This paper investigates the elastic lateral-torsional instability of shear deformable fixed arches having a monosymmetric cross-section when subjected to a localized uniform radial load. Hitherto, this topic has not been addressed in the open literature. The complex in-plane internal actions in a fixed arch with a monosymmetric section are produced by a localized uniform radial load and are affected by the arc length of localized load segment. When the in-plane internal actions reach certain magnitudes, the fixed arch may fail suddenly in a lateral-torsional instability mode. The lateral-torsional instability loads of such arches considering shear deformations under a localized uniform radial load are difficult to obtain and are investigated in this paper. The strain-displacement relationships for the longitudinal normal axial and shear strains in the arch with a monosymmetric section are derived. In-plane analyses for the internal forces produced by the localized uniform radial load are firstly carried out. The analytical solution for the lateral-torsional instability load accounting for shear deformations and monosymmetry is then obtained using the principle of stationary potential energy together with the Rayleigh-Ritz method and compared with ANSYS numerical results. It is found that the monosymmetry parameter, the shear deformations, the slenderness ratio and the arc length of the localized load segment have considerable effect on the lateral-torsional instability load of fixed arches with a monosymmetric section.

本文研究了具有局部对称径向载荷的具有单对称横截面的可剪切变形的固定拱的弹性横向扭转不稳定性。迄今为止，公开文献中尚未解决该主题。具有单对称截面的固定拱形中复杂的平面内部作用是由局部均匀的径向载荷产生的，并且受局部载荷段的弧长影响。当平面内的内部作用达到一定程度时，固定弓可能会在横向扭转不稳定模式下突然失效。难以获得在局部均匀径向载荷作用下考虑剪力变形的这种拱的横向扭转不稳定性载荷，并对其进行了研究。推导了具有单对称截面的拱中的纵向法向轴向应变和剪应变的位移关系。首先对由局部均匀径向载荷产生的内力进行平面分析。然后，利用平稳势能原理和瑞利-里兹方法，获得了考虑了剪切变形和单对称性的横向扭转失稳载荷的解析解，并与ANSYS数值结果进行了比较。结果表明，局部载荷段的单对称性参数，剪切变形，细长比和弧长对具有单对称截面的固定拱的横向扭转失稳载荷有很大影响。首先对由局部均匀径向载荷产生的内力进行平面分析。然后，利用平稳势能原理和瑞利-里兹方法，获得了考虑了剪切变形和单对称性的横向扭转失稳载荷的解析解，并与ANSYS数值结果进行了比较。结果表明，局部载荷段的单对称性参数，剪切变形，细长比和弧长对具有单对称截面的固定拱的横向扭转失稳载荷有很大影响。首先对由局部均匀径向载荷产生的内力进行平面分析。然后，利用平稳势能原理和瑞利-里兹方法，获得了考虑了剪切变形和单对称性的横向扭转失稳载荷的解析解，并与ANSYS数值结果进行了比较。结果表明，局部载荷段的单对称性参数，剪切变形，细长比和弧长对具有单对称截面的固定拱的横向扭转失稳载荷有很大影响。然后，利用平稳势能原理和瑞利-里兹方法，获得了考虑了剪切变形和单对称性的横向扭转失稳载荷的解析解，并与ANSYS数值结果进行了比较。结果表明，局部载荷段的单对称性参数，剪切变形，细长比和弧长对具有单对称截面的固定拱的横向扭转失稳载荷有很大影响。然后，利用平稳势能原理和瑞利-里兹方法，获得了考虑了剪切变形和单对称性的横向扭转失稳载荷的解析解，并与ANSYS数值结果进行了比较。结果表明，局部载荷段的单对称性参数，剪切变形，细长比和弧长对具有单对称截面的固定拱的横向扭转失稳载荷有很大影响。