A Two-Stage Procedure for Optimum Design of Plate Girders Using a Meta-heuristic Algorithm

Document Type : Research Article


1 Department of Civil Engineering, Faculty of Engineering, Ardakan University, Ardakan, Iran

2 International Institute of Earthquake Engineering and Seismology, Tehran, Iran


The main aim in the design of welded plate girders is to minimize the weight of the beam while satisfying design requirements which turns the design procedure into a nonlinear and complex optimization problem. In this paper, a two-stage optimization procedure is introduced to find the best design of welded plate girders in terms of both safety and economy. The total weight of the girder is considered as the objective function where some predefined constraints are applied using penalty functions to restrict the solution space. In the first stage, the theoretical optimum values of girder dimensions are obtained using the Artificial Bee Colony (ABC) algorithm based on the optimum use of steel material while satisfying restrictions on the flexural and shear strength, permissible deflection, and proportioning limits. Since the plate dimension values obtained by the first stage may not be available in the market, the second stage of optimization is carried out to reach a safe and economical design by considering available plate dimension values. The critical ratio of the designing procedure is obtained equal to one, which is the ideal design. To demonstrate the effectiveness of the proposed method, two examples are considered at the end of this article. The results show that the dimension of the plate girder calculated by the proposed approach is more economical and practical than that obtained by the traditional trial and error techniques.


Main Subjects

[1] R. Razani, G.G. Goble, Optimum design of constant-depth plate girders, Journal of the Structural Division, 92(2) (1966) 253-382.
[2]  A.K. Azad, S.A. Al-Ghamdi, Optimization of built-up nonuniform steel I-beams, Journal of Structural Engineering, 112(8) (1986) 1982-1986.
[3] H. Adeli, K. Mak, Interactive optimization of plate girder bridges subjected to moving loads, Computer-aided design, 22(6) (1990) 368-376.
[4] M.A. Bhatti, A. Al-Gahtani, Optimum design of welded plate girders subjected to highway bridge loading, WIT Transactions on The Built Environment, 14 (1970).
[5] S.A. Alghamdi, Design optimization of non-uniform stiffened steel plate girders—a computer code, Advances in Engineering Software, 34(6) (2003) 357-386.
[6]  S. Alghamdi, On the design optimization of built-up stiffened steel beams with buckling and frequency constraints, Structural and Multidisciplinary Optimization, 28 (2004) 296-305.
[7] R. Abspoel, F. Bijlaard, Optimization of plate girders, Steel construction, 7(2) (2014) 116-125.
[8] D.D. Thang, M.-S. Koo, A. Hameed, Optimum cost design of steel box-girder by varying plate thickness, KSCE Journal of Civil Engineering, 13 (2009) 31-37.
[9] M.U. Saleem, N. Khurram, H.J. Qureshi, Z.A. Kazmi, Z.A. Siddiqui, Optimisation of flange and web slenderness for pre-engineered built-up steel sections, Proceedings of the Institution of Civil Engineers-Structures and Buildings, 172(8) (2019) 599-608
[10]  G. Pachideh, M. Kafi, M. Gholhaki, Evaluation of cyclic performance of a novel bracing system equipped with a circular energy dissipater, in:  Structures, Elsevier, 2020, pp. 467-481.
[11]  G. Pachideh, M. Gholhaki, M. Kafi, Experimental and numerical evaluation of an innovative diamond-scheme bracing system equipped with a yielding damper, Steel and Composite Structures, 36(2) (2020) 197.
[12] K.-C. Fu, Y. Zhai, S. Zhou, Optimum design of welded steel plate girder bridges using a genetic algorithm with elitism, Journal of Bridge Engineering, 10(3) (2005) 291-301.
[13] Y.I. Musa, M.A. Diaz, Design optimization of composite steel box girder in flexure, Practice Periodical on Structural Design and Construction, 12(3) (2007) 146-152.
[14] P.M. Raju, G.R. Rao, G.H. Kumari, E. Gowthami, MATHEMATICAL MODEL FOR ESTIMATION OF SELF WEIGHT OF FLEXURAL STEEL MEMBERS, Int. J. Optim. Civil Eng, 7(2) (2017) 241-255.
[15] C. Cakiroglu, G. Bekda┼č, S. Kim, Z.W. Geem, Optimisation of Shear and Lateral–Torsional Buckling of Steel Plate Girders Using Meta-Heuristic Algorithms, Applied Sciences, 10(10) (2020) 3639.
[16] D. Karaboga, B. Akay, A comparative study of artificial bee colony algorithm, Applied mathematics and computation, 214(1) (2009) 108-132.