Flexural-torsional Buckling Research Articles

Post-buckling strength of steel tee columns

This paper examines the effects of torsional post-buckling on the strengths of tee section steel columns which fail in local, torsional, or flexural modes. Flexural–torsional buckling is not considered, but the post-buckling movement of the effective centroid and the ensuing bending effects are.It is shown that the elastic torsional buckling loads of tee section columns are greater than or equal to their local buckling loads, while their torsional and local post-buckling behaviours are very similar. Design codes which require separate account to be taken of torsional and local buckling duplicate their allowances for these effects and ignore the torsional post-buckling strength.It is found that the effective section method used in most codes to allow for local buckling and post-buckling is probably conservative, and that allowances for the movement of the centroid are over-conservative.It is suggested that close design approximations for the strengths of tee section columns can be obtained by ignoring the effects of movement of the centroid and torsional buckling, and instead using the lower of the axial compression section resistance determined for the effective section and the member resistance calculated by ignoring local buckling.

A new slenderness-based approach for the web crippling design of plain channel steel beams

In this paper, the web crippling strength of cold-formed steel plain channel beams subjected to concentrated loads is evaluated on the basis of numerical models and available test results. The design equations existing in current steel codes display many coefficients, have not theoretical background and overlook the slenderness concept, which is a trademark of safety checking rules related with other failure modes such as column flexural-torsional buckling, web shear buckling and plate buckling. The main objective is to show that such slenderness-based approach is possible for web crippling design. Firstly, some considerations about the web crippling of cold-formed steel beams are drawn and a brief review is made. Secondly, the equations for web crippling design available in current Eurocode 3 and AISI steel codes are described. Then, the numerical model is explained in detail. On the basis of numerical and experimental results, it is shown that an approach based on the slenderness concept leads to fairly good estimates of web crippling load. Finally, some conclusions are drawn.

Thin-Walled Cold-Formed Steel Beams with Holes in Lateral Flexural-Torsional Buckling

In this paper the study on lateral flexural-torsional buckling of steel sigma-cross-section beams with web holes will be presented. The analysis of corresponding stability problem is based on general approach derived for a group of beams including at least mono-symmetric sections loaded transversally to their plane of symmetry. The effective flexural and torsional stiffness of steel beams with holes has been verified by tests. The results of theoretical analysis were compared with specification design procedure and also with actual behaviour of set of beams investigated by experiments. The study conclusions aim to become the background of the supplements to specified provisions for the design of steel structures.

Improved design rules for fixed ended cold-formed steel columns subject to flexural–torsional buckling

This paper has presented the details of an investigation into the flexural and flexural–fl buckling behaviour of cold-formed structural steel columns with pinned and fixed ends. Current design rules for the member capacities of cold-formed steel columns are based on the same non-dimensional strength curve for both fixed and pinned-ended columns. This research has reviewed the accuracy of the current design rules in AS/NZS 4600 and the North American Specification in determining the member capacities of cold-formed steel columns using the results from detailed finite element analyses and an experimental study of lipped channel columns. It was found that the current Australian and American design rules accurately predicted the member capacities of pin ended lipped channel columns undergoing flexural and flexural torsional buckling. However, for fixed ended columns with warping fixity undergoing flexural–torsional buckling, it was found that the current design rules significantly underestimated the column capacities as they disregard the beneficial effect of warping fixity. This paper has therefore proposed improved design rules and verified their accuracy using finite element analysis and test results of cold-formed lipped channel columns made of three cross-sections and five different steel grades and thicknesses.

Elastic Flexural-Torsional Buckling of Beam-Column with Equal-Leg Angle Cross-Section

The flexural-torsional buckling of equal-leg angle member under compression is analyzed and calculated. Based on General bending theory and the section properties of angle, the governing equations of the spatial buckling are presented and the formula of Wagner effect coefficient is deduced. The method can also be used for beam-columns with any type section, and the computational efficiency is much higher than numerical methods. The critical buckling loads of equal-leg angle members with different sizes are calculated and the column curves of critical load and slenderness ratio are plotted which will guide efficiently the actual engineering design.

Schifflerised angle sections for triangular-based communication towers

This paper is concerned with the use of Schifflerised angle sections for triangular-based lattice communication towers. The torsional-flexural buckling properties of conventional 90°, 60° and schifflerised angles are compared. The experimental results obtained from the compression tests conducted on three different sizes of schifflerised angle sections are compared with the analytical results predicted from finite element analysis and with the capacities predicted from the procedure given in the literature. The capacity of schifflerised angles are underestimated by the methods suggested in the literature. The FE model non-linear analysis predicts the failure loads closer to the test results with a variation of −3 to 10%. The strength of schifflerised angles is 5 to 20% higher compared to conventional 90° angles. The behaviour of 60 m high three-legged triangular communication tower with schifflerised angles for leg members and conventional equal angles for all other members tested at Tower Testing and Res...

Postbuckling failure analysis of pultruded FRP beams under uniform bending

The postbuckling behaviour of Pultruded Fibre-Reinforced Plastic (PFRP) beams in uniform major-axis bending is analysed through a nonlinear finite element (FE) analysis including initial out-of-straightness. Two wide-flange shapes by two pultruders are analysed for six values of the beam slenderness, involving 24 FE models. The limiting imperfection amplitudes reported by the pultruders are shown to yield extremely low ultimate bending moments, associated with unrealistic failure mechanisms and strong interaction between local and flexural–torsional buckling modes. Conversely, reduced imperfection amplitudes reported in the literature are found to lead to well documented failure mechanisms and to a small influence of the buckling mode interaction. The influence of the warping restraints at the beam end sections is also discussed.

An Experimental Study on the Performance of Fixed-End Supported PFRP Channel Beams under Flexure

The experimental investigation on the fixed-end supported PFRP channel beams subjected to three-point loading is presented. The objectives of this study are to evaluate the effects of the span on the structural behaviors, the critical buckling loads and the modes of failure of the PFRP beams, and to compare the obtained deflections with those obtained from the Timoshenko’s shear deformation beam theory equation in order to check the adequacy of the equation. The beam specimens have the cross-sectional dimensions of 152 43 10 mm with span-to-depth ratio ranging from 16 to 33. A total of twenty-two specimens were performed. Based on the experimental results, it was found that the loads versus mid-span vertical deflection relationships of the beam specimens are linear up to the failure, but the load versus mid-span lateral deflection relationships are geometrically nonlinear. The general modes of failure are the flexural-torsional buckling. Finally, the Timoshenko’s shear deformation beam equation can satisfactorily predict the vertical deflection of the beams within acceptable engineering error.

Flexural-torsional buckling tests of cold-formed steel compression members at elevated temperatures

Current design standards do not provide adequate guidelines for the fire design of cold-formed steel compression members subject to flexural-torsional buckling. Eurocode 3 Part 1.2 (2005) recommends the same fire design guidelines for both hot-rolled and cold-formed steel compression members subject to flexural-torsional buckling although considerable behavioural differences exist between cold-formed and hot-rolled steel members. Past research has recommended the use of ambient temperature cold-formed steel design rules for the fire design of cold-formed steel compression members provided appropriately reduced mechanical properties are used at elevated temperatures. To assess the accuracy of flexural-torsional buckling design rules in both ambient temperature cold-formed steel design and fire design standards, an experimental study of slender cold-formed steel compression members was undertaken at both ambient and elevated temperatures. This paper presents the details of this experimental study, its results, and their comparison with the predictions from the current design rules. It was found that the current ambient temperature design rules are conservative while the fire design rules are overly conservative. Suitable recommendations have been made in relation to the currently available design rules for flexural-torsional buckling including methods of improvement. Most importantly, this paper has addressed the lack of experimental results for slender cold-formed steel columns at elevated temperatures.

Structural assessment of a modern heritage building

A structural assessment study on “Palazzo del Lavoro” in Turin, a masterpiece by Pier Luigi Nervi, was carried out within a National Research Project dedicated to the analysis of modern heritage architecture in Italy. Based on the original design documentation collected through records, a complete finite element model of the building was generated. The study included detailed models of the main structural members, represented by monumental reinforced concrete columns, a mushroom-type steel roof and reinforced concrete ribbed gallery slabs, and the main non-structural systems, constituted by continuous gallery-to-roof glazed façades. The results of the linear and non-linear analyses developed by these models, aimed at fully understanding the original design concept of the various members, as well as at evaluating their current static and seismic safety conditions, are reported in this paper. The non-linear computations include a buckling analysis of the slender steel beams constituting the roof, and an “integral” seismic pushover analysis of the monumental columns. The results of the analyses highlight safe conditions and good performance objectives in general, but for some important exceptions. Indeed, the roof beams failed to pass the verifications on global and local panel flexural–torsional buckling, and some cantilever beams of the gallery floors showed poor shear resistance. Retrofit hypotheses are also formulated for these elements, so as to help the entire structure to comply with the requirements of the new Italian Technical Standards.

Flexural-Torsional Buckling of Double-Angle Compression Members

The evaluation for double-angle compression members is a tedious procedure and is not an easy task for practicing engineers. In this study, a computer program has been developed to calculate the Pu based on the AISC specifications. It is found that the calculated value is quite close to the tabulated one if effective length (KL) is longer than 10 feet. However, the Pu is not tabulated for effective length less than 10 feet in some lager sections. It is found that the differences between the calculated value and the interpolated value could be as much as 20%. Unfortunately, the difference errors are not on conservative side and the use of interpolated values is not acceptable in practice. This study evaluates all double-angle compressive formulas provided by the AISC manuals and the comparisons among them are presented. The Pu versus KL curves, in which effective lengths less than 10 feet are added and plotted. Some supplementary tabulated values, which required in routine design and not listed in current AISC design manuals, are also furnished. This study will fulfill the needs for those who seek higher performance and wider coverage when evaluating the design of double-angle compression members under flexural-torsion condition.

Flexural-Torsional Buckling Analysis of Steel Beams under Transverse Loads in High Temperature

Flexural-torsional buckling of steel beams in high temperature is studied by adopting the method of theoretical analysis. The flexural-torsional buckling critical moment equations of steel beams under concentrated transverse loads are driven in high temperature ranging from 20°C to 300°C. In order to verify the validity of the theoretical analysis equations, a steel beam model under concentrated transverse load is designed. The flexural-torsional buckling critical moments and critical stresses are calculated under different temperature conditions. The influence of load point on flexural-torsional buckling critical moment and critical stress are obtained. The variation tendency of flexural-torsional buckling critical moment and critical stress against temperature are also presented.

Finite Element Modeling of Stability of Beam-Column Supports for Field Fabricated Spherical Storage Pressure Vessels

Spherical pressure vessels in large sizes are generally supported on legs or columns evenly spaced around the circumference. The legs are attached at or near the equator of the sphere. This research work focussed on flexural-torsional buckling of beam-column supports of field fabricated spherical pressure vessels using finite element analysis. Flexuraltorsional buckling is an important limit state that must be considered in structural steel design and it occurs when a structural member experiences significant out-of-plane bending and twisting. This research has therefore considered the total potential energy equation for the flexural-torsional buckling of a beam-column element. The energy equation was formulated by summing the strain energy and the potential energy of the external loads. The finite element method was applied in conjunction with the energy method to analyze the flexural-torsional buckling of beam-column supports. To apply the finite element method, the displacement functions are assumed to be cubic polynomials, and the shape functions used to derive the element stiffness and element geometric stiffness matrices. The element stiffness and geometric stiffness matrices were assembled to obtain the global stiffness matrices of the structure. The final finite element equation obtained was in the form of an eigenvalue problem. The flexural-torsional buckling loads of the structure were determined by solving for the eigenvalue of the equation. The resulting eigenvalue equation from the finite element analysis was coded using FORTRAN 90 programming language to aid in the analysis process. To validate FORTRAN 90 coding developed for the finite element analysis and the methodology, the results given by the software were compared to existing solutions and showed no significant difference P > 0.05.

Design of Cold-Formed Thin-Walled Steel Fixed-Ended Channels with Complex Edge Stiffeners under Axial Compressive Load by Direct Strength Method

The stability bearing capacity of axially compressive loaded fixed-ended channels with complex edge stiffeners were analyzed by direct strength method in this paper. A total of 292 examples with different parameters were selected to be studied by nonlinear finite element analysis. As the members with fix-ends, the failure modes include local and flexural-torsional interactive buckling, distortional and flexural-torsional interactive buckling. The revised direct strength method was put forward. After revise, the formula is in good agreement with experimental results. It is shown that direct strength method is valid for predicting the stability capacity of axially loaded fixed-ended channel columns with complex edge stiffeners. We suggest using the DSM3 to calculate the cold-formed thin-walled steel fixed-ended channels with complex edge stiffeners under axial compressive load.

Elastic Stability of Circular Arches with the Open Thin-walled Monosym-metric Section Considering the Prebuckling Deformation

The effect of prebuckling in-plane deformations on the elastic flexural-torsional buckling of arches is studied in this paper. Nonlinear strain-displacement relations considering initial curvature effects and higher order prebuckling de-formation terms with curvature in deriving process are substituted into the second variation of the total potential to obtain the buckling energy equation. The analytical solutions for the flexural-torsional buckling moment of arches in uniform bending, containing the effects of the prebuckling deformation, are proposed. Also, the influence of the higher order prebuckling deformation terms with the curvature effects is investigated according to the ratio of the minor axis flexural stiffness to the major axis flexural stiffness.

Experimental investigation of inelastic buckling of built-up steel columns

This paper experimentally investigated the buckling capacity of built-up steel columns mainly, Cruciform Columns (CC) and Side-to-Side (SS) columns fabricated from two Universal Beam (UB) sections. A series of nine experimental tests comprised of three UB sections, three CC sections and three SS sections with different lengths were tested to failure to measure the ultimate axial capacity of each column section. The lengths used for each category of columns were 1.8, 2.0, and 2.2 m with slenderness ratios ranging from 39-105. The measured buckling loads of the tested specimens were compared with the predicted ultimate axial capacity using Eurocode 3, AISC LRFD, and BS 5959-1. It was observed that the failure modes of the specimens included flexural buckling, local buckling and flexural-torsional buckling. The results showed that the ultimate axial capacity of the tested cruciform and side-by-side columns were higher than the code predicted design values by up to 20%, with AISC LRFD design values being the least conservative and the Eurocode 3 design values being the most conservative. This study has concluded that cruciform column and side-to-side welded flange columns using universal beam sections are efficient built-up sections that have larger ultimate axial load capacity, larger stiffness with saving in the weight of steel used compared to its equivalent universal beam counterpart.

Moment gradient correction factor and inelastic flexural–torsional buckling of I-girder with corrugated steel webs

Corrugated steel plates have several advantages such as high resistance for shear without stiffeners, minimization of welding process, and high fatigue resistance. To take advantage of these benefits, several researchers have attempted to use corrugated steel plate as a web for I-girders. The flexural–torsional buckling is the major design aspect of such I-girders. However, the flexural–torsional buckling of the I-girder with corrugated steel webs still needs to be investigated especially for a real loading condition such as non-uniform bending. This paper investigated the flexural–torsional buckling strength of an I-girder with corrugated steel webs under linear moment gradient by using finite element analysis. From the results, it was found that the buckling behavior of the I-girder with corrugated steel webs differed depending on the number of periods of the corrugation. Also, a simple equation for the moment gradient correction factor for the I-girder with corrugated steel webs was suggested. The inelastic flexural–torsional buckling strength of the I-girder with corrugated steel webs was then discussed based on current design equations for ordinary I-girders and inelastic finite element analysis considering initial imperfection and residual stresses.

Global buckling of thin-walled simply supported columns: Analytical solutions based on shell model

In this paper global buckling (i.e., flexural, pure torsional, or flexural–torsional buckling) of thin-walled columns is discussed. The considered problem is the most basic one: the column is simply supported and subjected to a uniform concentric compressive force. The column's cross-section is an arbitrary open thin-walled cross-section. For the critical forces of this problem classical analytical solutions are known. In the presented research alternative formulae are derived on the basis of modeling the member as a set of flat plane elements (or strips). As it is found, the derivations can be carried out in various ways, among which eight options are considered. The resulted critical force formulae are briefly discussed in this paper. Extensive numerical studies are also completed; these studies are summarized in a companion paper.

Global buckling of thin-walled simply supported columns: Numerical studies

In this paper numerical studies on global buckling of thin-walled members are presented. Various methods are used including classical analytical solutions, the semi-analytical finite strip method, the generalized beam theory, shell finite element method and the recently derived shell-model-based analytical formulae. Critical forces are calculated for flexural, pure torsional and flexural–torsional buckling of columns with various thin-walled cross-sections, the results are compared to each other and conclusions are drawn. As it is proved by the studies, the various methods yield similar results in many cases, but significant differences sometimes occur. The differences in the critical forces are due to various factors, these factors are fully explored and illustrated. Guidance is also given on how to minimize the differences between the various methods.

Flexural-torsional buckling strength of I-girders with discrete torsional braces under various loading conditions

Torsional bracing systems have been used widely in I-girder bridges to increase the flexural-torsional buckling strength and distribute the load to the adjacent girders. To evaluate the required stiffness of the bracing and the flexural-torsional buckling strength of the I-girder with a multiple torsional bracing system, the equivalent continuous torsional bracing concept is often adopted regardless of the type of torsional bracing system. However, a previous study on the I-girder with discrete torsional bracings under uniform bending reported that the equivalent continuous torsional bracing concept has certain limitations on discrete torsional bracing problems and it needs to be investigated for general loading cases. This article presents an analytical solution for the elastic flexural-torsional buckling strength and stiffness requirements of I-girders with discrete torsional bracings under various loading conditions. First, a review was performed of the previous study on the elastic critical buckling moment and torsional stiffness requirement of the I-girder with discrete torsional bracings under uniform bending. This solution was then extended for various loading conditions. From the derived analytical solutions, the equivalent moment factor was proposed for practical engineering purposes and the proposed solutions were verified by comparing them with the results of finite element analysis and those of other previous studies. Finally, non-linear finite element analyses including the effects of the initial imperfection and residual stresses were conducted to examine the inelastic buckling strengths of I-girders with discrete torsional bracings under various loading conditions. The results showed that the buckling curves from the current design specification provide reasonably conservative flexural-torsional buckling strengths of the I-girder with discrete torsional bracings when the proposed elastic solutions are applied to obtain the buckling parameters.