Steel I-section Research Articles

Design recommendations for stainless steel I-sections under concentrated transverse loading

Recent investigations have highlighted the need for improved provisions for determining the resistance of stainless steel I-sections under concentrated transverse loading. Such provisions, which reflect the particular characteristics of the material, have been developed and are described herein. A review of the existing European design formulae for members under concentrated transverse loading is firstly presented. Then a series of parametric studies, based on validated finite element models are described covering I-sections with a range of web slenderness values and different stainless steel grades. On the basis of the numerical results, together with existing experimental data, revised design equations are presented and assessed through reliability analysis performed in accordance with Annex D of EN 1990. The new provisions yield enhanced ultimate load predictions and are expected to be included in the next revision of EN 1993-1-4.

Out-Of-Plane Buckling of Steel I-Section Circular Arches

Circular arches subjected to in plane loading are restrained with discrete lateral bracing to improve their out of plane stabilities in many cases. The arch segment between two adjacent bracing may buckle out of plane if the effective length of the arch segment is sufficiently large. But replacing the flat web with corrugated web will increase the out of plane stability of the circular arches. This paper investigates the out of plane elastic buckling of steel I-section circular arches with flat web and sinusoidal corrugated web. This study considers pin-ended and fixed circular steel arches with a sinusoidal corrugated web under a uniform radial load or uniform vertical load to elucidate numerically their different failure modes. Arches subjected to in-plane loading may suddenly deflect laterally and twist out of loading plane and fail in an out-of-plane elastic buckling mode.

Web compression buckling capacity prediction for unstiffened I-sections with opposite patch loading

Two web compression buckling capacity prediction methods are introduced for unstiffened steel I-sections subject to opposite patch loading applied to the flanges. The methods are generally posed as a function of loaded width to web depth ratio, and are applicable for opposite patch loading applied at the interior of a wide flange section or at the end of it, where the web has a free edge. The proposed methods include three parts: 1) an expression for predicting the squash load, 2) an expression for predicting the elastic buckling load, and 3) a resistance function. The squash load is calculated using an empirically derived effective width concept based on observations at the ultimate load from an extensive experimental database and validated numerical simulations. Web slenderness is defined as the square root of the ratio of the web squash load to the web critical elastic buckling load. The critical elastic buckling load is defined consistently with that obtained with a plate buckling energy solution for patch loading on infinitely long strips and considers the shortened web buckling half-wavelength resulting from flange rotational restraint provided to the web. The methods are validated with existing experimental data and shell finite element collapse simulations, and are shown to be more accurate and more widely applicable than current American Institute for Steel Construction (AISC) Specification provisions.

Experimental study for strengthening octagonal castellated steel beams using circular and octagonal ring stiffeners

Castellated beams made by cutting web of hot rolled steel I-section in particular zigzag pattern and recollecting the two parts by welding, to form a castellated beam with hexagonal openings, or more increasing of section depth by placing expansion plates between these parts to fabricate castellated beam with octagonal openings. The main advantage of fabrication this type of beam is increasing section depth, which leads to improve its behavior compared with original beam. So as to use the castellated beams with expansion plates into its best advantages, the failure modes due to web opening need to be avoided. This paper aims to provide added strength of castellated beams with expansion plates by using two types of stiffeners (circular and octagonal ring) around octagonal web opening. This strengthening technique was suggested to reinforce web portion and avoid failure due to web-post buckling. Standard (IPE140) were chosen as a parent section for fabricating four specimens as well as original beam. The important observation through this study is that using ring stiffener leads to have significant effect on ultimate strength. In case of using circular ring stiffeners, the ultimate strength was increased up to (188%) compare with original beam. Whereas the increment in ultimate load at using octagonal ring stiffeners was reach to about (77.6%). Consequent, using circular ring stiffeners to reinforced this type of beams was more efficient than using octagonal ring stiffeners. It is worthwhile to mention that it can be used (37%) as additional steel material (Expansion plates and ring stiffeners) for increasing the load capacity of castellated beams up to (288%) relative to original beam.

Evaluating long-duration blast loads on steel columns using computational fluid dynamics

Long-duration blasts are typically defined by positive pressure durations exceeding 100 ms. Such blasts can generate dynamic pressures (blast winds) capable of exerting damaging drag loads on comparatively slender structural components such as columns. With limited drag coefficient availability for specific structural geometries, Computational Fluid Dynamics (CFD) can be the only satisfactory approach for analysing blast loading on user-specified, finite geometries. The ability to analyse long-duration blasts with commercially available CFD programmes is still not confidently offered, with no prior studies examining the accuracy of modelling interaction with relatively much smaller, finite geometries. This paper presents a comparative investigation between numerical and experimental results to assess the predictive capacity of inviscid Eulerian CFD as a method for calculating long-duration blast drag loading on finite cross-sectional geometries. Full-scale long-duration blast experiments successfully measured surface pressure–time histories on a steel I-section column aligned at four orientations. Calculated pressure–time histories on exposed geometry surfaces demonstrated good agreement although reduced accuracy and under-prediction occurred on shielded surfaces manifesting as overestimated net loading. This study provides new understanding and awareness of the numerical capability and limitations of using CFD to calculate long-duration blast loads on intricate geometries.

An assessment of the lateral-torsional buckling and post-buckling behaviour of steel I-section beams using a geometrically exact beam finite element

The goal of this paper is twofold. The first goal is to show that geometrically exact beam finite elements can be successfully employed to determine, accurately, the behaviour of steel I-section beams undergoing large displacements and finite rotations. For this purpose, a two-node geometrically exact beam element is presented and validated, which can handle arbitrary initial configurations (e.g. curved configurations), plasticity, geometric imperfections and residual stresses. The second goal is to employ the proposed element to assess the behaviour of I-section beams undergoing lateral-torsional buckling. In particular, the element is used to determine (i) elastic non-linear bifurcation loads (i.e., bifurcation loads accounting for pre-buckling deflections), (ii) large displacement elastic post-buckling paths including geometric imperfection effects and (iii) large displacement elastoplastic equilibrium paths accounting for geometric imperfections and residual stresses. Three support/loading cases are examined, namely: (i) simply supported beams under uniform moment, (ii) simply supported beams subjected to a mid-span vertical force and (iii) cantilevers subjected to a free end vertical force. Besides I-sections with standard height-to-width ratios, wider flange sections are also considered and it is demonstrated that, for the latter, the post-buckling behaviour is quite different from that of standard sections and an increase in the load carrying capacity is observed, which is not predicted by the current Eurocode 3 [1] provisions. Based on the results obtained, a set of relevant conclusions are drawn.

Weak axis response of steel I-sections subjected to close-in detonations

The response of I-shaped, or wide-flange, sections subjected to close-in detonations has been evaluated through numerical simulations. A simulation approach for close-in detonation, which includes two stages, is suggested. The first stage includes the modelling of the detonation process through computational fluid dynamics (CFD) and the second stage includes only the free vibrations of the structural member. The suggested approach is validated by a comparison with two experimental results for close-in detonations. Then, a parametric study for I-sections with their weak axis subjected to close-in detonations has been performed. Various spherical charges and standoff distances have been studied, with scaled distances in the range of 0.15–0.29 m/kg1/3. Bare members and members strengthened with stiffeners have been simulated. The influence of charge and standoff distance, and the addition of stiffeners on several parameters affecting deformation and folding angles, has been studied. The effect of localized pressure confined between the flanges and the stiffeners at the midspan, which can lead to increased total and local deformations, is illustrated. Finally, an alternative strengthening method, in which the flanges are connected with bars, is presented as an optional stiffening technique.

Formulae for determining elastic local buckling half-wavelengths of structural steel cross-sections

Formulae for determining elastic local buckling half-wavelengths of structural steel I-sections and box sections under compression, bending and combined loading are presented. Knowledge of local buckling half-wavelengths is useful for the direct definition of geometric imperfections in analytical and numerical models, as well as in a recently developed strain-based advanced analysis and design approach (Gardner et al., 2019a, 2019b). The underlying concept is that the cross-section local buckling response is bound by the theoretical behaviour of the isolated cross-section plates with simply-supported and fixed boundary conditions along their adjoined edges. At the isolated plate level, expressions for the half-wavelength buckling coefficient kLb, which defines the local buckling half-wavelength of a plate as a multiple of its width b, taking into account the effects of the boundary conditions and applied loading, have been developed based on the results of finite strip analysis. At the cross-sectional level, element interaction is accounted for through an interaction coefficient ζ that ranges between 0 and 1, corresponding to the upper (simply-supported) and lower (fixed) bound half-wavelength envelopes of the isolated cross-section plates. The predicted half-wavelengths have been compared against numerical values obtained from finite strip analyses performed on a range of standard European and American hot-rolled I-sections and square/rectangular hollow sections (SHS/RHS), as well as additional welded profiles. The proposed approach is shown to predict the cross-section local buckling half-wavelengths consistently to within 10% of the numerical results.

Numerical study of full-scale CFRP strengthened open-section steel columns under transverse impact

In recent years, externally bonded fibre reinforced polymer (FRP) material has gained popularity as an efficient means of strengthening existing civil engineering infrastructure. In the case of steel structures, FRP has frequently been deployed to strengthen against static and fatigue loads. However, the understanding of the effect of impact load on strengthened structures is still in its early stages. In parallel with this, most of the existing studies on impact have concentrated on small scale elements. Thus, the study presented here is aimed at examining the effectiveness of carbon fibre reinforced polymer (CFRP) in strengthening full-scale steel I-section columns against impact load. To achieve this aim, a non-linear finite element model built using ABAQUS was validated against experimental tests and then used to simulate the strengthening technique. The model included failure criteria of all investigated materials (steel, CFRP and adhesive material). Various parameters including boundary conditions, preloading level, kinetic energy, impact location and impact direction were examined. The CFRP strengthening technique was found to be highly effective in preventing column failure whether by global buckling failure or transverse shear failure. In addition the strengthened columns exhibited a reduced axial and transverse displacement by more than 70% in many cases.

Testing and numerical analysis of stainless steel I-sections under concentrated end-one-flange loading

A comprehensive investigation into the structural behaviour of austenitic stainless steel welded I-section beams under concentrated transverse end-one-flange loading is reported herein. Ten physical experiments are first described. The experimental results are then presented in terms of the full load-web shortening responses, ultimate loads, out-of-plane deformation fields and failure modes. An extensive finite element modelling study accounting for geometric, material and contact non-linearities was also performed. After successful model validation against the test results, a parametric investigation was conducted considering a range of bearing lengths, different distances of the bearing load to the member end and web slenderness values. The combined experimental and numerical data set was used to assess current European and North American design provisions for the resistance of stainless steel welded I-sections to concentrated end-one-flange loading. The results show that the current design formulae generally lead to safe-sided but rather scattered and conservative capacity predictions with considerable scope for the development of improved design formulae.

Strength optimization of structural elements by means of optimal control

This paper investigates the optimal shaping of the web height of an I-section steel portal frame. The problem is formulated as a control theory task. From a mathematical perspective, the task involves solving the multipoint boundary value problem for the system of forty-three differential equations. The solution is compared to results obtained from the finite element software Abaqus.

Ultimate strength capacity of composite self-compacting castellated steel beams

Castellated steel profile sections can be used in order to increase the flexure strength of composite concrete-steel beams for building large spans. Castellated beams are fabricated by cutting I-section steel girders in a special manner before welding to produce an opening throughout the web. The depth of the new section is enhanced by a specific percentage, which increases the performance of the beam against bending. Castellated beams can be used compositely in long span floors where floor beam heights are kept to a minimum by passing services through the web-openings. This paper will focus on the composite behaviour of specimens in two types of concrete with different strengths. The ultimate strength for these types of structures with different degrees of castellation will be considered. The study consisted of two parts: the first part tested six specimens using push out test specimens to understand the real behaviour of their shear connectors. The second part tested eight specimens under a third point static load. Three of the push out test specimens were of normal concrete, and the others were self-compacting concrete.Four of the composite beam specimens were normal concrete slabs, while the other four specimens were made from self-compacting concrete. The experimental programme also included fabrication of I-section steel beams with different castellation degrees of 0%, 25%, 33.8%, and 50%. The effects of concrete type and degree of were thus studied. It was found that the maximum load capacity was significantly affected by these parameters such that it was increased with both the increase of compressive strength of the concrete and the degree of castellation. The push out test showed that the slip behaviour was linear below 70 to 80% of the ultimate load capacity. At this linear stage, the amount of slip is very low and rarely exceeds 0.5 mm.

Laser-welded stainless steel I-section beam-columns: Testing, simulation and design

The stability and design of laser-welded stainless steel I-section beam-columns are explored in this study. Owing to the high precision and low heat input of laser-welding, structural cross-sections produced using this fabrication method have smaller heat affected zones, lower thermal distortions and lower residual stresses than would typically arise from traditional welding processes. Eighteen laser-welded stainless steel beam-columns were tested to investigate the member buckling behaviour under combined compression and bending. Two I-section sizes were considered in the tests: I-50 × 50 × 4 × 4 in grade EN 1.4301 and I-102 × 68 × 5 × 5 in grade EN 1.4571 austenitic stainless steel. The two cases of minor axis bending plus compression and major axis bending plus compression with lateral restraints were investigated. The initial loading eccentricities in the beam-column tests were varied to provide a wide range of bending moment-to-axial load ratios. The test results obtained herein and from a previous experimental study were used to validate finite element (FE) models, which were subsequently employed for parametric investigations to generate further structural performance data over a wider range of cross-section sizes, member lengths and loading combinations. The obtained test and FE results were utilized to evaluate the accuracy of the beam-column capacity predictions according to the current European and North American design provisions and a recent proposal by Greiner and Kettler. Finally, an improved approach for the design of stainless steel I-section beam-columns is proposed.

Long-duration blast loading & response of steel column sections at different angles of incidence

This paper reports experimental results pertaining to the effects of planar long-duration blast waves interacting with steel I-section column elements about different angles of incidence. Long-duration blast waves are typically defined by a positive pressure phase duration in excess of 100 ms, characteristic of very large explosion events such as industrial accidents. Blasts of this magnitude result in large impulses and dynamic pressures with the potential to exert high drag forces on column elements within an open frame structure. Due to relatively small dimensions in comparison to the blast wavelength, individual column elements are predominantly subjected to translational drag loading. Blast drag loading is complex to characterise, generally requiring approximation using drag coefficients, although proposed values in literature display inconsistency and typically lack provision for multi-axis interaction with I-shape geometries. Four full-scale long-duration experiments investigated blast interaction and elastic structural response of two steel I-section columns as a function of orientation to the incident shock wave. Drag coefficients were calculated as a function of I-section orientation using experimental pressure data and compared to values proposed in literature. It was found that drag coefficients proposed in literature have the potential to under-predict drag loading for certain oblique I-section orientations examined in these experiments. Importantly, intermediate oblique I-section orientations recorded higher loading and exhibited higher drag coefficients compared to orthogonal orientations, resulting in larger structural elastic response. Results from this experimental work have confirmed that I-section columns are axis-sensitive to blast wave direction giving rise to varying magnitudes of drag loading and structural response.

Validation of a general design procedure for the transverse impact capacity of steel columns

There has been considerable interest over the past decade in the transverse impact response of steel columns and composite steel-concrete columns. While several researchers have developed analytical procedures for specific types of steel sections, a unified design approach has yet to be established. The present paper develops a generalised rigid-plastic procedure to calculate the design transverse impact capacity for a wide range of steel and composite column sections. The design procedure is specifically developed to align with current international hot-rolled steel design specifications, including those in Australia, North America, the European Union and China. A database of 320 impact experiments is collated from the literature, and used to validate the general design procedure. It is demonstrated that the procedure provides robust transverse impact capacity predictions for solid rectangular steel sections, steel I-sections, circular and rectangular steel hollow sections, concrete filled circular and rectangular steel hollow sections and concrete filled double skin steel hollow sections. In some cases stainless steel members were additionally included.

Experimental and numerical study of stainless steel I-sections under concentrated internal one-flange and internal two-flange loading

The behaviour and design of stainless steel I-section beams under concentrated transverse loading are investigated in this study. Twenty-four experiments on stainless steel I-sections, formed by the welding of hot-rolled plates, were performed. The tests were conducted under two types of concentrated transverse loading – internal one-flange (IOF) and internal two-flange (ITF) loading. The experimental set-up, procedure and results, including the full load-displacement histories, ultimate loads and failure modes, are reported. A complementary nonlinear finite element modelling study was also carried out. The models were first validated against the results of the experiments. A parametric investigation into the influence of key parameters such as the bearing length, web slenderness and level of coexistent bending moment, on the structural response was then performed. Finally, an assessment of current design provisions for the resistance of stainless steel welded I-sections to concentrated loading is presented. The results show that the current design formulae yield safe-sided, but generally rather scattered and conservative capacity predictions, with considerable scope for further development.

Buckling Resistance Criteria of Prismatic Beams Under Biaxial Moment Gradient

Laterally and torsionally unrestrained steel I-section beams are susceptible to torsional deformations between supports; therefore, according to Part 1-1 of Eurocode 3, they need to be designed to resist lateral-torsional buckling. Eurocode’s steelwork design criteria require safety checking based on two stability interaction formulae utilizing the so-called equivalent uniform moment factors and the cross-section resistance formula that, in the case of moment gradient, refer to the beam end section. Uncoupling the beam stability resistance criterion and the cross-section resistance criterion may result in a nonuniform safety assessment of I-section beams. Finite element simulations of the beam resistance for different moment gradient ratios are performed. Verification of the buckling resistance is conducted by varying the following parameters: the slenderness ratio, the location of maximum end moments about both axes and the section depth-to-width ratio (i.e., considering rolled I- and H-sections). The variation in the accuracy of the current Eurocode resistance evaluation method is identified, and an approach for a better equalization of the safety predictions is suggested by considering different values of the most important factors influencing the stability performance of steel I-section beams.

Mechanism analysis of steel frames considering moment–shear interaction

Considering the interaction of flexural moment and shear force in the steel frames with haunch or intermediate beam length and eccentrically braced frames with intermediate link length is a major concern of the structural analysis and design. This article contains two stages. In the first stage, to investigate the moment–shear interaction for the highly ductile steel I-sections, a study is carried out using finite element analysis and a simple and practical relationship is developed. In the second stage, a simple approach based on virtual work method for assemblage of interconnected rigid bodies is employed to consider collapse mechanisms with mixed hinges. Using this approach, the applicability of the proposed relationship is demonstrated for a one-bay portal frame by considering all possible collapse mechanisms including those containing mixed hinges. Some numerical examples are presented using the proposed approach. Results indicate that, in general, the effect of moment–shear interaction on the load capacity of the structures cannot be ignored, and the capacity could be estimated, without using step-by-step analysis. Finally, by satisfying kinematic compatibility requirements and normality condition, simplified relations are derived to estimate post-mechanism deformations of plastic hinges for a prescribed lateral drift.

The continuous strength method for lateral-torsional buckling of stainless steel I-beams

Stainless steel is now widely used in construction as structural members in recognition to its unique beneficial properties such as corrosion resistance, higher strength, ductility, and negligible maintenance cost. Recent research on stainless steel has led to the evolution of a deformation based design rule, the Continuous Strength Method (CSM), which has been shown to perform well in predicting cross-sectional resistances but still requires considerable research to be used in predicting member resistances. The current paper proposes a new design method for lateral-torsional buckling (LTB) behaviour of welded stainless steel I-sections combining CSM design philosophy and traditional Perry-type concept used for column buckling. As part of the numerical study presented herein, nonlinear finite element (FE) models were developed and validated using available test results. Once the FE modelling technique was validated, a large number of reliable numerical results were generated to investigate effects of various factors on the resistance of members subjected to LTB. Obtained results showed that the cross-section slenderness λ¯p and the non-dimensional proof stress e have significant influences on LTB resistance. Effects of e was appropriately incorporated by introducing a correction factor to modify λ¯p. As LTB curves were mostly affected by λ¯p, it was included in the equation for calculating imperfection parameter ηcsm,LT, which is a key parameter to include member imperfections in Perry-type design equations. This new approach ensures appropriate utilization of strain hardening for stocky cross-sections and allows to avoid the complex process of calculating effective geometric properties for slender sections. All available test and generated numerical results were used to assess the performance the current European, the Australian and the proposed CSM based design rules for LTB. Comparisons clearly showed that the proposed approach performed significantly well in predicting the LTB response of stainless steel I-sections.

Ultimate capacity of I-sections under combined loading – Part 2: Parametric studies and CSM design

The second part of the study on the ultimate capacity of hot-rolled steel I-sections under combined compression and bending moment, focussing on parametric studies and design, is presented herein. An extensive numerical parametric study was carried out, using the verified finite element (FE) models from the companion paper, to generate further structural performance data for specimens with different steel grades, cross-section slendernesses and loading cases. The numerical results together with the experimental results were then used to assess the accuracy of two codified design methods: the European Standard EN 1993-1-1 (2005) and the American Specification AISC-360-16 (2016). The design strengths predicted by the current design standards were found to be generally rather conservative and scattered when applied to non-slender cross-sections, owing principally to the neglect of material strain hardening and reserve capacities between the classification limits. To improve the accuracy and efficiency of the design rules, the continuous strength method (CSM) – a deformation-based design approach which relates the resistance of a cross-section to its deformation capacity – was extended to cover the design of hot-rolled steel I-sections under combined loading, underpinned by both the experimentally and numerically derived ultimate capacities. Overall, the CSM was shown to offer more accurate and consistent predictions than the current design provisions. Finally, reliability analysis was performed to evaluate the reliability level of the design rules.