Keywords: cellular beams, optimum structural design, minimum weight design, combinatorial optimization, stochastic search techniques, harmony search algorithm.

Cellular beams became increasingly popular as an efficient structural form in steel construction since their introduction in 1987. They have been used in over 3500 projects in over twenty countries. Their sophisticated design and profiling process provides greater flexibility in beam proportioning for strength, depth, size and location of circular holes. The main goal of manufacturing these beams is to increase overall beam depth, the moment of inertia and section modulus, which results in greater strength and rigidity. Cellular beams can be used in a variety of applications. They are used as primary or secondary floor beams in order to achieve long spans and service integration. Cellular beams are used as roof beams beyond the range of portal-frame construction, and are the perfect solution for curved roof applications, combining weight savings with a low-cost manufacturing process. Cellular beams provide a very economical method of producing tapered members, which have been used extensively in sports stadiums.

In this study the design problem of cellular beams is formulated as an optimum design problem. The designation of an I-Beam from which the cellular beam is to be produced, the cell diameter and the total number of cells along the beam is taken as a design variables. Design constraints include the displacement limitations, overall beam flexural capacity, beam shear capacity, overall beam buckling strength, web post flexure and buckling, Vierendeel bending of upper and lower tees, local buckling of compression flange and practical restrictions between cell diameter and the spacing between cells. Due to the fact that the steel sections are to be selected from an available steel sections set and cell dimensions are to decided among the practically preferred values the design problem turns out to be discrete nonlinear programming problem.

Solution of this combinatorial optimization problem is carried out using harmony search algorithm which is one of the recent additions to stochastic search techniques. This approach is conceptualized using the musical performance process that takes place when a musician searches for a perfect state of harmony. Jazz improvisation seeks to find musically pleasing harmony similar to the optimum design process which seeks to find optimum solution. In the process of musical production a musician selects and brings together a number of different notes from the whole notes and then plays these with a musical instrument to find out whether it gives a pleasing harmony. The musician then tunes some of these notes to achieve a better harmony. Similar to this process the harmony search algorithm randomly selects values for each design variable from their possible value set and then brings them together to obtain a candidate solution for the optimum design problem. This candidate solution is then checked whether it satisfies the objective function or not, similar to the process of finding out whether euphonic music is obtained or not. A number of design examples considered has shown that the harmony search technique is quite robust and effective in finding the optimum steel section, cell diameter and number of holes in cellular beams.

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