Effects of movement and rotation of supports on nonlinear instability of fixed shallow arches

In practice, the foundations of arch bridges or other arch structures may have non-uniform settlements leading to uneven movements or rotations of the supports of the arch. The uneven movements and rotations of the supports influence the deformations and internal forces produced by the external load as well as the in-plane non-linear instability behaviour of arches significantly. Little research is reported about effects of support movements and rotations on the nonlinear in-plane instability of shallow arches in the opening literature insofar. This paper focuses on effects of uneven movements and rotations of the supports on the in-plane nonlinear instability of fixed shallow arches. New analytical solutions for the limit point instability load of the fixed shallow arches under a uniformly localized radial load incorporating the influences of uneven movements and rotations of the supports are derived. Comparisons against the finite element results show the analytical solutions are adequately accurate. It is found that the uneven support movements and rotations have significant effects on the nonlinear in-plane instability behaviour of fixed shallow arches. It is also found that the in-plane nonlinear instability load of a fixed shallow arch decreases with an increase of the magnitudes of uneven movements and rotations of the support.