Optimum design of geometrically nonlinear steel frames with semi-rigid connections using improved harmony search method

Abstract

The improved harmony search method based optimum design algorithm is presented for geometrically non-linear steel frames with semirigid connections. In the analysis of steel frames the real behaviour of connections are generally idealized either pinned or fully rigid. The rigid connection idealization indicates that relative rotation of the connection does not exist and the end moment of the beam is entirely transferred to the column. In contrast to the rigid connection assumption, the pinned connection idealization indicates that any restraint does exist for rotation of the connection and the connection moment is zero. Although these idealizations simplify the analysis and design process, the predicted response of the frame may be different from its real behaviour. Numerous experimental studies proved that all beam-to-column connections posses some flexural stiffness between these two extreme assumptions. The term semi-rigid is used to express the real connection behaviour. The moment-rotation relationship is the most important factor for the semi-rigid connection behaviour. The modelling of beam-to-column connections and predicting the real behaviour of them have been demonstrated by a number of experimental and numerical works. Moreover, experimental studies proved that moment-rotation curves of semi-rigid connections are non-linear. The nonlinearity of connection behaviour is due to a number of factors such as material discontinuity of the connection subassemblage, local yielding of some component part and local buckling of a plate element. Several mathematical models are developed to curve fit the experimental data of beam-to-column connections. These models vary from a linear model to polynomial and exponential models. In this study, the semi-rigid connections are modelled with the Frye-Morris polynomial model because of its easy implementation. The non-linear analysis of steel frames with semirigid connections includes both the geometrical nonlinearity of beam-column members and non-linearity due to end connection flexibility of beam members. The columns of frames are continuous and do not have any internal flexible connections. However, the beams possess semi-rigid end connections, but have small axial forces with a geometric non-linearity of little importance. Based on these considerations, two types of members are defined to design of steel frames with semi-rigid connections. These are beamcolumn member and beam member with semi-rigid end connections. Classical harmony search method is recently developed metaheuristic algorithm which simulates the process of producing a musical performance. The harmony search is quite sensitive to the tuning parameters which are harmony memory size, harmony memory consideration rate and pitch adjusting rate. The constant values are used for the tuning parameters in the pure harmony search algorithm. Since the values of these parameters are selected depending on the problem, the efficiency of the harmony search algorithm is directly affected by the tuning parameter values. In order to eliminate the parameter dependent character of the pure harmony search algorithm, pitch adjusting rate is updated in each search step. Therefore, the effectiveness of the classical harmony search algorithm is increased. The optimum design algorithm aims at obtaining minimum-weight steel frames by selecting from standard set of steel sections such as European wide flange beams (HE sections). Strength constraints of Turkish Building Code for Steel Structures (TS648) specification and displacement constraints are used in the optimum design formulation. The robustness of improved harmony search algorithm, in comparison with classical harmony search and genetic algorithms, is verified with a benchmark example. The comparisons revealed that the improved harmony search algorithm yielded lighter frames for the presented example.

Keywords

• Steel frames, Semi-rigid connections, Improved harmony search, Optimum design

Geometrik bakımdan lineer olmayan yarı-rijit birleşimli çelik çerçevelerin gelişmiş armoni arama yöntemiyle optimum tasarımı

Öz

Bu çalışmada geometrik bakımdan lineer olmayan yarı-rijit birleşimli çelik çerçevelerin gelişmiş armoni arama yöntemi ile optimum tasarımı için bir algoritma sunulmuştur. Armoni arama; müzisyenlerin en iyi armoniyi bulmak için izledikleri yol ile optimizasyon problemleri arasında benzerlik kuran bir yöntemdir. Gelişmiş armoni arama yöntem ile optimum tasarım esnasında kullanılan arama parametresinin her arama işlemi sonrasında güncellenmesi sağlanarak klasik armoni aramadan daha etkili bir yöntem elde edilmeye çalışılmıştır. Tasarım işleminde amaç gerilme ve deplasman sınırlayıcıları altında minimum ağırlıklı çelik çerçevenin elde edilmesidir. Gerilme sınırlayıcıları olarak çelik yapıların hesap ve yapım kuralları yönetmeliğindeki (TS 648) eksenel kuvvet ve eğilmeye maruz çubukların gerilme tahkiki formülleri kullanılmıştır. Çelik çerçevelerin analizinde hem çerçeve elemanlarının geometrik bakımdan lineer olmama etkileri hem de kiriş-kolon birleşimlerinin yarı-rijit davranışı hesaba katılmıştır. Gelişmiş armoni arama yönteminden elde edilen sonuçları kıyaslamak için daha önce genetik algoritma ve klasik armoni arama yöntemiyle optimum tasarımı yapılmış bir çelik çerçeve kullanılmıştır. Bu kıyaslamalar sonucunda gelişmiş armoni arama ile daha hafif çerçevelerin elde edildiği görülmüştür.

Anahtar Kelimeler

• Çelik çerçeveler, Yarı-rijit birleşimler, Gelişmiş armoni arama, Optimum tasarım