Column Slenderness Ratio Research Articles

Ultimate strength of stiffened panels with a crack and pits under uni-axial longitudinal compression

ABSTRACT An experimental programme and nonlinear finite element analysis are carried out to examine the ultimate strength characteristics of stiffened panels with a crack and pits, under uni-axial longitudinal compressive loads. The test results are used to validate the finite element models. A series of nonlinear finite element analysis is performed with the validated models to illustrate the ultimate strength reduction by varying the relative position between crack and pits, length of crack and pit characteristics. The present results are compared with the earlier results with either crack or pits, confirming the complexity of stiffened panel collapse behaviour. Including the effect of the crack and pits on the plate and column slenderness ratio, a formula has been introduced to predict the ultimate strength of the stiffened panel with the average error less than 10%.

Local-overall interactive buckling of high strength steel welded I-section columns under axial compression

In this study, the investigation on the overall-local interactive buckling performance of high strength steel welded I-section columns was carried out. Finite element models of steel columns of different yield strength (235 MPa, 460 MPa, 500MPa, 690 MPa, 800MPa, 960 MPa) were constructed considering geometric imperfection and residual stresses, and verified against the existing test results. Effect of geometric imperfection including global imperfection and local imperfection was found to be largely dependent on the nominal slenderness ratio of columns (λn). Local imperfection present prominent influence for the case of λn lower than 0.4, while global imperfection for the case of λn exceeding 0.95. Effect of four types of residual stress patterns on ultimate capacity were compared, the disparity of which was around 10%. Comprehensive effect of imperfections on local buckling load was found to be smaller resulted from higher steel grade; whilst that on stiffness became more pronounced. Based on the test data of stub columns, new predict formulas were proposed for the local post-buckling strength using effective width method and direct strength method respectively. Continuing the investigation of stub columns, the formulas for interactive buckling resistance of high strength steel welded I-section around the weak axis were studied, where column curve b in Eurocode3 was suggested to be adopted.

Compressive behaviour of slender FRP-confined concrete-encased cross-shaped steel columns

Fibre-reinforced polymer (FRP)-confined concrete-encased cross-shaped steel columns (FCCSCs) consist of a square FRP outer tube with round corners, a cross-shaped inner steel section and concrete filled in the between. The unique configuration of FCCSCs ensures that the concrete in the columns is well confined despite the square column shape, as demonstrated by the relevant existing research. The existing work on FCCSCs, however, has been limited to the behavior of short FCCSCs under axial compression. With their optimal configuration, the use of FCCSCs means that considerably reduced section dimensions may be adopted for the same load demand, leading to relatively slender columns in practice. In addition, the load eccentricity is an important parameter to consider in the column design. This paper presents the first-ever experimental study on the behaviour of slender FCCSCs. The test variables in this study included the load eccentricity, the slenderness ratio of the column and the thickness of FRP tube. The test results confirm the excellent structural performance of slender FCCSCs, and show that the load capacity of FCCSCs decreases with the slenderness ratio and the load eccentricity. Nevertheless, the confinement effects on the behavior of FCCSCs were found to be remarkable even when the column slenderness ratio and load eccentricity are large.

Influence of chord compactness and slenderness on axial compression behavior of built-up battened CFS columns

This study presents the behavior of built-up cold-formed steel (CFS) columns under axial compression loading. Two CFS unstiffened channel sections arranged in the toe-to-toe configuration are used as the chord members interconnected by the batten plates. An extensive parametric study has been conducted on 230 numbers of built-up battened CFS columns using a finite element software ABAQUS. The numerical models developed have been calibrated against the test results available on CFS battened columns with plain channels in the back-to-back arrangement reported in the literature. The main parameters varied in the numerical models are the width-to-thickness ratios of chords, overall column slenderness ratios, and the toe-to-toe spacing of chords. The behavior of built-up columns is studied in terms of peak axial compressive strengths, mode of failure, post-peak resistance, and lateral drift. The chord width-to-thickness ratios have a predominant effect on the peak axial stresses of short columns, and a meager effect on long columns. Also, large lateral displacements can be avoided by restricting the overall column slenderness to 75. Numerical results are compared with the design strengths predicted by North American Standards (NAS) and Eurocode (EC3). Both these standards are found to be un-conservative in predicting the axial strengths of short built-up columns in the range of 15–30%. Finally, the design recommendations are proposed for built-up battened CFS columns with channel chords in toe-to-toe configuration, which are verified through reliability analysis as well.

Numerical modelling of concrete-filled stainless steel slender columns loaded eccentrically

Purpose This paper is aimed at clarifying the behaviour of concrete-filled stainless steel tube (CFSST) slender columns. Based on the review of previous works, it can be found that the pieces of research on the behaviour of CFSST slender columns are very rare and the existing studies, to the author’s knowledge, have not covered this topic in greater depth. The purpose of this paper is to investigate the structural response and strength capacity of eccentric loaded long CFSST columns. Design/methodology/approach In this paper, a new finite element (FE) model is presented for predicting the nonlinear behaviour of CFSST slender columns under eccentric load. The FE model developed accounts for confinement influences of the concrete in-filled material. In addition, the initial local and overall geometric imperfections were introduced in the numerical model in addition to the inelastic response of stainless steel. The interaction between the stainless section and concrete in-filled was modelled using contact pair algorithm. The FE model was then verified against an experimental work presented in the literature. The ultimate strengths, axial load–lateral displacement and failure mode of CFSST slender columns predicted by the FE model were validated against corresponding experimental results. Findings The simulation results show that the improvement in the column strengths (compared to hollow section) is less significant when the composite columns have small width-to-thickness ratio. Finally, comparisons were made between the results obtained from FE simulation and those computed from the Eurocode 4 (EC4). It has been found that the EC4 predictions in most analysed cases are conservative for composite columns analysed under a combination of axial load and uniaxial or biaxial bending. However, the conservatism of the code is reduced with a higher slenderness ratio of the composite columns. Practical implications The simulation results throughout this research were compared with the corresponding Eurocode predictions. Originality/value This paper provides new findings about the structural behaviour of CFSST columns.

Thin-Walled Steel Stiffened Square Box Columns with Uniform and Graded Thickness under Bidirectional Cyclic Loading

In this paper, the overall hysteretic behavior of uniform (BB) and proposed graded-thickness (BGB) thin-walled steel square box columns under constant axial force and circular bidirectional cyclic lateral loading is investigated. First of all, the adopted finite element model (FEM) in ABAQUS is verified with the experimental results in the literature and employed for the analysis. Second, the proposed BGB column, with the same cross-section size and volume of material equivalent to the BB column, is evaluated. Then, the strength and ductility deterioration of both BB and BGB columns under circular bidirectional cyclic loading path over the unidirectional path are emphasized. Finally, an intensive parametric study is conducted to investigate the effect of main design parameters including: width-to-thickness ratio parameter (Rf), column slenderness ratio parameter (λ), magnitude of axial load (P/Py), and number of loading cycles (N) on the overall hysteretic behavior of BB and BGB columns under constant axial force and circular bidirectional cyclic lateral loading. Subsequently, design formulae have been derived to predict the ultimate strength and ductility capacities of the BB and BGB columns.

Compressive behavior of built-up closed box section columns consisting of two cold-formed steel channels

Abstract Thirty specimens of built-up closed box sections consisting of two cold-formed steel channels of various cross sections (B92 and B143), lengths (3000, 1500, 450, and 270 mm), and thicknesses (1.2 and 1.5 mm) were tested subject to concentric and eccentric axial compression. Failure modes were analyzed and load vs. displacement curves were obtained. The test results indicate that the failure modes of long and medium columns subject to concentric axial compression are flexural buckling about the weak axis, whereas that of the short column is excessive local buckling; specimens subject to eccentric axial compression about the strong and weak axes exhibited flexural-torsional buckling and flexural buckling, respectively. Finite element (FE) models were established and verified. Detailed parameter studies were performed to evaluate the accuracy of code equations for a wide range of parameters. The FE analysis results indicate that the concentric axial compression strength of the columns decreased with an increase in the slenderness ratio of column or the web height-to-thickness ratio; increasing the flange width can significantly increase the stability and strength of the column; the eccentric axial compression strength of the column about the weak axis decreased faster than that about the strong axis. Finally, the effectiveness of the design methods, i.e., the effective ratio of width-to-thickness method in the Chinese code, effective width method, direct strength method, and load and resistance factor design in North American specifications to predict the strength of this type of built-up column is evaluated. For the B92 series columns and B143 series column with slenderness ratio of the column greater than 92, it is conservative to use design methods to calculate the concentric axial compression strength of the column. Additionally, it is conservative to use the design methods to calculate the eccentric axial compression strength of the columns.

Structural Behaviour of Slender PVC Composite Columns Filled with Concrete

In this study, the performance of slender PVC-concrete columns was investigated using variables including concrete filling compressive strength, column slenderness ratio, and PVC section compactness ratio. The specimens were subjected to uniaxial compression in two loading modes; in the first mode, a PVC tube was utilised to enhance the concrete core as a composite element, and in the second mode, a PVC tube was utilised to confine the concrete core only. Nine PVC-concrete sections with different polyvinyl chloride tube characteristics and different filled concrete compressive strengths were considered in several fabricated slender PVC-concrete columns. The column lengths were varied so that overall column buckling could be investigated. The results showed that the composite mode columns exhibited more strength improvement than those in confined mode. Experimentally predicated effective flexural stiffness was thus normalised in terms of filling concrete stiffness and PVC tube stiffness, and the normalised results indicated that effective flexural stiffness depends on the mode (confining or composite), PVC and filling concrete strength, and column slenderness ratio.

Ultimate strength prediction of T-bar stiffened panel under longitudinal compression by data processing: A refined empirical formulation

In the present study, a data processing technique was introduced to develop a closed form shape empirical formulation in predicting ultimate strength of structures. The proposed method was verified by applying a ship's stiffened panel as an applied example. In particular, a refined empirical formulation in predicting the ultimate strength of stiffened panel subjected to longitudinal compression was proposed. Recently, Kim et al. (2017) observed that the ultimate strength behaviours fluctuated in small value of column slenderness ratio and urged the need for a more accurate empirical formulation. In order for an accurate ultimate strength behaviour of stiffened panel to be obtained, a total of 10,500 cases of numerical simulation results using the ANSYS Finite Element Method (FEM) were employed by considering the relevant size change of stiffened panels including plate thickness, web thickness, flange thickness, height of web, and breadth of flange. The simulation results were processed, in the case of initial imperfection, only for average level of initial deflection to plate. On the other hand, initial distortion to stiffener elements and no residual stress by welding were considered in this study. A detailed data processing technique and detailed modelling procedures, i.e, the scenario selection, FE modelling, FE analysis, were documented. From the obtained data processing results by this study, we have found that four (4) important parameters, i.e., P1=λ,P2=β,P3=hw/twandP4=Ipz/Isz are to be considered for the formulation of empirical formulation in predicting ultimate strength of stiffened panel under longitudinal compression (σxu/σYeq). The proposed new empirical formulation revealed positive agreement with ANSYS FEM results (R2 = 0.98 for overall case).

Laboratory and numerical based analysis of floating sand columns in clayey soil

The inclusion of sand columns results in enhancing the bearing capacity of clayey soil, increase the rate of consolidation, presentation of liquefaction in loose sandy soils and provide lateral resistance against the horizontal movement. This research aims at investigating the effects of floating columns in clayey soil with silty deposits by developing small scale laboratory models. The effects of sand columns on soils of different shear strengths, slenderness ratio (L/D) of columns were investigated. Group effect was also investigated by varying spacing between the columns. Experimental results were compared with the numerical analysis results. A 15-noded triangular mesh was generated using a finite element tool PLAXIS 2D. Finite element analysis was performed using Mohr’s Coulomb’s criterion considering undrained analysis for soft clayey soil and drained analysis for sand columns. It was concluded that the sand columns can significantly increase the ultimate loading capacity of soft soils. Results show that critical length for floating column ranges from 4 to 5.5 times the diameter of the column, beyond which bulging occurs and loading capacity decreased. The effect of group was also investigated and observed that with high spacing between the sand columns, the group efficiency decreased. The axial capacity of sand columns decreases while increasing spacing between the columns.

Thin-Walled Steel Tubular Circular Columns with Uniform and Graded Thickness under Bidirectional Cyclic Loading

Abstract Thin-walled steel tubular circular columns are becoming an increasingly attractive choice as cantilever bridge piers due to their architectural, structural and constructional advantages. This paper aims to evaluate the strength and ductility of thin-walled steel tubular circular columns with uniform thickness (BC) and graded thickness (BGC) under bidirectional cyclic lateral loading in the presence of constant axial force. The analysis is carried out using a finite-element model (FEM) which is substantiated based on the experimental results in the literature. Then, the proposed BGC column with size and volume of material equivalent to the BC column is investigated. As a part of this research, a comprehensive parametric study is carried out to investigate the effects of main design parameters including: radius-to-thickness ratio parameter (Rt), column slenderness ratio parameter (λ), magnitude of axial load (P/Py), and number of loading cycles (N) on the strength and ductility of both BC and BGC columns under bidirectional cyclic lateral loading. Finally, design formulae of ultimate strength and ductility of BC and BGC columns are derived.

Reliability Analysis of a Solid Timber Column Subjected to Axial and Lateral Loading

In this paper, a reliability analysis of a solid timber column of square cross section subjected to axial and lateral loading in accordance with the design requirements of Eurocode 5 is carried out. Compression and bending were the two failure criteria considered in the reliability investigation. The First Order Reliability method was employed to solve the limit state functions formed from the two failure criteria and was coded in MATLAB for quick estimation of the reliability indices. The results obtained showed that both the load and slenderness ratios have effects on the reliability of a solid timber column. The results of the sensitivity analysis carried out on the stochastic variables showed that the reliability indices decreased with increase in slenderness ratio for 3m, 4m and 5m length of column considering both the compression and bending failure modes and decreased with increase in load ratio for 3m, 4m and 5m length of column considering both the compression and bending failure modes. The reliability indices also decreased with increase in length of column mode and decreased with increase in ratio considering bending failure mode. The reliability indices were also found to decrease with increase in load ratio for varying values of axial and lateral loads at constant slenderness ratio and length of column considering compression and bending failure modes. The choice of adequate and suitable dimensions having a lower slenderness ratio will enhance the reliability of the column. Keywords- Reliability analysis, solid timber column, Eurocode 5, failure criteria, slenderness ratio

Simplified method for analysis of circular steel tubed-reinforced-concrete columns under eccentric compression

This paper develops a simple and general approach to analyse circular steel tubed- reinforced-concrete (TRC) columns including calculations of peak loads and plots of ascending branch of load-deflection curves. The proposed model relates cross-sectional capacity to actual column capacity by introducing a stability parameter so that column N-M curves can be determined directly. This stability parameter is calculated by establishing a rational mid-height deflection limit, which can be obtained through strain-compatibility and geometric relationship. It also provides a theoretical background to the classical Rankine formula. Moreover, a smooth transition of load-carrying capacity from short to slender columns is obtained. To generate the load-deflection curves, mid-height deflection is increased from 0 to the deflection limit while cross-sectional capacity is kept the same. The proposed method is validated against three series of test data including a total number of 40 TRC columns. It shows that the predictions compare well with the test results in three aspects, namely, mid-height deflection at peak load, peak load and ascending branch of the load-deflection curve. Moreover, the proposed method has a wide range of applications for TRC columns filled with both normal and high strength concretes with column slenderness ratio ranging from low to high. Most importantly, this model can be implemented using spreadsheet, which provides a simple and robust numerical tool for engineers to determine strength of TRC columns.

Numerical Investigation on Ultimate Compressive Strength of Welded Stiffened Plates Built by Steel Grades of S235–S390

The welded stiffened plate is widely used in naval architecture and offshore engineering as a basic structural member. The aim of this study is to investigate the effect of welding residual stress and steel grade on the ultimate strength of stiffened plates under uniaxial compressive load by non-linear finite element analysis. Nineteen stiffened plates built with three types of stiffeners with various column slenderness ratios provided in the ISSC’2000 VI.2 benchmark calculations are employed in the present study. The commercial finite element code ABAQUS is applied to simulate the collapse behavior of the stiffened plates and verified against the benchmark calculations. Fabrication-related imperfections, such as initial deflections and residual stresses, are accounted for in the simulations. The ultimate strength of stiffened plates built in common shipbuilding steels, namely S235, S315, S355 and S390, are investigated by varying the yield strength of materials in the simulation. Analysis of the numerical results shows that the welding residual stress reduces the ultimate strength of stiffened plates, and increase in yield strength of the material can effectively improve the ultimate strength of common ship stiffened plates; and quantitative analyses of their influences have also been performed.

Behaviour and design of circular hollow section steel columns strengthened by infilling concrete under preload

The objective of this work is to develop design guidance for existing hollow steel columns that are retrofitted by infilling concrete into the tubes. The primary challenge is the unknown effect of the existing preload on the steel columns prior to the concrete infill. Composite performance and buckling behaviour of circular hollow section (CHS) steel columns strengthened by infilling concrete under preload was experimentally and numerically investigated in this study. A total of 34 CHS steel columns were tested under pin-ended boundary conditions, and the overall buckling failure modes and corresponding ultimate buckling resistances were recorded. Prior to the member testing, material properties of the steel columns and the infilled concrete were attained. By means of the finite element (FE) software package ABAQUS, elaborate FE models for the CHS columns strengthened by infilling concrete were developed and validated against the obtained test results, which were further verified with other available test data. Using the validated FE models, systematic parametric studies were conducted to examine the influences of the major factors affecting the ultimate capacities of the CHS columns strengthened by infilling concrete, including preload ratios, steel and concrete strengths, steel ratios, initial global imperfections, eccentricity ratios and column slenderness ratios. The obtained test and numerical results were therefore utilised to develop design criteria for predicting the overall buckling resistance of CHS steel columns strengthened by infilling concrete. In view of the difficulty of determining the key parameters in practice and the uncertainty of the strengthening process, a new simplified design coefficient was proposed, taking into account the influence of the preload. It has been demonstrated that accurate and reasonable strength predictions can be provided by the proposed design method.

Mechanical properties of wood columns with rectangular hollow cross section

Abstract A rectangular hollow wood column made of Spruce-Pine-Fir (SPF) lumbers was developed, for the purpose of improving the utilization efficiency of timber. The present work conducted experimental investigations of the columns under centrically and eccentrically compression. A wide range of slenderness ratios of columns and eccentricities of loads was considered to carefully examine the failure modes in columns. The results indicated that combined material failures and buckling failures were observed for the intermediately slender columns under axial compression, while buckling failures were observed for the long columns. The ultimate strength of columns under axial compression significantly decreased with the increase of slenderness ratios. The predicted results by the tangent modulus theory closed to those of experiments. The bending failure, which underwent a pronounced nonlinear process, was the major characteristic of the intermediately slender column with an eccentric compressive load. Typically, the load carrying capacity of columns showed a decreasing trend with an increasing in eccentric ratios. Both the secondary bending and material nonlinearity were important factors that impacted the nonlinear response of the column. An analytical model was proposed for evaluating the load carrying capacity of the rectangular hollow columns under the interaction between compression and bending. There was good agreement between the results of the experiments and calculations.

Buckling strength and ductility evaluation of thin-walled steel stiffened square box columns with uniform and graded thickness under cyclic loading

Thin-walled steel stiffened square box columns are becoming an increasingly attractive choice as cantilever bridge piers due to their architectural, structural and constructional advantages. This paper investigates the behavior of thin-walled steel columns with uniform square box sections (B) and newly proposed graded-thickness square box sections (GB) under constant axial and cyclic lateral loading. The analysis is carried out using a finite-element model (FEM) which takes into account the effect of both material and geometric nonlinearities. First, the accuracy of the employed FEM is verified based on the experimental results. Then, a GB column with size and volume of material equivalent to a B column is introduced. The proposed GB column is proved to have significant improvements in strength, ductility, and post-buckling behavior as compared to its counterpart B column. As a part of this research, a comprehensive parametric study is carried out to investigate the effects of main key parameters including: the width-to-thickness ratio parameter (Rf), the column slenderness ratio parameter (λ), the magnitude of axial load (P/Py), and the number of loading cycles (N) on the strength and ductility of the B and GB columns. Finally, a series of proposed formulae for strength and ductility evaluation of the B and GB columns is given.

Generation of pressure–impulse diagrams for failure modes of RC columns subjected to blast loads

The Pressure–Impulse (P-I) diagram is generally accepted as a useful tool that permits easy assessment of structural responses to a specified load. To predict the failure characteristics of typical reinforced concrete (RC) columns subjected to blast loads, P-I diagrams considering different failure modes were generated with a high efficient procedure by employing an improved nonlinear analytical approach. In the nonlinear analytical approach that was improved from the Timoshenko beam theory, failure criteria to determine typical bending failure, diagonal failure and direct shear failure modes of RC columns were defined, respectively. The proposed efficient procedure was compiled to generate the P-I diagram by successively circular the improved nonlinear approach which was validated by conducting field blast tests. Parametric studies were carried out to investigate the effects on the failure characteristics of RC columns in the generated P-I diagram, including blast loads distribution, axial compression ratio, slenderness ratio, cross-section bend capacity and shear capacity. The analytical results demonstrate that the diagonal shear failure is most likely to occur on the typical RC columns subjected to blast loads. The bending failure basically occurred when the axial compression ratio and slenderness ratio of RC columns are large to a certain extent.

Axial compressive performance of circular CFST columns partially wrapped by carbon FRP

To explore the axial compression property and failure mechanism of concrete-filled steel tubular (CFST) columns partially wrapped by carbon-fibre-reinforced polymer (FRP), a series of tests using carbon-FRP-strengthened circular CFST stubs and slender columns imposed with axial loads were conducted. The effects of various parameters including steel yield stress, number of carbon-FRP layer, slenderness ratio of the composite column, and spacing of carbon-FRP strip on the axial load bearing capacities of the tested specimens were studied. Moreover, the axial compression behaviour of the circular CFST columns with carbon-FRP composites was evaluated in terms of axial compression force (N)–longitudinal shortening displacement (δ) curves, axial stiffness, strain response, strength enhancement indexes, and ductility indexes. Subsequently, a nonlinear finite element (FE) analysis modelling concerning the surface contact action of carbon-FRP-strengthened circular CFST columns was established and validated experimentally. The experimental and analytical results indicate that strengthening the circular CFST stub columns using carbon-FRP wraps could improve their axial load bearing capacities and prevent outward local bulges for the thin-walled steel tubes. Only a slight effect was observed when laterally confined carbon-FRP strips were used for the type of slender composite columns. Finally, several simplified empirical formulas for predicting the axial load bearing capacity of the circular CFST column partially wrapped by carbon-FRP are proposed.

Structural performance of frames with concrete-filled steel tubular columns and steel beams: Finite element approach

Composite columns such as concrete-filled steel tube (CFST) were adopted in many building constructions in recent years because of carrying high loading with the ability to resist buckling and small cross-sectional area. The high behavior of the CFST columns is due to the interaction between steel and concrete which called the composite action. This type of composite column without main and tie reinforcements embedded in concrete gives high axial compression strength to resist the external loadings with the economic sectional area. The work presented in this article includes simulation models that tested by other researchers and a parametric study on the performance of frames that connected steel beam by composed columns of circular CFST that subjected to lateral loading. A finite element (FE) approach is adopted to simulate the models by ANSYS software. All models consider the linear and nonlinear material analysis of the concrete and steel. The validity of the developed model was examined by comparing with the experimental data founded in the literature. Different parameters such as the ratio of the axial load, the slenderness ratio of CFST column, the linear stiffness ratio of the beam–column, the steel yield strength of the beam, the steel yield strength of the tube, and concrete strength on the performance of the composite frames were also studied and the load-deformation performance was obtained over the different cases of the study. Analysis results by FE modeling were in good agreement with the experimental results.