弹性地基上框架结构内力计算方法

将框架结构的地基梁单元细分,由弹性力学中的地基沉陷公式求得与细分后梁单元结点相对应的地基柔度矩阵,对柔度矩阵求逆得到地基刚度矩阵,与框架结构刚度矩阵叠加形成总体刚度矩阵;设置虚梁考虑边荷载;通过求解确定地基集中反力为受拉的结点,消除这些结点对地基刚度的贡献,进而考虑地基与地基梁的脱开问题;由梯形分布荷载作用下的梁单元固端剪力系数矩阵,建立由结点处地基集中反力求地基分布反力的关系式,形成了完善的半解析弹性地基上框架结构内力与地基反力求解方法,算例表明该方法有很好的精度。同时通过算例发现,不同地基模型对结构的总沉陷影响较大,但对结构内力、地基反力和沉陷差影响较小。

Calculation method of internal force of frame structures on elastic foundations

The foundation beam elements of a frame structure were subdivided as required.The foundation stiffness matrix was obtained by inversing the flexibility matrix of the subdivided foundation beam of the frame structure.The flexibility matrix was established from foundation settlement in elastic mechanics.The total stiffness matrix was formed by the stiffness matrix of the foundation beam and frame structure.Side loads were exerted by the virtual beam.The tensile separation of the beam from the foundation was considered by the transformation of the concentrated reaction force to contribution of tensile nodes to foundation stiffness.The relationship between the distributed subgrade reaction force and the concentrated reaction force was developed by a coefficient matrix of shear force at a fixed end of the beam under trapezoidal distributed loading.Finally,a complete semi-analytical method for frame structures on elastic foundations was established.An example shows that the method has high accuracy,and various foundation models have significant influence on the total settlement of the structure and insignificant influence on the structural internal force,foundation reaction force,and subsidence difference.