考虑不均匀沉降对非理想支承梁的受力影响

Influence of Differential Settlement on Girder with Non-ideal Support

针对两端存在一定转动刚度的非理想支承梁,为了分析支座沉降时端部转动刚度对该结构受力的影响,建立两端存在转动弹性支承的梁式结构模型。利用结构边界处变形协调条件给出梁式结构的一般力学方程,然后求解得出该方程中的相关系数表达式,并针对多跨梁式结构简化给出了方程中由转动刚度表示的修正自由项,得到在支座移动时的该模型的解析公式。结合数值试验,分别通过一个三跨梁式桥在不同的支座出现不均匀沉降时的数值分析来验证理论公式的准确性和端部不同转动约束刚度的单跨结构在支座移动时其受力变化规律。研究表明:支座移动时,引起该类模型的附加内力,且要考虑模型若由多跨结构简化而来需要修正力法方程的自由项;由于转动支承的存在产生附加内力大小随转动刚度增大而增大,而随着转动刚度的变化,该类结构附加内力大小出现非线性变化。

For the girder structure with some rotational stiffness at the boundary, the girder structure with some rotational stiffness is established for the differential settlement. The mechanical equation of the structure is derived based on deformation compatibility condition. The correlation coefficients of mechanical equation are derived based on energy principle,and especially the correction of the free term are derived for multi-span continuous beam. Then the explicit formulas of the internal forces are derived. The accuracy of the theoretical method proposed is proved by the finite element method of a three span continuous beams, and the change regulation is analyzed by one span beam with different when there is differential settlement. The results show that additional internal forces of the girder structure with some rotational stiffness may be induced by differential settlement. To obtain the additional internal forces by the mechanical equation, the free term needs to correct for continuous beam; because the existence of the rotary support additional internal force is proportional to rotational stiffness, and with the rotation stiffness change, this kind of structure additional internal force is in the nonlinear change.