The Effects of Changing the Support Point in a Given Cross Section on Structural Stability
Source abstract
Abstract
The aim of this study was to examine the effect of a change of the beam support point within the same support cross section and that of a change in the location of load application points on critical load values. In the literature on the stability of structures, the problem of a change of a rod system’s support point (within the same cross section) is neglected. Solely the effect of a change in load application points on the critical load value is considered. In this study, displacement differential equations describing the general stability loss problem for any nonprismatic thin-walled beam were derived. To solve the equations an approximation method (described in earlier papers by the authors), using the Chebyshev series of the first kind to approximate the sought functions, was employed. In the provided numerical examples the buckling problem was solved for nonprismatic I-beams with a bisymmetric cross section and a monosymmetric cross section. The determined critical load values were compared with the results obtained using the finite element method and the commercial Sofistik software. The results obtained in this study show the significant effect of beam support point location (within the same cross section), as well as the effect of load application point location, on critical load values.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Engineering Applied Research · Structural Load-Bearing Analysis · Structural Analysis of Composite Materials
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Faculty of Civil Engineering, Wrocław University of Science and Technology, 50-370 Wrocław, Poland
References (44)
Show source-provided references
1. Vibration and buckling behaviours of thin-walled composite and functionally graded sandwich I-beams10.1016/j.compositesb.2019.02.033 ↗
2. Lateral-torsional buckling of singly symmetric tapered beams: Theory and applications
3. Analytical solutions attempt for lateral torsional buckling of doubly symmetric web-tapered I-beams10.1016/j.engstruct.2013.06.036 ↗
4. Lateral-torsional buckling of singly symmetric web-tapered thin-walled I-beams: 1D model vs. shell FEA10.1016/j.compstruc.2006.08.079 ↗
5. Lateral-torsional buckling of tapered thin-walled beams with arbitrary cross-sections10.1016/j.tws.2012.06.007 ↗
6. Inelastic buckling of tapered monosymmetric I-beams10.1016/0141-0296(89)90021-7 ↗
7. An analytical study on the lateral-torsional buckling of linearly tapered cantilever strip beams10.1142/S0219455407002368 ↗
8. Lateral-torsional buckling of nonprismatic I-beams10.1061/(ASCE)0733-9445(1996)122:7(748) ↗
9. Elastic stability of tapered I-beams10.1061/JSDEAG.0003184 ↗
10. Elastic behavior of tapered monosymmetric I-beams10.1061/JSDEAG.0004130 ↗
11. Kuś, J. (2012). Stability of Beams with Tapered Cross Sections. [Doctoral Dissertation, Opole University of Technology]. (In Polish).
12. Lateral-torsional buckling steel beams with simultaneously tapered flanges and web10.12989/scs.2015.19.4.897 ↗
13. Critical moments in the lateral torsional buckling of steel I-beams with linearly variable web depth and flange width
14. Theoretical and numerical stability analyses of unrestrained, mono-symmetric thin-walled beams10.1016/S0143-974X(02)00007-X ↗
15. Lateral buckling of tapered thin walled bi-symmetric beams under combined axial and bending loads with shear deformations allowed10.1016/j.engstruct.2018.03.009 ↗
16. Lateral-torsional stability of steel web-tapered I-beams10.1061/(ASCE)0733-9445(1998)124:10(1208) ↗
17. Critical Lateral-Torsional Buckling Moments of Steel Web-Tapered I-beams10.2174/1874836801004010105 ↗
18. Lateral-torsional buckling of functionally graded tapered I-beams considering lateral bracing
19. A novel approach for lateral buckling assessment of double tapered thin-walled laminated composite I-beams
20. Exact stiffness matrices for lateral–torsional buckling of doubly symmetric tapered beams with axially varying material properties10.1007/s40996-020-00402-z ↗
21. Lateral-torsional stability analysis of a simply supported axially functionally graded beam with a tapered I-section10.1007/s11029-020-09859-5 ↗
22. Improved finite element model for lateral stability analysis of axially functionally graded nonprismatic I-beams10.1142/S0219455419501086 ↗
23. Lateral stability analysis of steel tapered thin-walled beams under various boundary conditions10.29252/nmce.3.1.13 ↗
24. Lateral buckling of web-tapered I-beams: A new theory10.1016/j.jcsr.2008.01.014 ↗
25. The lateral torsional buckling of steel beams with limited ability to rotate on their supports
26. Improved formulation for spatial stability and free vibration of thin-walled tapered beams and space frame10.1016/S0141-0296(98)00140-0 ↗
27. Flexural-torsional stability of thin-walled functionally graded open-section beams10.1016/j.tws.2016.09.021 ↗
28. Lateral buckling analysis of thin-walled functionally graded open-section beams10.1016/j.compstruct.2016.10.017 ↗
29. Buckling of thin-walled beams with open and generically variable section10.1016/0045-7949(92)90470-K ↗
30. Nonlocal elasticity theory for lateral stability analysis of tapered thin-walled nanobeams with axially varying materials10.1016/j.tws.2020.107268 ↗
31. Soltani, M., Atoufi, F., Mohri, F., Dimitri, R., and Tornabene, F. (2021). Nonlocal analysis of the flexural-torsional stability for FG tapered thin-walled beam-columns. Nanomaterials, 11.10.3390/nano11081936 ↗
32. Stability of beams with tapered I-sections
33. Latalski, J., and Zulli, D. (2020). Generalized Beam Theory for Thin-Walled Beams with Curvilinear Open Cross-Sections. Appl. Sci., 10.10.3390/app10217802 ↗
34. A geometrically nonlinear shell theory for thin-walled tubes and beams subjected to large displacements and cross-section deformation10.1016/j.tws.2025.113583 ↗
35. Application of Chebyshev series to solution of non-prismatic beam vibration problems10.1006/jsvi.1999.2348 ↗
36. Dynamic stability problem of non-prismatic rod10.1006/jsvi.2001.3954 ↗
37. Lateral stability of bending non-prismatic thin-walled beams using orthogonal series10.1016/j.proeng.2015.07.134 ↗
38. An analysis of the effect of a change in the support point location on the vibration of thin-walled beams10.1142/S021945542150125X ↗
39. Analysis of thin-walled beams with variable monosymmetric cross section by means of Legendre polynomials
40. Effect of a “slight” curvature of the axis of a thin-walled nonprismatic beam on its free vibration
41. The torsion of thin-walled rods with variable cross-section
42. Construction of a recurrence relation of the lowest order for coefficients of the Gegenbauer series
43. Paszkowski, S. (1975). The Numerical Application of Chebyshev Polynomials and Series, Polish Scientific Publishers. (In Polish).
44. (2025, September 02). Wolfram. Mathematica 12, Available online: https://www.wolfram.com/mathematica/.