FORCES IN PRESTRESSED CONCRETE BRIDGES CONSTRUCTED BY FREE CANTILEVERING

Abstract

There are many problems of free cantilevered prestressed concrete to be solved by more convenient methods. One of these is the determination of the internal forces during the assembly and post-tensioning of the cantilevers. This question is also called the determination of the elastic shortening loss in already anchored tendons. A system of equations for the tendon forces as unknowns using the force method for the states of the construction of the cantilevers is written. The analytical solution of this equation is enabled by the recognition that the coefficient matrix of the system is a one-pair matrix modified by a diagonal matrix. Using the statement according to which the inverse matrix of a one-pair matrix is a symmetric tridiagonal matrix and vice versa the elements of the inverse of the one-.pair matrix in the coefficient matrix can be produced. The task finally can be reduced to the inversion of the symmetric tridiagonal matrix modified by a diagonal matrix. This further problem can be solved by means of one-pair matrices formed by quantities gained by a recursive algorithm. The importance of the result consists in the fact that the internal forces of a free cantilevered structure in an arbitrary stage of construction can be written in case of any parameters (changing cross-section, length of segments, number of tendons, etc.)