Influence of mesh division of frame on steel quantity

In order to save the usage quantity of steel, a method of optimizing the steel quantity for per unit area of reinforced concrete frame structure was proposed. The main technical route was to explore the influence of the size of both slabs and beams as well as the number variation of columns on the internal force distribution and steel quantity of components. The uniform mesh division for the longitudinal length was conducted for a rectangular building with the given longitudinal and transverse length, where each mesh node was equipped with a column. And thus, n meshes with the same area were obtained from each mesh dividing. Generally, with increasing n, the steel quantity of slabs will reduce, while that of both beams and columns will increase. Therefore, there exists an n value which can make the total steel quantity of slabs, beams and columns reach the extreme values. A layer of reinforced concrete frame structure was simulated, and the formulas for the steel quantity of slabs, beams and columns were derived. Moreover, the function relationship between n and steel volume V of three components was obtained, which could be further converted into the relationship between the steel quantity m for per unit area and n. Through taking n as the optimization variable, the function change and the minimum value were attained with Matlab. Finally, the demonstration was performed through the typical example.