Solving of buckling characteristic of elastically supported shallow arch under concentrated load(PDF)
长安大学学报（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]
- Issue:
- 2017年04期
- Page:
- 112-118
- Research Field:
- Publishing date:
Info
- Title:
- Solving of buckling characteristic of elastically supported shallow arch under concentrated load
- Author(s):
- PAN Quan; YI Zhuang-peng; ZENG You-yi; YAN Dong-huang
- School of Civil Engineering and Architecture, Changsha University of Science and Technology, Changsha 410114, Hunan, China
- Keywords:
- bridge engineering; shallow arch; vertical elastic support; nonlinear stability; equilibrium path; critical load
- PACS:
- U441.2
- DOI:
- -
- Abstract:
- To find a research method that can solve the nonlinear stability of elastically supported arch with arbitrary arch axis under arbitrary load, the buckling characteristics of a planar shallow arch with vertical elastic supports at both ends of an arbitrary axis under a concentrated load were investigated in this research. The nonlinear equilibrium equations of dimensional normalization were derived and the distribution characteristics of buckling paths and critical loads were studied by an example. The analytical results were compared and validated with the finite element analysis results. The buckling modes of the beam, which has the same elastic supports as shallow arch, were applied as shape functions to expand the arch axis, external load and structural deformation without any truncations. Then the equilibrium equations of basic equilibrium states, primary buckling and bifurcated buckling were obtained. The corresponding relationship among the external load, the structural displacement and internal force of structure was established, and the equilibrium paths and critical loads of the primary and bifurcated buckling of shallow arches were further achieved. The effects of elastic stiffness parameters on equilibrium paths and ultimate load under two kinds of buckling conditions were analyzed. The results show that these two results match well with each other, and the presented method can trace the whole buckling process of shallow arch structure. The primary buckling and bifurcated buckling exist simultaneously. When elastic supports change from symmetry to asymmetry, the primary equilibrium paths split into basic paths and independent separated paths at specific locations. Some bifurcated equilibrium paths transfer to primary one with the appearance and disappearance of corresponding critical load points. The critical loads are only sensitive to the smaller elastic constraint parameters. When constraint stiffness increases to a certain extent, the critical load will no longer change with the constraint stiffness. The solving equations for planar buckling of vertically supported shallow arch with elastic supports and arbitrary arch axis under a concentrated load deduced in this paper can eventually provide a reference to realize the analytical solution of nonlinear stability of shallow arch with elastic supports and arbitrary arch axis under arbitrary loads.
Last Update: 2017-07-17