In-plane strength and design of parabolic arches

In the current AASHTO LRFD, the arch design formula is based on the bilinear interaction relationship between two extreme cases of the axial and the flexural strength. However, this method is not suitable for the design of the shallow arch which may buckle in a symmetric snap-through mode. Also, the use of the constant reduction factor for the design of arches leads to a conservative design. This paper investigates the in-plane buckling strength and design of parabolic arches. Firstly, the thresholds for the different buckling modes of shallow parabolic arches are summarized and boundaries for the deep and shallow arches are reported. The inelastic strengths of parabolic deep arches based on the finite element analyses are then compared with those presented in AASHTO LRFD. From the results, it is found that AASHTO LRFD provides good predictions of buckling strengths for the parabolic arches under only axial compression, while the bilinear interaction relationship provides conservative values for the in-plane strength of parabolic arches due to the use of constant reduction factors that can be applied regardless of loading and boundary conditions. The modified formulas for reduction factors are proposed for various loading and boundary conditions in this study. It is found that modified formulas for reduction factors show good match with the results obtained from finite element analyses.