Assessment of the flexural buckling resistance of bisymmetrical I-section beam-columns using FEM is widely discussed in the paper with regard to their imperfect model. The concept of equivalent geometric imperfections is applied in compliance with the so-called Eurocode’s general method. Various imperfection profiles are considered. The global effect of imperfections on the real compression members behaviour is illustrated by the comparison of imperfect beam-columns resistance and the resistance of their perfect counterparts. Numerous FEM simulations with regard to the stability behaviour of laterally and torsionally restrained steel structural elements of hot-rolled wide flange HEB section subjected to both compression and bending about the major or minor principal axes were performed. Geometrically and materially nonlinear analyses, GMNA for perfect structural elements and GMNIA for imperfect ones, preceded by LBA for the initial curvature evaluation of imperfect member configuration prior to loading were carried out. Numerical modelling and simulations were conducted with use of ABAQUS/Standard program. FEM results are compared with those obtained using the Eurocode’s interaction criteria of Method 1 and 2. Concluding remarks with regard to a necessity of equivalent imperfection profiles inclusion in modelling of the in-plane resistance of compression members are presented.

Steel prismatic elements of equal flanges double-tee section subject to major axis bending and compression, unrestrained in the out-of-plane direction between the supports, are vulnerable to buckling modes associated with minor axis flexural and torsional deformations. When end bending moments are acting alone on the quasi-straight member, the sensitivity to lateral-torsional buckling (LTB) is very much dependent upon the ratio of section minor axis to major axis moments of inertia, and additionally visibly dependent upon the major axis moment gradient ratio. In the case of major axis bending with the presence of a compressive axial force, even of rather small value in relation to the section squash resistance, there is a drastic reduction of structural elements in their realistic lengths to maintain a tendency to fail in the out-of-plane mode, governed by the large twist rotation. Increasing the load effects ratio of dimensionless axial force to dimensionless maximum major axis bending moment, the buckling mode goes away from that of lateral-torsional one, starting to become that closer to the minor axis flexural buckling (FBZ) mode. Different aspects of the flexural-torsional buckling (FTB) resistance of the typical rolled H-section beam-column with regard to the General Method (GM) formulation, developed by the authors elsewhere and based on the parametric finite element analysis, are dealt with in this paper. Investigations are concerned with different member slender ratio, different moment gradient ratios and different load effects ratio. Final conclusions are related to practical applications of the proposed format of General Method in relation to the effect of large displacements on the FTB resistance reduction factor described through the dimensionless measure of action effects and the FTB relative slenderness ratio of quasi-straight beam-columns.

The use of old building design codes and improper execution of recent seismic design practices have caused large amount of substandard and vulnerable reinforced concrete RC building stock majority of which are built with weak beam-column joint connections defect (i.e. joint panel having no transverse reinforcement and built in low strength concrete). In order to understand the seismic response and damage behaviour of recent special moment resisting frame SMRF structures with the defect of weak beam-column joints, shake table tests have been performed on two 1:3 reduced scaled, two story RC frame models. The representative reference code design and weak beam-column joint frame models were subjected to uni-directional dynamic excitations of increasing intensities using the natural record of 1994 Northridge Earthquake. The input scaled excitations were applied from 5% to 130% of the maximum input peak ground acceleration record, to deformed the test models from elastic to inelastic stage and then to fully plastic incipient collapse stage. The weak beam-column frame experienced column flexure cracking, longitudinal bar-slip in beam members and observed with cover concrete spalling and severe damageability of the joint panels upon subjected to multiple dynamic excitations. The deficient frame was only able to resist 40% of the maximum acceleration input as compared to the code design frame which was able to resist about 130%. The seismic performance of considered RC frames was evaluated in terms of seismic response parameters (seismic response modification, overstrength and displacement ductility factors), for critical comparison.

This paper presents a numerical investigation into the high strength steel (HSS) welded Isection overall buckling performance with respect to the major axis under combined axial compression and bending. The validation of FE models compared with the existing test data to verify the appropriateness of the element division and boundary condition was firstly conducted. In line with the FE arrangement verified, separate 890 numerical models, covering a broader range of eight steel grades (460 MPa, 500 MPa, 550 MPa, 620 MPa, 690 MPa, 800 MPa, 890 MPa and 960 MPa), different overall slenderness and various eccentricities were designated. Subsequently, the comparison of the resistance prediction codified design rules in EN1993-1-1, ANSI/AISC 360-10 and GB50017-2017 was preferentially operated, by the instrumentality of the normalized axial compression-bending moment curves. The results graphically revealed that, the provision given in ANSI/AISC 360-10 concerned in the present work was the most loose, whereas, the corresponding content set out in EN1993-1-1 and GB50017-2017 was relatively on the safe side. Taking account of the FE results, the conservative shortcomings of the considered rules in EN1993-1-1 and GB50017-2017 were further highlighted. Especially, the disparity of EN1993-1-1 and numerical results was higher to 27%, from the perspective of a definition given in the present work. In contrast, the provision in ANSI/AISC 360-10 yielded a relatively accurate prediction, on average. Based on the numerical program, an alternative formula for the HSS welded I-section beam-columns with a general expression form was sought, which intimately reflected the effect of overall slenderness.

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.