Elastic-plastic stability of shear-deformable circular arches

Abstract

Shear deformations affect the stability of arches. This paper investigates the in-plane elastic-plastic stability and design of pin-ended circular arches including shear deformations. The elastic buckling axial forces for symmetric and anti-symmetric buckling are first studied for radially compressed arches and arches uniformly loaded along the horizontal projection, formulas are proposed so that they are used to compute the normalized slenderness and the moment amplification factors respectively. The strength reduction factors of axially compressive arches are studied during which the effect of accompanying bending moments has been excluded, a formula for the strength reduction factors (SRF) of arches with uniform axial forces are proposed. This study verified that the effect of shear deformation can be fully included by the normalized slenderness. The SRF is also modified to make it applicable for real arches where axial forces are always varied along the arch centroid line. Then the moment amplification factor of arches subjected to uniformly distributed loads along the horizontal projection, are derived theoretically and validated by FE predictions. Finally, based on the modified SRF and the moment amplification factor, an interactive axial force-bending moment stability design equation is developed, which considers the effect of shear deformations and provides excellent predictions for the in-plane strength of shear-deformable pin-ended circular arches in bending and compression.