Genetic programming based formulation of rotation capacity of wide flange beams
Introduction
The behaviour of a wide flange beam can be generalized into: Elastic, Inelastic and Plastic categories as shown in Fig. 1. In any case the failure of a beam will be due to one of the following: local plate buckling of the compression flange, local plate buckling of the web in flexural compression, or lateral–torsional buckling. The plastic behaviour category is of special concern in this study as it permits moment redistribution in indeterminate structures [1].
The estimation of plastic rotation capacity is of significant importance for plastic and seismic analysis and design of steel structures. Similarly the moment redistribution in a steel structure also depends on the rotation capacity of the section. Thus the determination of rotation capacity of steel structures becomes an important task.
This study focuses on the explicit formulation of available rotation capacity of wide-flange steel beams using genetic programming. Theoretical, empirical and approximate methods have been proposed for the determination of available rotation capacity of wide-flange steel beams in literature which have been reported by Gioncu and Petcu 2., 3.. Guzelbey et al. [4] have developed an alternative approach for the prediction of rotation capacity of wide-flange beams using neural networks (NN) based on experimental results collected from literature. The proposed NN model showed perfect agreement with experimental results () where its accuracy was also quite high. Moreover Guzelbey et al. [4] have also presented the proposed NN model in explicit form as a mathematical function. This study investigates another alternative soft computing approach for the formulation rotation capacity which is genetic programming (GP) that is presented for the first time in this field. The results of the proposed GP formulation based on experimental studies are compared with numerical results and existing analytical equations. The proposed GP formulation is quite accurate, fast and practical.
Section snippets
Definition of rotation capacity
There are various definitions of rotation capacity in the literature as a non-dimensional parameter.
According to Lay and Galambos [5] rotation capacity is, , in which is the elastic rotation at the initial attainment of the plastic moment and is the plastic rotation at the point when moment drops below .
A widely used definition for rotation capacity is proposed by ASCE (Fig. 2):
where refers to the theoretical rotation at which the full plastic capacity is achieved
Overview of genetic programming
GP is an extension to Genetic Algorithms proposed by Koza [14]. Koza, The early pioneer defines GP as a domain-independent problem-solving approach in which computer programs are evolved to solve, or approximately solve, problems based on the Darwinian principle of reproduction and survival of the fittest and analogues of naturally occurring genetic operations such as crossover (sexual recombination) and mutation. GP reproduces computer programs to solve problems by executing the following
Numerical application
The main task of this article is the GP-based formulation of rotation capacity of wide-flange steel based on experimental results from the literature. Therefore an extensive literature survey has been performed for experimental results shown in Table 1. The experimental results in this field are dispersed. Standard beams are used in experimental studies (SB1, SB2) shown in Fig. 6, Fig. 7. SB1 is used in the experimental studies given in Table 1. The geometry of cross-section variables of tested
Discussion of results
The results of the proposed GP formulation are compared with experimental results in Table 5. The accuracy of the GP formulation is also evaluated with numerical results of the same experimental database obtained by DUCTROT and existing analytical equations proposed by Kemp and Li. The results of the proposed GP formulation are found to be by far more accurate than numerical results and existing analytical equations. It should be noted that tests 50, 51, 56 and 69 exceed maximum limits for
Conclusion
This paper presents a new and efficient approach for the formulation of available rotation capacity of wide-flange beams using GP for the first time in literature. The proposed GP formulation is an empirical formulation based on experimental results collected from literature. The proposed GP formulation shows very good agreement with experimental results (). Numerical results of the same experimental database used for GP formulation are obtained by a specialized computer program (DUCTROT)
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