The main aim of the study is an assessment of models suitability for steel beams made of thin-walled cold-formed sigma profiles with respect to different numerical descriptions used in buckling analysis. The analyses are carried out for the sigma profile beam with the height of 140 mm and the span of 2.20 m. The Finite Element (FE) numerical models are developed in the Abaqus program. The boundary conditions are introduced in the formof the so-called fork support with the use of displacement limitations. The beams are discretized using S4R shell finite elements with S4R linear and S8R quadratic shape functions. Local and global instability behaviour is investigated using linear buckling analysis and the models are verified by the comparison with theoretical critical bending moment obtained from the analytical formulae based on the Vlasow beam theory of the thin-walled elements. In addition, the engineering analysis of buckling is carried out for a simple shell (plate) model of the separated cross-section flange wall using the Boundary Element Method (BEM). Special attention was paid to critical bending moment calculated on the basis of the Vlasov beam theory, which does not take into account the loss of local stability or contour deformation. Numerical shell FE models are investigated, which enable a multimodal buckling analysis taking into account interactive buckling. The eigenvalues and shape of first three buckling modes for selected numerical models are calculated but the values of critical bending moments are identified basing on the eigenvalue obtained for the first buckling mode.

Elastic lateral-torsional buckling of double-tee section structural steelworks has been widely investigated with regard to the major axis bending of single structural elements as a result of certain loading conditions. No specific attention has been paid to the general formulation in which an arbitrary span load pattern was associated with unequal end moments as a result of the moment distribution between structural members of the load bearing system.Anumber of analytical solutionswere developed on the basis of the Vlasov theory of thin-walled members. Since the accurate closed-form solutions of lateral-torsional buckling (LTB) of beams may only be obtained for simple loading and boundary conditions, more complex situations are treated nowadays by using numerical finite element methods (FEM). Analytical and numerical methods are frequently combined for the purpose of: a) verification of approximate analytical formulae or b) presentation the results in the form of multiple curve nomograms to be used in design practice. Investigations presented in this paper deal with the energy method applied to LTB of any complex loading condition of elements of simple end boundary conditions, bent about the major axis. Firstly, a brief summary of the second-order based energy equation dealt with in this paper is presented and followed by its approximate solution using the so-called refined energy method that in the case of LTB coincides with the Timoshenko’s energy refinement. As a result, the LTB energy equation shape functions of twist rotation and minor axis displacement are chosen such that they cover both the symmetric and antisymmetric lateral-torsional buckling modes. The latter modes are chosen in relation to two lowest LTB eigenmodes of beams under uniform major axis bending. Finally, the explicit form of the general solution is presented as being dependent upon the dimensionless bending moment equations for symmetric and antisymmetric components, and the in-span loads. Solutions based on the present investigations are compared for selected loading conditions with those obtained in the previous studies and verified with use of the LTBeam software. Conclusions are drawn with regard to the application of obtained closed-form solutions in engineering practice.

This paper reports an experimental on the flexural performance of prestressed concrete-encased high-strength steel beams (PCEHSSBs). To study the applicability of high-strength steel (HSS) in prestressed concrete-encased steel beams (PCESBs), one simply supported prestressed concrete-encased ordinarystrength steel beam (PCEOSSB) and eight simply supported PCEHSSBs were tested under a four-point bending load. The influence of steel strength grade, I-steel ratio, reinforcement ratio and stirrup ratio on the flexural performance of such members was investigated. The test results show that increasing the I-steel grade and I-steel ratio can significantly improve the bearing capacity of PCESB. Increasing the compressive reinforcement ratio of PCEHSSB can effectively improve its bearing capacity and ductility properties, making full use of the performance of HSS in composite beams. Increasing the hoop ratio has a small improvement on the load capacity of the test beams; setting up shear connectors can improve the ductile properties of the specimens although it does not lead to a significant increase in the load capacity of the combined beams. Then, combined with the test data, the comprehensive reinforcement index considering the location of reinforcement was proposed to evaluate the crack resistance of specimens. The relationship between the comprehensive reinforcement index and the crack resistance of specimens was given.

In investigations constituting Part I of this paper, the effect of approximations in the flexural-torsional buckling analysis of beam-columns was studied. The starting point was the formulation of displacement field relationships built straightforward in the deflected configuration. It was shown that the second-order rotation matrix obtained with keeping the trigonometric functions of the mean twist rotation was sufficiently accurate for the flexural-torsional stability analysis. Furthermore, Part I was devoted to the formulation of a general energy equation for FTB being expressed in terms of prebuckling stress resultants and in-plane deflections through the factor k ₁. The energy equation developed there was presented in several variants dependent upon simplified assumptions one may adopt for the buckling analysis, i.e. the classical form of linear eigenproblem analysis (LEA), the form of quadratic eigenproblem analysis (QEA) and refined (non-classical) forms of nonlinear eigenproblem analysis (NEA), all of them used for solving the flexural-torsional buckling problems of elastic beamcolumns. The accuracy of obtained analytical solutions based on different approximations in the elastic flexural–torsional stability analysis of thin-walled beam-columns is examined and discussed in reference to those of earlier studies. The comparison is made for closed form solutions obtained in a companion paper, with a scatter of results evaluated for k ₁ = 1 in the solutions of LEA and QEA, as well as for all the options corresponding to NEA. The most reliable analytical solution is recommended for further investigations. The solutions for selected asymmetric loading cases of the left support moment and the half-length uniformly distributed span load of a slender unrestrained beam-column are discussed in detail in Part II. Moreover, the paper constituting Part II investigates how the buckling criterion obtained for the beam-column laterally and torsionally unrestrained between the end sections might be applied for the member with discrete restraints. The recommended analytical solutions are verified with use of numerical finite element method results, considering beam-columns with a mid-section restraint. A variant of the analytical form of solutions recommended in these investigations may be used in practical application in the Eurocode’s General Method of modern design procedures for steelwork.

Closed form solutions for the flexural-torsional buckling of elastic beam-columns may only be obtained for simple end boundary conditions, and the case of uniform bending and compression. Moment gradient cases need approximate analytical or numerical methods to be used. Investigations presented in this paper deal with the analytical energy method applied for any asymmetric transverse loading case that produces a moment gradient. Part I of this paper is devoted entirely to the theoretical investigations into the energy based out-of-plane stability formulation and its general solution. For the convenience of calculations, the load and the resulting moment diagram are presented as a superposition of two components, namely the symmetric and antisymmetric ones. The basic form of a non-classical energy equation is developed. It appears to be a function dependent upon the products of the prebuckling displacements (knowfrom the prebuckling analysis) and the postbuckling deformation state components (unknowns enabling the formulation of the stability eigenproblem according to the linear buckling analysis). Firstly, the buckling state solution is sought by presenting the basic form of the non-classical energy equation in several variants being dependent upon the approximation of the major axis stress resultant M_�� and the buckling minor axis stress resultant M_z. The following are considered: the classical energy equation leading to the linear eigenproblem analysis (LEA), its variant leading to the quadratic eigenproblem analysis (QEA) and the other non-classical energy equation forms leading to nonlinear eigenproblem analyses (NEA). The novel forms are those for which the stability equation becomes dependent only upon the twist rotation and its derivatives. Such a refinement is allowed for by using the second order out-of-plane bending differential equation through which the minor axis curvature shape is directly related to the twist rotation shape. Secondly, the effect of coupling of the in-plane and out-of-plane buckling forms is taken into consideration by introducing approximate second order bending relationships. The accuracy of the classical energy method of solving FTB problems is expected to be improved for both H- and I-section beam-columns. The outcomes of research presented in this part are utilized in Part II.