element method. The progressive local and post-local buckling of thin steel tube walls under stress gradients is simulated by gradually redistributing normal stresses within the steel tube walls. New efficient Müller's method algorithms are developed to iterate the neutral axis depth in the cross-sectional analysis and to adjust the curvature at the columns ends in the axial load–moment interaction strength analysis of a slender beam-column to satisfy equilibrium conditions. Analysis procedures for determining the load–deflection and axial load–moment interaction curves for high strength thin-walled rectangular CFST slender beam-columns incorporating progressive local bucking and initial geometric imperfections are presented. The new numerical model developed is shown to be efficient for predicting axial load–deflection and axial load–moment interaction curves for high strength thin-walled rectangular CFST slender beam-columns. The verification of the numerical model and parametric studies is given in a companion paper.

Assessment of RC columns subjected to horizontal and vertical ground motions recorded during the 2009 L’Aquila (Italy) earthquake

In the aftermath of recent earthquakes there has been substantial field evidence demonstrating that the collapse of several existing structures was caused by the effects of the vertical component of seismic ground motions. Such field evidence has not yet been supported by comprehensive analytical assessment and experimental tests. The present work focuses on preliminary analyses of the seismic response of reinforced concrete (RC) members subjected to horizontal (HGMs) and vertical (VGMs) ground motions recorded during the 2009 L’Aquila (Italy) earthquake. Normalised axial loads in beam–columns as well as the peak ground acceleration ratios between horizontal and vertical ground accelerations are emphasised as they are considered parameters of paramount importance for the assessment of structural components and systems subjected to combined horizontal and vertical ground motions (HVGMs). Results of extensive parametric nonlinear dynamic analyses carried out on simplified structural models are discussed in detail. The sample models comprise cantilever RC columns and a two-storey, two-bay plane frame designed for gravity loads. The structural response quantities for the performed analyses are expressed in terms of axial loads, axial deformations, bending moment-axial load interaction and shear demand/capacity ratios. It is found that the variation of axial loads is significant in columns under HVGMs, especially in compression. For values of normalised axial loads ( ν ) corresponding to actual RC columns in framed building structures, e.g., normalised axial load ν > 0.10 , the average increase of the compression load ranges between 174% ( ν = 0.20 ) and 59% ( ν = 0.50 ). For high values of normalised axial loads the computed axial load-bending moment pairs lie beyond the threshold interaction curves and, in turn, the RC members may fail. The shear demand-to-supply ratio is also detrimentally affected by the high fluctuations of axial loads in the columns. Net tensile forces were computed for columns with low-to-moderate axial gravity preload. In multi-storey framed buildings, the response of central columns is significantly affected by the HVGMs. Reliable seismic performance assessment of framed systems requires that combined HGMs and VGMs should be accounted for in the analyses. Further experimental and numerical research is needed to formulate efficient mechanical models to evaluate the shear capacity of structural members of existing RC framed buildings under earthquake loading.

High strength circular concrete-filled steel tubular slender beam–columns, Part I: Numerical analysis

High strength circular concrete-filled steel tubular (CFST) slender beam–columns are frequently used in high-rise composite buildings because they possess higher strength and stiffness than normal strength ones. Most nonlinear inelastic methods of analysis for circular CFST slender beam–columns have not considered the effects of high strength materials and concrete confinement that significantly increases the strength and ductility of the concrete core. As a result, these methods produce computational solutions that deviate considerably from experimental results. This paper presents a new numerical model for predicting the nonlinear inelastic behavior of high strength circular CFST slender beam–columns under axial load and bending. The numerical model developed not only accounts for confinement effects on the concrete core and circular steel tubes but also incorporates initial geometric imperfections of beam–columns. Axial load–moment–curvature relationships obtained from the fiber element analysis of column cross-sections are utilized to determine the equilibrium states in the inelastic stability analysis of slender beam–columns. Computational algorithms are developed for determining the axial load–deflection and axial load–moment interaction curves for slender beam–columns. The numerical model is implemented in a computer program, which is shown to be an efficient and accurate simulation tool that can be used to investigate the fundamental behavior of high strength circular CFST slender beam–columns. The verification and applications of the numerical model are given in a companion paper.