CALCULATION OF REINFORCED CONCRETE CROSS-ROD SYSTEMS TAKING INTO ACCOUNT CRACKING

Abstract

Crack formation changes the rigidity of the elements of the reinforced concrete cross-rod system. This, in turn, leads to a significant redistribution of loads between individual elements.Programs used to calculate reinforced concrete systems usually take into account the changes in the bending stiffnesses of the finite elements (bars) as a result of cracking.However, these programs do not take into account the change in torsional stiffnesses due to the formation of cracks. This leads to errors in the calculation of the loads, sometimes significant.

When calculating cross-rod systems by the classic method of displacement and the method of finite elements, the same number of unknowns is obtained. Therefore, their use is almost equivalent.

In a cross-rod system, the forces at either end of the element can be of different signs and can also vary significantly in magnitude. Therefore, when 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. Or for a more accurate calculation, each rod should be divided into several finite elements, which significantly increases the number of unknown variables.

To eliminate this drawback, the article proposes a method for calculating cross-rod systems using the classical method of displacement, but the table values of bending moments and reactions on the supports are determined taking into account the stiffness variability along the length of each element. Thus, with the same number of unknowns, it becomes possible to take into account the change in both torsional and bending stiffness along the length of each element. In this case, the length of the element can be divided into any number of sections without increasing the number of unknown systems of equations. These stiffness changes are easily recorded as a calculation subroutine. Given that solid slabs can also be calculated using the approximation in the form of a cross-rod system, the developed technique can also be used to design solid reinforced concrete slabs.