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对于有沉重负荷的上层地板或平板的支柱,多数具有相同的长度、横截面和结构特性。但是,有时某些支柱由于长度、截面积和面惯矩的差异而具有不同的结构特性。在这种情况下,确定板上载重的位置于某一侧,就可以把支柱上载重的差异减至最小。 这个问题如果采用能量原理,很易解决,它比采用复杂的FEA法解决得更快。为了推导这个方程,可取四条不等长的支柱,支承一刚性平板,另附加一重量。例如设一个机械零件于板的某一位置上,以便把支柱承重差异减至最小。这个理想化的结构,可用具有刚度为K_1至K_4的弹簧作为支柱昼出。以板的中心为原点组成x—y—z坐标系,极长为2a,宽为2b,附加的重量P_1置于板面(x_1,y_1)点上,板重P_2在板中心。板的变位轮廓如图中虚线所示。再者,板视为不变形的刚体。
For pillars with heavy loads on the upper floor or slab, most have the same length, cross-section, and structural characteristics. However, sometimes some pillars have different structural characteristics due to differences in length, cross-sectional area, and surface moment of inertia. In this case, determining the position of the board’s loading weight on one side can minimize the difference in the loading weight of the pillars. This problem is easily solved if it uses the energy principle. It solves it faster than the complex FEA method. In order to derive this equation, four pillars of unequal length can be used to support a rigid flat plate with an additional weight. For example, a mechanical part is placed at a position on the board to minimize the difference in pillar load. This idealized structure can be used as a pillar with a spring having a stiffness of K_1 to K_4. The x-y-z coordinate system is formed with the center of the plate as the origin, the length is 2a, and the width is 2b. The additional weight P_1 is placed on the plate surface (x_1, y_1), and the plate weight P_2 is in the center of the plate. The displacement profile of the plate is shown by the dotted line in the figure. In addition, the board is regarded as a rigid body that is not deformed.