Burulmaya maruz kalan dairesel içi boş kesitlerin efektif en kesit tasarımı

Year 2025, Volume: 4 Issue: 1, 32 - 55, 30.06.2025

Mirali Nuraliyev , Hamza Kemal Akyıldız , Mehmet Akif Dundar

https://doi.org/10.70700/bjea.1653488

Abstract

Bu çalışma, burulmaya tabi dairesel boşluklu kesitlerin burulma rijitliğini artırırken ağırlıklarını azaltmaya yönelik olarak, dairesel boşluklu kesitlerin optimal etkili kesit boyutlarını belirlemek için analitik yöntemler geliştirmeye adanmıştır. Bu amaçla, içi boş dairesel kesit tasarımına referans teşkil edecek içi dolu dairesel bir kesitin yarıçapı belirlenmiş ve bu kesite dayalı olarak “Eşdeğer Kesit 1” ve “Eşdeğer Kesit 2” olmak üzere iki farklı içi boş dairesel kesit tasarım modeli geliştirilmiştir. Kesitler arasındaki eşdeğerlik, mekanik ve geometrik parametrelerin karşılaştırılması yoluyla sağlanmıştır. “Eşdeğer Kesit 1” modeli kullanılarak elde edilen tasarım sonuçları, bu modelin önemli ölçüde malzeme tasarrufu sağladığını ve bu malzeme tasarrufunun %70'e kadar çıkabildiğini ortaya koymuştur. Buna ek olarak, “Eşdeğer Kesit 2” modeli kullanılarak elde edilen sonuçlar, içi dolu dairesel kesit ile aynı ağırlığa sahip olarak tasarlanan içi boş dairesel kesitlerde maksimum kayma gerilmesinin %77, maksimum birim burulma açısının ise %90 azaldığını ve bu iyileşmelerin sonucunda da burulma rijitliğinin 9 kat arttığını göstermiştir. Burulma yüklemesine maruz kalan içi boş dairesel kesitlerin efektif en kesit boyutlarını belirlemeye yönelik türetilen analitik ifadeler, pratik mühendislik tasarımlarında kullanılabilirliklerini sağlamak amacıyla erişime sunulmuştur. Bu sonuçlar, optimize edilmiş kesit tasarımlarının burulma dayanımını artırırken malzeme kullanımını önemli ölçüde azalttığını ve mühendislik uygulamalarında yapısal verimliliği artırabileceğini ortaya koymuştur.

Keywords

Analitik yöntem , İçi dolu dairesel kesit , İçi boş dairesel kesit , Burulma , Efektif en kesit tasarım

Effective cross-section design of circular hollow sections subjected to torsion

Abstract

This study has been devoted to developing analytical methods for determining the optimal effective cross-sectional dimensions of circular hollow sections subjected to torsion, with the aim of enhancing their torsional rigidity while reducing their weight. To this end, the radius of a solid circular section, which serves as a reference for the circular hollow section design, has been determined, and two different circular hollow section design models, namely “Equivalent Section 1” and “Equivalent Section 2,” have been developed based on this reference section. The equivalence between the sections has been ensured through the comparison of mechanical and geometric parameters. The design results obtained using the “Equivalent Section 1” model have demonstrated that this model achieves significant material savings, with the material savings reaching up to 70%. Furthermore, the results obtained using the “Equivalent Section 2” model have shown that, despite being designed with the same weight as the solid circular section, the circular hollow sections reduce the maximum shear stress by 77% and the maximum unit twist angle by 90%, resulting in a ninefold increase in torsional rigidity. The analytical expressions derived to determine the effective cross-sectional dimensions of circular hollow sections subjected to torsion have been made available to ensure their applicability in practical engineering designs. These findings have revealed that optimized cross-sectional designs can significantly enhance torsional resistance while reducing material use, thereby improving structural efficiency in engineering applications.

Keywords

Analytical method , Circular solid section , Circular hollow section , Torsion , Effective cross-section design

References

• Ashby MF. Overview No. 92: Materials and shape. Acta Metallurgica et Materialia 1991;39:1025–39. https://doi.org/10.1016/0956-7151(91)90189-8.
• Chan TM, Gardner L, Law KH. Structural design of elliptical hollow sections: a review. Proceedings of the Institution of Civil Engineers-Structures and Buildings 2010;163:391–402. https://doi.org/10.1680/stbu.2010.163.6.391.
• Wardenier J, Packer JA, Zhao X-L, Van der Vegte GJ. Hollow sections in structural applications. Bouwen met staal Rotterdam,, The Netherlands; 2002.
• Devi SM, Devi SV, Singh TG. Behaviour and design of high strength steel circular hollow section member under pure torsion. Thin-Walled Structures 2024;195:111387. https://doi.org/https://doi.org/10.1016/j.tws.2023.111387.
• Meng X. Testing, simulation and design of high strength steel tubular elements. Ph.D Dissertation, Imperial College of London, 2020. https://doi.org/10.25560/84566.
• Smith A. 100 Years of the Forth Bridge. Construction History 1991;7:118–20.
• Gere JM, Timoshenko SP. Mechanics of Materials, wadsworth. Inc, Belmont, California 1984:351–5.
• Timoshenko SP, Gere JM. Theory of elastic stability. Courier Corporation; 2012.
• Ashby MF. Materials selection in conceptual design. Materials Science and Technology 1989;5:517–25. https://doi.org/10.1179/mst.1989.5.6.
• Ashby MF. Overview No. 80: On the engineering properties of materials. Acta Metallurgica 1989;37:1273–93. https://doi.org/10.1016/0001-6160(89)90158-2.
• Devi SV, Singh KD. The continuous strength method for circular hollow sections in torsion. Eng Struct 2021;242:112567. https://doi.org/10.1016/j.engstruct.2021.112567.
• Ghavami P. Torsion in Circular Sections. In: Ghavami P, editor. Mechanics of Materials: An Introduction to Engineering Technology, Cham: Springer International Publishing; 2015, p. 163–76. https://doi.org/10.1007/978-3-319-07572-3_7.
• Devi SV, Singh TG, Singh KD. Cold-formed steel square hollow members with circular perforations subjected to torsion. J Constr Steel Res 2019;162:105730. https://doi.org/https://doi.org/10.1016/j.jcsr.2019.105730.
• Ridley-Ellis DJ, Owen JS, Davies G. Torsional behaviour of rectangular hollow sections. J Constr Steel Res 2003;59:641–63. https://doi.org/https://doi.org/10.1016/S0143-974X(02)00060-3.
• Han L-H, Yao G-H, Tao Z. Performance of concrete-filled thin-walled steel tubes under pure torsion. Thin-Walled Structures 2007;45:24–36. https://doi.org/https://doi.org/10.1016/j.tws.2007.01.008.
• Beck J, Kiyomiya O. Fundemental pure torsional properties of concrete filled circular steel tubes. Doboku Gakkai Ronbunshu 2003;2003:285–96.
• Byrne JG, Carré BA. Torsional Stress Concentrations at Rounded Corners of Rectangular Hollow Sections. Journal of Mechanical Engineering Science 1962;4:334–40. https://doi.org/10.1243/JMES_JOUR_1962_004_045_02.
• Abramyan BL. Torsion and bending of prismatic rods of hollow rectangular section. 1951.
• Marshall J, Engineering U of StrathclydeD of C. Aspects of Torsion of Structural Rectangular Hollow Sections. 1972.
• Marshall J. Derivation of Torsion Formulas for Multiply Connected Thick-Walled Rectangular Sections. J Appl Mech 1970;37:399–402. https://doi.org/10.1115/1.3408519.
• Arrayago I, Rasmussen KJR, Real E. Full slenderness range DSM approach for stainless steel hollow cross-sections. J Constr Steel Res 2017;133:156–66. https://doi.org/https://doi.org/10.1016/j.jcsr.2017.02.002.
• Gardner L. The continuous strength method. Proceedings of the Institution of Civil Engineers-Structures and Buildings 2008;161:127–33. https://doi.org/10.1680/stbu.2008.161.3.127.
• Rusch A, Lindner J. Remarks to the Direct Strength Method. Thin-Walled Structures 2001;39:807–20. https://doi.org/https://doi.org/10.1016/S0263-8231(01)00023-4.
• Zhang P, Alam MS. Accuracy of Buckling Strength Curves Using Direct Strength Method in Estimating Axial Strengths of Cold-Formed Steel Members under Compression: Critical Review. Journal of Structural Engineering 2023;149:04022262.
• Gardner L. The continuous strength method. Proceedings of the Institution of Civil Engineers-Structures and Buildings 2008;161:127–33.
• Gere JM, Goodno BJ. Mechanics of Materials, SI Edition. Cengage Learning; 2012.
• Gere JM, Timoshenko SP. Mechanics of Materials. ed. Boston, MA: PWS 1997.
• Bozacı A, Koçaş İ, Çolak ÖÜ. Makina elemanlarının projelendirilmesi. Çağlayan Kitabevi; 2012.
• Erdem KOÇ. Makina Elemanları Çözümlü Problemler. Akademisyen Kitabevi; 2019.