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.     

Flexural buckling of fire exposed aluminium columns

In order to study buckling of fire exposed aluminium columns, a finite element model is developed. The results of this model are verified with experiments. Based on a parametric study with the finite element model, it is concluded that the simple calculation model for flexural buckling of fire exposed aluminium columns in EN 1999-1-2 does not give an accurate prediction of the buckling resistance in fire. This paper proposes an alternative design model, which takes into account the shape of the stress–strain relationships of aluminium alloys at elevated temperatures. Predictions of this model agree well with that of the finite element model.     

Proposed design methods for lateral torsional buckling of unrestrained steel beams in fire

The behaviour of unrestrained steel I-beams has been studied by means of numerical analysis and published experimental results. The numerical model was developed using a commercial finite element program, MSC.MARC Mentat. A series of different UB and UC sections and different spans, subjected to both uniform moment and midspan point loads, are considered. The numerical predictions of the buckling moments are then compared with published experimental results. Consequently, a new approach is proposed to provide more accurate and safe predictions of the fire resistance of unrestrained beams, as well as to overcome certain weaknesses in the EC3:1.2 [European committee for standardization (CEN). Eurocode 3: Design of steel structures, Part 1.2: General rules — structural fire design, EN 1993-1-2. Brussels (Belgium); 2005] design formula. In addition, to provide a quick and simple design approach for engineers, a straightforward and rational method known as the Rankine method is introduced to predict the LTB failure load of steel beams in fire. It is shown that the Rankine approach generally provides a good lower bound value for numerical predictions.     

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.     

Capacity reduction and fire load factors for LRFD of steel columns exposed to fire

Capacity reduction and fire load factors corresponding to the load and resistance factor design (LRFD) format are developed for steel columns exposed to fire. A sample deterministic framework to determine fire and steel temperatures and the capacity of steel columns is adopted for this analysis to structure the methodology. A specific number of parameters that affect the structural response, including the fire load, ratio of floor area to the total area of the fire compartment, opening factor, thermal absorptivity of compartment boundaries, thickness, density and thermal conductivity of insulation, dead load, and live load are taken as random variables. Mechanical and sectional properties of steel (e.g., yield strength, cross-sectional area, etc.), are also considered to be random variables. The effect of active fire protection systems (e.g., sprinklers, smoke and heat detectors, fire brigade, etc.), in reducing the probability of occurrence of a severe fire is included. Given the choice of framework and based on detailed reliability analyses, it is shown that the capacity reduction and fire load factors should vary depending on the presence of active fire protection systems in a building.     

Performance-based analysis of cylindrical steel containment Vessels exposed to fire

This paper reports the results of a numerical investigation on the structural safety assessment of a nuclear cylindrical steel containment vessel exposed to an accidental external fire condition. A coupling procedure is proposed, linking the modeling of a nearly compressible flow with input energy given by a combustion model (CFD model) and a structural thermo-mechanical analysis (FEM model), allowing an accurate evaluation of a fluid-thermo-mechanical response for the entire duration of the simulated accident. The time-temperature evolution of the burned gases, resulting from the combustion of a hydraulic leakage pool, is performed by the CFD model. The FEM model is used to obtain (i) temperature variation and, (ii) thermo-mechanical behavior and ultimate strength of the vessel. The obtained results indicate that the suggested methodology can provide reliable fire-safety analyses, ensuring that the main safety (load-bearing and containment) functions of the installation are not impaired during accidental events.     

On the buckling of axially restrained steel columns in fire

This paper describes the behaviour of restrained steel columns in fire. It follows the introduction of extra load into the column through the axial restraint of the surrounding cooler structure and the consequential buckling. Key to this understanding is the post-failure behaviour and re-stabilisation of the column, which is discussed with reference to a finite element model and an analytical model. Through bi-directional control of the temperature, the finite element model allows the snap-back behaviour to be modelled in detail and the effects of varying slenderness and load ratio are investigated. The analytical model employs structural mechanics to describe the behaviour of a heated strut, and is capable of explaining both elastic and fully plastic post-buckling behaviour.Through this detailed explanation of what happens when a heated column buckles, the consequences for steel-framed building design are discussed. In particular, the need to provide robustness is highlighted, in order to ensure that alternative load paths are available once a column has buckled and re-stabilised. Without this robustness, the dynamic shedding of load onto surrounding structures may well spread failure from a fire’s origin and lead to progressive collapse.     

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.     

Lateral-torsional buckling of stainless steel I-beams in case of fire

This work presents a numerical study of the behaviour of stainless steel I-beams subjected to lateral-torsional buckling in case of fire and compares the obtained results with the beam design curves of Eurocode 3.New formulae for lateral-torsional buckling, that approximate better the real behaviour of stainless steel structural elements in case of fire are proposed. These new formulae were based on numerical simulations using the program SAFIR, which was modified to take into account the material properties of the stainless steel.     

Local buckling of steel plates in rectangular CFT columns with binding bars

This paper presents a theoretical study on the elastic local buckling of steel plates in rectangular concrete-filled steel tubular (CFT) columns with binding bars under axial compression. It is assumed that the unloaded edges of the steel plate are elastically restrained against rotation, whereas the loaded edges are clamped. Based on the energy method, the formulas for elastic local buckling strength of the steel plate in rectangular CFT columns under axial compression are derived, which are calibrated with the experimental results. Then the formulas are employed to study the elastic local buckling of steel plates in rectangular CFT columns with binding bars under axial compression. It is shown that the binding bars can increase the local buckling coefficient, which results in improvement of the capacity of the steel plate to resist local buckling. Finally, appropriate spacing of binding bars, appropriate limitation for aspect ratio and corresponding appropriate limitation for width-thickness ratio are suggested for rectangular CFT columns with binding bars under axial compression.     

Nonlinear behaviour of unprotected composite slim floor steel beams exposed to different fire conditions

An efficient nonlinear 3D finite element model has been developed to investigate the structural performance of composite slim floor steel beams with deep profiled steel decking under fire conditions. The composite steel beams were unprotected simply supported with different cross-sectional dimensions, structural steel sections, load ratios during fire and were subjected to different fire scenarios. The nonlinear material properties of steel, composite slim concrete floor and reinforcement bars were incorporated in the model at ambient and elevated temperatures. The interface between the structural steel section and composite slim concrete floor was also considered, allowing the bond behaviour to be modelled and the different components to retain its profile during the deformation of the composite beam. Furthermore the thermal properties of the interface were included in the finite element analysis. The finite element model has been validated against published fire tests on unprotected composite slim floor steel beams. The time–temperature relationships, deformed shapes at failure, time–vertical displacement relationships, failure modes and fire resistances of the composite steel beams were evaluated by the finite element model. Comparisons between predicted behaviour and that recorded in fire tests have shown that the finite element model can accurately predict the behaviour of the composite steel beams under fire conditions. Furthermore, the variables that influence the fire resistance and behaviour of the unprotected composite slim floor steel beams, comprising different load ratios during fire, cross-section geometries, beam length and fire scenarios, were investigated in parametric studies. It is shown that the failure of the composite beams under fire conditions occurred for the standard fire curve, but did not occur for the natural fires. The use of high strength structural steel considerably limited the vertical displacements after fire exposure. It is also shown that presence of additional top reinforcement mesh is necessary for composite beams exposed to short hot natural fires. The fire resistances of the composite beams obtained from the finite element analyses were compared with the design values obtained from the Eurocode 4 for composite beams at elevated temperatures. It is shown that the EC4 predictions are generally conservative for the design of composite slim floor steel beams heated using different fire scenarios.     

Local buckling of structural steel shapes

The objectives of this paper are to (1) provide analytical expressions for the elastic cross-section local buckling stresses, including element interaction, of hot-rolled steel structural shapes, and (2) compare these local buckling results to the assumptions inherent in the local slenderness limits of the US AISC structural steel specification. The cross-section local buckling stress is determined by finite strip analysis (FSA). Local stability of each cross-section in the AISC shapes database (excluding pipes) is considered in axial compression, as well as positive and negative bending about the major and minor geometric axes. Local buckling stresses are converted into plate buckling coefficients (k’s) and simplified expressions are provided for all observed k’s. The new k’s explicitly include elastic web-flange interaction amongst the elements comprising the cross-section. The k values from the FSA are compared to those inherently assumed in the AISC Specification, significant differences are observed.     

Experimental study on local buckling of fire-resisting steel columns under fire load

The structural behavior of stub columns using fire-resistant steel has been investigated experimentally under uniform fire load. The newly-developed fire-resistant steel is proven to have higher strength at elevated temperature than that of conventional steel. Also, the requirement of fire-protection in the fire-resisting steel can be released or relaxed as compared with conventional steel structures. However, the design criteria for the application of the fire-resisting steel in steel columns are still limited. To examine the structural behavior of this type of steel columns under fire load, a total of 24 stub column specimens, including both box columns and H columns, reached their limit states due to axial load under fire condition. The main purpose of these studies is to evaluate the variations of the ultimate strength of steel columns due to different width-to-thickness ratios under specified elevated temperature; in addition, to investigate the reduction effects on column strength resulting in the increasing temperature; and finally, to establish the design guidelines of steel columns using fire-resisting steel. From the experimental results, it is found that the ultimate loads of the stub columns decrease while the width-to-thickness ratios or the temperature increases. However, with the increase of temperature, the effect of the width-to-thickness ratio on ultimate strength decreases. It is also found that the effect of the width-to-thickness ratio on the ultimate strength of box column at elevated temperature is more significant than that of H column. Based on these studies, design guidelines are proposed for the requirement of the width-to-thickness ratios of both box column and H column fabricated from fire-resisting steel.     

Practical method for calculating the buckling temperature of the web-post in a cellular steel beam in fire

Buckling behaviors of web-posts in a cellular steel beam at elevated temperatures in a fire were studied using the Finite Element Method (FEM) analysis and available analytical models. The buckling temperatures obtained by the analytical models differed greatly to those obtained from the FEM simulation. Among these analytical models, the buckling temperature obtained through the strut model based on BS5950-1 agreed with the FEM result the best. It is more reasonable to take the width of the compression stress band in the web-post as the effective width of the strut. Numerical parametric studies showed that the width of the compression stress band varied with the opening diameter, the opening distance and the web thickness. A simplified method was proposed to calculate the effective width of the strut. The accuracy of the strut model integrating the new effective width was validated against the FEM simulations. The obtained buckling temperature of the web-post using the modified strut model agreed well with the FEM simulation result.     

Behavior of steel columns in a fire with partial damage to fire protection

An experimental study is performed on two specimens in a furnace to investigate the fire behaviour of steel columns with partial loss of fire protection. The steel columns are connected by flush end-plates at two ends and the axial load is kept constant with a load ratio of 0.55 subjected to an elevation of temperature. The specimens are protected with 20 mm thickness of fire protection. The damaged length of fire protection is 7% of the complete length of the column for specimen S-1 and 14% for S-2 at the two ends of the steel columns. The temperature of atmosphere around the specimens in the furnace is assumed to follow the ISO834 standard temperature and the temperatures and displacements are measured in the experiment. The temperature distribution along the steel column is modelled by finite element analysis and compared with the measured results. A continuum model is presented to predict the ultimate load capacity or critical temperature of the columns with fire protection damage. Analyses are carried out on the specimens and compared with the experiment. Experimental and analytical results showed that the fire resistance of steel columns with partial damage to the fire protection is reduced. The damage length of the fire protection has a great effect on the fire resistance of steel columns. The failure of the specimens mainly resulted from the buckling or yielding at the portion where the fire protection is damaged.     

Local buckling restraint condition for core plates in buckling restrained braces

Buckling Restrained Braces (BRBs) are commonly used as bracing elements in seismic zones. A key limit state governing BRB design is to prevent flexural buckling. However, when the wall thickness of the steel tube restrainer is relatively small compared to the cross-section of the core plate, the restraint conditions against the local buckling of the core plate can be critical for the stability and strength of the BRB. In this study, cyclic loading tests and numerical analyses of BRBs were carried out using various tube restrainer configurations to investigate the influence of local buckling of the restrainer on BRB strength and ductility.     

Shear buckling strength and design of curved corrugated steel webs for bridges

This paper presents the shear buckling strength and design of curved corrugated steel webs for bridges considering material inelasticity. The inelastic buckling strength is determined from buckling curves based on the proposed shear buckling parameter, which is a function of the elastic shear buckling strength of steel web and the material shear yielding strength. A finite element analysis is carried out to study the geometric parameters affecting the shear buckling strength of curved corrugated steel webs for bridges. Based on the numerical results, a shear buckling parameter formula is proposed with no need to calculate either local, global, or interactive buckling parameters. But it depends on the geometric properties of the curved corrugated web profile. Another formula is presented to maximize the shear buckling capacity of curved corrugated web. The proposed formulae agreed well with the published experimental data. The curved corrugated webs produce a tremendous increase in the shear buckling strength and considerable weight saving in regard to the corresponding trapezoidal corrugated webs. The corrugation angle has a considerable effect on the behavior of curved corrugated webs, where higher corrugation angles produce a tremendous increase in the shear buckling strength of curved corrugated webs. It was found that the proposed approach provides a good prediction for the shear buckling strength of curved corrugated steel webs of bridges.     

Behaviour of welded top-seat angle connections exposed to fire

Beam-to-column connections have been found to significantly influence the structural behaviour at ambient and elevated temperatures. When steel-framed structures are exposed to fire, the load-bearing capacity is decreased and the behaviour of the joints is of particular concern. To account for the extensive applications of welded connections, eight experimental tests were carried out in this study on two different types of beam-to-column angle connections to investigate their fire resistance capacity. Failure characteristics and fracture modes of specimens were studied, and results are presented in the form of temperature–rotation curves. In addition, the influence of different parameters such as thickness of the angles, the value of the applied moment, and other geometrical and mechanical characteristics of the connections was investigated.     

Experimental analysis on cold-formed steel beams subjected to fire

The great majority of the studies in this area emphasise further the structural behaviour of cold-formed steel members by means of analytical approximation and purely numerical methods. In addition, they generally only take into account the structural behaviour of members with just one profile. On the contrary, this paper reports a series of flexural tests under fire conditions focused on cold-formed galvanised steel beams consisting on compound cold-formed steel profiles which are often used in floors and roofs of warehouses and industrial buildings. The main objective of this research was to assess the failure modes, the critical temperature and the critical time of the studied beams. Other important goals of this research work were also to investigate the influence of the cross-sections, the axial restraint to the thermal elongation of the beam and the rotational stiffness of the beam supports. Finally, the results showed above all that the critical temperature of a cold-formed steel beam might be strongly affected by the axial restraint to the thermal elongation of the beam.     

Fire-resistance study of restrained steel columns with partial damage to fire protection

In order to analyze the behavior of steel columns in fire with partial damage of fire protection, an analytical model is presented based on the differential equation of equilibrium, which may be used to predict the ultimate load bearing capacity of steel columns fixed at two ends and to predict the critical temperature of axially restrained steel columns. The imperfection of initial flexure of steel columns is taken into account in the model. The yielding of the edge fiber at the mid-span of a column subjected to elevated temperature is taken as the failure criteria for the fire resistance of the column. A numerical application is carried out to demonstrate the effect of the damage of fire protection on the ultimate load bearing capacity and axial force increase of axially restrained steel column in fire. Comparing with FEM, the model proposed in the paper has been validated and good agreement has been found.