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本文采用拟夹层板法来分析计算两向正交斜放网架,给出了这种网架连续化后的六阶基本偏微分方程式。对第一类和第二类简支边界条件的矩形平面网架,分别求得了基本方程式的解析解。其中第二类简支网架的解答,是以第一类简支网架的重三角级数解为特解,叠加两组互相交叉的单三角级数解为齐次解,再采用边界配点法求得。文中对两类简支网架的内力和挠度作了对比,说明两者差异较大,在靠近边界和角部处更是明显。与此同时,文中还研讨了网架剪切变形对内力和挠度的影响。通过算例说明,按本文方法的计算结果与精确的空间桁架位移法的计算结果比较吻合,能满足工程计算精度的要求。为便于设计中应用,编制了与实际情况比较符合的第二类简支网架的内力和挠度计算图表。
In this paper, the method of pseudo-sandwich plate is used to analyze and calculate the two-dimension orthogonal oblique grids, and the sixth-order basic partial differential equation after this grid is continuous is given. For the rectangular plane grids of the first and second simple supported boundary conditions, the analytical solutions of the basic equations are obtained. The answer to the second type of simply-supported grids is the special solution of the triangular series solution of the simple support grid of the first type. The two overlapping sets of single-trigonometric series solutions are homogeneous solutions, and then the boundary collocations are used. The law seeks. In this paper, the internal forces and deflections of the two types of simple support grids are compared, which shows that the differences between the two are relatively large, and they are even more obvious near the boundary and corners. At the same time, the influence of shear deformation of the grid on internal forces and deflections is also discussed. The example shows that the calculation results of this method are in good agreement with the exact space truss displacement method and can meet the requirements of engineering calculation accuracy. In order to facilitate the application in design, the internal force and deflection calculation charts of the second type of simple support nets that are in line with the actual situation are compiled.