Out-Plane Buckling of Arches with Variable Cross-Section
Abstract
:1. Introduction
2. Basic Assumptions and Cross-Sectional Features
- (1)
- The cross-section of the arch remains perpendicular to the arch axis throughout the buckling process.
- (2)
- An exponential function with the base of the natural constant e is employed as the variable cross-sectional form.
- (3)
- The span and height of the arch are significantly larger than the dimensions of the arch’s cross-section are assumed.
- (4)
- The cross-section of the arch is assumed to be rectangular, exhibiting continuous and uniform variations along its length.
- (5)
- The material of the arch is assumed to be uniform, isotropic, and exhibits linear elasticity. The elastic modulus is represented as E, and the shear modulus as G.
3. Analysis of Variable Cross-Section
4. Out-Plane Buckling
4.1. Internal Force and Normal Stress of Variable Cross-Sectional Arch
4.2. Critical Out-Plane Buckling Load of Variable Cross-Sectional Arch
5. Comparisons with Finite Element (FE) Results
5.1. Numerical Model of the Arch with Variable Cross-Section
5.2. Comparative Analysis with Finite Element Results
6. Parametric Analysis
6.1. Parametric Analysis of Stresses and Internal Forces
6.2. Parametric Analysis of Critical Buckling Load
7. Conclusions
- (1)
- As the cross-sectional height ratio of the variable cross-sectional arch increases, the segments of the arch axis experiencing compressive stress increase, while the segments experiencing tensile stress gradually decrease. These result in a more uniform distribution of stress in the arch.
- (2)
- Through the analysis of the effects of the in-plane slenderness ratio S/rxm, the localized parameter c/Θ, the flexibility coefficient of the flexibility coefficient of elastic rotation constraint ζ, and the variation of internal forces along the arch axis, it can be observed that compared to arches with a uniform cross-sectional height ratio he/h0 = 1, variable cross-sectional arches with he/h0 greater than 1 exhibit larger axial compression Nc/Q and smaller bending moment 4 Mc/(QL). However, for variable cross-sectional arches with he/h0 less than 1, the axial compression Nc/Q is smaller, and the bending moment 4 Mc/(QL) is larger. Therefore, properly designed variable cross-sectional arches exhibit more uniform internal force distribution and better pre-buckling performance.
- (3)
- Through the parametric analysis of the critical out-plane buckling load, it has been found that compared to arches with a uniform cross-section height ratio of he/h0 = 1, variable cross-section arches with a cross-section height ratio he/h0 greater than 1 can achieve a larger critical out-plane buckling load, indicating a higher level of stability. These findings provide valuable insights for structural design.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Coefficients A11, A12, A13, A21, A22 and A23
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Jiang, A.; Deng, D.; Dai, W.; You, X.; Lu, H. Out-Plane Buckling of Arches with Variable Cross-Section. Buildings 2023, 13, 2838. https://doi.org/10.3390/buildings13112838
Jiang A, Deng D, Dai W, You X, Lu H. Out-Plane Buckling of Arches with Variable Cross-Section. Buildings. 2023; 13(11):2838. https://doi.org/10.3390/buildings13112838
Chicago/Turabian StyleJiang, Angfeng, Deyuan Deng, Wei Dai, Xiuwen You, and Hanwen Lu. 2023. "Out-Plane Buckling of Arches with Variable Cross-Section" Buildings 13, no. 11: 2838. https://doi.org/10.3390/buildings13112838