Thin-walled Steel Members Research Articles

Theoretical calculation methods of stable bearing capacity for thin-walled shells with corrosion and variable temperature

AbstractThin-wall shells (steel plates, steel cylindrical shells, steel spherical shells, etc.) are widely used in many engineering fields such as construction, machinery, chemical industry, navigation, and aviation because of their light weight and high strength. Their failure modes under static pressure or impact dynamic load are mostly buckling instability, and the failure is very sudden, often causing structural failure or even catastrophic accidents without obvious symptoms. In this framework, the significance of this paper is that it considers the influence of external environment corrosion on steel shells' bearing capacity using plate and shell classical stability theory, and investigates the stable bearing capacity of thin-wall steel shells in view of corrosion impact. By this approach, a theoretical calculating method for the time-varying stable bearing capacity of plate and shell thin-walled steel members under the simultaneous action of corrosion and temperature changes is obtained, providing a useful theory for complex engineering practices such as corrosion and temperature changes, including fire actions. Noted that for this method with no analytical solution found, its numerical solutions are given in the appendixes.

Simulating the hysteretic behaviour of thin-walled H-Section steel members using the geometrically exact beam theory

Based on Gonçalves's geometrically exact beam theory considering cross-section deformation, the warping and distortional deformation of thin-walled members are described in this paper by means of a combination of section deformation modes. By integrating with the J2 elastic‒plasticity theory for the steel, a numerical model is established for the hysteretic behaviour of thin-walled steel members. Four classes of H-section members are selected on account of the design codes, and the influence of section warping and distortion deformation modes on the calculation of the hysteretic behaviour of components with different section types is analysed. The crucial aspect lies in the bending hysteresis behaviour around the strong and weak axes of the cross-section for H-beam steel members subjected to typical thin-walled members with relatively large widths and thicknesses. Test results on the hysteretic behaviour of H-section steel members are compared with those calculated from the proposed model in terms of the hysteric behaviour of components, strength degradation, energy-dissipating capacity, etc. These findings validate the correctness and feasibility of the established non-linear analysis model for thin-walled members.

Geometric Nonlinear Analysis of Angle Section Elements Based on Updated Lagrangian Formulation and Rigid Body Rule

Angle cross-section members are widely used in various transmission towers owing to their convenient connections, easy availability, simple production processes, and high efficiency. Such members are very susceptible to nonlinear behavior when subjected to abnormal or extreme loads. In this work, a new geometric stiffness matrix for thin-walled steel members with an angle cross-section is derived based on the principle of virtual displacement, rigid body rule and updated Lagrangian equations. The generalized displacement control (GDC) method is employed to deal with the issues of non-convergence at the extreme value point and rebound point in the geometric nonlinear analysis, which offers clear physical meaning and can adjust the loading direction. The geometric and the traditional elastic stiffness matrices derived in this work are applied during the prediction phase, while only the traditional elastic stiffness matrix is used in the correction phase. The comparisons of the results obtained by the proposed method with those in the previous literature and ANSYS numerical solutions show that the proposed method is sufficient to ensure the accuracy and applicability for addressing the structural geometrically nonlinear issues.

Rapid evaluation of lateral-torsional buckling of European standard I-section cantilevers

Lateral-torsional buckling (LTB) is the primary failure mode for thin-walled steel members where the cantilever beams experience nonuniform twisting and buckling about their weak axes. Much research exists in the literature, and modern codes have presented simple formulations for calculating of elastic LTB load of simply-supported beams. However, there are limited numbers of treatments for predicting of elastic LTB load of cantilevers, most of which are numerical, because as different from the simply supported beams, the LTB failure mode of the thin-walled cantilevers is much more complicated. The present study aims to develop a simplified equation for calculating the elastic LTB of the cantilevers with the European standard I-section. First, an analytical model considering first-order bending distribution, load height level, and monosymmetry property of the section has been introduced. Then, a simplified formula for cantilevers has been introduced utilizing the analytical model and two dimensionless coefficients called the slenderness and the load case parameters. The presented analytical solutions were verified with the finite element analysis (FEA), and the effects of slenderness and loading positions on the LTB behavior of cantilevers with European standard I-section have been investigated. It is found analytical solutions are quite compatible with FEA, and the proposed equation could be safely used for calculating the elastic LTB of the cantilevers.

Enhancements to the Direct Strength Method of cold-formed steel member design

The design of thin-walled cold-formed steel members must consider various forms of buckling. The Direct Strength Method simplifies strength prediction with a common approach utilizing adaptations of the Winter plate buckling formula. Recent modifications to the Direct Strength Method were developed for flexural members not symmetric about the axis of bending, which introduced a new general form to the direct strength equation. The versatility of this form provides one strength curve for the entire range of slenderness, including inelastic reserve strength. This new form was investigated for local and distortional buckling of compression members, members with holes, beam–columns, and beam–columns with holes. The proposed formulas for members without holes gave strength predictions nearly identical to the current AISI expressions. For members with holes, the proposed strength predictions were compared to test data and showed improvement over the current AISI expressions. Shear buckling strength was also investigated using the new direct strength equation form which gave equivalent predictions. Enhancement to the global buckling strength curve for flexural members was explored for alignment with column buckling and to facilitate further consistency for global buckling of beam–columns. The proposed enhancements provide improvements with a consistent set of simpler equations, advancing a new cleaner appearance to the Direct Strength Method.

Efficient stress integration algorithm of memory surface model with shrinking rule under plane stress field

Reliable nonlinear finite element analysis (FEA) of steel structures requires a constitutive model capable of predicting the cyclic plasticity of structural steels. Steel structure members are typically composed of multiple thin steel plates. The FEA of such structures has frequently used shell elements to capture the bending deformation and reduce the computational complexity, where its stress state can be regarded as the plane stress field. This study provides a constitutive model with a memory surface under a plane stress field for the cyclic plasticity of structural steels. A noble computationally efficient algorithm for stress integration and consistent tangent operator was proposed, where the constitutive equations were linearized after solving some unknown variables. The proposed model was implemented in the Abaqus FEA code. The residual-force convergence rate of the consistent tangent operator is investigated using a single-shell element under simple boundary conditions, where the consistent tangent operator achieves more than a quadratic convergence. The proposed model was validated by comparing the experimental results and FEA results with the proposed model for thin-walled steel members under cyclic loading. The average difference in peak forces between FEA and experimental results was 11.5 % for the local buckling tests and 8.4 % for the shear buckling tests at most. These results suggest that the proposed model provides an accurate prediction for other thin-walled steel structures under cyclic loading.

Influence of Adhesive Layer Thickness on the Effectiveness of Reinforcing Thin-Walled Steel Beams with CFRP Tapes-A Pilot Study.

When reinforcing thin-walled steel members with composite tapes, two issues often overlooked in published scientific papers should be considered, namely the correct thickness of the adhesive layer and the optimum bond length of the CFRP tape. In this article, the authors focused on the first of these issues. For this purpose, eight beams with a thin-walled box cross-section and a length of 3 m were subjected to bending in a four-point scheme. Six beams were reinforced with Sika CarboDur S512 composite tape, and two beams without reinforcement were tested as reference members. Three thicknesses of the adhesive layer (SikaDur-30) were analyzed: 0.6 mm, 1.3 mm and 1.75 mm. In addition to examining the effect of the thickness of the adhesive layer on displacements and deformations of thin-walled steel members, the load value at which the composite tape peeled off was also analyzed. Numerical analyses were then carried out in Abaqus, the outcomes of which showed good agreement with the laboratory results. Both numerical and laboratory results have shown that the thickness of the adhesive layer had a minor effect on the reduction in deformation and displacement of the tested beams. At the same time, with the increase in the thickness of the adhesive layer, the value of the load at which the CFRP tapes detached from the beam surface significantly decreased.

An assessment of different direct strength methods for cold-formed thin-walled steel beam-columns under compression and major axis bending

This paper assesses a number of direct strength methods (DSM) for thin-walled steel members under combined major axis bending and compression. These methods consist of two ways of calculating the compression – bending moment (P-M) interaction surface (plastic or first yield) of the cross-section, and the following three methods of operating on the P-M surface: using a compound value of the surface; converting a beam-column to an equivalent beam; and converting a beam-column to an equivalent column. The aim of this research is to identify the most consistently accurate and easy to implement DSM equations to calculate the resistance of thin-walled steel beam-column members, by comparison against numerical simulation results, obtained using a validated ABAQUS model. The numerical simulations investigated the effects of changing different design parameters to ensure a sufficient dataset for each failure mode, including section size, member length, flange restraint, load eccentricity and yield strength. Based on an evaluation of the mean and standard deviation of ratios of the calculated resistances to ABAQUS simulation results, it has been found that for global buckling, any of the methods can produce accurate results. For local buckling, the standard deviation values for all the methods are similar, about 0.05. However, when judging the mean values, the best methods are the equivalent beam method using plastic P-M surface, with a mean value of 0.995. For distortional buckling, upon modification of the existing DSM equations for pure bending using the plastic P-M surface, the equivalent beam method gave an average of 0.998 and a standard deviation of 0.102. Overall, the equivalent beam method using the plastic P-M surface is the most consistently accurate method.

Ultimate and post-ultimate behaviour of thin-walled cold-formed steel open-section members under eccentric compression. Part I: Collapse mechanisms database (theoretical study)

The paper investigates the possibility to use the local plastic mechanisms to characterize the ultimate strength of short thin-walled cold-formed steel members subjected to eccentric compression and presents a database of local plastic mechanisms of failure for lipped channel section columns subjected to eccentric compression about minor axis. The background of yield line analysis related to thin-walled steel members is presented. Also, the buckling behaviour of examined members is briefly discussed. The geometries of the theoretical models of local plastic mechanisms for those members, for a wide range of applied eccentricities, are presented in detail. Comparative diagrams of equilibrium paths obtained from FE simulations together with post-ultimate curves derived via yield line analysis are shown based on developed mechanisms models. At the end, some conclusions concerning the applicability of presented mechanisms models for determination of load-carrying capacity of structures under investigation are derived.

Local-distortional and Overall Interactive Buckling of Unstiffened Open Cross-section Thin-walled Steel Members

The difference between local and distortional buckling of thin-walled cold-formed steel sections with stiffened elements, of both compression and bending members are take-in-to consideration applying relevant design formulas available in the codes. However, for unstiffened elements or for those not stiffened enough, the difference between distortional and local buckling modes is quite confusing.

A simplified method for calculating non-uniform temperature distributions in thin-walled steel members protected by intumescent coatings under localized fires

This paper presents a method to calculate the non-uniform temperature field of steel members protected by intumescent coatings under localized fires. In this proposed method, the steel member is divided into a number of segments along the length according to the localized fire temperature field, and each segment divided into plate elements with different surrounding fire temperatures. The temperature of each plate element is assumed uniform and is calculated by the lumped mass equation with the thermal conductivity of intumescent coatings approximated using a three-stage thermal conductivity model. Heat conduction between different steel plate elements is ignored. Comparisons of steel temperature results between measured results and the proposed simplified temperature calculation method show very good agreement in temperature distributions along the steel member length, in the cross-section and detailed temperature–time relations at critical and high temperature locations, with differences in calculated and measured average temperatures in different segments being less than 7.2 %. Comparisons of load carrying capacities of axially-loaded steel members using measured temperature distributions and calculated temperature distributions show small (<6%) differences.

Direct strength method for cold-formed steel beams with non-uniform temperatures

This paper presents the results of finite-element simulations leading to the development of a design method using the direct strength method (DSM) for transversely loaded thin-walled steel beams prone to local and distortional buckling failures at elevated temperatures. The systematic and extensive numerical parametric study covers different dimensions of thin-walled steel sections, different temperature distributions in the steel cross-section, different steel grades and different load ratios. The main findings are that DSM is a suitable method for thin-walled steel members with non-uniform elevated temperature distributions in the cross-section. Based on using the plastic moment capacity of the cross-section at elevated temperatures, the DSM equations in the existing specification by the American Iron and Steel Institute, as published in 2016, are sufficiently accurate for local buckling. For distortional buckling, a set of new DSM equations is proposed. The proposed DSM equations are then used to derive partial safety factors for structural resistance for conditional probabilities of structural failure of 0.1, 0.01 and 0.001 after flashover.

Study of post-fire mechanical properties of the light composite slabs after suffering hydrocarbon fire

The post-fire mechanical behaviours of the composite floors consisting of lightweight aggregate concrete and thin-walled steel members were experimentally studied, and the test result of the composite floor specimens was discussed. The experimental results showed that the residual load-bearing capacity of the composite slabs after suffering hydrocarbon fire can be effectively improved by increasing the wall thickness of transverse sub-members appropriately. The ultimate load of the composite slab specimens after fire with using the commonly used stud shearing connectors was larger than that with using the shear keys made with thin-walled steel plate.

Study of post-fire mechanical behaviours of the light prefabricated composite floors after fire

The post-fire mechanical properties of a prefabricated composite slabs consisting of thin-walled steel members and lightweight aggregate concrete was experimentally studied, and the displacements of the composite floor specimens was discussed. The experimental results showed that the ultimate load of the composite slab specimens after fire with using the stud shearing connectors was greater than that with using the new type shear keys made with thin-walled steel plate. The global stiffness and load-bearing capacity of the composite slabs after suffering hydrocarbon fire can be effectively improved by increasing the wall thickness of transverse sub-members appropriately.

Imperfection sensitivity analysis and DSM design of web-stiffened lipped channel columns experiencing local-distortional interaction

Cold-formed thin-walled steel members are commonly subjected to initial imperfection, which will greatly affect their load-carrying capacity. In this study, the load-carrying capacity and imperfection sensitivity of fixed-ended cold-formed steel web-stiffened lipped channel columns subjected to local-distortional (L-D) interactive failure (including secondary local bifurcation interaction (SLI), true L-D interaction (TI) and secondary distortional bifurcation interaction (SDI)) are investigated. A new imperfection simulation method combining finite element analysis (FEA) with the constrained finite strip method (cFSM) was firstly proposed, and then validated using experimental data from literatures. Next, 224 geometries of columns experiencing L-D interactive failure were chosen by the cFSM and their load-carrying capacity under normal state P num (with unavoidable minor initial imperfection) and those under imperfect state P imperfect (with various imperfections) were respectively obtained using FEA. The most unfavorable imperfection patterns for L-D interactive failure were summarized by comparing the P imperfect and P num of the members. Furthermore, the quality of the DSM-based design approaches for L-D interactive failure were evaluated by comparing P num with the failure load predictions of the selected columns provided by these design approaches. • An imperfection simulation method that combined FEM and constrained FSM was proposed. • The effects of imperfections on the thin-walled columns affected by L-D interaction were studied. • The accuracy and applicability of design approaches based on DSM were evaluated.

Experimental and numerical evaluation of inelastic lateral-torsional buckling of I-section cantilevers

A primary failure mode for thin-walled steel members is lateral-torsional buckling (LTB), in which steel cantilever beams experience nonuniform twisting and buckling about their weak axes. Analytical and numerical studies related to the elastic LTB of cantilevers abound. However, comprehensive analytical and experimental studies focusing on the inelastic LTB behaviour of cantilevers are rare. Therefore, this study intends to establish a numerical procedure verified with experimental results to evaluate the inelastic LTB strength of steel cantilevers with an I-section. First, an experimental study was performed, in which nine steel cantilever beams with different slenderness and load-height levels were tested. Load–displacement behaviours of steel cantilevers were investigated by measuring lateral and vertical displacements and rotations under the effect of a monotonic end-point load. Subsequently, a two-step numerical procedure is introduced. The elastic LTB loads and the related mode-shapes were determined in the first step, and the nonlinear load-deflection behaviours were evaluated in the second step based on the Riks method. Finally, numerical and experimental results were compared, thereby demonstrating that the presented numerical analysis can be used for predicting the buckling loads, vertical displacements, and torsional rotations at an acceptable level in the design stage.

Controlling Measure for Distortional Buckling of Cold-formed Thin-walled Steel Lipped Channel Members

This paper proposed a structural measure according to add batten sheets between two lips to controlling distortional buckling of cold-formed thin-walled steel members with lipped channel section, and the effectiveness was verified through existing tests. At the same time, the stiffness requirements of batten sheets were presented. The structural measures of adding batten sheets between two lips can effectively prevent the rotation of partially stiffened elements, and the distortional buckling load and bearing capacity of the members have been greatly improved. The test shows that the batten sheets with a certain distance and stiffness can improve the bearing capacity of the member or avoid the occurrence of distortional buckling.

Behavior of thin-walled beam-column modular connection subject to bending load

Abstract Steel modular construction has the potential to meet the growing infrastructure needs of the big cities and hence, the demand for modular construction is on the rise. This paper introduces a unique and innovative modular construction technique which involves the use of thin-walled hollow structural steel members and a state-of-the-art cast-steel connector, namely VectorBloc connector. The performance of the beam-column connections to be used in this modular construction largely determines its performance and success. In the present study, uniaxial and biaxial bending behavior of a typical corner beam-column connection made of thin-walled hollow structural steel members and VectorBloc connector was studied through full-scale tests and nonlinear finite element method. This beam-column connection will be used for constructing an assisted living facility. This study concludes that the design loads of the proposed assisted living facility can be safely carried by the VectorBloc connection. However, the weight of the VectorBloc connector can be reduced to 80% without compromising the design requirements of the assisted living facility. This study also concludes that the VectorBloc connection can be considered as a rigid connection. However, effective bracings against horizontal displacements must be provided in the structure in which the connection is intended to be used.

On Problem of Torsional Characteristics of Thin-walled Steel Beams with Web Openings

The current trend in the design of steel structures leads, due to the saving of the material, to the frequent use of thin-walled cold formed steel sections. The thin-walled cold-formed steel profiles are often manufactured with web holes. In the design of such a thin-walled steel members with web openings arises a question of correct determination of the real crosssectional properties. This paper focuses on the problem of the real torsional characteristics determination, which are parameters needed for the design of members subjected to the bending with respect to lateral torsional buckling or for the design of the compressed members prone to torsional buckling or flexural torsional buckling. These torsional characteristics include St. Venant torsion constant and warping constant. In the forthcoming European Standard specifying the rules for the design of beams with holes, it is recommended to use the cross-sectional characteristics of the most weakened section of the member with web openings. This paper deals with the possibility of introduction of “substitute cross-section” whose cross-sectional characteristics are determined as the weighted average of the properties of full section and the most weakened section. The solution with substitute cross-section is validated by the series of tests focusing on the experimental verification of the both real torsional stiffness –- St. Venant torsion stiffness and warping torsion stiffness. Based on the results of test series with twisted beams freely supported in torsion, the St. Venant torsion constant is being derived, respectively from the results of the test series with twisted beams fixed in torsion (the warping is restrained at both beam ends), the warping constant is being derived. Both torsional characteristics are verified by tests executed on three different lengths (L=2.0m, L=3.0m and L=4.0m) of beams with sigma cross-section with large circular web openings.

Branch-switching procedure for post-buckling analysis of thin-walled steel members at elevated temperature

The paper investigates the effects of the geometrical imperfections in buckling analyses of plated steel elements at elevated temperatures and provides an alternative branch-switching procedure to perform post-buckling analyses without introducing initial imperfections into the model. This procedure is appealing since the choice of appropriate imperfections in classical analyses is not straightforward, above all at elevated temperature. Several numerical analyses show that the choice of the imperfections is not trivial and that the buckling mode may vary with temperature. They also show that the proposed branch-switching procedure is an interesting preliminary tool to understand the instability behaviour of steel structural members.