Finite Element Modeling of Stability of Beam-Column Supports for Field Fabricated Spherical Storage Pressure Vessels
- 1 Department of Mechanical Engineering, University of Ibadan, Ibadan, Nigeria
- 2 Department of Mechanical Engineering, University of Ibadan, Ibadan, Nigeria
Abstract
Spherical pressure vessels in large sizes are generally supported on legs or columns evenly spaced around the circumference. The legs are attached at or near the equator of the sphere. This research work focussed on flexural-torsional buckling of beam-column supports of field fabricated spherical pressure vessels using finite element analysis. Flexuraltorsional buckling is an important limit state that must be considered in structural steel design and it occurs when a structural member experiences significant out-of-plane bending and twisting. This research has therefore considered the total potential energy equation for the flexural-torsional buckling of a beam-column element. The energy equation was formulated by summing the strain energy and the potential energy of the external loads. The finite element method was applied in conjunction with the energy method to analyze the flexural-torsional buckling of beam-column supports. To apply the finite element method, the displacement functions are assumed to be cubic polynomials, and the shape functions used to derive the element stiffness and element geometric stiffness matrices. The element stiffness and geometric stiffness matrices were assembled to obtain the global stiffness matrices of the structure. The final finite element equation obtained was in the form of an eigenvalue problem. The flexural-torsional buckling loads of the structure were determined by solving for the eigenvalue of the equation. The resulting eigenvalue equation from the finite element analysis was coded using FORTRAN 90 programming language to aid in the analysis process. To validate FORTRAN 90 coding developed for the finite element analysis and the methodology, the results given by the software were compared to existing solutions and showed no significant difference P > 0.05.
- R. R. Erin, “Elastic Flexural-Torsional Buckling Analysis Using Finite Element Method and Object-Oriented Technology with C/C++,” Master’s Thesis, University of Pittsburgh, Pittsburgh, 2002.
- N. S. Trahair, “Flexural Torsional Buckling of Structures,” CRC Press, Boca Raton, 1993.
- W. F. Chen and E. M. Lui, “Structural Stability Theory and Implementation,” Prentice-Hall, Upper Saddle River, 1987.
- A. Javidinejad, “Buckling of Beams and Columns under combined Axial and Horizontal Loading with various Axial Loading Application Locations,” Journal of Theoretical and Applied Mechanics, Vol. 42, No. 4, 2012, pp. 19-30.
- N. S. Trahair and K. J. R. Rasmussen, “Finite Element Analysis of the Flexural Buckling of Columns with Oblique Restrains,” Research Report No. R835, The University of Sydney, Sydney, 2006. http://www.civil.usyd.edu.au
- F. Mohria, C. Bouzerira and M. Potier-Ferry, “Lateral Buckling of Thin-Walled Beam-Column Elements under Combined Axial and Bending Loads,” Thin-Walled Structures, Vol. 46, No. 3, 2008, pp. 290-302. doi:10.1016/j.tws.2007.07.017
- L. Graham-Brady, B. W. Schafer and J. Li, “Analysis of Post-Buckling Behaviour of Beam-Column Structures via Stochastic Finite Elements,” 16th ASCE Engineering Mechanics Conference, Seattle, 16-18 July 2003.
- P. N. Jiki, “Stability of Matrices for Lateral Buckling Analysis of Beams,” Nigerian Journal of Technology, Vol. 25, No. 1, 2006, pp. 36-43.
- Y. L. Pi and N. S. Trahair, “Prebuckling Deflections and Lateral Buckling II: Applications,” Journal of Structural Engineering, Vol. 118, No. 11, 1992, pp. 2967-2986. doi:10.1061/(ASCE)0733-9445(1992)118:11(2967)
- Z. Yuan, “Advanced Analysis of Steel Frame Structures Subjected to Lateral Torsional Buckling Effects,” Doctor’s Thesis, Queensland University of Technology, Brisbane, 2004.