Parametric study of the structural and in-plane buckling analysis of ogee arches

As part of a pilot project an ogee arch is being studied as a self-supporting skin skylight for the Housing and Building National Research Center’s (HBRC) patio. The ogee arch consists of a pair of two tangential circular arcs making an arch shape. The geometry of the arch depends on several interrelated variables including the angles subtended by the arcs, the ratio of the radii of the two arcs, and the height of the arch. This paper provides curves for designing the geometry of ogee arches. The structural analysis of two-hinged ogee arches under different cases of loading is outlined deriving expressions for the horizontal base thrust and plotting their graphs. A parametric study of the antisymmetric in-plane buckling behavior of ogee arches is presented using a finite element eigenvalue buckling analysis for several cases of loading. The finite element models consist of beam elements and have varying geometrical dimensions representing different shapes of ogee arches. The structural response of the arches is verified through a linear finite element analysis. The results of the buckling analysis are verified through a nonlinear finite element analysis with initial imperfections. It is found that the buckling load is a function of the ratio of the height-to-base radius of the arch and expressions for the lower bound buckling load are derived as a function of this height-to-base radius ratio.