Keywords: plasticity, reliability analysis, shakedown analysis, residual strain energy, optimal design, bounding theorems.

One side in structural plasticity the static and kinematic limit theorems provide appropriate tools to solve complex problems [1,2]. Since the shakedown analysis provides 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 [1,3] suggested that the complementary strain energy of the residual forces could be considered an overall measure of the plastic performance of structures and the plastic deformations should be controlled by introducing a limit for magnitude of this energy. The skeletal structures (trusses, frames, grids) are very often used in structural engineering. The main structural elements of steel framed multi-storey structures are the columns and the beams. Their connections can be semi-rigid. This circumstance can influence significantly the behaviour of the structure therefore has to be taken into account in the analysis and design. Due to the different behaviour of the beam elements of the skeletal structures for compression and tension the stability problems need a certain care. The national standards give appropriate tools to solve the problem.

The aim of this paper is to take into consideration the influence of the limited load carrying capacity of the connections on the plastic limit state of elasto-plastic steel (or composite) trusses and frames under multi-parameter static loading and probabilistically given conditions during the design. In addition to the plastic shakedown analysis and optimal design to control the plastic behaviour of the structure, bound on the complementary strain energy of the residual forces is also applied. This bound has a significant effect on the load parameter [3]. The different behaviours of the beam elements in compression and tension are taken into consideration by the reduced load carrying capacity in compression. The calculation is based on the requirements of the Eurocode. If the design uncertainties (manufacturing, strength, geometrical) are expressed by the calculation of the complementary strain energy of the residual forces the reliability based extended shakedown analysis and optimal design problems can be formed. Numerical procedures are elaborated which are based on a direct integration technique and the uncertainties are assumed to follow a Gaussian distribution. The formulations of the problems yield to nonlinear mathematical programming which are solved by the use of sequential quadratic algorithm. The nested 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 G. Augusti, G.I. Schueller, M. Ciampoli, (Editors), "ICOSSAR 2005", Millpress, Rotterdam, 2323-2330, 2005.

3

J. Lógó, M. Movahedi Rad, J. Knabel, Z. Hortobágyi, "Reliability Based Limit Analysis and Shakedown of Framed Structures with Limited Residual Strain Energy Capacity", in B.H.V. Topping, M. Papadrakakis, (Editors), "Proceedings of the Ninth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 161, 2008. doi:10.4203/ccp.88.161

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