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[1] Topping, B.H.V. & Robinson, D.J., Optimization of timber framed structures. Computers & Structures, 18(6), pp. 1167–1177, 1984. 90161-5 [Crossref]
[2] Kaziolasa, D.N., Bekasb, G.Ȁ., Zygomalasc, I. & Stavroulakisd, G.E., Life Cycle Analysis and Optimization of a Timber Building. 7th International Conference on Sustainability in Energy and Buildings, Energy Procedia, 83, pp. 41–49, 2015. https://doi. org/10.1016/j.egypro.2015.12.194
[3] Stanić, A., Hudobivnik, B. & Brank, B., Economic-design optimization of cross laminated timber plates with ribs. Composite Structures, 154, pp. 527–537, 2016. [Crossref]
[4] Pech, S., Kandler, G., Lukacevic, M. & Füssl, J., Metamodel assisted optimization of glued laminated timber beams by using metaheuristic algorithms. Engineering Applications of Artificial Intelligence, 79, pp. 129–141, 2019. pai.2018.12.010 [Crossref]
[5] Jelušič, P. & Kravanja, S., Optimal design of timber-concrete composite floors based on the multi-parametric MINLP optimization. Composite structures, 179, pp. 285–293, 2017. [Crossref]
[6] Jelušič, P., Determining optimal designs of timber beams with non-uniform cross-section. High Performance and Optimum Design of Structures and Materials III, WIT Transactions on the Built Environment, 175, pp. 169–175, 2019.
[7] Kravanja, S. & Žula, T., Optimization of a timber hall structure. High Performance and Optimum Design of Structures and Materials IV, WIT Transactions on the Built Environment, 196, pp. 183–192, 2020.
[8] Eurocode 2. Design of concrete structures, European Committee for Standardization, Brussels 2004.
[9] Eurocode 3. Design of steel structures, European Committee for Standardization, Brus- sels 2005.
[10] Eurocode 5. Design of timber structures, European Committee for Standardization, Brussels 2008.
[11] Kravanja, Z. & Grossmann, I.E., New Developments and Capabilities in PROSYN – An Automated Topology and Parameter Process Synthesizer. Computers chem. Eng., 18, pp. 1097–1114, 1994. [Crossref]
[12] Kravanja, S., Kravanja, Z. & Bedenik, B.S., The MINLP optimization approach to structural synthesis, Part I: A general view on simultaneous topology and parameter optimization. Int. J. Numer. Methods Eng., 43, pp. 263–292, 1998. https://doi.org/10.1002/ (sici)1097-0207(19980930)43:2<263::aid-nme412>3.0.co;2-u
[13] Kravanja, S., Soršak, A. & Kravanja, Z., Efficient multilevel MINLP strategies for solving large combinatorial problems in engineering. Optim. Engng., 4, pp. 97–151, 2003. [Crossref]
[14] Brooke, A., Kendrick, D. and Meeraus, A., GAMS – A User’s Guide, Scientific Press, Redwood City, CA, 1988.
[15] WolframAlpha computational intelligence, https://www.wolframalpha.com/.
[16] Vratuša, S. & Premrov, M., Projektiranje lesenih konstrukcij. Projektiranje gradbenih konstrukcij po Evrokod standardih, Inženirska zbornica Slovenije, pp. 5/1–5/117, 2009.
[17] Kravanja, Z., Challenges in sustainable integrated process synthesis and the capabilities of an MINLP process synthesizer MipSyn. Comput. Chem. Eng., 34(11), pp. 1831–1848, 2010. [Crossref]
[18] Drudd, A.S., CONOPT – A Large-Scale GRG Code, ORSA J. Comput., 6, 207–216, 1994.
[19] Abadie, J. & Carpentier, J., Generalization of the Wolfe reduced gradient method to the case of nonlinear constraints, Optimization, Academic Press, New York, 1969.
[21] Land, A.H. & Doig, A.G., An Automatic Method for Solving Discrete Programming Problems, Econometrica, 28(3), pp. 497–520, 1960. [Crossref]
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Open Access
Research article

Optimization of a Single-Storey Timber Building Structure

Stojan Kravanja,
Tomaž Žula
Faculty of Civil Engineering, Transportation Engineering and Architecture, University of Maribor, Slovenia
International Journal of Computational Methods and Experimental Measurements
|
Volume 9, Issue 2, 2021
|
Pages 126-140
Received: N/A,
Revised: N/A,
Accepted: N/A,
Available online: N/A
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Abstract:

The paper deals with the optimization of a single-storey timber building structure designed from timber portal frames connected with steel purlins, rails and façade columns. While the portal frames are made of the glued laminated timber with rectangular cross-sections, purlins, rails and façade columns are made of commercially available steel I-profiles. The portal frames are supported by square concrete pad foundations. The building structure is optimized by a mixed-integer non-linear programming (MINLP). The optimization model is developed. The objective function defines the material costs of the structure. The objective function is subjected to structural analysis and design constraints defined according to Eurocode standards. The Modified Outer-Approximation/Equality-Relaxation algorithm (OA/ER) and the linked multi-level strategy are applied. The optimization determines the minimum material costs of the structure, the optimal number of glulam frames and steel members and all standard/discrete cross- sections. A numerical example at the end of the paper shows the efficiency of the proposed optimization approach.

Keywords: Cost optimization, Mixed-integer non-linear programming (MINLP), Steel structures, Structural optimization, Timber building, Timber structures
Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

References
[1] Topping, B.H.V. & Robinson, D.J., Optimization of timber framed structures. Computers & Structures, 18(6), pp. 1167–1177, 1984. 90161-5 [Crossref]
[2] Kaziolasa, D.N., Bekasb, G.Ȁ., Zygomalasc, I. & Stavroulakisd, G.E., Life Cycle Analysis and Optimization of a Timber Building. 7th International Conference on Sustainability in Energy and Buildings, Energy Procedia, 83, pp. 41–49, 2015. https://doi. org/10.1016/j.egypro.2015.12.194
[3] Stanić, A., Hudobivnik, B. & Brank, B., Economic-design optimization of cross laminated timber plates with ribs. Composite Structures, 154, pp. 527–537, 2016. [Crossref]
[4] Pech, S., Kandler, G., Lukacevic, M. & Füssl, J., Metamodel assisted optimization of glued laminated timber beams by using metaheuristic algorithms. Engineering Applications of Artificial Intelligence, 79, pp. 129–141, 2019. pai.2018.12.010 [Crossref]
[5] Jelušič, P. & Kravanja, S., Optimal design of timber-concrete composite floors based on the multi-parametric MINLP optimization. Composite structures, 179, pp. 285–293, 2017. [Crossref]
[6] Jelušič, P., Determining optimal designs of timber beams with non-uniform cross-section. High Performance and Optimum Design of Structures and Materials III, WIT Transactions on the Built Environment, 175, pp. 169–175, 2019.
[7] Kravanja, S. & Žula, T., Optimization of a timber hall structure. High Performance and Optimum Design of Structures and Materials IV, WIT Transactions on the Built Environment, 196, pp. 183–192, 2020.
[8] Eurocode 2. Design of concrete structures, European Committee for Standardization, Brussels 2004.
[9] Eurocode 3. Design of steel structures, European Committee for Standardization, Brus- sels 2005.
[10] Eurocode 5. Design of timber structures, European Committee for Standardization, Brussels 2008.
[11] Kravanja, Z. & Grossmann, I.E., New Developments and Capabilities in PROSYN – An Automated Topology and Parameter Process Synthesizer. Computers chem. Eng., 18, pp. 1097–1114, 1994. [Crossref]
[12] Kravanja, S., Kravanja, Z. & Bedenik, B.S., The MINLP optimization approach to structural synthesis, Part I: A general view on simultaneous topology and parameter optimization. Int. J. Numer. Methods Eng., 43, pp. 263–292, 1998. https://doi.org/10.1002/ (sici)1097-0207(19980930)43:2<263::aid-nme412>3.0.co;2-u
[13] Kravanja, S., Soršak, A. & Kravanja, Z., Efficient multilevel MINLP strategies for solving large combinatorial problems in engineering. Optim. Engng., 4, pp. 97–151, 2003. [Crossref]
[14] Brooke, A., Kendrick, D. and Meeraus, A., GAMS – A User’s Guide, Scientific Press, Redwood City, CA, 1988.
[15] WolframAlpha computational intelligence, https://www.wolframalpha.com/.
[16] Vratuša, S. & Premrov, M., Projektiranje lesenih konstrukcij. Projektiranje gradbenih konstrukcij po Evrokod standardih, Inženirska zbornica Slovenije, pp. 5/1–5/117, 2009.
[17] Kravanja, Z., Challenges in sustainable integrated process synthesis and the capabilities of an MINLP process synthesizer MipSyn. Comput. Chem. Eng., 34(11), pp. 1831–1848, 2010. [Crossref]
[18] Drudd, A.S., CONOPT – A Large-Scale GRG Code, ORSA J. Comput., 6, 207–216, 1994.
[19] Abadie, J. & Carpentier, J., Generalization of the Wolfe reduced gradient method to the case of nonlinear constraints, Optimization, Academic Press, New York, 1969.
[21] Land, A.H. & Doig, A.G., An Automatic Method for Solving Discrete Programming Problems, Econometrica, 28(3), pp. 497–520, 1960. [Crossref]
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Kravanja, S. & Žula, T. (2021). Optimization of a Single-Storey Timber Building Structure. Int. J. Comput. Methods Exp. Meas., 9(2), 126-140. https://doi.org/10.2495/CMEM-V9-N2-126-140
S. Kravanja and T. Žula, "Optimization of a Single-Storey Timber Building Structure," Int. J. Comput. Methods Exp. Meas., vol. 9, no. 2, pp. 126-140, 2021. https://doi.org/10.2495/CMEM-V9-N2-126-140
@research-article{Kravanja2021OptimizationOA,
title={Optimization of a Single-Storey Timber Building Structure},
author={Stojan Kravanja and Tomaž žUla},
journal={International Journal of Computational Methods and Experimental Measurements},
year={2021},
page={126-140},
doi={https://doi.org/10.2495/CMEM-V9-N2-126-140}
}
Stojan Kravanja, et al. "Optimization of a Single-Storey Timber Building Structure." International Journal of Computational Methods and Experimental Measurements, v 9, pp 126-140. doi: https://doi.org/10.2495/CMEM-V9-N2-126-140
Stojan Kravanja and Tomaž žUla. "Optimization of a Single-Storey Timber Building Structure." International Journal of Computational Methods and Experimental Measurements, 9, (2021): 126-140. doi: https://doi.org/10.2495/CMEM-V9-N2-126-140
KRAVANJA S， ŽULA T. Optimization of a Single-Storey Timber Building Structure[J]. International Journal of Computational Methods and Experimental Measurements， 2021， 9(2)： 126-140. https://doi.org/10.2495/CMEM-V9-N2-126-140