Novel Optimum Design and Sensitivity Assessment for Concrete ‎Beams Using FRP Bars

Document Type : Original Article

Authors

1 Graduate School of Engineering, Kobe University, Japan

2 Faculty of Civil, Water and Environmental Engineering, Shahid Beheshti University, Tehran, Iran

Abstract

Optimization of structural elements is one of the most important topics in structural engineering, ‎with a wide range of applications, including concrete beams reinforced with fiber-reinforced ‎polymer (FRP) bars. The increasing use of FRP reinforcement, owing to its corrosion resistance ‎and high strength-to-weight ratio, has created a need for efficient and economical design ‎approaches. Therefore, the objective of this paper is to employ the Lagrangian Multiplier Method ‎‎(LMM) to obtain a minimum-cost design of singly reinforced concrete beams with rectangular ‎cross-sections. In this study, the costs of concrete and FRP materials are formulated as objective ‎cost functions to be minimized, while the ultimate flexural strength of the beam is considered the ‎primary design constraint. The optimization problem is solved analytically, and optimum designs ‎are derived in closed-form solutions using the LMM framework. The applicability of the proposed ‎formulation is demonstrated through a real-life design example of a singly reinforced concrete ‎beam, showing that the minimum-cost design can be effectively achieved while satisfying ‎structural performance requirements. The derived design relations and optimization curves provide ‎a practical and efficient tool for engineers seeking economical and reliable FRP-reinforced concrete ‎beam designs.‎

Keywords

References

ACI. (2014). ACI 318-14 Building Code Requirements for Structural Concrete and Commentary BT - Building Code Requirements for Structural Concrete (ACI 318-14) and Commentary. In Building Code Requirements for Structural Concrete (ACI 318-14) and Commentary.
ACI Committee 440. (2015). Guide for the design and construction of structural concrete reinforced with FRP bars. American Concrete Institute.
Adamu, A. & Karihaloo, B. L. (1994). Minimum cost design of RC beams using DCOC Part I: Beams with freely-varying cross-sections. Structural Optimization. https://doi.org/10.1007/BF01743718
Adamu, A., Karihaloo, B. L. & Rozvany, G. I. N. (1994). Minimum cost design of reinforced concrete beams using continuum-type optimality criteria. Structural Optimization. https://doi.org/10.1007/BF01742512
Al-Salloum, Y. A. & Husainsiddiqi, G. (1994). Cost-Optimum Design of Reinforced Concrete (RC) Beams. ACI Structural Journal, 91(6), 647–655. https://doi.org/10.14359/1539
Arora, J. S., Elwakeil, O. A., Chahande, A. I. & Hsieh, C. C. (1995). Global optimization methods for engineering applications: A review. In Structural Optimization. https://doi.org/10.1007/BF01743964
Atabay, Ş. (2009). Cost optimization of three-dimensional beamless reinforced concrete shear-wall systems via genetic algorithm. Expert Systems with Applications. https://doi.org/10.1016/j.eswa.2008.02.004
Bakis, C. E., Bank, L. C., Brown, V. L., Cosenza, E., Davalos, J. F., Lesko, J. J., Machida, A., Rizkalla, S. H. & Triantafillou, T. C. (2002). Fiber-Reinforced Polymer Composites for Construction—State-of-the-Art Review. Journal of Composites for Construction. https://doi.org/10.1061/(ASCE)1090-0268(2002)6:2(73)
Bordignon, R. & Kripka, M. (2012). Optimum design of reinforced concrete columns subjected to uniaxial flexural compression. Computers & Concrete, 9(5), 327–340. https://doi.org/10.12989/cac.2012.9.5.327
Ceranic, B. & Fryer, C. (2000). Sensitivity analysis and optimum design curves for the minimum cost design of singly and doubly reinforced concrete beams. Structural and Multidisciplinary Optimization. https://doi.org/10.1007/s001580050156
Chakrabarty, B. K. (1992). Models for optimal design of reinforced concrete beams. Computers & Structures, 42(3), 447–451. https://doi.org/10.1016/0045-7949(92)90040-7
de Medeiros, G. F. & Kripka, M. (2013). Structural optimization and proposition of pre-sizing parameters for beams in reinforced concrete buildings. Computers & Concrete, 11(3), 253–270. https://doi.org/10.12989/cac.2013.11.3.253
Fedghouche, F. & Tiliouine, B. (2010). Minimum cost design of RC Rectangular sections in bending under ultimate loads. Proceedings of the 5th International Conference on Advances in Mechanical Engineering and Mechanics, ICAMEM 2010 Hammamat, Tunisia.
Fedghouche, Ferhat & Tiliouine, B. (2012). Minimum cost design of reinforced concrete T-beams at ultimate loads using Eurocode2. Engineering Structures. https://doi.org/10.1016/j.engstruct.2012.04.008
Fernandez, I., Bairán, J. M. & Marí, A. R. (2015). Corrosion effects on the mechanical properties of reinforcing steel bars. Fatigue and σ–ε behavior. Construction and Building Materials, 101, 772–783. https://doi.org/10.1016/J.CONBUILDMAT.2015.10.139
Hollaway, L. C. (2010). A review of the present and future utilisation of FRP composites in the civil infrastructure with reference to their important in-service properties. In Construction and Building Materials. https://doi.org/10.1016/j.conbuildmat.2010.04.062
Kao, C.-S. & Yeh, I.-C. (2014). Optimal design of reinforced concrete plane frames using artificial neural networks. Computers and Concrete, 14(4), 445–462. https://doi.org/10.12989/cac.2014.14.4.445
Mukherjee, A. & Deshpande, J. M. (1995a). Application of artificial neural networks in structural design expert systems. Computers & Structures, 54(3), 367–375. https://doi.org/10.1016/0045-7949(94)00342-Z
Mukherjee, A. & Deshpande, J. M. (1995b). Application of artificial neural networks in structural design expert systems. Computers & Structures, 54(3), 367–375. https://doi.org/10.1016/0045-7949(94)00342-Z
Mukherjee, Abhijit & Deshpande, J. M. (1995). Modeling Initial Design Process using Artificial Neural Networks. Journal of Computing in Civil Engineering, 9(3), 194–200. https://doi.org/10.1061/(ASCE)0887-3801(1995)9:3(194)
Ozbay, E., Oztas, A. & Baykasoglu, A. (2010). Cost optimization of high strength concretes by soft computing techniques. Computers and Concrete. https://doi.org/10.12989/cac.2010.7.3.221
Ozturk, H. T., Durmus, A. & Durmus, A. (2012). Optimum design of a reinforced concrete beam using artificial bee colony algorithm. Computers and Concrete. https://doi.org/10.12989/cac.2012.10.3.295
Öztürk, H. T., Türkeli, E. & Durmuş, A. (2016). Optimum design of RC shallow tunnels in earthquake zones using artificial bee colony and genetic algorithms. Computers and Concrete. https://doi.org/10.12989/cac.2016.17.4.435
Rahmanian, I., Lucet, Y. & Tesfamariam, S. (2014). Optimal design of reinforced concrete beams: A review. Computers and Concrete. https://doi.org/10.12989/cac.2014.13.4.457
Saini a, B., Sehgala, V. K., Gambhirb & M.L. (2006). GENETICALLY OPTIMIZED ARTIFICIAL NEURAL NETWORK BASED OPTIMUM DESIGN OF SINGLY AND DOUBLY REINFORCED CONCRETE BEAMS. ASIAN JOURNAL OF CIVIL ENGINEERING (BUILDING AND HOUSING, 7(6), 603–619.
Saini, B., Sehgal, V. K. & Gambhir, M. L. (2007). Least-cost design of singly and doubly reinforced concrete beam using genetic algorithm optimized artificial neural network based on Levenberg-Marquardt and quasi-Newton backpropagation learning techniques. Structural and Multidisciplinary Optimization. https://doi.org/10.1007/s00158-006-0081-3
Todeschini, C. E., Bianchini, A. C. & Kesler, C. E. (1964). Behavior of Concrete Columns Reinforced with High Strength Steels. ACI Journal Proceedings, 61(6), 701–716. https://doi.org/10.14359/7803
 
 
 
 
Interdisciplinary Journal of Civil Engineering
Volume 1, Issue 4 - Serial Number 4
October 2025
Pages 412-427

Files

Share

How to cite

Statistics