CALCULATION OF REINFORCED CONCRETE FRAMES WITH REGARD TO CRACKING

Abstract

Summary. It is known that in the elements of reinforced concrete frames during the formation of cracks, the stiffness characteristics change, which in turn leads to a significant redistribution of forces between the individual elements. Software complexes usually used in the engineering of reinforced concrete constructions take into account the change in bending stiffnesses of rod finite elements as a result of cracking. In this case, in order to obtain sufficient accuracy, as a rule, one element of the frame (column, transom) is split into several finite elements, which significantly increases the number of unknowns in the system of equations. In addition, almost all software complexes do not take changes in the torsional stiffness of rod elements as a result of cracking into consideration.
 Calculation of plane and spatial frames by classical displacement method and finite element method does not practically differ in terms of the number of unknowns in the system of equations. In a frame consisting of individual rods (columns, transoms), the forces at the different ends of each rod can differ significantly. Therefore, if the stiffness changes as a result of cracking (in an iterative process), the stiffness of the entire rod has to be changed, and this also leads to significant errors. To calculate accurately, we have to divide each rod into a certain number of finite elements, which greatly increases the number of unknowns.
 To eliminate this disadvantage, the paper proposes a method for calculating spatial and planar frameworks using the classical method of displacements. But in this case the values of bending moments and reactions on the supports are determined taking into consideration the variable stiffness along the length of each element. Thus, without increasing the number of unknowns, it is possible to take into consideration the stiffness variable along the length of the rod. Moreover, dividing the length of the element into any number of sections does not increase the number of unknowns, while refining the calculation results with regard to cracking. Changing the stiffnesses can be written as a fairly simple subprogram in the general calculation program. On the example of the simplest spatial frame, the importance of dividing the rod into several sections with different stiffnesses is shown. In this case, the number of unknown systems of equations does not increase.
 Keywords. Reinforced concrete frame; displacement method; finite element; stiffness; cracking.