Effective Width Formula Research Articles

Local and post-local buckling behavior of welded square high-strength steel tubes with concrete-infilled restraints

Concrete-filled high-strength steel tubular members gain increasing popularity as the building height and bridge span increase. The slender sections and higher stress levels, however, make the high-strength steel plates more susceptible to local buckling. This paper reports an experimental and numerical investigation on local and post-local buckling behavior of welded square high-strength steel tubes with concrete-infilled restraints. Sixteen high-strength steel tubes with nominal yield strengths of 460, 500, and 550 MPa with concrete-infilled restraints were tested. The experimental results reveal that the post-buckling reserve strength of steel tubes with slender sections increases with the increase in plate slenderness regardless of steel grade. A total of 168 numerical models were subsequently established using the verified finite element method. Based on the finite element analysis results, the slenderness limits and effective width formula were proposed for both high-strength and normal-strength steel tubes with concrete-infilled restraints. Available test data of steel-only-loaded concrete-filled steel tubular specimens constitutes an experimental database to evaluate the reliability of the existing slenderness limits and effective width formulas. The comparison result shows that GB 50936, AS/NZS 2327, and AISC 360-16 overestimate the slenderness limits, while Song et al. underestimate the slenderness limit excessively. The proposed slenderness limit (λpl = 0.500) is more consistent with the experimental results with a reasonable conservative level. The mean ratio of predicted post-buckling strengths by the proposed effective width formula to experimental results is 0.94, with a standard deviation of 0.073. The proposed slenderness limit and effective width formula provide a more accurate prediction and, therefore, are recommended in design.

Local buckling behaviour of stainless-clad bimetallic steel built-up square hollow section stub columns

The local buckling behaviour and design of built-up square hollow section (SHS) stub columns made of the stainless-clad (SC) bimetallic steel is addressed in this paper by experimental and numerical investigations. A total of seven stub column specimens fabricated from hot-rolling bonded SC bimetallic steel plates with nominal thicknesses of 8 mm and 13 mm were tested and analysed.​ Precise measurements of dimensions and geometrical imperfections of the specimens were conducted with the assistance of a non-contact 3D laser scanner. The scanned data was processed by a novel approach to provide a more accurate analysis of imperfections. Finite-element (FE) models with geometric imperfections obtained from 3D-scanned data were developed and validated against the dependent test results herein and independent ones. Comprehensive parametric studies considering various clad ratios, normalized plate slendernesses and steel grades were carried out by using the verified FE models. The applicability of current codified design methods to the SC bimetallic steel SHS stub columns was evaluated through comparisons with the numerical results. A normalized slenderness limit as well as an effective width formula were proposed based on the parametric studies and the evaluation of existing design methods. With improved efficiency and consistency, the design methods proposed herein can be utilized in the future application of the SC bimetallic steel structures.

Experimental and numerical investigation of axial compressive strength of unstiffened slender tapered-webs

This study investigates the axial compressive strength of unstiffened slender webs in prismatic tapered steel members utilizing the newly proposed buckling coefficients raised in companion research. An experimental program is performed using three specimens that are axially loaded. A three-dimensional numerical finite element model is established considering both material and geometrical nonlinearities. The finite element model is successfully calibrated to simulate the experimental tests. New procedures are proposed to predict the web's effective width in the same AISC generalized effective width formula. The new procedures are validated against both the experimental results and the finite element models. The developed finite element models are used to expand the validation range of the proposed method to include wider ranges of geometrical variables of columns. The new procedures are found conservative for higher width-to-thickness ratios and tapering ratios. A correction factor is proposed to account for these conservative results and the corrected predictions are compared to both finite element and experimental results showing a better correlation.

Fully nonlinear analysis of steel-concrete composite girder with web local buckling effects

A reliable and advanced program for nonlinear inelastic analyses of steel girders and steel-concrete composite girders subjected to flexural loadings has been developed in the current article. Effects of geometric nonlinearities, material nonlinearities, and residual stresses on flexural behaviors of different steel girders and steel-concrete composite girders have been thoroughly investigated. The concrete slab and steel I-beam cross-sections are discretized into fiber elements to formulate an equivalent effective cross-section. The P − δ effect of beam-column elements is investigated by using stability functions, wherein the plasticity spreading phenomena in the element cross-section are captured at different integration points along the longitudinal direction of the element based on constitutive relations in each fiber. The local buckling phenomenon that possibly occurs in web plates of noncompact composite sections has been considered by considering its effective width formulas for the first time. The generalized displacement control method is applied to solve nonlinear equilibrium equations. The proposed program validated by experimental results shows its accuracies in capturing the structure behaviors and its efficiencies in computing time compared with finite element analyses performed in ABAQUS. Different parametric studies are conducted yielding notable observations. The proposed program might be used as an efficient tool in practical advanced analyses and designs of steel girders and steel-concrete composite girders with high nonlinearities and complexity.

Local buckling of steel plates in concrete-filled steel tubular columns at elevated temperatures

Local buckling remarkably reduces the strength of steel plates in rectangular thin-walled concrete-filled steel tubular (CFST) columns at ambient temperature. This effect is more remarkable at elevated temperature. However, there have been very limited experimental and numerical investigations on the local and post-local buckling behavior of steel plates in CFST columns at elevated temperatures. This paper presents numerical studies on the local and post-local buckling behavior of thin steel plates under stress gradients in rectangular CFST columns at elevated temperatures. For this purpose, finite element models are developed, accounting for geometric and material nonlinearities at elevated temperatures. The initial geometric imperfections and residual stresses presented in steel plates are considered. Based on the finite element results, new formulas are proposed for determining the initial local buckling stress and post-local buckling strength of clamped steel plates under in-plane stress gradients at elevated temperatures. Moreover, new effective width formulas are developed for clamped steel plates at elevated temperatures. The proposed formulas are compared with existing ones with a good agreement. The effective width formulas developed are used in the calculations of the ultimate axial loads of rectangular CFST short columns exposed to fire and the results obtained are compared well with the finite element solutions provided by other researchers. The initial local buckling and effective width formulas can be implemented in numerical techniques to account for local buckling effects on the responses of rectangular thin-walled CFST columns at elevated temperatures.

Material properties and compressive local buckling response of high strength steel square and rectangular hollow sections

An experimental investigation into the structural performance of compressed high strength steel (HSS) square and rectangular hollow sections is described in this paper. Both hot-rolled and cold-formed HSS sections were examined. In total six S460NH and five S690QH hot-rolled section sizes and three S500MC, two S700MC and four S960QC cold-formed section sizes were tested. The experimental programme comprised tensile coupon tests on flat and corner material, measurements of geometric imperfections, full cross-section tensile tests and stub column tests. The results of the experiments presented in this paper have been combined with other available test data on high strength steel sections, and used to assess the existing design guidelines for high strength steels given in Eurocode 3. The focus has been on the material ductility requirements, the Class 3 slenderness limit for internal elements in compression and the effective width formula for Class 4 internal elements in compression.Reliability assessments of the Class 3 slenderness limit (both the current value of 42 and a proposed value of 38) and the effective width formula for Class 4 internal elements in compression were carried out. The analysis indicated that, based on the assembled test data considered in this study, and the assumptions made regarding the statistical distributions of material and geometric properties, a partial safety factor greater than unity is required for HSS. Similar findings have also recently been presented for ordinary strength steels.

Experiments on cold-formed ferritic stainless steel slender sections

The usage of stainless steel in construction has been increasing owing to its corrosion resistance, aesthetic appearance and favourable mechanical properties. The most common stainless steel grades used for structural applications are austenitic steels. The main drawback of these grades relies on their nickel content (around 8–10%), resulting in a relatively high initial material cost. Other stainless steel grades with lower nickel content such as the ferritic steels offer the benefits of stainless steels in terms of functional qualities and design but within a limited cost frame. Hence, ferritic stainless steels may be a viable alternative for structural applications. Given the fact that little experimental information on ferritic stainless steels is currently available, the purpose of this investigation is to report a series of material and cross-section tests on ferritic grade EN 1.4003 (similar to 3Cr12) stainless steel square and rectangular hollow sections to enable a better understanding of their material response and structural performance. Four different cross-section geometries have been tested under pure compression and in-plane bending. Measurements of geometric imperfections and material properties are also presented. The obtained test results are used to assess the adequacy of the slenderness limits and effective width formula given in EN 1993-1-4 to ferritic stainless steels, those proposed by Gardner and Theofanous and Zhou et al. design approach.

Strength design curves and an effective width formula for cold-formed steel columns with distortional buckling

Distortional buckling mode of cold-formed steel thin-walled member is an unstable behavior, and in some cases it may govern the load-carrying capacity of the member. The source, evolution and performance of the formulas and test data for the two strength design curves developed by Hancock are studied, for predicting the load-carrying capacity in the distortional mode. A proposed strength design curve based on available test data and Hancock׳s strength design curves are then compared with the current design methods, the Direct Strength Method and the Effective Width Method, which are incorporated in the “North American specification for the design of cold-formed steel structural members” (AISI-NAS: 2007), “cold-formed steel structures” (AS/NAS 4600: 2005), and the Chinese “Technical specification for low-rise cold-formed thin-walled steel buildings” (JGJ 227-2011). The results indicate that the current design standards adopted the two strength design curves for the DSM and EWM, but they have some differences at the partial extent. A novel formula is proposed for dealing with this problem. The range of applicability of the proposed strength equation is extended from that in AS/NZS 4600 and is shown to be more accurate than AS/NZS 4600 when compared with that in the NAS S100.

Testing and numerical modelling of lean duplex stainless steel hollow section columns

Stainless steels are employed in a wide range of structural applications. The austenitic grades, particularly EN 1.4301 and EN 1.4401, and their low-carbon variants EN 1.4307 and EN 1.4404, are the most commonly used within construction, and these typically contain around 8%–11% nickel. The nickel represents a large portion of the total material cost and thus high nickel prices and price volatility have a strong bearing on both the cost and price stability of stainless steel. While austenitic stainless steel remains the most favourable material choice in many applications, greater emphasis is now being placed on the development of alternative grades with lower nickel content. In this study, the material behaviour and compressive structural response of a lean duplex stainless steel (EN 1.4162), which contains approximately 1.5% nickel, are examined. A total of eight stub column tests and twelve long column tests on lean duplex stainless steel square (SHS) and rectangular hollow sections (RHS) are reported. Precise measurements of material and geometric properties of the test specimens were also made, including the assessment of local and global geometric imperfections. The experimental studies were supplemented by finite element analysis, and parametric studies were performed to generate results over a wider range of cross-sectional and member slenderness. Both the experimental and numerical results were used to assess the applicability of the Eurocode 3: Part 1-4 provisions regarding the Class 3 slenderness limit and effective width formula for internal elements in compression and the column buckling curve for hollow sections to lean duplex structural components. Comparisons between the structural performance of lean duplex stainless steel and that of other more commonly used stainless steel grades are also presented, showing lean duplex stainless steel to be an attractive choice for structural applications.

Strength of Concrete-Filled Steel Box Columns with Buckling Effects

This paper studies the ultimate strength and ductility of short concrete-filled thin-walled steel box columns with local buckling effects using a nonlinear fibre element analysis technique. New effective width formulas for determining the ultimate strengths of steel plates with geometric imperfections and residual stresses in concrete-filled thin-walled steel box columns are incorporated in the fibre element analysis program to account for the effects of local buckling. The progressive local and post-local buckling is simulated by gradually redistributing the normal stresses within the steel box. Performance indices are employed to quantitatively evaluate the section and ductility performance of composite columns. The effects of local buckling, steel ratios and steel yield strengths on the strength and ductility of concrete-filled steel box columns are investigated. It is demonstrated that local buckling significantly reduces the ultimate strength of thin-walled high-strength steel box columns filled with concrete. The 4% limit on the steel ratio or the 0.2 limit on the steel contribution ratio imposed on composite column sections in current design codes leads to the use of very slender steel plates in concrete-filled steel box columns. It is suggested that the section performance index of concrete-filled steel box columns should be as high as 0.5 for a better structural performance. The use of high strength steels in concrete-filled steel box columns significantly increases the ultimate strengths of the columns but reduces their ductility.

Local buckling of steel plates in concrete-filled thin-walled steel tubular beam–columns

The availability of high strength steels and concrete leads to the use of thin steel plates in concrete-filled steel tubular beam–columns. However, the use of thin steel plates in composite beam–columns gives a rise to local buckling that would appreciably reduce the strength and ductility performance of the members. This paper studies the critical local and post-local buckling behavior of steel plates in concrete-filled thin-walled steel tubular beam–columns by using the finite element analysis method. Geometric and material nonlinear analyses are performed to investigate the critical local and post-local buckling strengths of steel plates under compression and in-plane bending. Initial geometric imperfections and residual stresses presented in steel plates, material yielding and strain hardening are taken into account in the nonlinear analysis. Based on the results obtained from the nonlinear finite element analyses, a set of design formulas are proposed for determining the critical local buckling and ultimate strengths of steel plates in concrete-filled steel tubular beam–columns. In addition, effective width formulas are developed for the ultimate strength design of clamped steel plates under non-uniform compression. The accuracy of the proposed design formulas is established by comparisons with available solutions. The proposed design formulas can be used directly in the design of composite beam–columns and adopted in the advanced analysis of concrete-filled thin-walled steel tubular beam–columns to account for local buckling effects.

Effects of plate slenderness on the ultimate strength behaviour of foam supported steel plate elements

Plate elements in fully profiled sandwich panels are generally subjected to local buckling failure modes and this behaviour is treated in design by using the conventional effective width method for plates with a width to thickness (b/t) ratio less than 100. If the plate elements are very slender (b/t > 1000), the panel failure is governed by wrinkling instead of local buckling and the strength is determined by the flexural wrinkling formula. The plate elements in fully profiled sandwich panels do not fail by wrinkling as their b/t ratio is generally in the range of 100 to 600. For this plate slenderness region, it was found that the current effective width formula overestimates the strength of the fully profiled sandwich panels whereas the wrinkling formula underestimates it. Hence a new effective width design equation has been developed for practical plate slenderness values. However, no guidelines exist to identify the plate slenderness (b/t) limits defining the local buckling, wrinkling and the intermediate regions so that appropriate design rules can be used based on plate slenderness ratios. A research study was therefore conducted using experimental and numerical studies to investigate the effect of plate slenderness ratio on the ultimate strength behaviour of foam supported steel plate elements. This paper presents the details of the study and the results.

Nonlinear analysis of concrete-filled thin-walled steel box columns with local buckling effects

Local buckling of steel plates reduces the ultimate loads of concrete-filled thin-walled steel box columns under axial compression. The effects of local buckling have not been considered in advanced analysis methods that lead to the overestimates of the ultimate loads of composite columns and frames. This paper presents a nonlinear fiber element analysis method for predicting the ultimate strengths and behavior of short concrete-filled thin-walled steel box columns with local buckling effects. The fiber element method considers nonlinear constitutive models for confined concrete and structural steel. Effective width formulas for steel plates with geometric imperfections and residual stresses are incorporated in the fiber element analysis program to account for local buckling effects. The progressive local and post-local buckling is simulated by gradually redistributing the normal stresses within the steel plates. Two performance indices are proposed for evaluating the section and ductility performance of concrete-filled steel box columns. The computational technique developed is used to investigate the effects of the width-to-thickness ratios and concrete compressive strengths on the ultimate strength and ductility of concrete-filled steel box columns. It is demonstrated that the nonlinear fiber element method developed predicts well the ultimate loads and behavior of concrete-filled thin-walled steel box columns and can be implemented in advanced analysis programs for the nonlinear analysis of composite frames.

Recent research advances on the ECBL approach. Part II: interactive buckling of perforated sections

Perforated cold-formed steel sections are often used in civil engineering as structural members for residential buildings and storage racks construction. In the case of buildings the perforations are provided to permit piping and bridging, while for rack systems they allow for simple connections between members. The load bearing capacity of these sections are influenced not only by the local buckling, global buckling and interaction between these two, but also by the reduction of cross-sectional properties due to perforations. Because of the wide variety in the size and configuration of perforations, it is impossible to provide a practical design procedure to calculate the ultimate strength of such a type of sections. The main objective of this paper is to calibrate an effective design width formula for the perforated sections and, using the ECBL approach, to evaluate an equivalent α imperfection factor for European buckling curves, in order to adapt them for sections with different perforation patterns.

Bending strength of hybrid cold-formed steel beams

For the purpose of determining the load-carrying capacity of cold-formed steel structural members, the effective width approach has been used. Since most studies were limited only to the structural members, which were assembled from the same material in a given section, this investigation was concentrated on a study of structural strength and behavior of hybrid cold-formed steel beams subjected dynamic loads. An investigation was also conducted to study the validity of effective design width formulas for the design of these specimens. The materials used in this study were 25 AK and 50 SK sheet steels. A total of 72 spot-welded closed-hat sections were tested under different strain rates. The results showed that the structural strengths including yield moment and ultimate moment of hybrid cold-formed steel beams increase with increasing strain rates. In the determination of the strength of hybrid sections, the effective cross-sectional area calculated on the basis of the dynamic yield stresses can be employed. A design procedure was also developed to compute the member strength of hybrid beams.

Theoretical study on the post-local buckling of steel plates in concrete-filled box columns

This paper presents a theoretical study on the post-local buckling behaviour of steel plates in welded steel box columns filled with concrete, by using the finite element method. The effects of various geometric imperfections, residual stresses and width-to-thickness ratios on the post-local buckling characteristics of steel plates in composite columns are investigated. A novel method is developed for evaluating the initial local buckling loads and post-local buckling reserve strength of steel plates with imperfections associated with a theoretical analysis. Two effective width formulas are proposed for the design of clamped steel plates restrained by concrete and are employed in the ultimate strength calculation of short concrete-filled steel box columns. The proposed design models are compared with existing experimental results with a good agreement.

Postbuckling behaviour of foam-filled, thin-walled steel beams

Sandwich construction is increasingly used as wall and roof cladding for building structures. Typically, a cladding panel may consist of two plane or profiled metal faces with a foamed plastic core. The core may be polyurethane, polyisocyanurate, polystyrene or phenolic resin. When such a panel is subject to static loading due, for instance, to wind, snow or temperature gradient, one face is compressed and becomes liable to local buckling. If this face has a trapezoidal or similar profile the failure mode is similar to that for profiled steel sheeting, though the failure stress is enhanced by the presence of the core. The compressed face element first forms a series of buckling waves which increase in amplitude in the postbuckling phase. Failure takes place when one buckle in the region of maximum bending moment cripples. In light gauge steel applications, the conventional design treatment for this phenomenon utilises the concept of effective width. In order to investigate the extension of the effective width concept to plate elements supported by plastic foam material, a series of tests were undertaken on foam-filled steel beams. This paper describes these tests and their interpretation in terms of an enhanced effective width formula.

Thin‐Walled Steel Box Columns under Biaxial Loading

A numerical method to investigate the ultimate strength behavior of thin‐walled steel box columns subjected to axial load and biaxial end moments is presented in this paper. The columns are of uniform cross section along the length and simply supported at the ends. The local buckling of the component plates is taken into account by applying the effective width formulas proposed in an earlier paper. Moment‐curvature‐thrust relationships for a locally buckled box section are developed by using the tangent stiffness method, and the column analysis is then carried out by integrating, numerically, the moment‐curvature‐thrust relationships along the length. Due allowance is made in the analysis to account for imperfections such as initial column deflections and welding residual stresses. The accuracy of the method is established by comparison with limited experimental results for uniaxially loaded columns. Results for biaxially loaded columns are presented in the form of interaction diagrams. Several parameters...

Local buckling of thin-walled steel box columns

The investigation presented in this paper is concerned with the ultimate strength of thin-walled steel box columns that are pinned at their ends and subjected to an eccentrically applied load. An effective width formula to account for local buckling and residual stresses is proposed and the formula along with the tangent stiffness method has been used to develop an analytical method for predicting the failure load of box columns. The accuracy of the present method is established by comparing the predicted values of failure loads with the corresponding experimental values and the results are presented in the form of design curves.

Behavior and Design of Thin‐Walled Columns

Features of the phenomenon of interactive buckling of thin‐walled columns are briefly reviewed. The theoretical results are compared with the recent test results from University of Sydney and earlier results from Cornell University. The agreement is very good indeed. The role of imperfections in producing scatter in the prediction of the ultimate capacity of the columns is illustrated. Design procedures, one developed at Cornell University in the seventies and the other recommended by the new American Iron and Steel Institute Code, are examined in the light of the new results. In order to account for the interaction of plate elements, it is suggested that exact local critical stress be used in the effective width formula. To obtain a reliable and safe estimate of the column strength, it is proposed that the collapse load given by the design methods be multiplied by an appropriate factor. This factor must be a function of the key parameters governing the problem. A statistically derived expression for this...