Master's Thesis

Girder Cross Section Shape and Reinforcement Optimisation

Final Thesis 2.34 MB Appendix 6.31 MB

Author of thesis: Ing. Roman Hanuš

Acad. year: 2025/2026

Supervisor: doc. Ing. Ivana Laníková, Ph.D.

Reviewer: Ing. Petr Šimůnek, Ph.D.

Abstract:

This diploma thesis focuses on the design and development of a computational optimization tool for reinforced concrete structural elements using the Microsoft Office Excel environment. The main objective of the thesis is the application of optimization methods while complying with the requirements of the ultimate limit state and serviceability limit state according to applicable standards. The proposed algorithm enables variable optimization of both the cross-sectional geometry and material distribution within a concrete member based on a defined objective function. The theoretical part addresses the calculation of cross-sectional properties of a general polygonal section, determination of the neutral axis position, and integration of stresses in the compressed concrete zone using a parabolic–rectangular stress–strain diagram. The practical part describes the implementation of the computational model and optimization algorithm using the Solver add-in in MS Excel, including a discussion of its limitations and practical challenges. The functionality of the developed tool is demonstrated through a case study of a reinforced concrete element of a hall structure. The thesis highlights the potential of accessible computational tools for the efficient and economical design of reinforced concrete structures.

Keywords:

Optimization, truss, roof, reinforced concrete, cross-section, shape, Microsoft Office Excel, Scia Engineer, Solver tool, gradient method, purpose function, model variables, constraints, optimal design, cost, area, optimization algorithm, hall, load, combinations, internal forces, bending, shear, ultimate limit state, serviceability limit state, ideal cross-section.

Date of defence

04.02.2026

Result of the defence

Defended (thesis was successfully defended)

znamkaAznamka

Grading

A

Process of defence

Prof. Halvoník Plochu betonu, průřezu jste měnil výšku na základě nějakého kritéria? Odpověděl Prof. Halvoník Při jakém průměru jste volil stykování výztuže 350 mm? Odpověděl Prof. Halvoník Máte nějaký výkres nejoptimálnějšího řešení? Odpověděl Doc. Novák Zajišťoval jste spojitost mezi jednotlivými částmi? Odpověděl Doc. Novák Omezení veličin. Jakým způsobem jste zajistil, že se jednotlivé veličiny ovlivňují? Odpověděl Doktorka Lakatosová Máte nosník štíhlý. Co si myslíte, že je kritické namáhání? Odpověděl s dopomocí

Language of thesis

Czech

Faculty

Department

Institute of Concrete and Masonry Structures

Study programme

Civil Engineering – Structural and Transport Engineering (NPC-SIK)

Composition of Committee

prof. Ing. Jaroslav Halvoník, Ph.D. (předseda)
prof. Ing. Jiří Stráský, DSc. (místopředseda)
doc. Ing. Ladislav Klusáček, CSc. (člen)
doc. Ing. Jan Koláček, Ph.D. (člen)
Ing. Adam Svoboda, Ph.D. (člen)
Ing. Pavlína Lakatosová, Ph.D. (člen)
doc. Ing. Lukáš Novák, Ph.D. (člen)

Supervisor’s report
doc. Ing. Ivana Laníková, Ph.D.

Grade proposed by supervisor: A

File inserted by supervisor Size
Posudek DP Hanuš.pdf 80,99 kB

Reviewer’s report
Ing. Petr Šimůnek, Ph.D.

Grade proposed by reviewer: A

File inserted by the reviewer Size
DP posudek oponenta Hanuš_Šimůnek.pdf 87,85 kB

Responsibility: Mgr. et Mgr. Hana Odstrčilová