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建筑物底层支柱下面的钢筋混凝土底板可视为弹性地基上的四边自由中点受集中力的正交异性板的弯曲问题。为了求得板中心的弯矩,应将集中力改为支柱横截面承受的分布力。该文建立了双参数弹性地基上的正交异性矩形薄板弯曲问题的一般解析解。可用以精确地求解矩形板在任意载荷作用下和任意边界的弯曲问题。以四边自由在中点附近承受局部均布载荷的方板为例进行了计算,并求得了板的最大弯矩。该文的一般解同样适用于单参数弹性地基以及各向同性板的情形。计算过程简单、便于应用。
Reinforced concrete slabs beneath the lower pillars of the building can be considered as bending problems of concentrated orthogonal orthotropic plates at the free midpoints of the four sides of the elastic foundation. In order to obtain the bending moment in the center of the plate, the concentration force should be changed to the distribution force that the cross-section of the pillar can bear. In this paper, a general analytical solution to the bending problem of orthotropic rectangular thin plates on two-parameter elastic foundations is established. It can be used to solve the bending problem of rectangular plates under arbitrary load and arbitrary boundary accurately. Taking square plates which are free to bear local uniform load around the midpoint as an example, the maximum bending moment of the plate is obtained. The general solution of this paper also applies to the case of one-parameter elastic foundation and isotropic plate. Calculation process is simple, easy to use.