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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 77
Edited by: B.H.V. Topping
Paper 69

Evaluation of the Post-Limit Stiffness of Beam-to-Column Semi-Rigid Joints using Genetic Algorithms

L.A.C. Borges+, L.R.O. de Lima*, L.A.P.S. da Silva+ and P.C.G. da S. Vellasco$

+Department of Civil Engineering, University of Coimbra, Portugal
*Department of Civil Engineering, PUC-Rio - Pontifical Catholic University of Rio de Janeiro, Brazil
$Structural Engineering Department, UERJ - State University of Rio de Janeiro, Brazil

Full Bibliographic Reference for this paper
L.A.C. Borges, L.R.O. de Lima, L.A.P.S. da Silva, P.C.G. da S. Vellasco, "Evaluation of the Post-Limit Stiffness of Beam-to-Column Semi-Rigid Joints using Genetic Algorithms", in B.H.V. Topping, (Editor), "Proceedings of the Ninth International Conference on Civil and Structural Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 69, 2003. doi:10.4203/ccp.77.69
Keywords: structural engineering, semi-rigid connections, steel structures, genetic algorithms, non-linear analysis, semi-rigid behaviour, connection stiffness.

This paper proposes the use of genetic algorithms to adjust the post limit stiffness of the mechanical springs, used in EUROCODE 3 model [1], to predict the full joint response. The developed software, NASCon [2,3], is able to evaluate, by means of a non-linear analysis, the EUROCODE 3 mechanical model behaviour by individually calibrating the post limit stiffness of each component according to their associated experimental evidence. This interactive procedure was implemented with the aid of a genetic algorithmic software, Evolver [4] producing promising results when compared to experimental tests.

Several investigations have been produced to determine the components post- limit stiffness from experimental data. This painstaking procedure has proved to be difficult, since each post-limit stiffness had to be manually adjusted when the component reached the plastic phase.

The endplate beam-to-column joints investigated in this paper are designed according to the component method philosophy proposed in EUROCODE 3.In this procedure, the joint overall response can be determined based on the mechanical properties of its parts (components). Therefore, the components are assembled into a mechanical model, consisting of extensional springs and rigid links. In general, each component (spring) is characterized by a non-linear force-displacement ($ F \times \Delta$) curve, adequately represented by a bi-linear approximation whenever only the resistance and the initial stiffness of the connection is required. In this procedure, the post-limit stiffness of the components is disregarded since perfect elastic-plastic behaviour is assumed. However, this method was shown to be unconservative, whenever ductility is a critical issue.

During the last thirty years there has been a growing interest in problem solving systems based on principles of evolution and hereditary: such as systems maintain a population of potential solutions, they have some selection process based on fitness of individuals, and some "genetic" operators that are inspired on the Darwin's principle of the species evolution and genetics. These systems are called Genetic Algorithms (GA).

In order to evaluate the global response of the joint, their full geometrical and mechanical properties should be considered. With these results in hand, the mechanical model of the joint can be characterised according to the type of connection. Finally, the component resistance is evaluated and the moment versus rotation curve of the joint may be obtained. The ratio $ k_p/k_e$ of all joint components represent the chromosome used in genetic algorithm. Within these values, the NASCon evaluates the moment versus rotation curve and then, the comparison with the experimental curve is performed. The fitness is measured through the distance between these two curves. The procedure continues with the genetic algorithm operating the changes in the chromosome (crossover and mutation) and a new iteration is performed. This interactive procedure was implemented with the aid of GA software, Evolver [4].

In this work five experimental data were used: one flush endplate joint, two extended endplate joints with backing plates and two welded joints.

The potential use of computational evolutionary for evaluation of structural and civil engineering problems has been fulfilled by the trustworthy results obtained with the semi-rigid joints. The main contribution of this work is to present the use of genetic algorithm as a design aid to predict the full response of the beam-to-column joints considering when appropriate, the components post-limit stiffness. Five joints were investigated: one flush endplate joint, two extended endplate and two welded joints. The results enable the determination of the post-limit stiffness for each relevant component, producing a very interesting tool to calibrate experimental results.

Eurocode 3, prEN 1993-1-8, Part 1.8: Design of Joints, Eurocode 3: Design of Steel Structures, Final draft (corrected), February 2002. CEN, European Committee for Standardization, Brussels, 2002.
Gervásio H., Simões da Silva L., Borges L. - Reliability Assessment of the Post-limit Stiffness and Ductility of Steel Joints - Proceedings of Third European Conference on Steel Structures, Coimbra, Portugal, vol. 2, p. 1027-1038, 2002.
Evolver 4.0 - Genetic Optimization Add-in for Microsoft Excel - Palisade Decision Tools, 1999.
Michalewicz, Zbigniew, "Genetic Algorithms + Data Structures = Evolution Programs", 3rd Revised and Extended Edition, Springer, 1996.

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