Keywords: non-linear geometric structural analysis, stability of asymmetric 3D frames, bracing of structures, modelling of connections.

The non-linear P-delta behaviour of three-dimensional frames with plan and elevation asymmetries is studied, using a parametric variation of geometry in plan and a stiffness variation with respect to the height. Eurocode 3 criteria for the second order analyses is briefly addressed in connection with the 2D frame classification with respect to sway behaviour; however for 3D structures the calculated carrying capacity is independent of this classification. So a parametric study of the critical load factor of asymmetric three-dimensional frames, unbraced and braced, permits characterisation of their carrying capacity with respect to overall structural stability.

Tall three-dimensional irregular or asymmetric steel frames often have their design controlled by structural stability requirements. This study departs from the previous works of the authors (Barros and Cesar [1], Cesar [2]) that used a calibration frame to assess the accuracy of some available commercial software (ANSYS, LUSAS and SAP 2000) as well as the author's software INST3D (Barros and Cesar [1]) in determining the critical load factors of side-sway prevention and side-sway free rectangular 3D metallic frames.

Two modeling aspects of the nodal connections between members of a calibration frame are assessed for the nodes modeled using laminar shell elements with the implicit formulation of thick plates and for the nodes modeled as elastic springs. The modelling of rigid nodes with additional metallic reinforcement elements leads to lower buckling loads than assuming full continuity at the node sections. Modifying the characteristics of the linking of the union of the beam to the column, one proves that the rigidity of these zones influences the performance of the structure. For lower spring stiffness, a non-linear initial behaviour of the frame carrying capacity was found for distinct buckling modes as stiffness increases, nevertheless the buckling loads approach a constant value for higher spring stiffnesses. The relative gain in the carrying capacity for the critical mode of the sidesway restrained frame and of the sidesway free frame, as spring stiffness increases, is smaller than 15% and than 20%, respectively. These may be considered as an upper bound of the gain in carrying capacity for the sidesway restrained frame and for the sidesway free frame, if semi-rigid connections would have been modelled for the links between the beam and the columns (Cesar [2], Cesar and Barros [3]).

For asymmetric 3D rectangular structures or 3D structures with unusual complex geometry, a second order 3D analysis permits the calculation of the carrying capacity from the true deformed configuration, independently from the EC3 sway classification. A five floor asymmetric building is used as a reference frame, pre-designed with commercial software using column profiles of HE series. A parametric study of the critical load parameter of this frame, with unbraced and braced configurations, was completed based upon the variation of the length of the beam members (frame spans L₁ and L₂) between the columns, on the definition of the space geometry of the structure (frame inter-story height H) and elevation asymmetry due to the inclusion of the rigid diaphragm slab L₃ solely in a certain number of floors. Some significant results have been graphically synthesized by Cesar [2] Cesar and Barros [3], comparing the evolution of critical buckling loads of six elevation asymmetry cases, unbraced and braced, for three inter-story heights and six frame spans. For unbraced configurations, it is verified that the value of the critical buckling load increases with the number of floors of slab L₃ until reaching a maximum value for two slab floors; for three slab floors the carrying capacity is practically of the same value, but when more than three slab floors are used a loss in the carrying capacity is observed. For braced configurations, a continuous increase in the critical buckling load with the number of floors of slab L₃ is distinctively observed: the carrying capacity practically doubles, for the range of parametric studies analysed.

1

Barros R.C. and César M.B., "Non-Linear Carrying Capacity of Asymmetric Three-Dimensional Braced Steel Frames", Editors: B. Topping and C. Mota Soares, Proceedings of The Seventh International Conference on Computational Structures Technology, Lisbon, Portugal, Paper 145, Civil-Comp Press, Scotland, U.K., 2004. doi:10.4203/ccp.79.145

2

César M.B., "Estudos Paramétricos sobre a Instabilidade de Pórticos Metálicos Bidimensionais e Tridimensionais", Tese de Mestrado em Estruturas de Engenharia Civil, Department of Civil Engineering, FEUP, Porto, Portugal, Dezembro 2004.

3

César M.B. and Barros R.C., "Modelação de Ligações em Pórticos Associada a Estudo Paramétrico do Comportamento Não Linear Geométrico de Pórticos Metálicos Tridimensionais Assimétricos", Congreso de Métodos Numéricos en Ingeniería, Granada, 4-7 July 2005, SEMNI, Spain, (in-press).

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £135 +P&P)