Keywords: reliability analysis, limit analysis, shakedown analysis, residual strain energy, Gaussian distribution, probability.

In classical plasticity the limit and the shakedown analysis are among the most important basic problems. For the application of the plastic analysis and design methods the control of the plastic behaviour of the structures is an important requirement. Since the shakedown and limit analysis provide no information about the magnitude of the plastic deformations and residual displacements accumulated before the adaptation of the structure, therefore for their determination several bounding theorems and approximate methods have been proposed. Among others Kaliszky and Lógó [1] suggested that the complementary strain energy of the residual forces could be considered as an overall measure of the plastic performance of structures and the plastic deformations should be controlled by introducing a limit for the magnitude of this energy. In engineering the problem parameters (geometric, material, strength, manufacturing) are given or considered with uncertainties. The analysis obtained and the design task is more complex and can lead to reliability analysis and design [2].

There are several engineering problems where the designer will face the problem of limited load carrying capacity of the connected elements of the structure. Such problem can be found during the rehabilitation of old buildings with composite plates (floors) or in the case of steel structures. The main structural elements of steel framed multi-storey structures are the columns, the beams and their connections. The assumption that the connections are either rigid or pinned has been widely applied in the past. The actual behaviour of the connections is however somewhere between these limits and they are semi-rigid [3,4]. These connections can significantly influence the behaviour of the structure and therefore they have to be taken into account in the analysis and design.

The aim of this paper is to analyze the influence of the limited load carrying capacity of the connections on the plastic limit state and shakedown of elasto-plastic steel (or composite) framed structures under multi-parameter static loading and probabilistically given conditions. In addition to the limit analysis and shakedown, to control the plastic behavior of the structure, a bound on the complementary strain energy of the residual forces is also applied. This bound has significant effect on the load parameter [5]. If the design uncertainties (manufacturing, strength, geometric) are expressed by the calculation of the complementary strain energy of the residual forces then a reliability based extended limit analysis and extended shakedown problems are formed. The formulations of the problems yield to nonlinear mathematical programming problems which are solved by the use of a sequential quadratic algorithm. The bi-level optimization procedure is governed by the reliability index calculation.

1

S. Kaliszky, J. Lógó, "Optimal Plastic Limit and Shakedown Design of Bar Structures with Constraints on Plastic Deformation", Engineering Structures, 19 (1), 19-27,1997. doi:10.1016/S0141-0296(96)00066-1

2

K. Dolinski, J. Knabel, "Reliability-oriented Shakedown Formulation", in ICOSSAR 2005, eds by G. Augusti, G.I. Schueller, M. Ciampoli, Millpress, Rotterdam, 2323-2330, 2005.

3

Eurocode 3, "Design of steel structures", Commission of the European Communities, 1999.

4

M. Iványi, "Semi-rigid Connections in Steel Frames", Part I. In "Semi-Rigid Connections in Structural Steelwork", CISM Courses and Lectures No. 419., eds. M. Ivanyi, C.C. Baniotopoulos, Springer-Wien New York, 2000.

5

J. Lógó, S. Kaliszky, M. Hjiaj, M. Movahedi Rad, "Plastic limit and shakedown analysis of elasto-plastic steel frames with semi-rigid connections", in DFE2008 Design, Fabrication and Economy, eds K. Jármai, J. Farkas, Horwood Limited Publishers, Chichester, 237-244, 2008.

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 £145 +P&P)