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.

实际上，拱桥或其他拱形结构的基础可能具有不均匀的沉降，从而导致拱形支架的运动或旋转不均匀。支架的不均匀运动和旋转会显着影响由外载荷产生的变形和内力，以及拱的平面内非线性不稳定性行为。迄今为止，在开篇文献中，关于支撑运动和旋转对浅拱的非线性平面内不稳定性影响的研究报道很少。本文重点研究支架不均匀运动和旋转对固定浅拱的面内非线性不稳定性的影响。推导了在均匀局部径向载荷作用下固定浅拱的极限点不稳定性载荷的新的解析解，其中考虑了支座不均匀运动和旋转的影响。与有限元结果的比较表明，解析解足够准确。研究发现，不均匀的支撑运动和旋转对固定浅拱的非线性面内失稳行为具有重要影响。还发现，固定的浅拱的面内非线性不稳定性载荷随着支座不均匀运动和旋转幅度的增加而减小。研究发现，不均匀的支撑运动和旋转对固定浅拱的非线性面内失稳行为具有重要影响。还发现，固定浅拱的平面内非线性不稳定性载荷随着支座不均匀运动和旋转的幅度的增加而减小。研究发现，不均匀的支撑运动和旋转对固定浅拱的非线性面内失稳行为具有重要影响。还发现，固定的浅拱的面内非线性不稳定性载荷随着支座不均匀运动和旋转幅度的增加而减小。