Pin-ended Columns Research Articles

Design Methods of Aluminium Pin-Ended Columns with Topology-Optimised Cross-Sections

This paper presents a numerical study of topology-optimised pin-end aluminium alloy columns using finite element analysis (FEA). The FEA models integrate geometric imperfections and material nonlinearity, and are validated against experimental findings from the existing literature. ABAQUS v.6.15 (release 2020) is used in preparing the FEA models and obtaining the analysis results. Furthermore, modern design methodologies including Eurocode 9, the direct strength method (DSM), and the continuous strength method (CSM) are employed to assess the maximum load capacity of such columns. Parametric investigations encompass diverse parameters such as varied cross-sections, column lengths, and global and local imperfections. By analysing a total of 288 FE models, incorporating 16 column cross-sections across two lengths with nine distinct imperfections, this study compares results with those derived from modern design methodologies. Thus, this research elucidates the behaviour of novel cross-sections and the application of contemporary design techniques in their analysis.

DSM-Based failure load prediction of CFS pin-ended singly symmetric columns buckling in flexural-torsional modes

Recently, the authors investigated the post-buckling behaviour, strength and Direct Strength Method (DSM) design of cold-formed steel (CFS) fixed-ended singly symmetric columns buckling in major-axis flexural-torsional modes (FMT), some of which were shown to experience interaction with minor-axis flexural (Fm) buckling − FMT-Fm (global-global) interaction. The main fruit of this investigation was the development of an efficient DSM-based design approach capable of predicting the failure loads of such columns, regardless of their failure mode nature (pure FMT or FMT-Fm interactive). This work extends the scope of the above study to singly symmetric columns with three types of pin-ended support conditions, all fixed with respect to torsion and having warping fully prevented. Columns with seven cross-section shapes are considered, having their wall dimensions, lengths and yield stresses selected to ensure covering wide FMT slenderness ranges and various ratios between the Fm and FMT buckling loads. Following an investigation on the elastic and elastic-plastic post-buckling behaviours of the selected pin-ended columns, paying attention to the possible occurrence of FMT-Fm interaction, parametric studies are carried out to gather extensive pin-ended column failure load data, including some potentially associated with FMT-Fm interactive collapses. Then, the assembled numerical failure loads are used to show that (i) the available DSM-based strength curves are only able to predict adequately part of them and, thus, (ii) novel DSM-based design curves are needed to estimate the failure loads of the remaining pin-ended singly symmetric columns buckling in FMT modes. After developing such curves and assessing their merits (safety and reliability), it is concluded that different DSM-based design curves/approaches must be employed for columns with each type of pin-ended support conditions.

Design procedures for cold-formed stainless steel built-up columns assembled from equal-leg angles

In this paper, the structural behaviour of cold-formed stainless steel (CFSS) built-up T- and cruciform-section columns is studied experimentally and numerically, and the effect of discrete fasteners on their flexural and torsional rigidity is considered. To build the singly symmetrical built-up T-section columns, two equal-leg angle sections made of lean-duplex grade EN 1.4162 were assembled back-to-back. The doubly symmetrical built-up cruciform-section columns were composed of four star-oriented equal-leg angle sections made of austenitic grade EN 1.4301. They were connected using M8 bolts of class 8.8. Two pin-ended built-up T-section columns with length of 1000 mm, and four built-up cruciform-section columns with lengths of 600 mm and 2400 mm with semi-rigid support conditions, were tested under pure axial compression. As observed in the tests, built-up T-section columns experienced flexural-torsional buckling failure, whereas built-up cruciform-section columns failed in torsional buckling mode. Finite element models were validated against the conducted experiments and used to perform a parametric study of the structural behaviour of CFSS built-up T- and cruciform-section columns. The study included the column length, cross-sectional dimensions and bolt spacing as variables. The experimental and numerical data, i.e., the column strengths and failure modes, were compared against the results obtained based on the European and North American Specifications alongside a recent method established for cold-formed carbon steel equivalents and based on the Direct Strength Method (DSM). It is shown that the DSM-based approach predicts the ultimate buckling resistances of the considered built-up columns more accurately than the available codified design methods.

Testing, FE modelling and design of pin-ended stainless steel equal-leg angle section columns and beam–columns

The behaviour and design of pin-ended stainless steel equal-leg angle section members under compression and compression plus minor-axis bending are investigated herein. The studied members are cylindrically pinned about the minor axis. An experimental investigation, including material testing, initial geometric imperfection measurements and physical tests on hot-rolled stainless steel equal-leg angle section members is first presented. Numerical models are developed and validated against the new experimental data. A numerical parametric study is then presented considering both hot-rolled and cold-formed stainless steel angle section columns alongside beam–columns with a wide range of slenderness values. Finally, new design proposals for pin-ended stainless steel equal-leg angle section members under compression and combined compression and minor-axis bending are developed and verified against the results of existing physical experiments, as well as the newly-generated test and numerical results. The proposed design rules are shown to offer substantially more accurate and consistent resistance predictions compared to existing codified design rules. The reliability of the new design provisions, with a recommended partial safety factor γM1=1.1, is verified following the EN 1990 procedure.

Flexural–torsional buckling of pin-ended press-braked S690 high strength steel angle section columns: Testing, modelling and design

This paper presents an experimental and numerical investigation into the flexural–torsional buckling behaviour and resistance of pin-ended press-braked S690 high strength steel angle section columns. An experimental programme was firstly conducted and included initial geometric imperfection measurements and twelve pin-ended column tests. The column test results, including the failure loads and deformations at the failure loads, load–mid-height torsional rotation curves and failure modes, were fully reported and discussed. The experimental programme was accompanied by a numerical modelling programme, where finite element models were developed and validated against the test results and then employed to perform parametric studies to expand the test data pool over a wider range of cross-section dimensions and member lengths. The obtained test and numerical data were then used to assess the relevant codified design rules, as provided in the European code, North American specification and Australian/New Zealand standard, and a DSM-based design approach. The assessment results revealed that all the codified design rules lead to excessively conservative and scattered resistance predictions for pin-ended press-braked S690 high strength steel angle section columns susceptible to flexural–torsional buckling, while the DSM-based design approach yields substantially improved resistance predictions, owing to the rational consideration of the length-dependent characteristic of flexural–torsional buckling and the interaction of flexural–torsional buckling with minor-axis flexural buckling.

Experimental and numerical tests of cold-formed square and rectangular hollow columns

This paper summarizes the results of experimental tests and finite element simulations aimed at investigating the buckling response of cold-formed square and rectangular hollow columns. The material stress–strain curves of the tested columns have been derived from testing 83 coupons sampled from the flat and corner parts of the cross-sections, along with coupons containing the weld in both longitudinal and perpendicular directions. The experimental stress–strain parameters have been statistically processed to calibrate the parameters of Ramberg-Osgood and Giuffrè-Menegotto-Pinto material models. The cross-sectional geometry and geometric imperfections have been also measured for all tested profiles. The buckling resistance of 21 different pin-ended columns has been experimentally measured in order to examine the influence of the steel grade (both S275 and S355), the normalized slenderness and the shape of cross-section. Finite element simulations of the tested members have been carried out to investigate the influence of residual stresses and out-of-straightness imperfections on the buckling resistance of hollow profiles. The buckling resistance evaluated on the basis of current EN1993-1–1 and the measured properties of the members are in very good agreement with the tested buckling resistances, even though slightly underestimating the resistance of stocky columns. The partial safety factor for flexural buckling has been evaluated using the method given by Annex D of EN 1990 and the results show that the computed average partial safety factor of curve “c” of EN1993-1–1 for cold-formed square and rectangular hollow columns is 0.92.

Global Stability Performance of Multi-Cellular T-Shaped CFST Slender Columns under Eccentric Compression

With the development of pre-fabricated composite structures, concrete filled steel tubular (CFST) columns have been widely used, and researches on T-shaped CFST slender columns have attracted much attention. Since ordinary T-shaped CFST columns have weak constraint on concrete at the sectional concave angle region and local buckling easily occurs in this region, a multi-cellular T-shaped concrete filled steel tubular (MCT-CFST) column was developed for improving the axial resistant performance. In this study, the global stability performance of MCT-CFST slender columns under uniaxial eccentric compression was investigated. Firstly, three pin-ended MCT-CFST slender columns were tested under eccentric compression with different eccentricities. Secondly, a refined finite-element (FE) model of MCT-CFST column was established, and the load–displacement curves, Mises stress and deformation diagrams from the FE analysis were compared with the experimental results to verify the validity of the FE model. Moreover, based on the validated FE model, a parametric analysis was carried out to study the effects of normalized slenderness ratio, thickness of steel plate and material strength on the global stability performance of MCT-CFST slender columns under combined axial and bending loads. Finally, [Formula: see text]-[Formula: see text] interaction curves were obtained from the numerical simulations, and these results were considered to provide valuable references for designing MCT-CFST slender columns in engineering practice.

Experimental and numerical study of 7A04-T6 extruded aluminium alloy lipped angle columns in axial compression

The behaviour and design method of 7A04-T6 high-strength extruded aluminium alloy lipped angle columns in axial compression are investigated. First, compressive tests on 27 pin-ended lipped angle columns of various dimensions were conducted. Measurement on initial geometric imperfections and tensile coupon tests were also performed. Second, the finite element (FE) models were developed to simulate the compressive behaviour of the tested specimens. The validated FE models were then used to carry out a parametric study covering a wide range of cross-sectional dimensions and column slendernesses. The obtained ultimate compressive strengths were compared with existing design codes in Europe, China, America and Canada for aluminium alloy structures. Furthermore, the direct strength method (DSM) codified in AISI S100-16 was also considered. In predicting the ultimate compressive strength, the elastic global buckling stress was determined from classical column buckling theory, while the elastic sectional buckling stress was given by energy method. The comparisons show that the compressive strengths of columns failing in flexural buckling are generally well predicted by existing design methods. For torsional–flexural buckling, the Eurocode 9 (EC9) generally gives more accurate predictions and the other design rules are relatively conservative, because an independent strength curve is adopted in EC9 and the interaction with local buckling is excluded. Finally, modified equations are proposed to improve the accuracy of DSM in predicting the compressive capacities of columns failing in distortional buckling and torsional–flexural buckling.

Experimental and numerical flexural buckling resistance of high strength steel columns and beam-columns

The use of high strength steel (HSS) has been consolidated around the world because of its numerous advantages mostly for high-rise buildings and large span bridges. As it provides the possibility of a design with slender sections, substantial reduction in the structure weight is expected, but special attention should be given to the stability of the HSS compression members. However, the existing design codes for HSS columns are limited and based on experimental data related to normal strength steel (NSS) materials, which is responsible for an inaccurate resistance prediction. In this sense, the present paper aimed to investigate the buckling behavior of S690 HSS welded I-section columns failing by flexural buckling around the both principal axes and beam-columns failing by lateral torsional buckling. The experimental campaign contemplated 4 pin-ended columns, in which 2 were tested about their major-axis and the other 2 about the minor-axis, and also 2 beam-columns, including supplementary experimental to measure the geometric imperfections, residual stresses and material properties of the S690 welded I-section columns and beam-columns. In the following, a numerical model was built and validated against the experimental results and afterwards employed to perform a sensitivity study considering different membrane residual stress patterns. Finally, the European [1,2], American [3], and Australian [4] codes were assessed by comparing the design resistances with the results from the experimental tests and the collected test data of relevant studies, showing in general a considerable level of conservatism.

Affordable Earthquake Building

Abstract: Nowadays springs are the main component in the structures. A new low-cost seismic isolation system which is related on spring tube bracings has been proposed and studied, and according to that study when springs are performed their designated jobs there is very little reason to spare them much thought. One area that you might not have considered the worth of springs within is the science of architecture, but actually springs are being used in buildings all around the world. As per the study, multiple compression-type springs are positioned in a special cylindrical tube to obtain a symmetrical response in tension and compression-type axial loading. An isolation floor, which consists of pin-ended steel columns and spring tube bracings, is constructed at the foundation level or any intermediate level of the building. An experimental campaign with three stages was completed to evaluate the capability of the system. First, the behavior of the spring tubes subjected to axial displacement reversals with varying frequencies was determined. In the second phase, the isolation floor was assessed in the quasi-static tests. Finally, a ¼ scaled 3D steel frame was tested on the shake table using actual acceleration records. The transmitted acceleration to the floor levels is greatly diminished because of the isolation story, which effects longer period and higher damping. There are no stability and self-centering problems in the isolation floor.

Buckling behavior and design of concentrically loaded T-section aluminum alloy columns

Tees are utilized as chord members in a number of arrangements of aluminum alloy trusses. The purpose of this study is to investigate the buckling behavior and design methods of concentrically loaded T-section aluminum alloy columns. Using column tests and finite element analysis, this study analyzed the buckling modes and ultimate strengths of high-strength aluminum alloy T-columns under axial compression and validated the numerical model against the experimental results. Comparisons with the current Eurocode 9 and Direct Strength Method (DSM) design rules were also conducted. Fixed- and pin-ended columns exhibit a quite different buckling behavior. The failure modes of flexural buckling about the two principal axes could be treated with sufficient safety and accuracy using the column design rules in Eurocode 9 and DSM. The effects of the effective centroid shift due to the local buckling of slender parts could be ignored. The Eurocode 9 and DSM leads to inaccurate and conservative results for fixed-ended columns failing by local-torsional buckling and flexural–torsional buckling. The paper recommends suggestions based on the DSM approach that improve the design strength predictions for aluminum alloy T-section columns.

Investigation on buckling behavior of T-shaped box-T section columns under axial load

Special-shaped columns (i.e., L-shaped, T-shaped, and cross-shaped) present the main advantages of avoiding column protrusion and enlarging the indoor space, and they also have large stiffness and strength in the direction of their longer sections. However, there is a lack of systematic research of the buckling performance of T-shaped column. In this paper, T-shaped box-T section columns, composed of one cold-formed box section and several T-sections, were concerned. The elastic buckling analysis of T-shaped box-T section columns was firstly conducted, and it is recommended to set stiffeners to restrain the distortional buckling of the first order buckling modes of the columns. Based on the elastic buckling analysis, 10 T-shaped box-T section columns with one stiffener were tested under axial load. The measured material properties, geometries, initial imperfections, failure modes, ultimate capacities, and loading histories of the specimens were reported and employed to validate the finite element (FE) models. The plane section assumption was confirmed for T-shaped box-T section columns based on the records of the strain gauges and the FE results. FE analysis was carried out to investigate the effects of initial geometric imperfections, residual stress, and stiffeners on the buckling performances of T-shaped box-T section columns. Totally 880 FE results of the pin-ended columns were employed to evaluate the design curves of the current specifications GB 50017-2017, EN 1993-1-1, and ANSI/AISC 360-16, and new design curves were also proposed.

Experimental and numerical investigation on cold-formed steel built-up section pin-ended columns

The thorough test programme and numerical simulation were conducted to examine the buckling behaviour and loading capacity of cold-formed steel (CFS) built-up section members subjected to axial compression. In the test programme, the folded-flange channels of steel grades G500 and G550 were designed to assemble the novel built-up section compressive members. Two types of built-up sectional profiles were formed by composing channels with self-tapping screws. A total of twenty-two built-up section specimens with member lengths varied from 300 to 1500 mm were compressively loaded under pin-ended supports. The initial geometric imperfection measurements, test rig arrangement, loading procedure and test results were fully reported. In the numerical simulation, the extensive parametric study incorporating 224 CFS built-up section columns was performed to further generate numerical data covering a broad range of sectional configurations and geometric parameters. After that, the comparisons of loading capacities obtained from experiments and numerical simulation with nominal compressive strengths calculated on the basis of direct strength method (DSM) as stipulated in the Australian/New Zealand Standard and the North American Specification were conducted to assess the applicability of the current design rules for CFS built-up section members under compression. The results manifest that the codified DSM equations are generally conservative and fairly scattered to predict the resistances of the newly designed built-up section columns. The modifications of codified DSM equations are thus proposed in this study for the CFS built-up open and closed section compressive members. It is found that the modified DSM formulae reliably provide overall precise and less scattered strength predictions.

Buckling behaviour of Q460GJ welded H-section columns subjected to minor axis under axial compression

To study the overall buckling behavior of Q460GJ steel columns around the minor principal axis under axial compression, experimental investigations were carried out on 8 pin-ended H-section steel columns. The main parameter of the specimens is slenderness λ, ranging from 36 to 86. Besides, material properties, initial geometrical imperfections and residual stresses of the specimens were measured. During the loading process, horizontal displacements at the mid-span of the specimens and the strain development were monitored. All the specimens failed with overall buckling and the bearing capacity was obtained. Moreover, a finite element model that considered initial geometric imperfections and residual stress was established and verified, and numerical studies were followed. The buckling factor φ - nondimensional slenderness λn relationship is compared with that in current design specifications. The curve “c” in the Chinese standard GB50017-2017 and curve “c” in Eurocode 3 are recommended to evaluate the overall buckling resistance of 460GJ welded H-section columns under axial compression conservatively.

The influence of the reinforced concrete deformability in the design of slender columns

This work aims to evaluate the influence of the main parameters related to the deformability of reinforced concrete columns in the design of pin-ended rectangular slender columns, under combined bending and axial force. For this, the objective is to analyse the influence of the elasticity modulus of the concrete and the type of coarse aggregate on the deformability of slender columns and consequent dimensioning, and to propose an adaptation of the parabolic law, inserting the influences of the coarse aggregate and the initial tangent modulus of elasticity in this equation, being able to use it to evaluate the local second order effects. Concrete characteristic strengths in the range 20–50 MPa (Group I) and 55–90 MPa (Group II) and CA-50 steel (fyk=500MPa) and their respective constitutive laws are considered. Geometric non-linearity is defined from the exact solution of the second-order differential equation for two simultaneous loading cases: geometric imperfection of the column axis and equal moments applied at its extremities. Physical non-linearity is defined from the moment–curvature diagram of the cross-section under the action of the compression force. The constitutive laws used in this diagram are: the bilinear law with horizontal threshold for steel, and for concrete in compression, the parabola-rectangle diagram on the dimensioning of the cross-section at the ultimate limit state under combined bending and axial force, and the law given in MC-90, MC-2010 [13], EC2-2010 [17] and in the Brazilian Bridge Standard ABNT NBR 7187 [20]. It is also examined the parabola of degree n, corrected for the local physical non-linearity consideration (i.e. of the column’s length). These laws explicitly or implicitly include the modulus of elasticity of concrete and the type of aggregate in it, through the factor αe defined in ABNT NBR 6118 [14]. The concrete strength in tension is disregarded in this work, that is, the tension-stiffening effect for the cracked column is taken equal to zero, which is on the safe side in case of slender columns, as its cracking moment increases with increasing axial compression force. Besides, this strength depends also on the height of the cross-section, frequently considered in prestressed beams. Another important parameter, besides the concrete characteristic strength, is the geometric ratio of the total reinforcement. Thus, it is possible to determine more precisely and securely the second order effect of the slender column, and the consequent variation in reinforcement in relation to the basic case in which αe=1. The results showed that the influence of the type of aggregate can be considered irrelevant for the determination of reinforcement of columns with low slenderness. However, for columns with high slenderness and high strength concrete, the type of aggregate had a significant influence on the design of these columns, where the column with aggregate αe=0,7 required twice the reinforcement compared to the column with aggregate αe=1. In addition, a parabolic law adapted to analyse the second order effects of slender columns is proposed with the replacement of fckby∝0∙αe∙fcd0.

Experimental investigation and design of cold-formed steel U-section columns with the local and global interactive buckling

To propose a design method for determining and designing cold-formed steel (CFS) U-section columns with the local and global (LG) interactive buckling, an experimental investigation and numerical simulation with pin-ended columns were carried out in this study. A total of 12 specimens were investigated, considering four cross-section dimensions. In addition, a finite element model (FEM) was established to simulate experimental specimens, the results of which were compared with those of the experiment. Furthermore, the width-to-height ratio, the key parameter effecting the buckling modes and ultimate capacity of CFS U-section columns, was analyzed in detail using a numerical simulation. Finally, based on the experimental and numerical results, an approach for calculating the ultimate capacity of CFS U-section columns was proposed. The accuracy and applicability of the proposed method were verified by the extensive experimental and finite element data. The results indicate that the design method can accurately predict the ultimate strength of CFS U-section columns with the LG interactive buckling.

Stability checks of columns and beams n braced Frames using elastic effective lengths.(Dept.C)

Checking for stability of columns and beams in braced frames is based on the elastic effective lengths. Simple design formulae. for checking the stability of the individual Pin-ended columns, are derived, where the effective length is equal to the line structure length. In this paper the problem of checking the stability of single braced frames, by using the equivalent column approach is considered. i.e the stability check of the total braced frame is replaced by stability cheeks of the individual Columns. Requirements necessary for the beans of a simple braced frame are sought, when the column is checked for stability using the elastic effective length.

Experimental and numerical investigations of hot-rolled stainless steel channel section columns susceptible to flexural buckling

A thorough testing and numerical modelling programme has been conducted to investigate the minor-axis flexural buckling behaviour and resistances of pin-ended hot-rolled stainless steel channel section columns. The testing programme included material coupon tests, membrane residual stress measurements, initial global and local geometric imperfection measurements and ten pin-ended channel section column tests about the minor principal axis. A membrane residual stress predictive model was developed based on the measured data. The testing programme was followed by a numerical modelling programme; finite element models were developed to simulate the test results and then adopted to perform parametric studies to generate further numerical data on hot-rolled stainless steel channel section columns over a wide range of cross-section dimensions and member effective lengths. The obtained test and numerical data were then adopted to assess the accuracy of relevant design rules for hot-rolled stainless steel channel section columns failing by flexural buckling about the minor principal axis, as given in the European code and American design guide. The assessment results revealed that (i) the European code yields many unsafe flexural buckling resistance predictions and (ii) the American design guide yields overly conservative and scattered flexural buckling resistance predictions. Finally, a revised Eurocode buckling curve was proposed and shown to offer accurate, consistent and safe-sided flexural buckling resistance predictions for hot-rolled stainless steel channel section columns over the whole considered range of member non-dimensional slendernesses. The reliability of the revised Eurocode buckling curve was also confirmed using statistical analyses based on EN 1990.

Experimental response of hot-rolled stainless steel angle columns

This paper reports on experiments addressing the buckling and collapse behaviour of pin-ended hot-rolled stainless steel equal-leg angle columns under pure axial compression, aiming to provide reliable experimental data needed to develop explicit design guidelines for hot-rolled stainless steel angle columns currently absent in European standard. The systematic experimental programme included two test groups of specimens with nominal dimensions of 60 ×60× 6 mm and 100 ×100× 10 mm produced from austenitic grade EN 1.4301, and involved tensile material tests, geometric imperfection measurements, residual stress measurements, 6 stub column tests and 20 global compression tests. A wide range of column slenderness ratios was carefully selected to account for both elastic and inelastic failure characteristics including flexural and flexural–torsional modes and the influence of the legs’ width-to-thickness ratios. The test setup and procedure together with the key experimental results and characterised failure modes, were fully reported and discussed. The test results were compared with those predicted using the design methods for compressed stainless steel angle columns provided in European and North American standards. It was observed that the specifications offer conservative strength predictions of the tested columns, primarily due to the lower distribution of initial geometric imperfections of tested columns in comparison with the permissible fabrication tolerances that are usually used as the basis of stability checks in codified design.

Experimental Investigation of Reinforced Concrete Columns with Steel Embedded Tubes

This study aimed to investigate the influence of longitudinal steel embedded tubes located at the center of the column cross-section on the behavior of reinforced concrete (RC) columns. The experimental program consisted of 8 testing pin-ended square sectional columns of 150×150 mm, having a total height of 1400 mm, subjected to eccentric load. The considered variables were the steel square tube sizes of 25, 51 and 68 mm side dimensions and the load eccentricity (50 and 150) mm. RC columns were concealed steel tubes with hollow ratios of 3%, 12% and 20% depending on tube sizes used. The experimental results indicated an improvement in the overall behavior of eccentric columns when steel embedded tubes are used. The maximum gain in strength was about 59% for the hollow ratio of 20% with e/h=1. The test results show that the inserted steel pipe improves strength, ductility and enables these columns to absorb more energy than a similar solid column.