Free vibration of simply supported steel I-girders with trapezoidal web corrugations
DOI:
https://doi.org/10.31181/rme200101141vKeywords:
Natural frequency; Trapezoidal web corrugations; I-girder; Stiffness matrix; Mass matrix.Abstract
Natural frequency is essential information required to perform the dynamic analysis. In this study, the straight I-girder element with trapezoidal web corrugations and singly symmetric cross-section is derived based on Kang and Yoo’s thin-walled curved beam with doubly symmetric cross-section theory. Each node of the element has seven degrees of freedom including one warping degree of freedom. Using Hamilton’s principle, governing linear dynamic differential equations of equilibrium, elastic element stiffness matrix, and consistent element mass matrix are established. Matlab code is employed for natural frequency analysis of simply supported steel I-girders with trapezoidal web corrugations. The results are compared with the natural frequencies related to ABAQUS software. Finally, it is found that the proposed equations provide a good prediction of natural frequency for the first three lateral bending modes and the first five torsional modes.
References
Abbas, H. H. (2003). Analysis and design of corrugated web I-girders for bridges using high performance steel. Ph.D. dissertation, Lehigh University, Bethlehem, Pa.
Inaam, Q., & Upadhyay, A. (2020). Behavior of corrugated steel I-girder webs subjected to patch loading: Parametric study. Journal of Constructional Steel Research, 165, 1058-1096.
Jager, B., Dunai, L., & Kövesdi, B. (2017). Flange buckling behavior of girders with corrugated web Part I: Experimental study. Thin-walled Structures, 118, 181-195.
Kang, Y. J., & Yoo, C. H. (1994). Thin-walled curved beams. I: Formulation of nonlinear equations. Journal of Engineering Mechanics, 120(10), 2072-2101.
Kang, Y. J., & Yoo, C. H. (1994). Thin-walled curved beams. II: Analytical solutions for buckling of arches. Journal of Engineering Mechanics, 120(10), 2102-2125.
Kövesdi, B., Jager, B., & Dunai, L. (2016). Bending and shear interaction behavior of girders with trapezoidally corrugated webs. Journal of Constructional Steel Research, 121, 383-397.
Lin, X., Far, H., & Ali Saleh. (2019). Structural Behaviour and Mechanical Properties of Welded Steel I-Girders with Corrugated Webs. International Journal of Steel Structures, 19(4), 1342-1352.
Lindner, J. (1990). Lateral torsional buckling of beams with trapezoidally corrugated webs. Stab Steel Struct Budapest, Hungary, 305-310.
Moon, J., Yi, J., Choi, B. H., & Lee, H. E. (2009). Shear strength and design of trapezoidally corrugated steel webs. Journal of Constructional Steel Research, 65(5), 1198-1205.
Nguyen, N. N., Kim, S. N., Han, S. R., & Kang, Y. J. (2010). Elastic lateral-torsional buckling strength of I-girder with trapezoidal web corrugations using a new warping constant under uniform moment. Engineering Structures, 32, 2157-2165.
Nguyen, V. H., Ton-That, H. L., Chau, D. T., & Dao, D. N. (2017). Nonlinear Static Bending Analysis of Functionally Graded Plates Using MISQ24 Elements with Drilling Rotations. International Conference on Advances in Computational Mechanics, ACOME, Springer, Singapore, 461-475.
Riahi, F., Behravesh, A., Fard, M. Y., & Armaghani, A. (2018). Shear Buckling Analysis of Steel Flat and Corrugated Web I-girders. KSCE Journal of Civil Engineering, 22, 5058-5073.
Say-Ahmed, E. Y. (2005). Lateral torsion–flexure buckling of corrugated web steel girders. Proceedings of the Institution of Civil Engineers - Structures and Buildings, 158(1), 53-69.
Ton, T. H. L. (2020). A new C0 third-order shear deformation theory for the nonlinear free vibration analysis of stiffened functionally graded plates. Facta Universitatis, Series: Mechanical Engineering, DOI: 10.22190/FUME200629040T.
Ton, T. H. L., Nguyen, V. H., & Chau, D. T. (2020). An Improved Four-Node Element for Analysis of Composite Plate/Shell Structures Based on Twice Interpolation Strategy. International Journal of Computational Methods, 17(6), 1950-1990.
Ton, T. H. L., Nguyen, V. H., & Chau, D. T. (2020). Nonlinear Bending Analysis of Functionally Graded Plates Using SQ4T Elements based on Twice Interpolation Strategy. Journal of Applied and Computational Mechanics, 6(1), 125-136.
Ton, T. H. L., Nguyen, V. H., Chau, D. T., & Huynh. V. C. (2018). Enhancement to four-node quadrilateral plate elements by using cell-based smoothed strains and higher-order shear deformation theory for nonlinear analysis of composite structures. Journal of Sandwich Structures & Materials, 22(7), 2302-2329.
