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

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/[Formula: see text] (where [Formula: see text] is the shear modulus, [Formula: see text] the St. Venant torsion constant, [Formula: see text] 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/[Formula: see text] for members with large cross-sectional torsional stiffness parameters (especially open cross-sections).