A theoretical method for calculating the collapse load of steel circular arches

Arches are frequently used in large span structures like bridges and roofs. Although these structural elements may be prone to various instability phenomena, stocky arches or slender arches with sufficient lateral bracing fail due to plastic collapse instead of in-plane buckling or out-of-plane buckling. The plastic collapse load can be obtained through limit load analyses, making full use of the plastic capacity of the cross-section and possible redistribution of internal forces after formation of the first hinge. This paper describes an analytical approach to obtain the plastic collapse load of circular steel arches subjected to vertical loading. The upper-bound theorem, lower-bound theorem and kinematic admissibility rules of plastic theory were employed to arrive at a plastic collapse load. Reduction of the full plastic moment capacity of the arch cross-section due to the presence of compressive forces was accounted for. An iterative procedure was found necessary to obtain the plastic collapse load since a non-linear relationship was observed between the acting loads and the reduced plastic moment capacity. Finite element analyses were performed to verify analytical results. Good agreement between the suggested iterative procedure and finite element computations was found. Design graphs were developed based on the iterative procedure.