Vol. 22, No. 1, pp. 116-129 (2026)
EFFICIENT CROSS-SECTIONAL ANALYSIS TECHNIQUE FOR
ARBITRARY-SHAPED STEEL SECTIONS USING
GAUSSIAN SEGMENTAL ELEMENTS
Wen-Long Gao 1, Liang Chen 1, *, A.H.A. Abdelrahman 2 and Si-Wei Liu 1
1 Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University,
Hung Hom, Kowloon, Hong Kong, China
2 Department of Structural Engineering, Faculty of Engineering, Mansoura University, Egypt
*(Corresponding author: E-mail:This email address is being protected from spambots. You need JavaScript enabled to view it.)
Received: 06 November 2025; Revised: 26 January 2026; Accepted: 6 February 2026
DOI:10.18057/IJASC.2026.22.1.10
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ABSTRACT
This research introduces an efficient cross-sectional analysis algorithm utilizing innovative Gaussian segmental elements for arbitrary-shaped steel sections. Steel members with arbitrary-shaped sections are gradually widely employed in engineering due to their mechanical benefits. Achieving accuracy in cross-sectional analysis remains crucial for the understanding of their comprehensive structural behavior and enhancing design optimization. Traditional fiber-based cross-sectional analysis methods prioritize accuracy but often compromise computational efficiency. The proposed algorithm leverages the Gaussian quadrature method, renowned for its precise approximation of definite integrals, to address complex cross-sectional geometries. In addition, a refined line-segment model is introduced to solve the overlapping problem by configuring eccentricities at the ends of segments. The paper elaborates on the derivation of the novel Gaussian segmental element designed for modeling the arbitrary-shaped section, determining the section properties, generating full yield surfaces, and calculating the moment-thrust-curvature relationships. Notably, the algorithm balances accuracy and computational efficiency by strategically selecting integration Gauss points and weights across thicknesses. Three groups of examples are provided to demonstrate the accuracy and efficiency of the proposed method for the cross-sectional analysis of arbitrary-shaped steel sections.
KEYWORDS
Arbitrary-shaped steel sections, Cross-sectional analysis, Yield surface, Moment-thrust-curvature, Gauss integration
REFERENCES
[1] P. Waldron, "Sectorial properties of straight thin-walled beams," Computers & Structures, vol. 24, no. 1, pp. 147-156, 1986/01/01/ 1986. doi: https://doi.org/10.1016/0045-7949(86)90344-5
[2] Y. Chai Hong and S. V. Acra, "Cross-sectional properties of thin-walled multi-cellular section," Computers & Structures, vol. 22, no. 1, pp. 53-61, 1986/01/01/ 1986. doi: https://doi.org/10.1016/0045-7949(86)90084-2
[3] T. J. Li, S. W. Liu, and S. L. Chan, "Cross-sectional analysis of arbitrary sections allowing for residual stresses," Steel and Composite Structures, vol. 18, no. 4, pp. 985-1000, 2015.
[4] S. Abdelmageed and T. Zayed, "A study of literature in modular integrated construction - Critical review and future directions," Journal of Cleaner Production, vol. 277, p. 124044, 2020/12/20/ 2020. doi: https://doi.org/10.1016/j.jclepro.2020.124044
[5] X. Du and J. F. Hajjar, "Three-dimensional nonlinear mixed 6-DOF beam element for thin-walled members," Thin-Walled Structures, vol. 164, p. 107817, 2021/07/01/ 2021. doi: https://doi.org/10.1016/j.tws.2021.107817
[6] W. McGuire, a. R. H. Gallagher, and R. D. Ziemian, Matrix Structural Analysis, 2nd Edition (Faculty Books. 7.). 2000.
[7] S.-W. Liu, Y.-P. Liu, and S.-L. Chan, "Advanced analysis of hybrid steel and concrete frames: Part 1: Cross-section analysis technique and second-order analysis," Journal of Constructional Steel Research, vol. 70, pp. 326-336, 2012/03/01/ 2012. doi: https://doi.org/10.1016/j.jcsr.2011.09.003
[8] L. Chen, W.-L. Gao, S.-W. Liu, R. D. Ziemian, and S.-L. Chan, "Geometric and material nonlinear analysis of steel members with nonsymmetric sections," Journal of Constructional Steel Research, vol. 198, p. 107537, 2022/11/01/ 2022. doi: https://doi.org/10.1016/j.jcsr.2022.107537
[9] L. Duan, J. T. Loh, and W. F. Chen, "Moment‐Curvature Relationships for Dented Tubular Sections," Journal of Structural Engineering, vol. 119, no. 3, pp. 809-830, 1993/03/01 1993. doi: 10.1061/(ASCE)0733-9445(1993)119:3(809)
[10] A. Liew, L. Gardner, and P. Block, "Moment-Curvature-Thrust Relationships for Beam-Columns," Structures, vol. 11, pp. 146-154, 2017/08/01/ 2017. doi: https://doi.org/10.1016/j.istruc.2017.05.005
[11] L. Chen, S. W. Liu, and S. L. Chan, "Divergence-free algorithms for moment-thrust-curvature analysis of arbitrary sections," Steel and Composite Structures, vol. 25, pp. 557-569, December10 2017 2017.
[12] M. Mohareb and F. Nowzartash, "Exact Finite Element for Nonuniform Torsion of Open Sections," Journal of Structural Engineering, vol. 129, no. 2, pp. 215-223, 2003/02/01 2003. doi: 10.1061/(ASCE)0733-9445(2003)129:2(215)
[13] K. Saadé, B. Espion, and G. Warzée, "Discussion of “Exact Finite Element for Nonuniform Torsion of Open Sections” by Magdi Mohareb and Farhood Nowzartash," Journal of Structural Engineering, vol. 130, no. 9, pp. 1420-1420, 2004/09/01 2004. doi: 10.1061/(ASCE)0733-9445(2004)130:9(1420)
[14] M. Mohareb and F. Nowzartash, "Closure to “Exact Finite Element for Nonuniform Torsion of Open Sections” by Magdi Mohareb and Farhood Nowzartash," Journal of Structural Engineering, vol. 130, no. 9, pp. 1420-1421, 2004/09/01 2004. doi: 10.1061/(ASCE)0733-9445(2004)130:9(1420.2)
[15] O. Bourihane, A. Ed-dinari, B. Braikat, M. Jamal, F. Mohri, and N. Damil, "Stability analysis of thin-walled beams with open section subject to arbitrary loads," Thin-Walled Structures, vol. 105, pp. 156-171, 2016/08/01/ 2016. doi: https://doi.org/10.1016/j.tws.2016.04.008
[16] A. Elkaimbillah, B. Braikat, F. Mohri, and N. Damil, "A one-dimensional model for computing forced nonlinear vibration of thin-walled composite beams with open variable cross-sections," Thin-Walled Structures, vol. 159, p. 107211, 2021/02/01/ 2021. doi: https://doi.org/10.1016/j.tws.2020.107211
[17] G. J. Hancock and K. J. Rasmussen, "Formulation and Implementation of General Thin-Walled Open-Section Beam-Column Elements in Opensees (No. R961)," 2016.
[18] Rinchen, G. J. Hancock, and K. J. R. Rasmussen, "Geometric and material nonlinear analysis of thin-walled members with arbitrary open cross-section," Thin-Walled Structures, vol. 153, p. 106783, 2020/08/01/ 2020. doi: https://doi.org/10.1016/j.tws.2020.106783
[19] L. Chen, H.-Y. Zhang, S.-W. Liu, and D. Ziemian Ronald, "Efficient Line-Element Method for the Second-Order Analysis of Steel Members with Nonsymmetric Thick-Walled Cross Sections," Journal of Structural Engineering, vol. 150, no. 2, p. 04023226, 2024/02/01 2024. doi: 10.1061/JSENDH.STENG-12543
[20] S.-W. Liu, W.-L. Gao, and R. D. Ziemian, "Improved line-element formulations for the stability analysis of arbitrarily-shaped open-section beam-columns," Thin-Walled Structures, vol. 144, p. 106290, 2019/11/01/ 2019. doi: https://doi.org/10.1016/j.tws.2019.106290
[21] Hou, Yong, Junying Min, Nan Guo, Jianping Lin, John E. Carsley, Thomas B. Stoughton, Heinrich Traphöner, Till Clausmeyer, and A. Erman Tekkaya. "Investigation of evolving yield surfaces of dual-phase steels." Journal of Materials Processing Technology, vol. 287, p. 116314, 2021/01/01 2021. doi: https://doi.org/10.1016/j.jmatprotec.2019.116314
[22] Skordeli, M-AA, and C. D. Bisbos. "Limit and shakedown analysis of 3D steel frames via approximate ellipsoidal yield surfaces." Engineering Structures, vol. 32, no. 6, p. 1556-1567, 2010/06/01 2010. doi: https://doi.org/10.1016/j.engstruct.2010.02.004
[23] Hoang, Hieu Nghia, Quoc Anh Vu, and Manh Hien Nghiem. "An Approximation of Yield Surface for Doubly Symmetrical Sections of Steel Structures." Periodica Polytechnica Civil Engineering, vol. 69, no. 1, P. 321-332, 2025. doi:https://doi.org/10.3311/PPci.36589
[24] Vu, Anh Q., Nghia H. Hoang, and Hien M. Nghiem. "An efficient method for yield and failure surfaces of the steel i-section." Advanced Steel Construction, vol. 16, no. 3, P. 246-254, 2020/09/01 2020. doi: https://doi.org/10.18057/IJASC.2020.16.3.6
[25] Rakici, Salih, and Fatmir Menkulasi. "Moment curvature response of composite UHPC filled hollow structural steel cross-sections." Engineering Structures, vol. 294, P. 116728, 2023/11/01 2023. doi: https://doi.org/10.1016/j.engstruct.2023.116728
[26] Chiorean, Cosmin G. "A computer method for moment-curvature analysis of composite steel-concrete cross-sections of arbitrary shape." Engineering Structures and Technologies, vol. 9, no. 1, P. 25-40. 2017/01/02 2017, doi: https://doi.org/10.3846/2029882X.2017.1299969.
[27] Sun, Zeyang, Yang Yang, Wenlong Yan, Gang Wu, and Xiaoyuan He. "Moment‐curvature behaviors of concrete beams singly reinforced by steel‐FRP composite bars." Advances in Civil Engineering, vol. 1,P. 1309629. 2017.doi: https://doi.org/10.1155/2017/1309629
[28] Abdallah, Maha Hussein, Hamdy M. Mohamed, Radhouane Masmoudi, and Ahmed Moussa. "Analytical modeling of moment-curvature behavior of steel and CFRP RC circular confined columns." Composite Structures, vol. 189, p. 473-487, 2018/04/01 2018, doi: https://doi.org/10.1016/j.compstruct.2018.01.110.
[29] Montuori, Rosario, and Vincenzo Piluso. "Analysis and modelling of CFT members: moment curvature analysis." Thin-Walled Structures, vlo. 86, p. 157-166. 2015/01/01 2015. doi: https://doi.org/10.1016/j.tws.2014.10.010
[30] Rodriguez-Gutierrez, J. A., and J. Dario Aristizabal-Ochoa. "Bending moment-axial force-curvature interactions for metal beam-column sections." Structures, vol. 10, p. 139-146. 2017/05/01 2017. doi: https://doi.org/10.1016/j.istruc.2017.03.003
[31] T. J. R. Hughes and W. K. Liu, "Nonlinear finite element analysis of shells: Part I. three-dimensional shells," Computer Methods in Applied Mechanics and Engineering, vol. 26, no. 3, pp. 331-362, 1981/06/01/ 1981. doi: https://doi.org/10.1016/0045-7825(81)90121-3
[32] E. Spacone, F. C. Filippou, and F. F. Taucer, "FIBRE BEAM–COLUMN MODEL FOR NON-LINEAR ANALYSIS OF R/C FRAMES: PART I. FORMULATION," Earthquake Engineering & Structural Dynamics, vol. 25, no. 7, pp. 711-725, 1996/07/01 1996. doi: https://doi.org/10.1002/(SICI)1096-9845(199607)25:7<711::AID-EQE576>3.0.CO;2-9
[33] N. R. B. K. Raju and J. Nagabhushanam, "Nonlinear structural analysis using integrated force method," Sadhana, vol. 25, no. 4, pp. 353-365, 2000/08/01 2000. doi: 10.1007/BF03029720
[34] C. M. Tiago and V. M. A. Leitão, "Application of radial basis functions to linear and nonlinear structural analysis problems," Computers & Mathematics with Applications, vol. 51, no. 8, pp. 1311-1334, 2006/04/01/ 2006. doi: https://doi.org/10.1016/j.camwa.2006.04.008
[35] E. Parente Jr, G. V. Nogueira, M. Meireles Neto, and L. S. Moreira, "Material and geometric nonlinear analysis of reinforced concrete frames," Revista IBRACON de Estruturas e Materiais, vol. 7, 2014.
[36] L. Chen, A. H. A. Abdelrahman, S.-W. Liu, D. Ziemian Ronald, and S.-L. Chan, "Gaussian Beam–Column Element Formulation for Large-Deflection Analysis of Steel Members with Open Sections Subjected to Torsion," Journal of Structural Engineering, vol. 147, no. 12, p. 04021206, 2021/12/01 2021. doi: 10.1061/(ASCE)ST.1943-541X.0003185
[37] W.-L. Gao, A. H. A. Abdelrahman, S.-W. Liu, and R. D. Ziemian, "Second-order dynamic time-history analysis of beam-columns with nonsymmetrical thin-walled steel sections," Thin-Walled Structures, vol. 160, p. 107367, 2021/03/01/ 2021. doi: https://doi.org/10.1016/j.tws.2020.107367
[38] S.-W. Liu, R. D. Ziemian, L. Chen, and S.-L. Chan, "Bifurcation and large-deflection analyses of thin-walled beam-columns with non-symmetric open-sections," Thin-Walled Structures, vol. 132, pp. 287-301, 2018/11/01/ 2018. doi: https://doi.org/10.1016/j.tws.2018.07.044
[39] S. W. Liu and R. D. Ziemian, "MSASect2 - Matrix Structural Analysis Software for Arbitrary Cross-sections. Retrieved from http://www.msasect.com," ed, 2023.
[40] AISC, Specifications for Structural Steel Buildings ANSI/AISC 360-16, American Institute of Steel Construction, Chicago, C. American Institute of Steel Construction. 2016.
[41] Structure Express, “SE::MC – Moment Curvature Analysis (V2015.06.01)”, 2024, software available at http://structurexpress.com/
[42] W. F. Chen. and and T. Atsuta, Theory of Beam Columns: In-Plane Behavior and Design. Ross Publishing, 1977.