Formation of Moments Influence Matrix in Frame Based on Graph of its Design Scheme

Abstract

A procedure is proposed for the automated construction of the bending moments influence matrix in the frame based on the graph of its discrete model. Forming the incidence matrix of the graph characterizing the topological structure of the design scheme of the frame, through matrix transformations of the displacement vectors, at the transition from local coordinate systems to a global system, it is possible to establish the relationship between the nodal displacements and the displacement increments of individual sections in the direction of the axis of the segment and perpendicular to it. The composition of only three initial matrices of the frame structure, the incidence matrix of the graph, the node coordinate matrix and the matrix of the frame model internal rigidity, solves the problem of automatic formation of the bending moments influence matrix with the help of a PC. The procedure proposed for the construction of the influence matrix, makes it possible to find the forces in the frame structure caused by external load, in the matrix form.