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Abstract

Elastic instability of steel I-section members has been investigated with regard to axial compression, major axis bending as well as compression and major axis bending, based on the Vlasov theory of thin-walled members. Investigations presented in this paper deal with the energy method applied to the flexural-torsional buckling (FTB) problems of any complex loading case that for convenience of predictions is treated as a superposition of symmetric and antisymmetric components. Firstly, the review of energy equation formulations is presented for the elastic lateral-torsional buckling (LTB) of beams, then the most accurate beam energy equation, so-called the classical energy equation formulated for bisymmetric I-section beams is extended to cover also the beam-column out-of-plane stability problems, referred hereafter to FTB problems. Secondly, for the simple end boundary conditions, the shape functions of twist rotation and minor axis displacement are chosen such that they cover both symmetric and antisymmetric lateral-torsional buckling modes in relation to two lowest eigenvalues of the beam LTB in major axis bending. Finally, the explicit form of the general solution is presented being dependent upon the dimensionless bending moment equations for symmetric and antisymmetric components, and the load factor where the lower k index identifies the load case.
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Authors and Affiliations

Marian Antoni Giżejowski
1
Anna Maria Barszcz
1
Zbigniew Stachura
2

  1. Warsaw University of Technology, Faculty of Civil Engineering, Al. Armii Ludowej 16, 00-637 Warsaw, Poland
  2. Warsaw University of Technology, Faculty of Civil Engineering, Al. Armii Ludowej 16, 00-637 Warsaw
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Abstract

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.
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Authors and Affiliations

Marian Antoni Giżejowski
1
Radosław Bronisław Szczerba
2
Zbigniew Stachura
2
Marcin Daniel Gajewski
2

  1. Warsaw University of Technology, Faculty of Civil Engineering, Al. Armii Ludowej 16, 00-637 Warsaw, Poland
  2. Warsaw University of Technology, Faculty of Civil Engineering, Al. Armii Ludowej 16, 00-637 Warsaw

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