Research PaperNo Access

Exact Matrix Stiffness Method for Out-of-Plane Buckling Analysis of Funicular Arches Considering Warping Deformations

Chuan-Hao Zhao

College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, P. R. China

Center for Balance Architecture, Zhejiang University, Hangzhou 310028, P. R. China

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Wen-Hao Pan

https://orcid.org/0000-0002-0280-4550

College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, P. R. China

Architectural Design and Research Institute of Zhejiang University Co., Ltd., Hangzhou 310028, P. R. China

Key Laboratory of Space Structures of Zhejiang Province, Hangzhou 310058, P. R. China

E-mail Address: pan_wh@zju.edu.cn

Corresponding author.

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Yao-Zhi Luo

College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, P. R. China

Key Laboratory of Space Structures of Zhejiang Province, Hangzhou 310058, P. R. China

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https://doi.org/10.1142/S0219455423500104Cited by:7 (Source: Crossref)

Abstract

The out-of-plane buckling behavior of arches is closely related to the element torsional behavior. The traditional 12-degree-of-freedom second-order element stiffness matrix which uses a simplified element torsional stiffness GJ/ $L$ $L$ (where $G$ $G$ is the shear modulus, $J$ $J$ the St. Venant torsion constant, $L$ $L$ the element length) may significantly underestimate the out-of-plane buckling loads of funicular arches. This paper presents a simple and effective exact matrix stiffness method (MSM) for the out-of-plane buckling analysis of funicular arches. The developed MSM uses a 14-degree-of-freedom second-order element stiffness matrix of three-dimensional beam-columns considering both torsion and warping deformations. The out-of-plane buckling analysis of funicular arches is performed by using the global structural stability stiffness matrix, which combines the transformed second-order element stiffness matrices. The proposed MSM with the exact 14-degree-of-freedom second-order element stiffness matrix for the out-of-plane buckling analysis is verified by comparing with some classical solutions of funicular circular and parabolic arches with box sections and I-sections. Further discussions show that the 14-degree-of-freedom second-order element stiffness matrix may be reduced to a simplified 12-degree-of-freedom form only by deriving the exact element torsional stiffnesses, which could be significantly larger than GJ/ $L$ $L$ for members with large cross-sectional torsional stiffness parameters (especially open cross-sections).

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