Géza Tassi’s research while affiliated with Budapest University of Technology and Economics and other places

Examples are shown for analytical solution of engineering structures. The basic procedures for statically indeterminate systems are the force method and the deformation method. The calculation leads to a linear system of equations. The coefficients of the systems are in many cases tridiagonal or one-pair matrices. The solving of this kind of problems is based on a theorem, which states that the inverse of each tridiagonal matrix is a one-pair matrix and vice versa. This enables us to find an analytical solution in numerous particular problems. Examples are taken from theory of reinforced concrete and from different girder and cable-stayed structures.

Advantageous moment distribution can be achieved by V-or Y-supported bridges. The structural model is a continuous girder with alternating spans. The application of the force method leads to a linear system of equations. The coefficient matrix of the system is a periodic tridiagonal matrix with alternating elements in the codiagonals. After rear-ranging the equations and the unknowns, the blocks of the inverse of the coefficient matrix can be expressed by applying the Sherman-Morrison formula. The elements of the Green-matrix are obtained in an explicit form. This enables the description of the influence line ordinates.

The adjustment of cable -stayed bridges needs the shortening or lengthening of several or all cables. Changing the length of a single cable produces the change in forces at other stays and at the stiffening girder. The calculation of the forces due to the adjustment of one stay seems to be advantageous by the force method. The paper gives an analytical way to the calculation of a bridge with a given arrangement. The chosen primary system leads to a system of equations having a pentadiagonal coefficient matrix. Because of the complexity of the task, even in the case of the regular form of the bridge, the solution is given by a recursion.

The paper is dealing with continuous post-tensioned girders in elastic range. Different load cases are considered: post-tensioning, total load, a single span loaded. The tendon layout is continuous or each span is supplied by an individual cable. The tendon is bonded by subsequent grouting, or unbonded. For the possibility of relatively simple comparison the solution is given analytically in closed formulae. The method gives a way to analyze many other cases.-The application of the force method leads to systems of linear equations the coefficients of which have remarkable properties. In the case of a continuous girder with a continuous tendon the matrix is a bordered uniform tridiagonal matrix. This property enables to calculate the inverse by help of the Chebyshev polynomials of the second kind. In the case of a continuous girder post-tensioned in each span separately the corresponding matrix is a two-by-two block matrix, the blocks of its inverse can be obtained in a relatively simple form. The final results can be expressed by means of hyperbolic and trigonometric functions.