Steel arches are applied in many engineering structures because of their excellent capacity to resist various transverse loadings. Modified (or normalized) slenderness plays an important role in the strength design of steel arches. The elastic lateral-torsional buckling load of steel arches is essential in calculating the modified slenderness for the out-of-plane strength design. This paper is concerned with analytical investigations of the elastic lateral-torsional buckling of steel pin-ended arches having in-plane rotationally restrained ends under an arbitrary radial concentrated load, which has not been reported in the literature. Nonuniform unsymmetrical distributed internal actions are produced by the arbitrary load and are significantly influenced by the load position. The arch suddenly reaches its ultimate resistance in a lateral-torsional buckling mode when the internal actions reach certain values. This paper conducts a theoretical investigation into the elastic lateral-torsional buckling of steel arches and derives the analytical solution for the buckling load based on accurate internal forces obtained by an exact prebuckling analysis. The fourth-order differential equations in terms of axial and radial displacements, which are successfully used for the prebuckling analysis of steel arches under symmetric loads, are found to be difficult to solve for steel arches under an arbitrary concentrated load. A proper method is explored and found useful for accurately determining the prebuckling internal forces. The analytical solutions for the elastic lateral-torsional buckling load based on the accurate prebuckling internal forces are compared with the independent finite-element results, and the comparisons show very good agreements between them. The effects of the load position on the lateral-torsional buckling loads of arches are investigated. It is found that the buckling loads are significantly influenced by changes in load position. The lateral-torsional buckling load increases as the load position moves away from the crown of the arch. The influence of the load position on the lateral-torsional buckling load of steel arches with a rectangular section is slightly significant than that of steel arches with an I-section. The elastic lateral-torsional buckling load obtained in this paper provides a sound basis for out-of-plane strength studies of steel arches in the future.

When an arch is subjected to a periodic load, it may lose in-plane stability dynamically owing to parametric resonance. Previous investigations have been concentrated on in-plane dynamic buckling of pin-ended shallow arches. However, in engineering practice, fixed arches with different rise-to-span ratios are often encountered. Little research on in-plane dynamic instability of deep fixed arches has been reported in the literature. This paper is concerned with experimental and analytical investigations for in-plane dynamic instability of fixed circular arches with rise-to-span ratios 1/8–1/2 under a central periodic load owing to parametric resonance. Experiments are carried out to determine the in-plane frequency and damping ratio of arches, to investigate critical regions of frequencies and amplitudes of the periodic load for in-plane dynamic instability of arches, and to explore effects of the rise-to-span ratio and additional weights on dynamic instability. The analytical method for determining the region of excitation frequencies and amplitudes of the periodic load causing in-plane instability of the arch is established using the Hamilton’s principle by accounting for effects of additional concentrated weights. Comparisons of analytical solutions with test results show that they agree with each other quite well. These results show that the rise-to-span ratio significantly influences the bandwidth of regions of critical excitation frequencies for in-plane dynamic instability of arches. The critical frequencies of the periodic load and their bandwidth increase with a decrease of the rise–span ratio of the arch, whereas the corresponding amplitude of the periodic load decreases at the same time. It is also found that the central concentrated weight influences in-plane dynamic instability of arches significantly. As the weight increases, the critical frequencies of excitation and their bandwidth for in-plane dynamic instability of arches decreases, whereas the corresponding amplitude of excitation increases.