摘要
考虑十字交叉条形基础截面剪切变形影响,利用Winkler地基Timoshenko梁无限长梁在集中力、集中力偶作用下的变形和内力关系,推导了带悬挑的半无限长梁的集中力、集中力偶作用下的悬挑系数计算公式。当条形基础抗剪刚度趋于无穷大时可退化成不考虑剪切变形影响的Euler梁理论结果,因此该文公式是一种通用公式。剪切变形对集中力的悬挑系数影响大、对集中力偶的悬挑系数影响小。对于节点较密、截面尺寸较大、对变形敏感的十字交叉条形基础,应该考虑截面的剪切变形影响。根据静力平衡条件和变形协调条件,建立了可同时考虑截面剪切变形和节点集中力、集中力偶作用的带悬挑十字交叉条形基础的节点荷载分配的统一公式。算例结果显示:虽然节点处作用的集中力偶较小,但其可以改变竖向荷载在节点x、y两方向上的分配,力偶数值越大,影响越明显。考虑条形基础截面剪切变形影响后,计算的节点荷载分配更均匀。
Considering the shear deformation effect of crossed foundation beams, and using the relationship between the load and deformation of an infinite length Timoshenko beam on Winkler foundation acted by a concentrated load and a moment, the cantilevering coefficients of a semi-infinite length Timoshenko beam on Winkler foundation acted by a concentrated load and a moment were derived. When the shear stiffness of a Timoshenko beam became into infinite, the cantilevering coefficients can be degenerated into those of an Euler beam without considering the shear deformation effect. Thus, the present formula was very general. The influence of shear deformation effect on the cantilevering coefficient of a concentrated load was great, and of concentrated moment was little. For those of the crossed foundations with dense nodes, large sectional dimensions, and sensitive to deflection, the shear deformation effect must be considered. According to static equilibrium conditions and deformation compatibility, the general formulae of nodal load distribution of a crossed foundation beam with cantilever were established, which can incorporate both the shear deformation effect and concentrated load & moment at the same time. Examples show that although the concentrated moment acted on the crossed foundation is small, but it can change the load distribution along the x, y axis. The larger of the concentrated moment, the more apparent of the influence. Considering the shear deformation effect, nodal load distribution becomes more uniform by calculations.
引文
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