Axial strength of cold-formed thin-walled steel channels under non-uniform temperatures in fire

This paper presents the results of a numerical investigation into the axial strength of cold-formed thin-walled channel sections (columns) under non-uniform high temperatures in fire. The non-uniform temperature distributions are based on the results of a thermal analysis of thin-walled stud panels carried out by the authors. The general finite-element package ABAQUS is used to obtain strengths of columns with different lengths at different fire exposure times. To aid development of a hand calculation method of column strength in fire, the accuracy of using two ways of simplifying the non-uniform temperature distribution is investigated. The ambient temperature design method for cold-formed thin-walled columns in Eurocode 3 Part 1.3 (EN1993-1-3, Eurocode 3: design of steel structures, Part 1.3: general rules, supplementary rules for cold formed thin gauge members and sheeting, European Commission for Standardisation, Brussels, 2001) is modified to take into account the change in the strength and stiffness of steel at elevated temperatures and thermal-bowing effects. The results of this design method are compared to the ABAQUS simulation results.     

Multiobjective optimization of cold-formed steel columns

The optimal design of cold-formed steel columns is addressed in this paper, with two objectives: maximize the local-global buckling strength and maximize the distortional buckling strength. The design variables of the problem are the angles of orientation of cross-section wall elements—the thickness and width of the steel sheet that forms the cross-section are fixed. The elastic local, distortional and global buckling loads are determined using Finite Strip Method (CUFSM) and the strength of cold-formed steel columns (with given length) is calculated using the Direct Strength Method (DSM). The bi-objective optimization problem is solved using the Direct MultiSearch (DMS) method, which does not use any derivatives of the objective functions. Trade-off Pareto optimal fronts are obtained separately for symmetric and anti-symmetric cross-section shapes. The results are analyzed and further discussed, and some interesting conclusions about the individual strengths (local-global and distortional) are found.     

Corner properties of cold-formed steel sections at elevated temperatures

This paper presents the mechanical properties of the corner parts of cold-formed steel sections at elevated temperatures. Light-gauge structural members are cold-formed which results the mechanical properties of the corner parts being different from the flat parts. However, previous research has focused on the investigation of the corner parts of cold-formed steel sections at normal room temperature and the performance of the corner parts at elevated temperatures is unknown. An appropriate model for fire resistant design of steel structures necessitates a correct representation of mechanical properties of structural steel at elevated temperatures. Therefore, experimental investigation on corner coupon specimens at different temperatures ranged from approximately 20 to 1000 °C was conducted to study the behaviour of the corner parts of cold-formed steel sections at elevated temperatures. Two kinds of corner coupon specimens, namely the inner corner coupon specimens and outer corner coupon specimens having the steel grade of G500 (nominal 0.2% proof stress of 500 MPa) and nominal thickness of 1.9 mm were tested. The test results were compared with the flat coupon specimens taken from the same cold-formed steel sections as the corner coupon specimens. A unified equation to predict the yield strength (0.2% proof stress), elastic modulus, ultimate strength and ultimate strain of the corner parts of cold-formed steel sections at elevated temperatures is thus proposed in this paper. Generally, it is shown that the proposed equation adequately predicts the test results of the corner coupon specimens. Furthermore, stress–strain curves at different temperatures are plotted and a stress–strain model is also proposed for the corner parts of cold-formed steel sections.     

Calculating the global buckling resistance of thin-walled steel members with uniform and non-uniform elevated temperatures under axial compression

This paper develops a method, based on the Direct Strength Method (DSM) global buckling curve, to calculate the global buckling ultimate strength of cold-formed thin-walled (CF-TW) steel members under uniform and non-uniform elevated temperatures. The assessment is carried out by checking the DSM curve-based results with numerical simulation results using the general finite element software ABAQUS. The numerical model has been validated against a series of ambient temperature and fire tests on panels made of two different lipped channel sections tested to their ultimate load carrying capacities at ambient temperature or to their fire resistance at different load levels. The validated numerical model has been used to generate a database of numerical results of load carry capacity of CF-TW members with different uniform and non-uniform temperature distributions in the cross-sections under different boundary and loading conditions and with different dimensions. It is concluded that the DSM global buckling column curve is directly applicable for uniform temperature but a simple modification is required for non-uniform temperature distributions.     

Experimental study on local buckling of axially compressed steel stub columns at elevated temperatures

There are few design provisions in codes and standards on local buckling of steel columns under fire conditions. To examine the local stability of steel stub columns at elevated temperatures, 12 stub columns were tested under simultaneous application of load and fire conditions. The test variables included Grade (type) of steel, buckling resistance, temperature and load levels. During fire tests, cross sectional temperatures, axial displacement, buckling deflection, and local buckling failure modes of flange and web of stub columns were recorded at various temperatures. Data from the tests is utilized to evaluate buckling resistance of flange and web both at room and elevated temperatures by applying the ultimate strain method and curve inflexion point method. Results from fire tests are utilized to validate a finite element model developed for tracing local buckling of steel columns at elevated temperatures. Results from fire tests and finite element analysis show that failure mode of columns at room and elevated temperatures follow similar pattern but the load bearing capacity of Q460 steel columns degrade much more rapidly under fire conditions than that of Q235 steel columns. Further, Eurocode 3 provisions for local buckling produce non-conservative results in certain situations.     

Buckling analysis of thin-walled cold-formed steel structural members using complex finite strip method

In this paper, a generalised complex finite strip method is proposed for buckling analysis of thin-walled cold-formed steel structures. The main advantage of this method over the ordinary finite strip method is that it can handle the shear effects due to the use of complex functions. In addition, distortional buckling as well as all other buckling modes of cold-formed steel sections like local and global modes can be investigated by the suggested complex finite strip method. A combination of general loading including bending, compression, shear and transverse compression forces is considered in the analytical model. For validation purposes, the results are compared with those obtained by the Generalized Beam Theory analysis. In order to illustrate the capabilities of complex finite strip method in modelling the buckling behavior of cold-formed steel structures, a number of case studies with different applications are presented. The studies are on both stiffened and unstiffened cold-formed steel members.     

An experimental study on the axial behaviour of cold-formed steel wall studs and panels

A full-scale experimental study on the structural performance of load-bearing wall panels made of cold-formed steel frames and boards is presented. Six different types of C-channel stud, a total of 20 panels with one middle stud and 10 panels with two middle studs were tested under vertical compression until failure. The measured stud failure load agrees well with analytical prediction. The load carrying capacity of a stud increases significantly when one- or two-side sheathing is used, although the latter is more effective. It is also dependent upon the type of board used. Whereas panels with either OSB (orient strand board) or CPB (cement particle board) sheathing have nearly identical load carrying capacity, panels with CSB (calcium silicate board) sheathing are considerably weaker. Screw spacing affects the load carrying capacity of a stud. When the screw spacing on the middle stud in panels with one-side sheathing is reduced from 600 to 300 mm, the stud load carrying capacity increases by 14.5, 20.6 and 94.2% for OSB, CPB and CSB sheathing, respectively.     

Application of the Direct Strength Method to local buckling resistance of thin-walled steel members with non-uniform elevated temperatures under axial compression

This paper assesses the applicability of the Direct Strength Method (DSM) to calculating the local buckling ultimate strength of cold-formed thin-walled (CF-TW) steel members with non-uniform elevated temperature distributions in the cross-section. The assessment was carried out by checking the DSM calculation results with numerical simulation results using the general finite element software ABAQUS which was validated against ambient and uniform elevated temperature tests on short lipped channel sections. The validated numerical model was used to generate an extensive database (372 models) of numerical results of load carry capacity of CF-TW members with different uniform and non-uniform temperature distributions in the cross-sections, under different boundary and loading conditions and with different dimensions and lengths. It was concluded that the DSM local buckling curve was directly applicable for columns with uniform temperature distributions in the cross-section. For columns with non-uniform temperature distributions, a modification to the local buckling curve was necessary and this paper has proposed a new curve.     

Design of high strength steel columns at elevated temperatures

The main objective of this paper is to study the behaviour and design of high strength steel columns at elevated temperatures using finite element analysis. In this study, equations predicting the yield strength and elastic modulus of high strength steel and mild steel at elevated temperatures are proposed. In addition, stress-strain curve model for high strength steel and mild steel materials at elevated temperatures is also proposed. The numerical analysis was performed on high strength steel columns over a range of column lengths for various temperatures. The nonlinear finite element model was verified against experimental results of columns at normal room and elevated temperatures. The effects of initial local and overall geometrical imperfections have been taken into consideration in the analysis. The material properties and stress-strain curves at elevated temperatures used in the finite element model were obtained from the proposed equations based on the material tests. Two series of box and I-section columns were studied using the finite element analysis to investigate the strength and behaviour of high strength steel columns at elevated temperatures. Both fixed-ended stub columns and pin-ended slender columns were considered. The column strengths predicted from the finite element analysis were compared with the design strengths predicted using the American, European and Australian specifications for hot-rolled steel columns at elevated temperatures by substituting the reduced material properties. In addition, the direct strength method, which was developed for the design of cold-formed steel columns at normal room temperature, was also used in this study to predict the high strength steel column strengths at elevated temperatures. The suitability of these design rules for high strength steel columns at elevated temperatures is assessed. Generally, it is shown that the American and European specifications as well as the direct strength method conservatively predicted the column strengths of high strength steel at elevated temperatures. The European Code predictions are slightly more conservative than the American Specification and the direct strength method predictions.     

Mechanical properties of cold-formed steels at elevated temperatures

Mechanical properties have an important role in the fire safety design of cold-formed steel structures due to the rapid reduction in mechanical properties such as yield strength and elastic modulus under fire conditions and associated reduction to the load carrying capacities. Hence there is a need to fully understand the deterioration characteristics of yield strength and elastic modulus of cold-formed steels at elevated temperatures. Although past research has produced useful experimental data on the mechanical properties of cold-formed steels at elevated temperatures, such data do not yet cover different cold-formed steel grades and thicknesses. Therefore, an experimental study was undertaken to investigate the elevated temperature mechanical properties of two low and high strength steels with two thicknesses that are commonly used in Australia. Tensile coupon tests were undertaken using a steady state test method for temperatures in the range 20–700 °C. Test results were compared with the currently available reduction factors for yield strength and elastic modulus, and stress–strain curves, based on which further improvements were made. For this purpose, test results of many other cold-formed steels were also used based on other similar studies undertaken at the Queensland University of Technology. Improved equations were developed to predict the yield strength and elastic modulus reduction factors and stress–strain curves of a range of cold-formed steel grades and thicknesses used in Australia. This paper presents the results of this experimental study, comparisons with the results of past research and steel design standards, and the new predictive equations.     

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

In recent times, light gauge cold-formed steel sections have been used extensively since they have a very high strength to weight ratio compared with thicker hot-rolled steel sections. However, they are susceptible to various buckling modes including a distortional mode and hence show complex behaviour under fire conditions. Therefore, a research project based on detailed experimental studies was undertaken to investigate the distortional buckling behaviour of light gauge cold-formed steel compression members under simulated fire conditions. More than 150 axial compression tests were undertaken at uniform ambient and elevated temperatures. Two types of cross sections were selected with nominal thicknesses of 0.60, 0.80, and 0.95 mm. Both low (G250) and high (G550) strength steels were used. Distortional buckling tests were conducted at six different temperatures in the range of 20-800 ^°C. The ultimate loads of compression members subject to distortional buckling were then used to review the adequacy of the current design rules at ambient and elevated temperatures. This paper presents the details of this experimental study and the results.     

Application of direct strength method to axially loaded perforated cold-formed steel studs: Distortional and local buckling

A study to develop methods of analyzing perforated, axially loaded, cold-formed steel studs using the provisions of the Direct Strength Method [American Iron and Steel Institute (AISI). North American Specification for the Design of Cold-Formed Steel Structural Members 2001 Edition with Supplement 2004 (AISI/COFS/NASPEC 2004) and Commentary (AISI/COFS/NASPEC 2004), Washington, DC; 2004] was undertaken using the Finite Strip Method as the method for determining the elastic buckling stresses. Several different models were developed to represent the effect of the web perforations. The capacities predicted using the Direct Strength Method for the limit states of distortional and local buckling were compared to capacities calculated using the equations contained in the AISI Specification [American Iron and Steel Institute (AISI). North American Specification for the Design of Cold-Formed Steel Structural Members 2001 Edition with Supplement 2004 (AISI/COFS/NASPEC 2004) and Commentary (AISI/COFS/NASPEC 2004), Washington, DC; 2004]. The limit state of longwave buckling is considered in a companion paper [Sputo T, Tovar J. Application of direct strength method to axially loaded perforated cold-formed steel studs: Part 1. Longwave buckling. Thin Walled Struct, submitted for publication]. The validity of the results is discussed and recommendations are made for the use of the Direct Strength Method for these members.     

Simulation of cold-formed steel beams in local and distortional buckling with applications to the direct strength method

A nonlinear finite element (FE) model is developed to simulate two series of flexural tests, previously conducted by the authors, on industry standard cold-formed steel C- and Z-section beams. The previous tests focused on laterally braced beams with compression flange details that lead predominately to local buckling failures, in the first test series, and distortional buckling failures, in the second test series. The objectives of this paper are to (i) validate the FE model developed for simulation of the testing, (ii) perform parametric studies outside the bounds of the original tests with a particular focus on variation in yield stress and influence of moment gradient on failures, and (iii) apply the study results to examine and extend the Direct Strength Method of design. The developed FE model shows good agreement with the test data in terms of ultimate bending strength. Extension of the tested sections to cover yield stresses from 228 to 506 MPa indicates that the Direct Strength Method is applicable over this full range of yield stresses. The FE model is also applied to analyze the effect of moment gradient on distortional buckling. It is found that the distortional buckling strength of beams is increased due to the presence of moment gradient. Further, it is proposed and verified that the moment gradient effect on distortional buckling failures can be conservatively accounted for in the Direct Strength Method by using an elastic buckling moment that accounts for the moment gradient. An empirical equation, appropriate for use in design, to predict the increase in the elastic distortional buckling moment due to moment gradient, is developed.     

Strength and behaviour of cold-formed steel offset trusses

Thirteen full-scale truss specimens fabricated with cold-formed steel C-sections were tested to study various practical strengthening techniques in order to achieve a desired behaviour and an increased capacity. Specimens were subjected to concentrated panel point loading simulating the realistic loading condition of a roof truss. Results revealed that local buckling of the top chord (LBTC) adjacent to the heel plate was the predominant failure mechanism. In instances where the heel plate was not adequately stiffened, the distortion or crippling of the plate occurred at failure. For the investigated pitches, an increase in specimen pitch resulted in an increase in the capacity. Strengthening both the top chord adjacent to the heel plate and the heel connection with both a shallow member and a heel plate stiffener resulted in the most significant increase in the capacity compared with the original truss configuration. Beam-column analysis of the top chords in the failure region was performed using both the conventional interaction design equations and the direct strength method as suggested in CSA S136-07.     

Finite element modelling of cold-formed steel beams under local buckling or combined local/distortional buckling

The finite element (FE) method is capable of solving the complex interactive buckling of cold-formed steel beams allowing for all important governing features such as geometrical imperfections, material nonlinearity, postbuckling, etc.; this is unlikely to be achieved by analytical methods. In this paper, two series of finite element models for buckling behaviour of laterally-restrained cold-formed steel Z-section beams have been developed with special reference to material and geometrical nonlinearities: one to allow for the possibility of combined local/distortional buckling and the other to allow for local buckling only. Four-point bending tests carried out by previous researchers have been used to verify the FE models. A simplified configuration of the test setup has been modelled in ABAQUS. In the local buckling FE models, distortional buckling has been restricted in the member using translational springs applied to the lip/flange corner of the beam. Predictions of load carrying capacity and deformed shapes exhibit excellent agreement with both the results from the more extensive models and laboratory tests. Further papers will exploit the developed FE models to investigate the different forms of buckling that occur in laterally-restrained cold-formed steel beams i.e. local, distortional and combined local/distortional.     

Effective width method to account for the local buckling of steel thin plates at elevated temperatures

The local buckling of thin steel plates exposed to fire is investigated using a finite element model. The reduction of strength and stiffness that occurs at elevated temperatures needs to be taken into account in the design, as it increases the susceptibility to local buckling of the plates thus affecting their load carrying capacity. The obtained results show that the current existing design method of Eurocode 3 to take into consideration the local buckling in the calculation of the ultimate strength of steel thin plates at elevated temperatures needs to be improved. These methods are based on the same principles as for normal temperature but using for the design yield strength of steel, at elevated temperatures, the 0.2% proof strength of the steel instead of its strength at 2% total strain as for the cases where the local buckling is not limiting the ultimate strength of the plates. This consideration, however, leads to an inconsistency if cross-sections are composed simultaneous of plates susceptible and not to local buckling. To address this issue, new expressions for calculating the effective width of internal compressed elements (webs) and outstand elements (flanges) are proposed, which have been derived from the actual expressions of the Part 1.5 of the Eurocode 3 and validated against numerical results. It is also demonstrated that it is not necessary to use for the yield stress at elevated temperatures the 0.2% proof strength of the steel instead of the yield stress at 2% total strain, given that the necessary allowances are considered in these new expressions, thus leading to a more economic design.     

Experimental and numerical study on a full scale apex connection of cold-formed steel portal frames

In this paper, experimental and theoretical studies performed on apex connection of an industrial portal frame constructed with cold-formed back-to-back double sigma profile rafters are presented. By those experiments performed, local buckling behavior of the apex plate and load–displacement behavior of the system were investigated under monotonic vertical loading. This investigation was conducted for conditions that the gap between rafter ends at the apex plate are 90, 180, 360, and 450 mm and apex plate is unstiffened/stiffened. Experimental results for the model with 360 mm gap were compared to those of nonlinear quasi-static finite element analyses performed using a finite element software and a good agreement between those results was observed. The connection׳s behavior is controlled by the apex plate. No significant damage occurred on the profiles after the tests. According to the results, it is sufficient to increase the gap between rafter ends up to not higher than 360 mm in order to maximize the general load carrying capacity of the system and the stability of out of plane local buckling behavior of the apex plate. Furthermore, although stiffener plate significantly restricted local buckling of apex plate, no remarkable effect of this enhancement was observed on the flexural capacity of the system.     

Investigation of concrete encased steel composite columns at elevated temperatures

This paper presents a nonlinear 3-D finite element model investigating the behaviour of concrete encased steel composite columns at elevated temperatures. The composite columns were pin-ended axially loaded columns having different cross-sectional dimensions, different structural steel sections, different coarse aggregates and different load ratios during fire. The nonlinear material properties of steel, concrete, longitudinal and transverse reinforcement bars as well as the effect of concrete confinement at ambient and elevated temperatures were considered in the finite element models. The interface between the steel section and concrete, the longitudinal and transverse reinforcement bars, and the reinforcement bars and concrete were also considered allowing the bond behaviour to be modelled and the different components to retain its profile during the deformation of the column. The initial overall (out-of-straightness) geometric imperfection was carefully included in the model. The finite element model has been validated against published tests conducted at elevated temperatures. The time–temperature relationships, deformed shapes at failure, time–axial displacement relationships, failure modes and fire resistances of the columns were evaluated by the finite element model. It has been shown that the finite element model can accurately predict the behaviour of the columns at elevated temperatures. Furthermore, the variables that influence the fire resistance and behaviour of the composite columns comprising different load ratios during fire, different coarse aggregates and different slenderness ratios were investigated in parametric studies. It is shown that the fire resistance of the columns generally increases with the decrease in the column slenderness ratio as well as the increase in the structural steel ratio. It is also shown that the time–axial displacement relationship is considerably affected by the coarse aggregate. The fire resistances of the composite columns obtained from the finite element analyses were compared with the design values obtained from the Eurocode 4 for composite columns at elevated temperatures. It is shown that the EC4 is conservative for all the concrete encased steel composite columns, except for the columns having a load ratio of 0.5 as well as the columns having a slenderness ratio of 0.69 and a load ratio of 0.4.     

Application of direct strength method to axially loaded perforated cold-formed steel studs: Longwave buckling

A study to develop methods of analyzing perforated, axially loaded, cold-formed steel studs using the provisions of the Direct Strength Method [3] was undertaken using the Finite Strip Method as the method for determining the elastic buckling stresses. Several different models were developed to represent the effect of the web perforations. The capacities predicted using the Direct Strength Method for the limit state of longwave buckling were compared to capacities calculated using the equations contained in the AISI Specification [3]. The limit states of local and distortional buckling are considered in a companion paper [12]. The validity of the results is discussed and recommendations are made for the use of the Direct Strength Method for these members.