An approach of web stiffener calculation in thin-walled columns
Abstract
This article presents an analytical approach for calculating web stiffeners in thin-walled columns. A novel method is introduced, which treats each bending point in the cross-section web as a separate stiffener. The advantages of this calculation method are discussed, highlighting its increased versatility in designing cross-section geometry. The load-bearing strength of axially compressed thin-walled closed cross-section columns, calculated using this method, is compared to analytical calculations based on the Eurocode 3-1-3 methodology and to the finite element method analysis. Calculation results of columns with cross-sections including shallow web stiffeners were up to 9.22% less conservative when compared to the Eurocode 3-1-3 methodology. The results demonstrate great compliance of the proposed method for column crosssections with deep stiffeners. Finite element method (FEM) analysis was performed to verify the calculated load bearing strengths of the columns according to both calculation methodologies. FEM analysis confirmed the reliance of the calculated results and showed, that the load bearing strengths calculated using the newly presented methodology were ranging from 88.77% to 97.86% of load bearing strength calculated using finite element method. These results proved, that the proposed method provides an accurate load bearing strength of thin-walled columns with web stiffeners.
Keyword : cold-formed structures, Eurocode, Finite element method, slender members, local buckling, distortional buckling, flexural buckling
How to Cite
Stulpinas, M., & Daniūnas, A. (2024). An approach of web stiffener calculation in thin-walled columns. Journal of Civil Engineering and Management, 30(6), 551–565. https://doi.org/10.3846/jcem.2024.21793
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Kotełko, M. (2007). Load-carrying capacity and energy absorption of thin-walled profiles with edge stiffeners. Thin-Walled Structures, 45(10–11), 872–876. https://doi.org/10.1016/j.tws.2007.08.038
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Li, Q. Y., & Young, B. (2023). Experimental and numerical studies on cold-formed steel battened columns. Engineering Structures, 288, Article 116110. https://doi.org/10.1016/j.engstruct.2023.116110
Li, Q. Y., & Young, B. (2024). Experimental and numerical investigation on cold-formed steel zed section beams with complex edge stiffeners. Thin-Walled Structures, 194, Article 111315. https://doi.org/10.1016/j.tws.2023.111315
Liu, C., Chen, X., Mao, X., He, L., & Yuan, J. (2023). Study on flexural and demountable behavior of a modular light-gauge steel framed wall. Journal of Civil Engineering and Management, 29(2), 143–156. https://doi.org/10.3846/jcem.2023.18351
Meza, F., J., & Becque, J. (2023). Numerical modelling of cold-formed steel built-up columns. Thin-Walled Structures, 188, Article 110781. https://doi.org/10.1016/j.tws.2023.110781
Meza, F., J., Becque, J., & Hajirasouliha, I. (2020). Experimental study of the cross-sectional capacity of cold-formed steel built—up columns. Thin-Walled Structures, 155, Article 106958. https://doi.org/10.1016/j.tws.2020.106958
Mojtabaei, S., M., Hajirasouliha, I., & Ye, J. (2021). Optimisation of cold-formed steel beams for best seismic performance in bolted moment connections. Journal of Constructional Steel Research, 181, Article 106621. https://doi.org/10.1016/j.jcsr.2021.106621
Mokhtari, F., & Imanpour, A. (2024). Hybrid data-driven and physics-based simulation technique for seismic analysis of steel structural systems. Computers & Structures, 295, Article 107286. https://doi.org/10.1016/j.compstruc.2024.107286
Natali, A., & Morelli, F. (2022). Experimental validation of dissipative reduced-section thin walled diagonals for seismic-resistant automated rack supported warehouses. Procedia Structural Integrity, 44, 2334–2341. https://doi.org/10.1016/j.prostr.2023.01.298
Rinchen, R., & Rasmussen, K. J. R. (2020). Experiments on long-span cold-formed steel single C-section portal frames. Journal of Structural Engineering, 146(1), Article 04019187. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002487
Sang, L., Zhou, T., Zhang, L., Chen, B., & Wang, S. (2022). Experimental investigation on the axial compression behavior of cold-formed steel triple-limbs built-up columns with half open section. Thin-Walled Structures, 172, Article 108913. https://doi.org/10.1016/j.tws.2022.108913
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Schafer, B., W. (2020, April 6). Intro to CUFSM. CUFSM – Cross-section elastic buckling analysis. Constrained and unconstrained finite strip method. https://www.ce.jhu.edu/cufsm/2020/04/06/intro-to-cufsm/
Schafer, B. W., Li, Z., & Moen, C. D. (2010). Computational modeling of cold-formed steel. Thin-Walled Structures, 48(10–11), 752–762. https://doi.org/10.1016/j.tws.2010.04.008
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Stulpinas, M., & Daniūnas, A. (2024). Selection of an optimum axially compressed closed cross-section thin-walled built-up column. In J. A. O. Barros, G. Kaklauskas, & E. K. Zavadskas (Eds.), Lecture notes in civil engineering, Vol. 392: Modern building materials, structures and techniques (MBMST 2023) (pp. 194–203). Springer, Cham. https://doi.org/10.1007/978-3-031-44603-0_19
Truong, D. N., & Chou, J. S. (2023). Integrating enhanced optimization with finite element analysis for designing steel structure weight under multiple constraints. Journal of Civil Engineering and Management, 29(8), 757–786. https://doi.org/10.3846/jcem.2023.20399
Weixin, M., Jurgen, B., Iman, H., & Jun, Y. (2015). Cross-sectional optimization of cold-formed steel channels to Eurocode 3. Engineering Structures, 101, 641–651. https://doi.org/10.1016/j.engstruct.2015.07.051
Wen, C.-B., Zhu, B.-L., Sun, H.-J., Guo, Y.-L., Zheng, W.-J., & Deng, L.-L. (2024). Global stability design of double corrugated steel plate shear walls under combined shear and compression loads. Thin-Walled Structures, 199, Article 111789. https://doi.org/10.1016/j.tws.2024.111789
Ye, J., Quan, G., Kyvelou, P., Teh, L, & Gardner, L. (2022). A practical numerical model for thin-walled steel connections and built-up members. Structures, 38, 753–764. https://doi.org/10.1016/j.istruc.2022.02.028
Zhang, X., & Rasmussen, K. (2014). Tests of cold-formed steel portal frames with slender sections. Steel Construction, 7, 199–203. https://doi.org/10.1002/stco.201410030
Zhang, J., H., & Young, B. (2018a). Experimental investigation of cold-formed steel built-up closed section columns with web stiffeners. Journal of Constructional Steel Research, 147, 380–392. https://doi.org/10.1016/j.jcsr.2018.04.008
Zhang, J., H., & Young, B. (2018b) Finite element analysis and design of cold-formed steel built-up closed section columns with web stiffeners. Thin-Walled Structures, 131, 223–237. https://doi.org/10.1016/j.tws.2018.06.008
Zhou, K., Li, Q. S., Zhi, L. H., Han, X. L., & Xu, K. (2023). Investigation of modal parameters of a 600-m-tall skyscraper based on two-year-long structural health monitoring data and five typhoons measurements. Engineering Structures, 274, Article 115162. https://doi.org/10.1016/j.engstruct.2022.115162
Alabi-Bello, M., A., Wang, Y., C., & Su, M. (2021). An assessment of different direct strength methods for cold-formed thin-walled steel beam-columns under com-pression and major axis bending. Structures, 34, 4788–4802. https://doi.org/10.1016/j.istruc.2021.10.027
ANSYS, Inc. (2013). ANSYS mechanical APDL verification manual.
Ananthi, G. B. G., Deepak, M. S., Roy, K., & Lim, J. B. P. (2021). Influence of intermediate stiffeners on the axial capacity of cold-formed steel back-to-back built-up unequal angle sections. Structures, 32, 827–848. https://doi.org/10.1016/j.istruc.2021.03.059
Bučmys, Ž., Daniūnas, A., Jaspart, J.-P., & Demonceau, J.-F. (2018). A component method for cold-formed steel beam-to-column bolted gusset plate joints. Thin-Walled Structures, 123, 520–527. https://doi.org/10.1016/j.tws.2016.10.022
Chen, J., He, Y., Jin, W. L. (2010). Stub column tests of thin-walled complex section with intermediate stiffeners. Thin-Walled Structures, 48(6), 423–429. https://doi.org/10.1016/j.tws.2010.01.008
Cheng, L., Qiu, C., & Du, X. (2024). A two-level performance-based plastic design method for multi-story steel frames with double-yielding systems. Soil Dynamics and Earthquake Engineering, 178, Article 108449. https://doi.org/10.1016/j.soildyn.2024.108449
Dar, M., A., Verma, A., Anbarasu, M., Pang, S., D., & Dar, A. R. (2022). Design of cold-formed steel battened built-up columns. Journal of Constructional Steel Research, 193, Article 107291. https://doi.org/10.1016/j.jcsr.2022.107291
Dong, S., Li, H., & Wen, Q. (2015). Study on distortional buckling performance of cold-formed thin-walled steel flexural members with stiffeners in the flange. Thin-Walled Structures, 95, 161–169. https://doi.org/10.1016/j.tws.2015.07.006
Dubina, D., & Ungureanu, V. (2023). Local/distortional and overall interactive buckling of thin-walled cold-formed steel columns with open cross-section. Thin-Walled Structures, 182, Article 110172. https://doi.org/10.1016/j.tws.2022.110172
European Committee for Standardization. (2006a). Eurocode 3: Design of steel structures – Part 1-3: General rules – Supplementary rules for cold-formed members and sheeting (EN 1993-1-3).
European Committee for Standardization. (2006b). Eurocode 3: Design of steel structures – Part 1-5: Plated structural elements (EN 1993-1-5).
European Committee for Standardization. (2018). Execution of steel structures and aluminium structures – Part 2: Technical requirements for steel structures (EN 1090-2:2018).
European Committee for Standardization. (2023). Eurocode 3: Design of steel structures – Part 1-14: Design assisted by finite element analysis (EN 1993-1-14).
Gurupatham, B. G. A., Roy, K., Raftery, G. M., & Lim, J. B. P. (2022). Influence of intermediate stiffeners on axial capacity of thin-walled built-up open and closed channel section columns. Buildings, 12(8), Article 1071. https://doi.org/10.3390/buildings12081071
Habashneh, M., Cucuzza, R., Domaneschi, M., & Movahedi Rad, M. (2024). Advanced elasto-plastic topology optimization of steel beams under elevated temperatures. Advances in Engineering Software, 190, Article 103596. https://doi.org/10.1016/j.advengsoft.2024.103596
Kherbouche, S., & Megnounif, A. (2019). Numerical study and design of thin walled cold formed steel built-up open and closed section columns. Engineering Structures, 179, 670–682. https://doi.org/10.1016/j.engstruct.2018.10.069
Kishino, V. H., Kishino, R. T., & Coda, H. B. (2022). A sequential investigation of the residual stresses and strains influence on the buckling of cold-formed thin-walled members. Thin-Walled Structures, 180, Article 109814. https://doi.org/10.1016/j.tws.2022.109814
Kotełko, M. (2007). Load-carrying capacity and energy absorption of thin-walled profiles with edge stiffeners. Thin-Walled Structures, 45(10–11), 872–876. https://doi.org/10.1016/j.tws.2007.08.038
Laghi, V., Babovic, N., Benvenuti, E., & Kloft, H. (2024). Blended structural optimization of steel joints for wire-and-arc additive manufacturing. Engineering Structures, 300, Article 117141. https://doi.org/10.1016/j.engstruct.2023.117141
Li, Z., & Schafer, B. W. (2010). Buckling analysis of cold-formed steel members with general boundary conditions using CUFSM conventional and constrained finite strip methods. In CCFSS Proceedings of International Specialty Conference on Cold-Formed Steel Structures (pp. 1971–2018). Missouri University of Science and Technology. https://scholarsmine.mst.edu/isccss/20iccfss/20iccfss-session1/2
Li, Q. Y., & Young, B. (2023). Experimental and numerical studies on cold-formed steel battened columns. Engineering Structures, 288, Article 116110. https://doi.org/10.1016/j.engstruct.2023.116110
Li, Q. Y., & Young, B. (2024). Experimental and numerical investigation on cold-formed steel zed section beams with complex edge stiffeners. Thin-Walled Structures, 194, Article 111315. https://doi.org/10.1016/j.tws.2023.111315
Liu, C., Chen, X., Mao, X., He, L., & Yuan, J. (2023). Study on flexural and demountable behavior of a modular light-gauge steel framed wall. Journal of Civil Engineering and Management, 29(2), 143–156. https://doi.org/10.3846/jcem.2023.18351
Meza, F., J., & Becque, J. (2023). Numerical modelling of cold-formed steel built-up columns. Thin-Walled Structures, 188, Article 110781. https://doi.org/10.1016/j.tws.2023.110781
Meza, F., J., Becque, J., & Hajirasouliha, I. (2020). Experimental study of the cross-sectional capacity of cold-formed steel built—up columns. Thin-Walled Structures, 155, Article 106958. https://doi.org/10.1016/j.tws.2020.106958
Mojtabaei, S., M., Hajirasouliha, I., & Ye, J. (2021). Optimisation of cold-formed steel beams for best seismic performance in bolted moment connections. Journal of Constructional Steel Research, 181, Article 106621. https://doi.org/10.1016/j.jcsr.2021.106621
Mokhtari, F., & Imanpour, A. (2024). Hybrid data-driven and physics-based simulation technique for seismic analysis of steel structural systems. Computers & Structures, 295, Article 107286. https://doi.org/10.1016/j.compstruc.2024.107286
Natali, A., & Morelli, F. (2022). Experimental validation of dissipative reduced-section thin walled diagonals for seismic-resistant automated rack supported warehouses. Procedia Structural Integrity, 44, 2334–2341. https://doi.org/10.1016/j.prostr.2023.01.298
Rinchen, R., & Rasmussen, K. J. R. (2020). Experiments on long-span cold-formed steel single C-section portal frames. Journal of Structural Engineering, 146(1), Article 04019187. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002487
Sang, L., Zhou, T., Zhang, L., Chen, B., & Wang, S. (2022). Experimental investigation on the axial compression behavior of cold-formed steel triple-limbs built-up columns with half open section. Thin-Walled Structures, 172, Article 108913. https://doi.org/10.1016/j.tws.2022.108913
Schafer, B. W. (2011). Cold-formed steel structures around the world. Steel Construction, 4(3), 141–149. https://doi.org/10.1002/stco.201110019
Schafer, B., W. (2020, April 6). Intro to CUFSM. CUFSM – Cross-section elastic buckling analysis. Constrained and unconstrained finite strip method. https://www.ce.jhu.edu/cufsm/2020/04/06/intro-to-cufsm/
Schafer, B. W., Li, Z., & Moen, C. D. (2010). Computational modeling of cold-formed steel. Thin-Walled Structures, 48(10–11), 752–762. https://doi.org/10.1016/j.tws.2010.04.008
Seyedabadi, M. R., Karrabi, M., Shariati, M., Karimi, S., Maghrebi, M., & Eicker, U. (2024). Global building life cycle assessment: Comparative study of steel and concrete frames across European Union, USA, Canada, and Australia building codes. Energy and Buildings, 304, Article 113875. https://doi.org/10.1016/j.enbuild.2023.113875
Stulpinas, M., & Daniūnas, A. (2024). Selection of an optimum axially compressed closed cross-section thin-walled built-up column. In J. A. O. Barros, G. Kaklauskas, & E. K. Zavadskas (Eds.), Lecture notes in civil engineering, Vol. 392: Modern building materials, structures and techniques (MBMST 2023) (pp. 194–203). Springer, Cham. https://doi.org/10.1007/978-3-031-44603-0_19
Truong, D. N., & Chou, J. S. (2023). Integrating enhanced optimization with finite element analysis for designing steel structure weight under multiple constraints. Journal of Civil Engineering and Management, 29(8), 757–786. https://doi.org/10.3846/jcem.2023.20399
Weixin, M., Jurgen, B., Iman, H., & Jun, Y. (2015). Cross-sectional optimization of cold-formed steel channels to Eurocode 3. Engineering Structures, 101, 641–651. https://doi.org/10.1016/j.engstruct.2015.07.051
Wen, C.-B., Zhu, B.-L., Sun, H.-J., Guo, Y.-L., Zheng, W.-J., & Deng, L.-L. (2024). Global stability design of double corrugated steel plate shear walls under combined shear and compression loads. Thin-Walled Structures, 199, Article 111789. https://doi.org/10.1016/j.tws.2024.111789
Ye, J., Quan, G., Kyvelou, P., Teh, L, & Gardner, L. (2022). A practical numerical model for thin-walled steel connections and built-up members. Structures, 38, 753–764. https://doi.org/10.1016/j.istruc.2022.02.028
Zhang, X., & Rasmussen, K. (2014). Tests of cold-formed steel portal frames with slender sections. Steel Construction, 7, 199–203. https://doi.org/10.1002/stco.201410030
Zhang, J., H., & Young, B. (2018a). Experimental investigation of cold-formed steel built-up closed section columns with web stiffeners. Journal of Constructional Steel Research, 147, 380–392. https://doi.org/10.1016/j.jcsr.2018.04.008
Zhang, J., H., & Young, B. (2018b) Finite element analysis and design of cold-formed steel built-up closed section columns with web stiffeners. Thin-Walled Structures, 131, 223–237. https://doi.org/10.1016/j.tws.2018.06.008
Zhou, K., Li, Q. S., Zhi, L. H., Han, X. L., & Xu, K. (2023). Investigation of modal parameters of a 600-m-tall skyscraper based on two-year-long structural health monitoring data and five typhoons measurements. Engineering Structures, 274, Article 115162. https://doi.org/10.1016/j.engstruct.2022.115162