A state-of-the-art is presented in the form of a literature review of over 100 papers which describe research on the flexural-torsional buckling of arches. Early research on the flexural-torsional buckling of arches mainly focused on elastic theoretical solutions and testing with more recent research focusing on finite element analysis, ultimate strength and design equations. This paper firstly presents research on the elastic flexural-torsional buckling of arches, including the effects of temperature, pre-buckling deflections and restraints. This is followed by finite element methods for the elastic flexural-torsional buckling of arches. Inelastic flexural-torsional buckling of arches and non-linear finite element analysis are described next, followed by research on testing of arches. Finally, proposed equations for the design of arches are presented. Closed form solutions for the elastic flexural-torsional buckling of arches are generally only possible for arches subjected to equal and opposite end moments (uniform bending) and to uniformly distributed radial loads (uniform compression). For other types of loading, the finite element method employing a linear buckling analysis can be used. The ultimate load capacity for arches can be determined from testing or by non-linear finite element analysis. The conclusions summarise each topic in detail and recommendations for future research are also presented.
Papangelis et al. (Wed,) studied this question.