UNIVERSAL METHOD OF CALCULATION OF MULTISPAN BEAMS

Abstract

The supporting structures of machines and mechanisms of metallurgical equipment, which are characterized by large dimensions, in the calculation scheme can be reduced to multispan beams, which are statically indeterminate. Traditionally, the disclosure of their static uncertainty is based on the graphoanalytical method, which is called "Equation of 3 moments". According to this method, the equations of three points are solved by constructing intermediate epure of bending moments, finding their areas and position of the centers of gravity. These procedures lead to an unreasonable increase in time to solve the problem. It is advisable to have an analytical method for detecting static uncertainty of multispan beams, which would be free from graphical constructions and would significantly reduce the time to solve the problem.
 At the present stage, the calculation of complex spatial structures is carried out using the calculation and software systems "LIRA", "SCAD" and others. However, this in no way limits the need for the application in engineering practice of simple analytical methods, which include a universal method for detecting static indeterminateness of multispan beams.
 Additional, to the static equations, the equations of displacement are compiled using the universal equation of the bent axis of the beam, and the number of beams can be any large. Different variants of boundary conditions are considered. The results of the considered examples prove the independence of the values ​of "extra" unknown from the stiffness of the beam.
 The universal method is quite optimal, as it uses a very simple universal equation of the bent axis of the beam and, with each subsequent additional equation of displacement differs from the previous one only by adding another item with a new load. This approach provides the optimal solution to almost any problem, by revealing the static indeterminateness of multispan beams.